AN12 and FM12 Abstracts

Abstracts are printed as submitted by the authors.

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Annual Meeting (AN12)

Invited Speakers .............................................................................4

Contributed Lectures .....................................................................7

Minisymposia ................................................................................30

Contributed Posters ...................................................................104

Financial Mathematics and Engineering (FM12)

Invited Speakers .........................................................................126

Contributed Lectures .................................................................128

Minisymposia ..............................................................................139

Contributed Posters ...................................................................159

Table of Contents

2 2012 SIAM Annual Meeting • SIAM Conference on Financial Mathematics and Engineering

SIAM PresentsSince 2008, SIAM has recorded many Invited Lectures, Prize Lectures, and selected Minisymposia from various conferences. These are available by visiting SIAM Presents (http://www.siam.org/meetings/presents.php).

AN12 Abstracts

2012 SIAM Annual Meeting • SIAM Conference on Financial Mathematics and Engineering 3

4 AN12 Abstracts

IC1On the Shape of Data

Topology is the mathematical discipline which studiesshape. Data sets typically come with a notion of distancewhich formalizes notions of similarity of data points. Theshape of the data is of a great deal of importance in under-standing it - cluster decompositions define subpopulationsof the data and presence of loops often is a clue to the pres-ence of periodic or recurrent behavior in it. In this talk,we will describe how topological methods can be adaptedto the study of data sets, with examples.

Gunnar E. CarlssonStanford Universitygunnar@math.stanford.edu

IC2Elliptic Curve Cryptography and Applications

In the last 25 years, Elliptic Curve Cryptography has be-come a mainstream primitive for cryptographic protocolsand applications. This talk will give a survey of ellipticcurve cryptography and its applications, including appli-cations of pairing-based cryptography which are built withelliptic curves. No prior knowledge about elliptic curvesis required for this talk. One of the information-theoreticapplications I will cover is a solution to prevent pollutionattacks in content distribution networks which use networkcoding to achieve optimal throughput. One solution isbased on a pairing-based signature scheme using ellipticcurves. I will also discuss some applications to privacy ofelectronic medical records, and implications for secure andprivate cloud storage and cloud computing.

Kristin LauterMicrosoft Researchklauter@microsoft.com

IC3Applying Mathematics to Better Understand theOcean

The ocean still represents a realm of discovery in manyimportant respects. We do not, for example, fully under-stand the magnitude of mixing in the ocean, and this lackof knowledge has real consequences for our ability to modeland predict future climate. In this talk I will describe howwe have been using ideas from dynamical systems to bringa new degree of clarity to this problem. I will discuss howthis has improved our theoretical understanding of someof the key processes driving ocean circulations and how wehave been literally applying mathematics to the ocean bydeploying floats in the Southern Ocean to map unstablemanifolds and calculate Lyapunov exponents.

Emily ShuckburghBritish Antarctic Survey, United Kingdomemily.shuckburgh@bas.ac.uk

IC4Image Processing and Computational Mathematics

Image processing has traditionally been studied as a formof signal processing, and a subfield of electrical engineering.Recently, with the advent of inexpensive and integratedimage capturing devices, leading to massive data andnovel applications, the field has seen tremendous growth.Within computational mathematics, image processing has

emerged not only as an application domain where compu-tational mathematics provide ideas and solutions, but alsoin spurring new research directions (a new ComputationalFluid Dynamics) in geometry (Total Variation regulariza-tion and Level Set methods), optimization (primal-dual,Bregman and Augmented Lagrangian methods, L1 convex-ification), inverse problems (inpainting, compressive sens-ing), and graph algorithms (high-dimensional data analy-sis). This talk gives an overview of these developments.

Tony ChanDepartment of MathematicsHong Kong University of Science and Technologytonyfchan@ust.hk

IC5Model-Assisted Effective Large Scale Matrix Com-putations

Advanced mathematical models very often require the solu-tion of (sequences of) large algebraic linear systems, whosenumerical treatment should incorporate problem informa-tion in order to be computationally effective. For instance,matrices and vectors usually inherit crucial (e.g., spectral)properties of the underlying continuous operators. In thistalk we will discuss a few examples where the performanceof state-of-the-art iterative linear system solvers can bedramatically enhanced by exploiting these properties. Ourpresentation will focus on structured linear systems stem-ming from the numerical discretization of systems of partialdifferential equations, as well as of optimal control prob-lems constrained by partial differential equations.

Valeria SimonciniUniversita’ di Bologna, Italyvaleria@dm.unibo.it

IC6Multiscale Problems Involving Disorder: A Math-ematical Perspective

The talk will review a series of recent works, includingworks in collaboration with X. Blanc, F. Legoll, PL. Lionsaddressing various aspects, both mathematical and numer-ical in nature,of some multiscale problems involving nonperiodic and random modelling. The problems consideredall originate from materials science at different scales. Thecommon motivation of the approaches presented is the wishto keep the computational workload as limited as possible,despite the presence of disorder (non periodicity, defects,randomness) in the problems.

Claude LeBrisCERMICS - ENPC, Francelebris@cermics.enpc.fr

IC7Freeform Architecture and Discrete DifferentialGeometry

The emergence of freeform structures in contemporary ar-chitecture raises numerous challenging research problemsmany of which are related to the actual fabrication andare of a mathematical nature. The speaker will report onrecent progress in geometric computing for freeform archi-tecture, with special emphasis on the close relation to dis-crete differential geometry. Specific topics to be addressedinclude: meshes with planar quadrilateral faces and cor-

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responding supporting structures, semi-discrete represen-tations for structures from single curved panels, panelingalgorithms and the design of self supporting surfaces. Thetransfer of research into the architectural practice will beillustrated at hand of selected projects.

Helmut PottmannKing Abdullah University of Sciencehelmut.pottmann@kaust.edu.sa

IC8Computing Essentials: What SIAM MembersShould Know About Emerging Architectures

For most of computing history programmers have experi-enced steady performance improvement with little effort,primarily due to increased clock speed and instruction levelparallelism: Riding the commodity performance curve waseasy. This has changed. Multicore and GPU processorspromise terascale laptop, petascale deskside and exascalecenter systems. But realizing this potential is challenging:Riding the new commodity performance curve requires par-allel execution. Furthermore, the number of components inhigh-end systems will increase soft and hard system errors.We discuss the essentials of how to develop algorithms andsoftware in order to realize parallel performance today andprepare for the future.

Michael A. HerouxSandia National Laboratoriesmaherou@sandia.gov

IC9Overcoming the Tyranny of Scales in SubsurfaceFlow and Reactive Transport Simulation

A grand challenge facing subsurface modelers is the dispar-ity between length and time scales at which fundamentalprocesses are controlled and those at which predictions areneeded. This presentation will describe the application ofmultiscale simulation methods to this challenge. Particu-lar focus will be given to 1) hybrid multiscale simulations,which directly couple pore- and continuum-scale models,and 2) integration of genome-scale microbial metabolismmodels into field-scale bioremediation analyses. We willpresent our multiscale analysis platform (or MAP), a com-munity resource for navigating the breadth of multiscalemethods and identifying which tools are best suited to spe-cific problems.

Timothy D. ScheibeHydrology Technical GroupPacific Northwest National Laboratorytim.scheibe@pnl.gov

IC10Network Formation and Ion Conduction inIonomer Membranes

Selective charge transport is an essential step in efficientenergy conversion. Ionomer membranes are formed fromcross-linked, charged polymers. They imbibe solvent toform nanoscaled network structures which lie at the heartof many energy conversion devices. Experimental datashows that the networks are hysteretic, evolving on timescales of minutes and hours, far outside the reach of molec-ular simulations. We present a novel reformulation of theclassical Cahn-Hilliard free energy that permits the inclu-sion of solvation energy and counter-ion entropy within a

continuum model. Gradient flows on the FunctionalizedCahn-Hilliard energy show bi-stability of bilayer, pore, andmicelle dominated networks. We present sharp interfacereductions, including classes of curvature driven flows thatcouple to the network structure.

Keith PromislowMichigan State Universitykpromisl@math.msu.edu

IP1On Mean Field Games

This talk will be a general presentation of Mean FieldGames (MFG in short), a new class of mathematical mod-els and problems introduced and studied in collaborationwith Jean-Michel Lasry. Roughly speaking, MFG aremathematical models that aim to describe the behaviorof a very large number of agents who optimize their de-cisions while taking into account and interacting with theother agents. The derivation of MFG, which can be justi-fied rigorously from Nash equilibria for N players games,letting N go to infinity, leads to new nonlinear systemsinvolving ordinary differential equations or partial differ-ential equations. Many classical systems are particularcases of MFG like, for example, compressible Euler equa-tions, Hartree equations, porous media equations, semilin-ear elliptic equations, Hamilton-Jacobi-Bellman equations,Vlasov-Boltzmann models... In this talk we shall explainin a very simple example how MFG models are derived andpresent some overview of the theory, its connections withmany other fields and its applications.

Pierre-Louis LionsCollege de Francepierre-louis.lions@college-de-france.fr

IP2Complex Adaptive Systems and the Challenge ofSustainability

The continual increase in the human population, magni-fied by increasing per capita demands on Earth’s limitedresources, raise the urgent mandate of understanding thedegree to which these patterns are sustainable. The scien-tific challenges posed by this simply stated goal are enor-mous, and cross disciplines. What measures of human wel-fare should be at the core of definitions of sustainability,and how do we discount the future and deal with problemsof intra-generational and inter-generational equity? Howdo environmental and socioeconomic systems become or-ganized as complex adaptive systems, and what are theimplications for dealing with public goods at scales fromthe local to the global? How does the increasing intercon-nectedness of coupled natural and human systems affectthe robustness of aspects of importance to us, and whatare the implications for management. What is the role ofsocial norms, and how do we achieve cooperation at theglobal level? All of these issues have parallels in evolu-tionary biology, and this lecture will explore what lessonscan be learned from ecology and evolutionary theory foraddressing the problems posed by achieving a sustainablefuture.

Simon LevinPrinceton University, USAslevin60@gmail.com

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IP3The Isoperimetric Problem Revisited: ExposingEulers 1744 Proof of Necessity as a Proof of Suffi-ciency, as Such the First and Shortest in History

In this talk the speaker will outline the remarkable lifeof the isoperimetric problem (Determine, from all simpleclosed planar curves of the same perimeter, the one thatencloses the greatest area) and argue that it has been themost influential mathematics problem of all time. In 1744Euler constructed multiplier theory to solve the isoperimet-ric problem; however he concluded that his theory was onlynecessary and not sufficient to prove that the circle was thesolution. Some 130 years later Weierstrass constructed hiselegant sufficiency theory for problems in the calculus ofvariations and used it to give the first complete proof thatthe circle solved the isoperimetric problem. The speakerwill demonstrate that Eulers original proof was merely anobservation away from establishing sufficiency. As such itshould be viewed as the first and shortest solution to theisoperimetric problem in history.

Richard A. TapiaRice UniversityDept of Comp & Applied Mathrat@rice.edu

IP4Complex Networks. A Tour d’ Horizon

The field of complex network is gently introduced. Theclassical concepts of small-world and scale-freeness arebriefly discussed. Then, the problem of communicabilityin complex networks is motivated and analyzed by consid-ering the use of matrix functions. The concept of networkcommunicability is then applied to a few real-world situa-tions. It motivates a new Euclidean metric for networks,which allows to embed every network into a hypersphere ofcertain radius. Finally we discuss dynamical processes onnetworks. In particular we show how to extend these con-cepts to the consideration of long-range interactions amongthe agents in complex networks. The consequences of theseextensions for real-world situations are briefly discussed.

Ernesto EstradaUniversity of Strathclydeernesto.estrada@strath.ac.uk

IP5Linear Algebra Methods for Data Mining with Ap-plications to Materials Science

The field of data mining is the source of many new, in-teresting, and sometimes challenging, linear algebra prob-lems. In fact, one can say that data mining and machinelearning are now beginning to shape a ”new chapter” innumerical linear algebra. We will illustrate the key con-cepts and discuss dimension reduction methods which playa major role in machine learning. The synergy betweenhigh-performance computing, efficient electronic structurealgorithms, and data mining, may potentially lead to ma-jor discoveries in materials. We will report on our first ex-periments in ‘materials informatics’, a methodology whichblends data mining and materials science.

Yousef SaadDepartment of Computer ScienceUniversity of Minnesotasaad@cs.umn.edu

IP6Multifidelity Modeling for Identification, Predic-tion and Optimization of Large-scale Complex Sys-tems

Often we have available several numerical models that de-scribe a system of interest. These numerical models mayvary in ”fidelity” or ”skill,” encompassing different reso-lutions, different physics, and different modeling assump-tions; they may also include surrogates such as reduced-order models. A multifidelity approach seeks to exploitoptimally all available models and data. This talk dis-cusses the key elements of multifidelity modeling: con-structing reduced-order models, quantifying model uncer-tainties, selecting models with appropriate fidelity for theprediction/decision task at hand, and synthesizing multi-fidelity information. We show the benefit of multifidelitymodeling for the tasks of prediction, design optimization,and uncertainty quantification.

Karen E. WillcoxMassachusetts Institute of Technologykwillcox@MIT.EDU

SP1AWM-SIAM Sonia Kovalevsky Lecture: The Roleof Characteristics in Conservation Laws

Sonya Kovalevsky, in the celebrated Cauchy-Kovalevskytheorem, made clear the significance of characteristics inpartial differential equations. In the field of hyperbolicconservation laws, characteristic curves (in one space di-mension) and surfaces (in higher dimensions) dominate thebehavior of solutions. Some examples of systems exhibitinteresting, one might even say pathological, characteristicbehavior. This talk will focus on ways that characteristicsin systems of conservation laws give information about thesystems being modeled.

Barbara Lee KeyfitzThe Ohio State UniversityDepartment of Mathematicsbkeyfitz@math.ohio-state.edu

SP2The John von Neumann Lecture: Liquid Crystalsfor Mathematicians

Liquid crystals form an important class of soft matter sys-tems with properties intermediate between solid crystalsand isotropic fluids. They are the working substance of liq-uid crystal displays, which form the basis of a huge multi-national industry. The lecture will describe these fascinat-ing materials, and what different branches of mathematics,such as partial differential equations, the calculus of vari-ations, multiscale analysis, scientific computation, dynam-ical systems, algebra and topology, can say about them.

John BallOxford Centre for Nonlinear PDE Mathematical InstituteOxfordball@maths.ox.ac.uk

SP3Past President’s Address: Reflections on SIAM,Publishing, and the Opportunities Before Us

Upon taking up the post of president I had, of course, for-

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mulated my priorities for SIAM. This talk provides a goodoccasion to revisit some of those. One area turned outto play a vastly larger role than I would have anticipated,namely mathematical publishing and many issues associ-ated with it, ethical, technological, economic, political, andscientific. The future of scholarly publishing is far fromclear, but one thing seems certain: big changes are neededand will be coming. We, as mathematicians, are majorstakeholders. We should also be major agents in guidingthese changes. I will present some of my observations andthoughts as we confront the opportunities before us.

Douglas N. ArnoldSchool of MathematicsUniversity of Minnesotaarnold@umn.edu

SP4W. T. and Idalia Reid Prize Lecture: Large Alge-braic Properties of Riccati Equations

In the eighties there was considerable interest in the alge-braic properties of the following Riccati equation

A∗X +XA−XBB∗X + C∗C = 0, (1)

where A,B,C ∈ A, a Banach algebra with identity, andthe involution operation ∗. Conditions are sought to ensurethat the above equation has a solution in A. The resultswere disappointing and the problem was forgotten untilthis century when engineers studied the class of spatiallydistributed systems. One application was to control forma-tions of vehicles where the algebraic property was essential.This case involves matrices A,B,C with components in ascalar Banach algebra. Positive results are obtained forboth commutative and noncommutative algebras.

Ruth CurtainUniversity of Groningen, Netherlandsr.f.curtain@math.rug.nl

SP5I.E. Block Community Lecture: Creating Reality:The Mathematics Behind Visual Effects

Film-makers have long realized one of the best ways toconvince audiences that a computer-generated effect, like astormy ocean, is real is to numerically solve physical equa-tions describing the motion, bringing mathematics andscientific computing into the forefront of animation. Aswe progress to solving more physics more accurately andfaster, a whole new way of working has emerged, ”virtualpractical effects”, where artists set up shots virtually asthey’d want to in the real world and let simulated physicstake over. I’ll demonstrate how a little mathematical anal-ysis can make a world of difference to making a film.

Robert BridsonUniversity of British Columbiarebridson@gmail.com

JP1Systemic Risk

What is systemic risk, how do we model it,how to we an-alyze it, and what are the implications of the analysis? Iwill address these issues both in a larger historical contextand within current research mathematical finance. The keyproperty of systems subject to systemic risk is their inter-

connectivity and the way individual risk can become over-all, systemic risk when it is diversified by inter-connectivity.I will discuss theoretical issues that come up with mean-field and other models and will also show results of numer-ical simulations.

George C. PapanicolaouStanford UniversityDepartment of Mathematicspapanico@math.stanford.edu

CP1A-Posteriori Verification of Optimality Conditionsfor Control Problems with Finite-DimensionalControl Space

In this paper we investigate non-convex optimal controlproblems.We are concerned with a-posteriori verification ofsufficient optimality conditions.If the proposed verificationmethod confirms the fulfillment of the sufficient conditionthen a-posteriori error estimates can be computed. A spe-cial ingredient of our method is an error analysis for theHessian of the underlying optimization problem.We deriveconditions under which positive definiteness of the Hessianof the discrete problem implies positive definiteness of theHessian of the continuous problem.The article is comple-mented with numerical experiments.

Saheed Ojo AkindeindeJohann Radon Institute for Computational andApplied Mathematics (RICAM)saheed.akindeinde@mathematik.uni-wuerzburg.de

Daniel WachsmuthRICAM, Linz, Austriadaniel.wachsmuth@oeaw.ac.at

CP1Modeling and Control of Nanoparticle Delivery toTumor Sites with Experimental Validation

Currently, experimental trials are underway to investigatethe therapeutic bioavailability of nanoparticles used in thetreatment of certain types of cancers. This presentationwill discuss the development of mathematical models topredict and controls to regulate the concentration of suchnanoparticles in a mammalian body post-injection. Theelimination of nanoparticles from the blood and into tar-geted tumors and the reticulo-endothelial system will beevaluated.

Scarlett S. Bracey, Katie A. Evans, D. Patrick O’Neal,Isidro B. MaganaLouisiana Tech Universityssf005@latech.edu, kevans@latech.edu, poneal@latech.edu,ibmagana@gmail.com

CP1Discrete Approximations of Controlled StochasticSystems with Memory

This paper considers discrete approximations of an opti-mal control problem in which the controlled state equationis described by a general class of stochastic functional dif-ferential equations with a bounded memory. Three differ-ent approximation methods, namely (i) semidiscretizationscheme; (ii) Markov chain approximation; and (iii) finite

8 AN12 Abstracts

difference approximation, are investigated.

Mou-Hsiung ChangU. S. Army Research OfficeMathematics Divisionmouhsiung.chang@us.army.mil

CP1Steady State Sets of Non-Linear Discrete-TimeControl Dynamical Systems with Singular Distur-bance

Finding steady state sets is an important topic in the studyof dynamical systems. In this paper, we concentrate our ef-forts to non-linear discrete-time control dynamical systemswith large singular disturbance that are modeled by mul-tiple valued iterative dynamical systems or set valued dy-namical systems. Because the traditional means of calculususually fails under the extensive influence of singularity, theuse of alternative methods such as multiple valued iterativedynamics modeling is necessary in general. Under the mul-tiple valued iterative dynamics modeling, the steady statesets of non-linear discrete-time control dynamical systemsturn out to be the locally maximal strongly full-invariantsets, and we discuss how to reach it in countable steps sothat the finite step approximation problem is well posed.We also discuss the invariant fractal structure that oftenarises due to the large singular disturbance.

Byungik KahngUniversity of North Texas at Dallasbyungik.kahng@unt.edu

CP1Sparsity-Promoting Optimal Control of Dis-tributed Systems

We design sparse and block sparse feedback gains that min-imize variance amplification of distributed systems. Wefirst identify patterns that strike a balance between thequadratic performance and controller sparsity. We thenoptimize the feedback gains subject to the structural con-straints determined by the identified sparsity patterns. Weemploy the alternating direction method of multipliers andexploit structure of sparsity-promoting terms to decomposethe minimization problem into sub-problems that can besolved analytically.

Fu LinElectrical and Computer EngineeringUniversity of Minnesotafu@umn.edu

Makan FardadElectrical Engineering & Computer ScienceSyracuse Universitymakan@syr.edu

Mihailo R. JovanovicElectrical and Computer EngineeringUniversity of Minnesotamihailo@umn.edu

CP1Exact Controllability of the Linear AdvectionEquation with Interior Controls

An exact controllability result is discussed for the following

controlled linear advection equation:

ρt + · (fρ) = χA(x)u(x, t), (2)ρ(x, 0) = ρ0(x);ρ|Γi = 0,

where ρ is the state, u(x, t) ∈ L2([0, τ ];A) is the controlinput, f(x) is a smooth vector field, Γi ⊂ X is the inflowportion of the boundary ∂X, and ρ0(x) is the initial state.The result states that the region of controllability in timeτ is the portion of X that is touched by solutions of theODE x = f(x);x(0) = x0 in time τ emanating from initialpoints x0 ∈ A. An explicit expression for the controllability(and by duality, the observability) gramian is shown, andsome ideas to use the gramians for optimal placement ofactuators and sensors will be discussed.

Rajeev RajaramKent State Universityrrajaram@kent.edu

CP1Solving Optimal Control Problems with ControlDelays Using Direct Transcription

Numerical solutions of optimal control problems with de-lays are important in industry. Solutions to these types ofproblems are difficult to obtain via analytic techniques. Di-rect Transcription is a popular numerical method used tocompute the solutions of optimal control problems. In thispaper we report on the progress and challenges of develop-ing a general purpose industrial grade direct transcriptioncode that can handle problems with both state and controlconstraints and delays.

Karmethia C. ThompsonNorth Carolina State UnivDepartment of Mathematicskcthomps@ncsu.edu

Stephen L. CampbellNorth Carolina State UniversityDepartment of Mathematicsslc@ncsu.edu

John T. BettsPartner of Applied Mathematical Analysis, LLCjohn.betts@comcast.net

CP2A Discrete Dynamical Systems Model to Study theInteraction Between Arctic Sea-Surface Tempera-ture and Sea-Ice Cover

We propose a mathematical model involving discrete dy-namical systems to understand the interaction betweensea-surface temperature and sea-ice cover over the ArcticOcean. In particular, we use ideas from dynamical systemssuch as bifurcations and basins of attraction of equilibriaalong with basic probability theory to make future projec-tions about the possibility of extinction of Arctic sea-icecover, one of the top five tipping points in the Earth’s cli-mate. Observed data from multiple sensors will be used tovalidate the model. The implications and caveats of thefuture projections made by our model will be explored.

Sukanya BasuGrand Valley State University,Allendale, MIbasus@gvsu.edu

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CP2Numerical Studies of Eor by Asp-Flooding

Of the new techniques leading to increase oil production,EOR, which uses chemical additives, is one of the mostpromising. Chemical flooding is a way to recover addi-tional oil after water-flooding. It involves adding sufficientamounts of chemical species to injected fluids to changephase properties in a way that will enhance oil recovery.However, it is still a big problem that how to appropriatelychoose the displacing fluids based on their properties andthe sequence in which these should be injected to produceoil out as much as possible. In this talk, we will presentour results for optimal profiles on Polymer-Water floodingas well as Alkaline-Surfactant-Polymer-Water flooding. Itwill be discussed for the cases of constant and variable con-centrations of injected chemicals. The research reportedhere has been made possible by a grant NPRP 08-777-1-141 from the Qatar National Research Fund (a member ofThe Qatar Foundation). The statements made herein aresolely responsibility of the authors.

Xueru DingTexas A&M University at Qatardxueru@gmail.com

Prabir DaripaTexas A&M Universitydaripa@math.tamu.edu

CP2Bregman Iterations for Geosounding Inversion

A novel algorithm for nonlinear inversion based on Breg-man iterations is applied to electrical, electromagnetic andresistivity soundings. Tikhonov’s inversion method, com-monly employed for solving inverse problems solving, pro-duces smooth, ”smeared” models. Several techniques havebeen proposed in order to improve the model developmentin layered models, particularly in geophysics. Some changethe norm to L1 or total variation, and others propose apiecewise-continuous model. In the case of L1 optimiza-tion, a computationally expensive solver is required. Breg-man iterative method has recently proposed for L1 mini-mization problems, particularly when a sparse representa-tion is required. An iterative, coordinate descent methodis implemented based on Bregman distance. Results forseveral data of electrical, electromagnetic and resistivitysoundings are presented.

Hugo HidalgoCICESE-Ciencias de la Computacionhugo@cicese.mx

Enrique Gomez-TrevinoCICESE-Geofisica Aplicadaegomez@cicese.mx

CP2High Frequency Acoustic Propagation Using LevelSet Methods

We discuss an application of the level set method to under-water acoustic propagation. The level set model provides away to compute acoustic wavefronts on a fixed grid, so thatthe user has more control over the accuracy of the final so-lution than with the standard Lagrangian approaches (i.e.,ray tracing). The method includes high order numericalboundary conditions for reflections from hard surfaces and

allows for arbitrary, range-dependent sound speed data asinput.

Sheri L. MartinelliBrown UniversityNaval Undersea Warfare Center Newportsheri.martinelli@navy.mil

CP2How Do You Determine Whether The Earth IsWarming Up?

How does one determine whether the extreme summer tem-peratures in Moscow of a few years ago was an extremeclimatic fluctuation or the result of a systematic globalwarming trend? It is only under exceptional circumstancesthat one can determine whether a climate signal belongsto a particular statistical distribution. In fact, climate sig-nals are rarely ”statistical;” other than measurement er-rors, there is usually no way to obtain enough field data toproduce a trend or tendency, based upon data alone. Wepropose a trend or tendency methodology that does notmake use of a parametric or statistical assumption. Themost important feature of this trend strategy is that it isdefined in very precise mathematical terms.

Juan M. RestrepoDepartments of Mathematics, Atmospheric Physics, andPhysicsUniversity of Arizonarestrepo@math.arizona.edu

Darin ComeauProgram of Applied MathematicsUniversity of Arizonadcomeau@math.arizona.edu

Hermann FlaschkaMathematics DepartmentUniversity of Arizonaflaschka@math.arizona.edu

CP2An Adaptive Strategy with Unconditional Con-vergence for Solving Nonlinear Coupled Flow andTransport Equations in Porous Media

We propose a new hybrid strategy for solving flow andtransport equations in porous media . At each iteration,after updating pressure from a reduced system of linearequations, we decompose the phases flow graph into itsstrongly connected components. Saturation field is up-dated by traversing the resulting graph from upstream todownstream. We update pressure and saturation simulta-neously in counter current flow regions identified by multi-cell components to resolve the tight coupling. The resultsshow that the algorithm is convergent for very large timestep sizes.

Mohammad ShahvaliStanford Universityshahvali@stanford.edu

Hamdi TchelepiStanford UniversityEnergy Resources Engineering Departmenttchelepi@stanford.edu

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CP2Use of Integral Transforms in Analyzing Nmr Data

In Nuclear Magnetic Resonance (NMR) applications tostudy porous media, the measured data is modeled asa Laplace transform of the probability density function(PDF) of relaxation times. In this presentation, we de-scribe a novel method to directly compute linear function-als of the PDF without computing the PDF. This methodinvolves a linear transform of the measured data using in-tegral transforms. Different linear functionals of the PDFcan be obtained by choosing appropriate kernels in the in-tegral transforms.

Lalitha Venkataramanan, Fred Gruber, Tarek HabashySchlumbergerlvenkataramanan@slb.com, lvenkataramanan@slb.com,lvenkataramanan@slb.com

CP3An Object-Oriented Linear System Solver for Mat-lab

The MATLAB backslash is an elegant interface to a suiteof high-performance methods for solving linear systemsand least-squares problems. However, its simplicity pro-hibits the reuse of its factorization for subsequent sys-tems. Naive MATLAB users also have a tendency totranslate mathematical expressions from linear algebra di-rectly into MATLAB, so that x = A−1b becomes theunfortunate x=inv(A)*b. To address this problem, anobject-oriented factorize method is presented. Via oper-ator overloading, solving two linear systems can be writtenas F=factorize(A); x=F\b; y=F\c, where A is factorizedonly once. The selection of the best factorization methodis hidden from the user. The expression x = A−1b trans-lates into x=inverse(A)*b, without computing the inverse.

Timothy A. DavisUniversity of FloridaComputer and Information Science and EngineeringDrTimothyAldenDavis@gmail.com

CP3Sign Patterns That Allow Strong Eventual Non-negativity

A sign pattern is potentially eventually nonnegative (po-tentially strongly eventually nonnegative) if there is a ma-trix with this sign pattern that is eventually nonnegative(eventually nonnegative and has some power that is bothnonnegative and irreducible). The study of potentiallyeventually nonnegative sign patterns is hindered by nilpo-tent matrices and matrices which have powers that are re-ducible with a nilpotent diagonal block. This talk presentsresults about potentially strongly eventually nonnegativesign patterns.

Craig EricksonIowa State Universitycraig@iastate.edu

Minerva CatralXavier Universitycatralm@xavier.edu

Leslie HogbenIowa State University,

American Institute of Mathematicshogben@aimath.org

Dale OleskyDepartment of Computer ScienceUniversity of Victoriadolesky@cs.uvic.ca

Pauline van den DriesscheDepartment of Mathematics and StatisticsUniversity of Victoriapvdd@math.uvic.ca

CP3Matrix Computation and Its Application to SignalProcessing

First part of this presentation aims to leverage com-puting of the determinant of a 3×3 matrix whose ithrow is defined by [a1i+a2i+a3i a1i−1+a2i−1+a3i−1

a1i−2+a2i−2+a3i−2] without expanding. Second part ofthis presentation is the application to signal processing,specifically to non-uniform sampling [Yih-Chyun Jenq,Perfect Reconstruction of Non-Uniformly Sampled Signal,IEEE Trans. Inst.&Meas. 1997].

Wei-Da HaoDepartment of Electrical Engineering and ComputerScienceTexas A/&M University-Kingsvillekfwh000@tamuk.edu

Yih-Chyun JenqDepartment of Computer and Electrical EngineeringPortland State Universityjenq@cecs.pdx.edu

David H. ChiangDepartment of Compuetr and Electrical EngineeringPortland State Universitychiang@ece.pdx.edu

CP3Classification of Potentially Eventually Exponen-tially Positive Sign Patterns of Small Order

A matrix A is eventually exponentially positive if there ex-ists a positive real number t0 such that for all t ≥ t0, e

tA >0. A sign pattern is a matrix having entries in +,−, 0. Asign pattern A is potentially eventually exponentially pos-itive (PEEP) if there exists a matrix A in the qualitativeclass of A such that A is eventually exponentially positive.A classification of all 2x2 and 3x3 PEEP sign patterns isgiven.

Xavier Martinez-Rivera, Marie ArcherIowa State Universityxaviermr@iastate.edu, mharcher@iastate.edu

Minerva CatralXavier Universitycatralm@xavier.edu

Craig EricksonIowa State Universitycraig@iastate.edu

Rana Haber

AN12 Abstracts 11

Florida Institute of Technologyrhaber2010@my.fit.edu

Leslie HogbenIowa State University,American Institute of Mathematicshogben@aimath.org

Antonio OchoaCalifornia State Polytechnic Universityaochoa@csupomona.edu

CP3Positive Semidefinite Zero Forcing

The zero forcing number Z(G) is used to study the max-imum nullity/minimum rank of the family of symmetricmatrices described by a simple, undirected graph G. Westudy the positive semidefinite zero forcing number Z+(G)and some of its properties. In particular, we determinethe maximum positive semidefinite nullity and positivesemidefinite zero forcing number for a number of graphfamilies appearing in the AIM minimum rank graph cata-log.

Travis PetersIowa State Universitytpeters@iastate.edu

CP3On Estimating Hitting and Commute Times forLarge Dense Digraphs

Recent studies have established that the lengths of random-commutes between a source-destination pair, in large denseundirected-graphs, can be well approximated in terms ofscaled degrees of the end-point vertices, which implicatesthe relevance of commute times as a distance in machinelearning tasks. In this work we generalize the approxima-tions to strongly connected directed-graphs, albeit in termsof the steady-state-stationary-probability distribution. Inso doing, we develop a theoretical framework for these ap-proximations, without resorting to the interplay betweenundirected graphs and electrical-networks, an analogy onwhich previous studies rely and, more importantly, onethat does not apply to directed-graphs.

Gyan Ranjan, Zhi-Li ZhangUniversity of MinnesotaComputer Sciencegranjan@cs.umn.edu, zhzhang@cs.umn.edu

Daniel L. BoleyUniversity of MinnesotaDepartment of Computer Scienceboley@cs.umn.edu

CP4Contour Detection and Completion for Inpaintingand Segmentation Based on Topological Gradientand Fast Marching Algorithms

We combine the topological gradient, a powerful methodfor edge detection in image processing, and a minimal pathmethod in order to find connected contours. The topolog-ical gradient provides a more global analysis of the im-age than the standard gradient, and identifies the mainedges. Then the fast marching algorithm identifies minimal

paths in the topological gradient image. This coupled al-gorithm quickly provides accurate and connected contours.We present applications to inpainting and segmentation.

Didier AurouxUniversity of Nice, Franceauroux@unice.fr

Laurent D. CohenCNRS, UMR 7534Universite Paris-Dauphine, CEREMADEcohen@ceremade.dauphine.fr

Mohamed MasmoudiUniversity of Toulousemasmoudi@math.univ-toulouse.fr

CP4Iterative Wavefront Reconstruction in AdaptiveOptics

Obtaining high resolution images of space objects fromground based telescopes is challenging, and often requirescomputational post processing using image deconvolutionmethods. Good reconstructions can be obtained if the con-volution kernel can be accurately estimated. The convolu-tion kernel is defined by the wavefront of light, and howit is distorted as it propagates through the atmosphere.We describe the wavefront reconstruction problem - a newlinear least squares model that exploits information frommultiple measurements.

Qing Chu, James G. NagyDepartment of Mathematics & Computer ScienceEmory Universityqchu@emory.edu, nagy@mathcs.emory.edu

CP4Parallel Markov Chain Monte Carlo Methods inOptical Tomography

Markov Chain Monte Carlo (MCMC) is a standard sam-pling method in Bayesian inference. However, it is slow be-cause it requires that the forward model is solved at everyiteration. Furthermore, the standard algorithm is inher-ently sequential. We will discuss successful parallelizationtechniques involving a single and a multiple chains methodthat both shorten computations and improve sample qual-ity. We will then show results from applying them to areal-world, optical tomography problem.

Kainan Wang, Wolfgang BangerthTexas A&M Universitykwang@math.tamu.edu, bangerth@math.tamu.edu

CP5Using An Old Traffic Flow Model to Gain New In-sights into a Biological Process

The use of a nonlinear PDE to model the elongation pro-cess on ribosomal RNA is discussed. Experimentally, themotion of a transcription complex experiences multiplepauses, and the density of elongating complexes may besufficiently high to experience traffic jams. The traffic flowmodel includes the presence of non-uniform distributionsof pauses along the rrn operon and is used to estimatethe instantaneous elongation rate. Discontinuous Galerkin

12 AN12 Abstracts

methods are used for the model simulations.

Lisa G. DavisMontana State Universitydavis@math.montana.edu

CP5Interior-Point Methods for An Optimal Control In-fluenza Model

We introduce a discrete optimal control problem in orderto minimize the number of infected individuals on a singleinfluenza outbreak. We evaluate the effect of social distanc-ing and antiviral treatment as control policies. We solve theproblem by using Forward-Backward and Interior-PointMethod. Our simulations show that Interior point methodgives more robust results than Forward-Backward method.Finally we introduce an isoperimetric constraint to con-sider limited resources.

Paula A. Gonzalez ParraUniversity of Texas at El Pasopaulag817@gmail.com

Leticia VelazquezDepartment of Mathematical SciencesThe University of Texas at El Pasoletivela@gmail.com

Sunmi LeeMathematical, Computational and Modeling SciencesCenter,Arizona State University,mathever@gmail.com

Carlos Castillo-ChavezArizona State University andDepartment of Mathematicsccchavez@asu.edu

CP5Modeling the Effect of a New Antibiotic on theTransmission of Antimicrobial Resistant Bacteriain a Hospital Setting

The increase in antibiotic resistance continues to pose apublic health risk as very few new antibiotics are beingproduced, and the prevalence of bacteria resistant to cur-rently prescribed antibiotics is growing. In this talk, we useboth deterministic and stochastic mathematical models toanalyze the benefits and limitations of the introduction of anew antibiotic in both a large hospital setting and a smallerunit within a hospital under different administration pro-tocols.

Michele JoynerEast Tennessee State Universityjoynerm@etsu.edu

Cammey ManningMeredith Collegemanningc@meredith.edu

Brandi CanterEast Tennessee State Universitycanterb@goldmail.etsu.edu

CP5Modeling Behavior: Using Game Theory and Pop-ulation Modeling to Explain Sub-Maximal Para-sitism

We examine the implications of spatial structure on theevolution of parasitism rates for a well-characterized in-teraction between a parasitoid wasp and host butterfly ona fragmented landscape. We present multiple evolution-ary hypotheses, formulated as mathematical models, andshow the extent to which landscape features (patch quality,density, and connectedness) and host attributes (dispersalability, reproductive success, mortality) affect the viabil-ity of this mechanism; thus unveiling the role of spatialprocesses in the interaction.

Kathryn MontovanCornell Universitykjs237@cornell.edu

CP6Modeling Cell Movement Through Collagen Usingthe Level Set Method

Cell movement affects different biological processes. In thebody, cells move through a three-dimensional network ofcollagen, filaments, and other proteins. We are modelingcell movement through a series of deformable obstacles rep-resenting this network. We use the level set method totrack the membrane of the cell and borrow concepts fromthe theory of beams to model the network. Our goal is touse the simulations to model the environment within thebody and to investigate variations of this environment oncell movement.

Magdalena StolarskaUniversity of St. ThomasDepartment of Mathematicsmastolarska@stthomas.edu

Matthew FoxUniversity of St. Thomasfox07210@stthomas.edu

CP6A Sparse Update Method for the in-Silico Manip-ulation of Biological Signaling Pathways

Radon Institute for Computational and Applied Mathe-matics Austrian Academy of Sciences Defective biologicalsignaling pathways are linked to various pathological con-ditions and the correction of dysfunctional qualitative be-haviour such as oscillation or bistability is a major goalof pharmaceutical and clinical research. Based on differ-ential equation models of the underlying biochemical re-action networks we formulate nonlinear inverse problemsand suggest a sparse update algorithm that determines acomprehensible number of candidate network interventionsites. The practicability of our approach is demonstratedby an example related to defective apoptotic signaling.

Philipp KueglerRICAM, Austrian Academy of SciencesAustriaphilipp.kuegler@oeaw.ac.at

CP6An Unbiased Estimator of Noise Correlations un-

AN12 Abstracts 13

der Signal Drift

Estimation of correlations in noises is important in large-scale modeling and data analysis. In neuroscience, smallcorrelations in noises (trial-to-trial response variations) candecrease coding capacity by sensory neurons dramatically.Although significant noise correlation has been reportedfrom almost all cortical areas, nonstationarity, such as adrift in signals (mean responses) might engender artificialcorrelations even if no actual correlation exists. Althoughattempts to estimate noise correlation under changing envi-ronments have been made, they were useful only for specificcases. This study presents consideration of a bivariate nor-mal distribution for activities of two neurons and advancesthe proposition of a semiparametric method for estimatingits covariance matrix in an unbiased fashion, whatever thetime course of the signal is.

Keiji MiuraJST PRESTO, Harvard Universitymiura@ecei.tohoku.ac.jp

CP6Using Maps to Predict Activation Order in Multi-phase Rhythms

We consider a network of three heterogeneous coupledunits, each described by a planar dynamical system ontwo timescales, motivated by recent models for respiratoryrhythmogenesis. Each unit’s intrinsic dynamics supportsan active state and an inactive state. We analyze solutionsin which the units take turns activating, allowing for anyactivation order, including multiple activations of two ofthe units between activations of the third. The analysisproceeds via the derivation of a set of explicit maps be-tween the pairs of slow variables corresponding to the in-active units on each cycle. Evaluation of these maps on afew key curves in their domains can be used to constrain allpossible activation orders in a given network and to obtainboundary curves between all regions of initial conditionsproducing different activation patterns.

Jonathan E. RubinUniversity of PittsburghDepartment of Mathematicsrubin@math.pitt.edu

CP6The Influence of Heart Rate Variability on Alter-nans Formation in the Heart

Sudden cardiac death is caused by ventricular fibrillation,which is directly linked to an alternation in action potentialduration (APD) at the cellular level, i.e. alternans. A com-mon technique for studying the initiation and of alternansis the restitution curve, i.e. the relationship between theAPD and the preceding diastolic interval. However, thistechnique was derived under periodic pacing condition, i.e.in the presence of feedback. However, in the heart, morecomplex stimulation regimes exist, including physiologicalheart rate variability (HRV). Here, we investigated the ef-fect of HRV on the alternans formation in the heart, bothat the cellular and whole heart levels.

Elena TolkachevaDepartment of Biomedical EngineeringUniversity of Minnesotatalkacal@umn.edu

CP7Estimation of 3D Microstructural Band Propertiesin Dual Phase Steel Assuming An Oriented Cylin-der Model

Oriented cylinders in an opaque medium represent mi-crostructural banding in steels. The medium is sliced andon the cut plane, rectangular projections of the cylindersare observed. The marginal distributions of the cylinderradii and heights, aspect ratio, surface area and volumeare estimated from the rectangle length and height distri-butions. This estimation procedure is used on real bandedmicrostructures for which nearly 90 µm of depth have beenobserved via serial sectioning.

Kimberly S. McGarrityMaterials innovation institute (M2i)Delft University of Technologyk.s.mcgarrity@tudelft.nl

Jilt Sietsma, Geurt JongbloedDelft University of Technologyj.sietsma@tudelft.nl, g.jongbloed@tudelft.nl

CP7Thermodynamically Compatible Model of YieldStress Polymeric Fluids

We want to present some results on mathematical model-ing of polymeric yield stress fluids which have the proper-ties of both elastic solids and fluids. We try to investigatethis problem using the approach of multiphase continuummechanics. We develop the two-phase solid-fluid modelwhich is thermodynamically compatible and its govern-ing differential equations can be written in a conservativeform. Such a model is convenient for application of ad-vanced high-accuracy numerical methods and modeling ofdiscontinuous solutions.

Ilya PeshkovEcole Polytechnique de Montrealilya.peshkov@polymtl.ca

Evgeniy RomenskiSobolev Institute of Mathematicsevrom@math.nsc.ru

Miroslav GrmelaEcole Polytechnique de Montrealmiroslav.grmela@polymtl.ca

CP7Temporal Coarse-Graining of High Frequency Dy-namics Using Parameterized Locally InvariantManifolds

A model is built for coarse representation of the dynam-ics of phase transitions at the atomistic level. The coarsemodel is based on the idea of Parameterized Locally Invari-ant Manifolds (PLIM). By considering fine dynamics as asystem of ODE, one generates an evolutionary set of closedequations for the coarse quantities. With the implementa-tion of PLIM, we observe the macroscopic features of thesystem, such as temperature, number of interfaces and thestress-strain curve.

Likun TanCarnegie Mellon Universitylikunt@andrew.cmu.edu

14 AN12 Abstracts

Amit Acharya, Kaushik DayalCivil and Environmental EngineeringCarnegie Mellon Universityacharyaamit@cmu.edu, kaushik@cmu.edu

CP7Dynamics of Light Beam Interaction at the Inter-face of Nonlinear Optical Media

The Dynamics of two or more light beams interacting at theinterface of linear and nonlinear optical media is studiednumerically and analytically. Some interesting new resultshave been obtained. The numerical Simulations agree withthe results of analytical model. This results can be used todevelop devices in optical beam switching.

Rajah P. VaratharajahNorth Carolina A&T State Universityrajah@ncat.edu

CP7Impact of Combined Irregularity on the TorsionalWave Propagation

In this paper, we study the propagation of torsional sur-face wave in a homogeneous layer over an initially stressedheterogeneous half space with linearly varying directionalrigidities, density and initial stress under the effect of var-ious combined irregularities at the interface. Dispersionequation in a closed form has been deduced for variouscases. For a layer over a homogeneous half space, the ve-locity of torsional surface wave coincides with that of theLove waves. The consolidated effect of combined irregular-ity, inhomogeneity, initial stress and wave number on thephase velocity of torsional wave is depicted by means ofgraphs.

Sumit K. Vishwakarma, Shishir GuptaIndian School of Mines, Dhanbad, Jharkhand,India-826004sumo.ism@gmail.com, shishir ism@yahoo.com

CP8Matrices, Kirchhoff Graphs and Reaction Net-works

This talk introduces the concept of a Kirchhoff graph forany rational matrix. Kirchhoff graphs represent the fun-damental theorem of linear algebra for the matrix; if thematrix is the stoichiometric matrix for a chemical reactionnetworks, they also satisfy the Kirchhoff laws for that reac-tion network. The construction of these graphs and someof their properties will be discussed.

Joseph D. FehribachDepartment of Mathematical SciencesWorcester Polytechnic Institutebach@wpi.edu

CP8Microscopic Theory of Brownian Motion Revisited

A single massive particle suspended in a non-interactingsolvent is studied. Microscopic expressions for the frictioncoefficient in the Langevin equation in the Brownian limitand the time autocorrelation function of the force on theBrownian particle in the frozen dynamics are presented.

Guided by these expressions, the limiting behaviors of Morikernel, which is numerically obtained from molecular dy-namics simulation results of the full dynamics, are observedand discussed.

Changho KimDivision of Applied MathematicsBrown Universitychangho kim@brown.edu

George E. KarniadakisBrown UniversityDivision of Applied Mathematicsgeorge karniadakis@brown.edu

CP8A Conjecture on the Structure of Mutually Unbi-ased Bases

The maximal size of a collection of mutually unbiased bases(MUBs) for a finite-dimensional, complex Hilbert space isonly known for certain dimensions. We offer a conjectureconcerning the structure of the space of MUBs and prove itfor dimension 2, which provides a new proof that the max-imum size of a collection of MUBs is 3. We also develop anew algorithm for generating random MUBs to numericallyexplore conjectures concerning MUBs.

Francis C. MottaColorado State Universitymotta@math.colostate.edu

CP8Recursive Fermi-Dirac Operator Expansions withApplications in Electronic Structure Theory

Recursive Fermi-Dirac operator expansion is an efficientway to calculate the density matrix in reduced complexityelectronic structure theory. In this work, the errors in therecursive expansion methods are analyzed and schemes forerror control developed. Besides error control, a scale-and-fold technique to accelerate the convergence of the recursiveexpansion for the zero temperature case will be presented.

Emanuel H. RubenssonUppsala Universityemanuel.rubensson@it.uu.se

CP8Block-Sparse Matrix-Matrix Multiplication withError Control for Quantum Chemistry Applica-tions

In quantum chemistry applications such as Hartree-Fock(HF) and Kohn-Sham density functional theory (KS-DFT)for large molecules, the structure of the involved matrices issuch that a sparse matrix representation is advantageous.Efficient matrix-matrix multiplication for such matrices isneeded in the computationally challenging density matrixconstruction operation. In this work, methods for matrix-matrix multiplication for this kind of matrices are devel-oped and evaluated, focusing on efficiency and error con-trol.

Elias RudbergDivision of Scientific Computing, Department of I.T.Uppsala Universityelias.rudberg@it.uu.se

AN12 Abstracts 15

CP9Time Reversed Absorbing Condition (trac): Appli-cations to Inverse Problems

We introduce time reversed absorbing conditions (TRAC)in time reversal methods. They enable one to “recreatethe past’ without knowing the source which has emittedthe signals that are back-propagated. Applications in in-verse problems are presented. The method does not relyon any a priori knowledge of the physical properties of theinclusion. Numerical tests with the wave equation illus-trate the efficiency of the method. This technique is fairlyinsensitive with respect to noise in the data.

Franck AssousAriel University Center40700 Ariel - Israelfranckassous@netscape.net

Frederic NatafLaboratoire J.L. Lionsnataf@ann.jussieu.fr

Marie KrayPierre-et-Marie Curie University, Paris, Francekray@ann.jussieu.fr

CP9Reducing Uncertainty in Stochastic Inverse Prob-lems Involving Sparse Data

This work presents an approach for augmenting theinformation in the posterior distribution accompanyingBayesian inverse problems. Dominant behavioral featuresof a particular system, captured using snapshots from aphysics based model, in conjunction with a “Gappy’ in-ner product are used to generate plausible surrogate data.Such data are incorporated into the likelihood function toreduce the uncertainty in the joint posterior over modelparameters. Numerical examples are provided for charac-terization and flaw identification.

Jose G. Cano, Christopher J. EarlsCornell Universityjgc86@cornell.edu, cje23@cornell.edu

CP9An Application of Particle Swarm Optimization toIdentify the Thermal Properties of Materials

Input your abstract, including TeX commands, here. Theabstract should be no longer than 75 words. Only inputthe abstract text. Don’t include title or author informa-tion here. An inverse analysis of identifying thermal prop-erties for materials is presented. It is shown that the physi-cal problem can be formulated as an optimization problemwith differential equation constraints. A particle swarm op-timization algorithm is developed for solving the resultingoptimization problem. The proposed algorithm providesa global optimum with highly-improved convergence per-formance. Numerical results are presented to demonstratethe performance of the proposed method. The comparisonto the modified genetic algorithm is also included.

Fung-Bao LiuDepartment of Mechanical and Automation EngineeringI-Shou Universityfliu@isu.edu.tw

CP9The Estimation of Uncertainty in the Solution ofIce Sheet Inverse Problems: Gaussian Linear Caseversus the Stochastic Newton MCMC Method

We consider the estimation of uncertainty in the solu-tion of ice sheet inverse problems within the frameworkof Bayesian inference. When the noise and prior probabil-ity densities are Gaussian, and the parameter-to-observablemap is linearized, the resulting posterior probability den-sity is Gaussian, with covariance given by the inverse of thelog-posterior Hessian. We compare solutions of ice sheet in-verse problems under the Gaussian-linear assumption withthe full non-Gaussian solution obtained by stochastic New-ton MCMC sampling, which employs local Hessian-basedGaussians as proposal densities.

Noemi PetraInstitute for Computational Engineering and Sciences(ICES)The University of Texas at Austinnoemi@ices.utexas.edu

James R. MartinUniversity of Texas at AustinInstitute for Computational Engineering and Sciencesjmartin@ices.utexas.edu

Georg Stadler, Omar GhattasUniversity of Texas at Austingeorgst@ices.utexas.edu, omar@ices.utexas.edu

CP9A Comparison of Deterministic and StochasticMeans for Damage Parameter Identification in aMultiphysics Context

A means for obtaining accurate damage parameter esti-mates resulting from complex, multi-modal likelihood func-tions common with multiphysics problems is presented.Noisy data in the form of fluid pressures resulting fromthe vibration of a damaged structure are generated fromsparse sensors in the fluid domain. A comparison betweena deterministic and stochastic means for solving the inverseproblem is described. Solution existence, uniqueness andstability will be discussed.

Heather M. Reed, Christopher J. EarlsCornell Universityhmr6@cornell.edu, cje23@cornell.edu

Jonathan NicholsNaval Research Laboratoryjonathan.nichols@nrl.navy.mil

CP93-D Constrained Joint Inversion of GeophysicalData for Crustal and Mantle Velocities in theSouthern Rio Grande Rift

We propose a novel approach for joint inversion of geophys-ical datasets to characterize velocity structure of the RioGrande Rift. The inverse problem is solved as in nonlinearprogramming with interior-point methods. We introducephysical bounds over the model parameters and a measureof differences in geological structure. Bound and structuralconstraints introduce a priori information to simulate thephysics of each dataset. Initial results reveal 3-D veloc-ity structure suggesting continuation of deformation and

16 AN12 Abstracts

extension of the Rift.

Anibal SosaComputational Science ProgramThe University of Texas at El Pasousosaaguirre@miners.utep.edu

Aaron Velasco, Lennox ThompsonDepartment of Geological SciencesThe University of Texas at El Pasoaavelasco@utep.edu, lethompson@miners.utep.edu

CP10Modeling and Analysis of Plant-Seed Bank Dynam-ics of a Disturbance Specialist in a Random Envi-ronment

A nonlinear stochastic integral projection model (SIPM)is introduced for the dynamics of a plant population witha seed bank. This plant population needs disturbancesto germinate, and these disturbances are governed by astochastic process. Under biologically-reasonable assump-tions we show that both the plant and the seed bank pop-ulations converge (in distribution)to a stationary distri-bution independent of initial populations. We also showhow changes in the parameters governing disturbance (fre-quency and intensity of disturbance)affect some of the char-acteristics of the long-term stationary distribution.

Eric A. EagerUniversity of Nebraska - Lincolns-eeager1@math.unl.edu

CP10Urinary Tract Infections in Meningioma Patients:Analysis of Risk Factors and Outcomes

Urinary tract infections account for approximately 35% ofall nosocomial infections and 75% are associated with theuse of urethral catheters. The goal of this study was toevaluate pre-operative factors associated with the risk ofa UTI and estimate the impact of UTIs on patient out-come and resource utilization. Perioperative UTIs werestrongly associated with specific comorbidities and post-operative complications. They significantly increase in-hospital length of stay and costs.

Miriam NunoDepartment of NeurosurgeryCedars Sinai Medical Centermiriamucla@gmail.com

CP10Finding Trends in Multiscale/Non-StationaryTime Series

We would like to define a trend to a a time series for whichthere is no information on its statistics or for which an ap-proximate or a precise functional relationship to time is notknown or safely assumed. An example where this arises isin the determination of whether meteorological variationscan be ascribed to simple fluctuations, or are instead man-ifestations of changes in the global climate trend. We in-troduce an adaptive non-parametric time series estimatorthat has a clear mathematical description and is capableof extracting a trend for this type of time series.

Juan M. RestrepoDepartments of Mathematics, Atmospheric Physics, and

PhysicsUniversity of Arizonarestrepo@math.arizona.edu

Darin ComeauProgram of Applied MathematicsUniversity of Arizonadcomeau@math.arizona.edu

Hermann FlaschkaMathematics DepartmentUniversity of Arizonaflaschka@math.arizona.edu

CP10Linear Regression Via the Singular Value Decom-position

Biased estimators for linear ill-posed problems are often ob-tained by truncating the SVD for the discrete system. Thetechnique is generally regarded as a determination of the”numerical rank” of the matrix, even though this ”rank”often depends on the right hand side vector. A betteridea is to truncate the rotated right hand side vector toeliminate components corrupted by measurement errors.The method also works well for well conditioned regressionproblems.

Bert W. RustNational Institute of Standards and Technnologybert.rust@nist.gov

CP10Large Deviations and Importance Sampling for aFeed-forward Network

We begin by considering a feed-forward network with a sin-gle server station serving jobs with multiple levels of prior-ity. The service discipline is preemptive in that the serveralways serves a job with the current highest priority level.For this system with discontinuous dynamics, we outlinethat the family of scaled state processes satisfy the samplepath large deviations principle using a weak convergenceargument. In the special case where the jobs have twodifferent levels of priority, we explicitly identify the expo-nential decay rate of the probability a rare event, namely,the total population overflow associated to the feed-forwardnetwork. We then use importance sampling - a variance re-duction technique - efficient for rare event probabilities tosimulate the exact probability of interest. We conclude byconfirming our theoretical results with numerical simula-tions.

Leila Setayeshgar, Hui WangBrown Universityleila setayeshgar@brown.edu, huiwang@cfm.brown.edu

CP10Demonic Fuzzy Operators: Illustration with FuzzyLogic

Fuzzy relations and fuzzy relational operators can be usedto define the fuzzy semantics of programming languages.The operators ∪fuz and fuz serve to give an fuzzy angelicsemantics, by defining a program to go right when thereis a possibility to go right. On the other hand, the fuzzydemonic operators fuz and fuz do the opposite: if thereis a possibility to go wrong, a program whose semantics

AN12 Abstracts 17

is given by these operators will go wrong; it’s the fuzzydemonic semantics. We will define these operators andillustrate them using fuzzy logic.

Fairouz TchierKing saud Universityftchier@ksu.edu.sa

CP11Fast Computation of the Zeros of a Polynomial

We present a new method for computing the zeros of apolynomial based on a factorization of the companion ma-trix into a product of n− 1 essentially 2× 2 matrices. Thezeros are computed by a non-unitary variant of Francis’algorithm that preserves the matrix factorization and con-sequently uses only O(n) storage and produces the rootsin O(n2) time.

Jared Aurentz, David S. WatkinsWashington State UniversityDepartment of Mathematicsjaurentz@math.wsu.edu, watkins@math.wsu.edu

Raf VandebrilKatholieke Universiteit LeuvenDepartment of Computer Scienceraf.vandebril@cs.kuleuven.be

CP11A One-Sided Convex Area Function for ImprovedVariational Grid Generation

The use of suitable convex area functionals in the contextof the variational grid generation problem has been studiedin detail. A fundamental theorem for this problem statesthat if Ω is a polygonal region for which there exists a con-vex grid, and f : R→ R is a C2 convex, strictly decreasingand nonnegative function, then it is possible to find a realnumber t such that the functional F : RN → R given byF (G) =

∑N

q=1 f(tαq) attains its minima in the open setof convex grids for Ω. Using this result, several global andlocal strategies for updating t have been proposed. In thispaper, by weakening the strictly decreasing hypothesis, wepropose a one-sided functional, for which f(x) is constantfor x larger that a given parameter α0. This new func-tional is also convex and shares many properties with theprevious ones, but since it focuses only on grid cells witharea values less that α0, it can be used in order to increasethe quality of very specific cells on convex grids. Somenumerical experiments show the quality grids that can beobtained with this new approach.

Guilmer Gonzalez, Pablo BarreraFacultad de Ciencias - UNAMguilmerg@yahoo.com, antoniolapetra@gmail.com

Francisco Dominguez-MotaFacultad de Ciencias Fisico-MatematicasUMSNHfrancisco.dmota@gmail.com

CP11A Scalable Reformulation of the Parallel Algorithmfor the Mixed Volume Computation

Efficient algorithms for computing mixed volumes havebeen implemented in DEMiCs and MixedVol-2.0. While

the approaches in those two packages are different, theyfollow the same theme and are both highly serial. To fitthe need for the parallel computing, a reformulation of thealgorithms is inevitable. In this talk, a reformulation of thealgorithm for the mixed volume computation rooted fromalgorithms in graph theory will be presented.

Tsung-Lin LeeNational Sun Yat-set Universityleetsung@math.nsysu.edu.tw

Tien-Yien LiDepartment of MathematicsMichigan State Universityli@math.msu.edu

Tianran ChenMichigan State Universitychentia1@msu.edu

CP11Accelerating Iterative Linear Solvers on GPU

In this talk we present new results on developing paral-lel iterative linear solvers on NVIDIA GPU. We have de-signed a new matrix vector multiplication kernel and otherBLAS 1/2 subroutines. Based on these subroutines, sevenKrylov solvers and two algebraic multigrid solvers were im-plemented. ILU(k), ILUT, approximate inverse, polyno-mial, domain decomposition and algebraic multigrid pre-conditioners were also developed. Besides, a parallel tri-angular solver was developed. The speedup of our solverswas up to 20.

Hui Liu, Song YuUniversity of Calgaryhui.jw.liu@gmail.com, soyu@ucalgary.ca

Zhangxin ChenUniversity of CalgaryDepartment of Chemical & Petroleum Engineeringzhachen@ucalgary.ca

Ben Hsieh, Lei ShaoUniversity of Calgarybhsieh@ucalgary.ca, jedyfun@gmail.com

CP11Nonoverlapping Domain Decomposition Precondi-tioners for Isogeometric Analysis

In this talk, we construct and study nonoverlapping do-main decomposition preconditioners for elliptic problemsdiscretized by NURBS-based Isogeometric Analysis. Weconsider nonoverlapping preconditioners for the reducedSchur complement system, in particular BDDC precondi-tioners defined by primal continuity constraints across thesubdomain interface. These constraints are associated tosubdomain vertices and/or averages or moments over edgesor faces of the subdomains, but have a higher multiplicityproportional to the splines regularity. By constructing ap-propriate discrete norms, we are able to prove that our iso-geometric BDDC preconditioner is scalable in the numberof subdomains and quasi-optimal in the ratio of subdomainand element sizes. Numerical experiments in 2D and 3Dthat confirm our theoretical estimates and also illustratethe preconditioner performance with respect to the polyno-mial degree and regularity of the NURBS basis functions,

18 AN12 Abstracts

as well as its robustness with respect to discontinuities ofthe elliptic coefficients across subdomain boundaries.

Luca F. PavarinoDepartment of MathematicsUniversity of Milan, Italyluca.pavarino@unimi.it

Lourenco Beirao Da VeigaUniversita’ degli Studi di Milanolourenco.beirao@unimi.it

Durkbin ChoDipartimento di MatematicaUniversita’ di Milano, Italydurkbin@imati.cnr.it

Simone ScacchiUniversita’ degli Studi di Milanosimone.scacchi@unimi.it

CP11Dynamic Implicit 3D Adaptive Mesh RefinementFor Non-Equilibrium Radiation Diffusion

We describe a highly effifficient solution method for thecoupled nonlinear time dependent non-equilibrium radia-tion diffffusion equations. This coupled system of nonlin-ear equations exhibits multiple temporal and spatial scalesrendering it a stiffff coupled system to solve. Fully im-plicit time integration schemes are combined with 3D par-allel adaptive mesh refinement with the resulting nonlin-ear systems at each timestep being solved with a JacobianFree Newton Krylov method which employs highly efficientphysics based multilevel preconditioners.

Bobby Philip, Zhen Wang, Manuel Rodriguez, MarkBerrillOak Ridge National Laboratoryphilipb@ornl.gov, wzg@ornl.gov, mrs@ornl.gov,berrillma@ornl.gov

Michael PerniceIdaho National Laboratorymichamichael.pernice@inl.gov

CP11Recursive Schur Decomposition

We will present a new preconditioner to solve the linearsystems of equations arising from the discretization of el-liptic partial differential equations (PDEs) using the finiteelement method. This is a recursive algorithm that uses(a) non-overlapping domain decomposition, (b) Schur de-composition, (c) Krylov subspace method and (d) a fastsolver such as multigrid. We will also describe the parallelimplementation of this algorithm. Although the algorithmis general enough to be applied to solve a wide variety ofelliptic PDEs, we will focus on a model Poisson problemfor demonstration purposes. The algorithm can also be ex-tended to other discretizations such as finite difference orfinite volume methods.

Rahul S. SampathORNLsampathrs@ornl.gov

Bobby Philip

Oak Ridge National Laboratoryphilipb@ornl.gov

Srdjan SimunovicComputer Science and MathematiOak Ridge National Laboratorysimunovics@ornl.gov

CP12Schur Complements and Block Preconditioners forCoupled Diffusion Systems

Discretization of systems of coupled PDE under finite ele-ments or finite differences gives rise to block-structured al-gebraic systems. Expensive to solve, these systems requireeffective preconditioning. Many of these preconditionersare based on block LU factorizations. In such factoriza-tions, one obtains the Schur complement by eliminating onefield in terms of the other. Preconditioners constructed inthis manner require the inverse of the Schur complement,which is very expensive to compute. We study a particularsimple strategy for approximating the Schur complementthat has some general applicability, giving examples bothof the resulting block preconditioner and solving the Schurcomplement system for some coupled PDE.

Geoffrey Dillon, Rob KirbyTexas Tech Universitygeoffrey.dillon@ttu.edu, robert.c.kirby@ttu.edu

CP12Absolutely Stable Explicit Difference Schemes Pos-sessing Unconditional Approximation. ParabolicEquation Case.

A difference scheme is proposed that is absolutely stableas implicit schemes and require the minimum number ofarithmetic operations as explicit schemes. It also proposesa version of the Du Fort - Frankel scheme possessing un-conditional approximation.

Isom JurayevUnemployedijurayev@yahoo.com

CP12Instability of the Finite-Difference Split-StepMethod on a Non-Constant-Amplitude Back-ground in the Nonlinear Schrodinger Equation(nls)

We consider the implementation of the split-step methodwhere the linear part of the NLS is solved by the Crank-Nicolson method employing finite-difference discretizationof the spatial derivative. The von Neumann analysis re-veals that this method is unconditionally stable on thebackground of a constant-amplitude plain wave. However,simulations show that the method can become unstable onthe background of a soliton. We present a theory explain-ing this instability. Both this theory and the instabilityitself are substantially different from those of the Fouriersplit-step method, which computes the spatial derivativeby spectral discretization.

Taras LakobaUniversity of VermontDepartment of Mathematics and Statisticstlakoba@uvm.edu

AN12 Abstracts 19

CP12Using the Reverse Heat Equation to ApproximateFields Using Gaussian Basis Functions

Field interpolation is any method for approximating aknown field as a linear combination of basis functions.This presentation explores a procedure using the reverseheat equation to produce high order representations ofthe known field. As an alternative to interpolation meth-ods, we will begin with a regularization of the known fieldand use direct, stable, explicit finite difference methodsto correct the regularization using the reverse heat equa-tion. This method achieves the predicted second, fourthand sixth order of accuracy.

Louis F. RossiUniversity of Delawarerossi@math.udel.edu

CP12Uniform Numerical Approximation of IntegrableEquations via Riemann-Hilbert Problems

The Riemann–Hilbert formulations of the Korteweg–deVries and the Painleve II transcendent have proved tobe computationally valuable. Borrowing ideas from themethod of nonlinear steepest descent, the resulting numer-ical schemes are seen to be asymptotically reliable. Herewe derive some sufficient conditions for a numerical methodto maintain accuracy throughout unbounded regions of theplane on which the differential equation is posed.

Thomas D. TrogdonDepartment of Applied MathematicsUniversity of Washingtontrogdon@amath.washington.edu

Sheehan OlverThe University of SydneySheehan.Olver@sydney.edu.au

CP12On the Numerical Solution of Initial-BoundaryProblem to One Nonlinear Parabolic Equation

In the presented work the numerical solution of initial-boundary problem to the following nonlinear parabolicequation

∂U

∂t= a (x, t, U)

∂2U

∂x2+ b (x, t, U)

(∂U

∂x

)2+ f (x, t)

is obtained. The coefficients a (x, t, U) and b (x, t, U) arerequired to be continuous and to have continuous partialderivative with respect to argument U . Additionally co-efficient a (x, t, U) is required to be positive. The func-tion f (x, t) is required to be continuous. For the men-tioned initial-boundary problem the difference scheme isconstructed and the theorem of existence of its solution andthe theorem of convergence of its solution to the solutionof the source problem are proved. The rate of convergenceis established and it is equal to O

(τ + h2

).

Mikheil TutberidzeIlia State UniversityAssociated Professormikheil.tutberidze@iliauni.edu.ge

CP12Investigations on Performances of ElectromagneticSolvers

Many efficient numerical methods have been developed andused for electromagnetic simulations in time and frequencydomains. Their performances are quite different based onmany details of the numerical methods, such as mesh, nu-merical orders and expansion bases, etc. This talk willinvestigate these factors and compare their performance indetail. Some simulation results will be presented using thesuitable solvers. Challenges for current solvers and possiblenew techniques to improve them will be discussed.

Jin XuChinese Academy of Sciencejin xu@hotmail.com

MiSun MinArgonne National LaboratoryMathematics and Computer Science Divisionmmin@mcs.anl.gov

CP13Data Mining Methods Applied to Numerical Ap-proximations for Pdes

Classical results analysis of numerical methods is very of-ten limited to the description of tables or graphs of isoval-ues. We propose a new method for numerical data analy-sis, based on exploratory data mining techniques that haveproven to be efficient in other areas producing bulimic data,like biology or marketing. Our approach allows us to ana-lyze and characterize the different sources of errors involvedin a given mathematical modeling process coupled with nu-merical approximations.

Joel ChaskalovicUPMC - Paris 6, Francej.chaskalovic@free.fr

Franck AssousAriel University Center40700 Ariel - Israelfranckassous@netscape.net

CP13Runge-Kutta Discontinuous Galerkin Method for2D Nonlinear Moment Closures for RadiativeTransfer

Radiative transport equation calculations have importantapplications in determining the interaction between highenergy particle propagation and body tissue in radiationdose therapy. We apply the Runge-Kutta discontinuousGalerkin (RKDG) method to moment models for the ra-diative transfer equation. Our goal is to resolve the timeevolution of isolated sources or beams of particles in hetero-geneous media on unstructured grids. The moment modelsconsidered are nonlinear hyperbolic balance laws.

Prince ChidyagwaiTemple UniversityDepartment of Mathematicsprince.chidyagwai@temple.edu

Benjamin SeiboldTemple Universityseibold@temple.edu

20 AN12 Abstracts

Philipp MonrealAachen Universitymonreal@mathcces.rwth-aachen.de

Martin FrankRWTH Aachen UniversityCenter for Computational Engineering Sciencefrank@mathcces.rwth-aachen.de

CP13The Ghost Solid Method Based Algorithms forElastic Solid-Solid Interaction

Three variations of Ghost Solid Method based algorithmsare developed for capturing the boundary conditions atthe solid-solid interface of isotropic, linearly elastic mate-rials, in a Lagrangian framework. The methods are exten-sively tested under 1D setting. The effect of using differentsolvers for these methods is discussed. The advantages anddisadvantages of each of these methods are analyzed. Pre-liminary results show that these methods can be extendedto multi-dimensional settings.

Abouzar KaboudianNUS Graduate School for Integrative Sciences andEngineeringNational University of Singaporeabouzar@nus.edu.sg

Boo Cheong KhooSingapore-MIT Alliancempekbc@nus.edu.sg

CP13Applying the Exterior Matrix Method to the In-clined Cable Problem

We apply the Exterior Matrix Method to find the approx-imate eigenfrequencies for serially connected inclined ca-bles. The dynamics of each satisfies a system of four partialdifferential equations, but even their linearization cannotbe solved in closed form. However, the Exterior MatrixMethod does not require the solution of governing equa-tions. The eigenfrequency information is embedded in a6 × 6 exterior matrix for each span, which are multipliedtogether to solve for the eigenfrequencies.

Matthew Manning, William PaulsenArkansas State Universitymatthew.manning@smail.astate.edu,wpaulsen@astate.edu

CP13Introduction to the Exterior Matrix Method

We will introduce the Exterior Matrix Method (EMM) tocompute the approximate eigenfrequencies for serially con-nected elements, each governed by a system of four firstorder linear partial differential equations. Ironically, thegoverning equations do not have to be solved to find theapproximate corresponding 6 × 6 exterior matrix. We cansolve the the approximate eigenfrequencies by multiplyingthe exterior matrices together. The procedure works evenif dissipative joints are added to the system.

William Paulsen, Matthew ManningArkansas State Universitywpaulsen@astate.edu,

matthew.manning@smail.astate.edu

CP13Highly Accurate Algorithm for Time-DependentPde’s

Standard space discretization of time-dependant pde’s usu-ally results in system of ode’s of the form

ut −Gu = s (3)

where G is a linear operator ( matrix ) and u is atime-dependent solution vector. Highly accurate methods,based on polynomial approximation of a modified expo-nential evolution operator, had been developed already forthis type of problems where G and s are constant. In thistalk we will discribe a new algorithm for the more generalcase where G and s depend on t and u. Numerical resultswill be presented.

Hillel Tal-EzerAcademic College of Tel-Aviv Yaffohillel@mta.ac.il

CP14Small Deformation Viscoplastic Dynamic SphereProblem

Developing benchmark solutions for problems in solid me-chanics is very important for the purpose of verifying com-putational physics codes. In order to test some physicscodes, we present a benchmark solution to the small de-formation dynamic sphere problem for an isotropic vis-coplastic material obeying the Bodner-Partom model. Thesolution takes the form of an infinite series of eigenfunc-tions. We demonstrate convergence under eigenmode, spa-tial, and time refinement, and then compare to numericalresults.

Brandon ChabaudPennsylvania State Universitychabaud@lanl.gov

Jerry Brock, Todd WilliamsLos Alamos National Laboratoryjsbrock@lanl.gov, oakhill@lanl.gov

CP14Tensor Product Decomposition Methods for NoiseReduction, Data Compression, and Projective In-tegration

Tensor product decomposition (TPD) methods are a pow-erful linear algebra technique for the efficient representa-tion of high dimensional data sets. In the simplest 2-Dcase, TPD reduces to the well-known singular value de-composition of matrices. We discuss the application ofTPD methods to data compression of 3-D Magnetohydro-dynamic and 6-D kinetic simulations of plasmas. We alsodiscuss the application of TPD methods in noise reduc-tion and projective integration of particle-based collisionaltransport computations.

Diego Del-Castillo-NegreteOak Ridge National Laboratorydelcastillod@ornl.gov

AN12 Abstracts 21

CP14Lime: Software for Robust and Flexible Multi-physics Coupling

Multiphysics code coupling aims at a synergistic unionof existing and emerging simulation capabilities with ro-bust and efficient coupling algorithms. Originally targetingnuclear reactor performance modeling, LIME representsa general multiphysics coupling capability. LIME’s algo-rithms span fixed-point coupling, placing no restrictionson models or methods, through Newton-based coupling,requiring residuals and exploiting any additional informa-tion and functionality codes expose. A rich suite of linearand nonlinear solvers is provided through LIME’s interfaceto the Trilinos Solver Framework.

Russell W. Hooper, Rodney Schmidt, Kenneth BelcourtSandia National Laboratoriesrhoope@sandia.gov, rcschmi@sandia.gov,kbelco@sandia.gov

CP14Application of a Perturbation Method to NonlinearParabolic Stochastic PDEs

We have applied the perturbation method developed byZhang and Lu in 2004, making use of the Karhunen-Loeveexpansion, to 2D parabolic equations having stochasticconductivity and nonlinear reaction. Some results areshown, demonstrating that in many cases the method pro-duces good approximations of the first and second momentsof solutions. Some analysis of computational complexityand convergence of the approximate solutions will be pre-sented.

Kevin LenthUniversity of Wyomingklenth@uwyo.edu

Victor E. GintingDepartment of MathematicsUniversity of Wyomingvginting@uwyo.edu

Peter PolyakovUniversity of Wyomingpolyakov@uwyo.edu

CP14Discontinuous Galerkin Methods for Modelling andSimulation of Transcription Processes

A Discontinuous Galerkin FEM is used for simulation ofa nonlinear PDE that models the motion of polymeraseson ribosomal RNA. Physically relevant pauses along therrn operon are incorporated into the model. These pausesresult in delays during the transcription process, possiblyaffecting protein production. The average delay experi-enced by a polymerase is estimated, and sensitivity anal-ysis is used to quantify the effects that location and timeduration of pauses have on the average delay.

Jennifer ThorensonMontana State Universitythorenso@math.montana.edu

CP14Reweighted l1 Minimization Method for SPDEs

We propose a method for the approximation of solutionsof PDEs with stochastic coefficients and “sparse” solutionsbased on l1 minimization. We employ reweighted iterationsto enhance the “sparsity” of the solution. Also, we usesampling points based on specific probability measure dueto the structure of the measurement matrix which dependson the gPC expansion of the solutions. This non-intrusivemethod is especially effective when the deterministic solveris very time consuming.

Xiu YangBrown Universityxiu yang@brown.edu

George E. KarniadakisBrown UniversityDivision of Applied Mathematicsgeorge karniadakis@brown.edu

CP15Identity Issues in Radial Basis Functions: RBFs AsModulated Sinc Functions in the Near-Equivalenceof Exponentially Convergent RBF Species

On a one-dimensional uniform, infinite grid, we show thatradial basis functions (RBFs) are well approximated bythe product of the sinc, sin(πx)/(πx), with a modulationπx/sinh(πx/ρ). This implies that Gaussian, sech, multi-quadric, inverse multiquadric and inverse quadratic RBFsare the same species,modulo tiny differences that disap-pear altogether in the ”flat limit”. Extensions to a nearlyuniform grid and to higher dimensions are also described..

John P. BoydUniversity of MichiganAnn Arbor, MI 48109-2143 USAjpboyd@umich.edu

CP15Error Bounds for Spline Interpolation Based Para-metric Model Order Reduction

Spline interpolation technique combined with balancedtruncation is con- sidered to reduce the order of parameterdependent large LTI-systems while preserving the param-eters as variables. Linear or cubic spline inter- polation isapplied to transfer functions of locally reduced order mod-els to deliver an approximation to the parameter dependentoriginal transfer function. This talk presents the proce-dures and the derivation of error bounds and demonstratesthe results on a numerical example.

Angelika Bunse-GerstnerUniversitaet BremenZentrum fuer Technomathematik, Fachbereich 3Bunse-Gerstner@math.uni-bremen.de

Than Son NguyenUniversitaet Bremen, Germanyson-nguyen@math.uni-bremen.de

CP15Chebyshev Interpolation for Functions with End-

22 AN12 Abstracts

point Singularities.

Functions defined on a finite interval which are boundedand singular at one or both endpoints may be effectivelydealt with by use of an exponential or double-exponentialtransform. This strategy involves transplantation of theproblem function to an infinite or semi-infinite interval,where a trade-off between domain-truncation and interpo-lation errors determines the overall rate of convergence.We shall systematically categorise the convergence theoryfor these situations, with a particular focus on Chebyshevinterpolation.

Mark RichardsonUniversity of Oxfordmark.richardson@maths.ox.ac.uk

CP15Finite Difference Weights and Superconvergence

Let z1, z2, . . . , zN be a sequence of distinct grid points. Afinite difference formula approximates the m-th derivativef (m)(0) as

∑wkf (zk). We derive an algorithm for finding

wk which uses fewer arithmetic operations and less memorythan the algorithm in current use (Fornberg, Mathematicsof Computation, vol. 51 (1988), p. 699-706). In addi-tion, the order of accuracy of the finite difference formulafor f (m)(0) with grid points hzk, 1 ≤ k ≤ N , is typicallyO(〈N−). However, the most commonly used finite differ-

ence formulas have an increased order of accuracy (super-convergence). Even unsymmetric finite difference formulascan exhibit such superconvergence, as shown by the explicitalgebraic condition that we derive.

Burhan SadiqDepartment of MathematicsUniversity of Michigan, Ann Arborbsadiq@umich.edu

Divakar ViswanathUniversity of Michigandivakar@umich.edu

CP15Jacobi 1825, Cauchy 1826, Poisson 1827

Fast-converging numerical algorithms are usually fast be-cause some function is analytic, and to quantify that fastconvergence, a powerful tool is contour integrals in thecomplex plane. We show how a formula in Jacobi’s 1825thesis in Berlin leads to:

• fast convergence of the periodic trapezoid rule

• Hermite integral formula

• Runge phenomenon

• potential theory

• Euler-Maclaurin formula

• Gauss quadrature

• spectral methods

• barycentric interpolation formula

• Chebfun

• (and maybe) hyperfunctions

Lloyd N. TrefethenOxford Universitytrefethen@maths.ox.ac.uk

CP15Barycentric Hermite Interpolation

For long it was believed that Newton interpolation was su-perior to Lagrange interpolation. However, the work ofBerrut and Trefethen has shown that Lagrange interpola-tion is as fast and typically more robust. Here we considerHermite interpolation: finding a polynomial interpolantthat matches the function values and derivatives at gridpoints. We derive an algorithm for barycentric Hermiteinterpolation. The algorithm is identical to the recentlypublished version of Butcher et al. (Numerical Algorithms2011). However our derivation is somewhat different andleads to an efficient method for updating Hermite inter-polants.

Divakar ViswanathUniversity of Michigandivakar@umich.edu

CP15Summability of Expansions on the Cylinder

We present a result regarding the Cesaro summability ofthe expansion of functions on the cylinder Bd × Im inorthogonal polynomials with respect to a product weightfunction. An upper bound for the critical index δ is ob-tained.

Jeremy WadePittsburg State Universityjwade@pittstate.edu

CP16Numerical Methods for High-Dimensional PdfEquations

We study the evolution equation of joint excitation-response PDF obtained by the Hopf functional approachfor various stochastic systems. Adaptive DiscontinuousGarlerkin and other methods are developed and comparedto solve this advection-type evolution equation. Also, someissues arising in this formulation are investigated includ-ing different high dimensionality in phase and parametricspace, and representation of multiple correlated randomprocesses. Various stochastic dynamical system such asnonlinear advection equation, tumor cell model, and LimitCycle Oscillator are tested.

Heyrim ChoBrown UniversityProvidence, RIheyrim cho@brown.edu

Daniele VenturiBrown Universitydaniele venturi@brown.edu

George E. KarniadakisBrown UniversityDivision of Applied Mathematicsgeorge karniadakis@brown.edu

CP16A Convergence Study for Spdes Using CombinedPolynomial Chaos and Dynamically Orthogonal

AN12 Abstracts 23

Schemes

We study the convergence properties of the recently de-veloped Dynamically Orthogonal (DO) field equations incomparison with the Polynomial Chaos (PC) method. Ahybrid method with PC is introduced to tackle the sin-gularity of the DO equations for the case of deterministicinitial conditions. An adaptive method in the basis is alsoproposed. The computational cost of DO is found to besmaller when compared to the cost of other methods in-cluding MC and PC.

Minseok ChoiBrown Universityminseok choi@brown.edu

Themis SapsisNew Yrok Universitysapsis@cims.nyu.edu

George E. KarniadakisBrown UniversityDivision of Applied Mathematicsgeorge karniadakis@brown.edu

CP16Variance Reduction in the Simulation of StochasticDifferential Equations

Variance reduction techniques are commonly used to en-hance the efficiency of Monte Carlo simulations. This talkfocuses on variance reduction for single and coupled sys-tems of stochastic ordinary differential equations. Variancereduction techniques such as antithetic variates and controlvariates will be described and results presented.

David J. HorntropDept of Mathematical Sciences, Center for Applied MathNew Jersey Institute of Technologydavid.horntrop@njit.edu

CP16Variance-Reduced Equation-Free Newton-KrylovMethods for Stochastic Fine-Scale Simulations

Equation-free methods promise a straightforward compu-tation of macroscopic steady states and their stability,based only on appropriately initialized short bursts of mi-croscopic simulation, which are used to compute residualsand Jacobian-vector products. One way to proceed is touse a Newton algorithm, in which the linear systems in eachNewton iteration are solved via a Krylov method. A ma-jor problem in a naive implementation of this approach isthe amplification of statistical noise in the Jacobian-vectorproducts when the microscopic model is stochastic. Thistalk discusses approaches to reduce the variance on theseJacobian-vector calculations significantly, yielding signifi-cant reductions in computational effort.

Giovanni SamaeyDepartment of Computer Science, K. U. Leuvengiovanni.samaey@cs.kuleuven.ac.be

CP16Stochastic Collocation Methods for Stochastic Dif-ferential Equations Driven by White Noise

We propose stochastic collocation methods for SODEs and

SPDEs driven by white noise using the Stratonovich formu-lation. To control the increasing dimensionality in randomspace generated by the increments of Brownian motion, weapproximate Brownian motion with a spectral expansion.We also use sparse grid techniques to further reduce thecomputational cost. Numerical examples demonstrate thevery high accuracy and efficiency of the proposed method,including equations driven by additive and multiplicativenoises.

Zhongqiang Zhang, Xiu YangBrown Universityzhongqiang zhang@brown.edu, xiu yang@brown.edu

Guang LinPacific Northwest National Laboratoryguang.lin@pnnl.gov

Boris RozovskyBrown UniversityBoris Rozovsky@brown.edu

George E. KarniadakisBrown UniversityDivision of Applied Mathematicsgeorge karniadakis@brown.edu

CP17Multigrid, Adaptive Discontinuous Galerkin Meth-ods for the Cahn-Hilliard Equation and a DiffuseInterface Model of Tumor Growth

We present a mixed discontinuous galerkin finite element(DG-FE), convex splitting scheme for the Cahn-Hilliard(CH) equation. Unconditional energy stability and uniquesolvability, as well as optimal convergence, are proven forthe scheme. An efficient non linear multigrid algorithmis used to solve the discrete equations. Also, a spatiallyadaptive, primitive-variable DG-FE scheme for a CH-typediffuse interface model for cancer growth is presented. Con-vergence under mesh modification is demonstrated, andsimulation results are provided.

Andreas AristotelousDuke UniversityStatistical and Applied Mathematical Sciences Instituteaaristot@math.duke.edu

Ohannes KarakashianDepartment of MathematicsThe University of Tennesseeohannes@math.utk.edu

Steven M. WiseMathematics DepartmentUniversity of Tennesseeswise@math.utk.edu

CP17An Efficient Scheme Involving Only Constant Coef-ficient Matrices for Coupled Navier-Stokes/Cahn-Hilliard Equations with Large Density Ratios

We present an efficient scheme for simulations of the cou-pled Navier-Stokes/Cahn-Hilliard equations for the phasefield approach. The scheme has several attractive features:(i) It is suitable for large density ratios, and numericalexperiments with density ratios up to 1000 have been pre-

24 AN12 Abstracts

sented; (ii) It involves only time-independent coefficientmatrices for all flow variables, which can be pre-computedduring pre-processing, so it effectively overcomes the per-formance bottleneck induced by variable coefficient matri-ces associated with the variable density and variable vis-cosity; (iii) It completely de-couples the computations ofthe velocity, pressure, and the phase field function. Simu-lations will be presented to demonstrate the effectivenessof current method for studying two-phase flows involvinglarge density ratios, moving contact lines, and interfacialtopology changes.

Suchuan DongPurdue Universitysdong@math.purdue.edu

CP17Application of Compact-Reconstruction WENOSchemes to the Navier-Stokes Equations

The Compact-Reconstruction WENO (CRWENO) schemewas constructed by applying the WENO algorithm on com-pact stencils and achieved high spectral resolution as wellas non-oscillatory behavior across discontinuities. The newscheme was analyzed for scalar conservation laws and theEuler equations. The CRWENO scheme demonstratedlower dissipation and dispersion errors for smooth and dis-continuous flows, compared to the WENO scheme. Inthe present study, the CRWENO scheme is applied to themulti-dimensional Navier-Stokes equations on curvilinearmeshes. Results are presented for steady flow over airfoilsas well as dynamic stall of a pitching airfoil. Flow prob-lems representative of direct numerical simulation (DNS) ofturbulent flows are attempted and the results from the CR-WENO scheme are compared with those from the WENOscheme.

Debojyoti GhoshApplied Mathematics & Statistics, and ScientificComputationUniversity of Marylandghosh@umd.edu

James BaederDepartment of Aerospace EngineeringUniversity of Marylandbaeder@umd.edu

CP17A Fast Perturbation Approach in Ensemble LevelUpscaling

Ensemble level upscaling is efficient upscaling of flow pa-rameters for multiple geological realizations. Solving theflow problem for all the realizations is time-consuming. Re-cently, different stochastic procedures have been combinedwith upscaling methods to efficiently compute the upscaledcoefficients for a large set of realization. In this work, weproposed a fast perturbation approach in the ensemble levelupscaling. We give a correction scheme to generate up-scaled parameters and use collocation and clustering tech-niques in stochastic space, which allow us to compute theupscaled permeabilities rapidly for all realizations. Thenumerical results will be present.

Yan LiChevronsdyanli@gmail.com

Yalchin EfendievDept of MathematicsTexas A&M Universityefendiev@math.tamu.edu

Yuguang ChenChevron Energy Technology CompanyYChen@chevron.com

Louis DurlofskyStanford Universitylou@stanford.edu

CP17Summation-by-Parts Operators and Weak InitialConditions for Time-Discretisation

During the last decade, stable high order finite differencemethods applied to initial-boundary-value-problems havebeen developed. The stability is due to the use of so-calledsummation-by-parts operators (SBP), penalty techniquesfor implementing boundary and interface conditions (SAT),and the energy method for proving stability. The so calledSBP-SAT technique has so far only been used to discretizethe initial-boundary-value-problem in space. In this talkwe will discuss the use of this technique also in time. Forlinear problems, the result will be a fully discrete and en-ergy stable method of very high order of accuracy. Wewill discuss stability, accuracy and efficiency aspects of thistechnique.

Jan Nordstromprofessor in scientific computingDepartment of Mathematics, Linkoping Universityjan.nordstrom@liu.se

Tomas LundquistDepartment of MathematicsLinkoping Universitytomas.lundquist@liu.se

CP17Partitioned Algorithms for the Numerical Solu-tion of the Fluid-Structure Interaction Problem inHaemodynamics

In this work we deal with the numerical solution of thefluid-structure interaction (FSI) problem arising in thehaemodynamic environment. The aim is to develop effi-cient partitioned algorithms for real haemodynamic appli-cations, where the non-linear finite elasticity is consideredfor the structure subproblem. We provide theoretical andexperimental results concerning the accuracy and efficiencyof the proposed schemes and finally we apply some of suchschemes to the case of human carotid geometries, in orderto compare the fluid-dynamics before and after the removalof the atheromasic plaque.

Christian VergaraUniversita’ degli Studi di BergamoBergamo, Italychristian.vergara@unibg.it

Fabio NobileCSQI – MATHICSE, EPF de Lausanne, CHfabio.nobile@polimi.it

Matteo Pozzoli

AN12 Abstracts 25

Universita’ degli Studi di Bergamo Bergamo, Italymatteo1.pozzoli@mail.polimi.it

CP18Guaranteed Biclustering Via Semidefinite Pro-gramming

Given a set of objects and a set of features exhibited bythese objects, biclustering seeks to simultaneously groupthe objects and features according to their expression lev-els. We pose this problem as that of partitioning a weightedcomplete bipartite graph such that the densities of the re-sulting subgraphs are maximized. We consider a noncon-vex quadratic programming formulation for this problemand relax to a semidefinite program using matrix lifting.We show that the correct partition of the objects and fea-tures can be recovered from the optimal solution of thesemidefinite relaxation in the case that the input instanceconsists of several disjoint sets of objects exhibiting similarfeatures.

Brendan P. AmesUniversity of Waterloobpames@gmail.com

CP18A Minty Variational Principle for Set-Valued Op-timization

Set-valued optimization is proving a valuable tool inmathematical finance (see e.g. F.Heyde et al. inMath.Meth.Oper.Res (2009) 69:159-179). Besides, inscalar and vector optimization, Minty variational principleproves to be a sufficient optimality conditions and ensuresgood properties of the primitive optimization problem. Wewant to develop a Minty variational principle for set-valuedoptimization, defining Dini-type derivative for set-valuedfunctions.

Giovanni CrespiUniversite de la Vallee d’Aosteg.crespi@univda.it

Carola SchrageMartin˘Luther˘University Halle˘Wittenbergcarolaschrage@googlemail.com

CP18Solving Games by Differential Equations in FiniteTime

New method to solve symmetric matrix games by differen-tial equations is described. It allows us to find out opti-mal mixed strategy in finite time, whilst the ODE-basedmethod, belonging to Brown and von Neumann, in generalcase consideres ODE on [0,∞) and gives only the value ofgame.

Koba GelashviliFull Professor, Computer Science Department,Ivane Javakhishvili Tbilisi State Universitykobage@gmail.com

CP18Solving Sup-T Equation Constrained OptimizationProblems

This work considers solving the sup-T equation constrained

optimization problems from the integer programming view-point. A set covering-based surrogate approach is proposedto solve the sup-T equation constrained optimization prob-lem with a separable and monotone objective function ineach of the variables. This is our first trial of develop-ing integer programming-based techniques to solve sup-Tequation constrained optimization problems. Our com-putational results confirm the efficiency of the proposedmethod and show its potential for solving large scale sup-T equation constrained optimization problems.

Cheng-Feng HuDept. of Industrial Management, I-Shou university,Taiwanchu1@isu.edu.tw

CP18A Joint Economic Production and Delivery Quan-tity Model With a General Transportation CostStructure

A joint economic production and delivery quantity modelin a delivery price-based supply chain is studied in thispaper. More specifically, a fixed lot sizing policy is imple-mented in the production system, while smaller shippingquantity with periodic dispatches is delivered to the cus-tomer. The considered cost includes setup cost to launchthe batch production, inventory carrying cost, and trans-portation cost, where the transportation cost is a generalfunction of the delivery quantity. A per unit time costmodel is developed and analyzed to determine the optimalproduction quantity for the production system and the de-livery quantity to the customer. Under some mild condi-tions, it can be shown that the joint cost function is convexand the optimal production quantity is dependent of thedelivery quantity. The computational study has demon-strated the significant impact of the joint decision modelon the operating cost. In particular, cost savings can bemore than 30% when inventory carrying cost and/or trans-portation cost are high.

Shine-Der LeeNational Cheng Kung UniversityDept. of Industrial & Information Managementsdlee@mail.ncku.edu.tw

Yen-Chen FuNational Cheng Kung UniversityDepartment of Industrial and Information Managementr3897101@mail.ncku.edu.tw

CP18Cyber-Insurance in Internet Security: The Prob-lem of Resolving Information Asymmetry

Internet users such as individuals and organizations aresubject to different types of epidemic risks such as worms,viruses, spams, and botnets. To reduce the probabil-ity of risk, an Internet user generally invests in tradi-tional security mechanisms like anti-virus and anti-spamsoftware, sometimes also known as self-defense mecha-nisms. However, such software does not completely elim-inate risk. Recent works have considered the problem ofresidual risk elimination by proposing the idea of cyber-insurance. In this regard, an important research problemis resolving information asymmetry issues associated withcyber-insurance contracts. In this paper we propose threemechanisms to resolve information asymmetry in cyber-insurance. Our mechanisms are based on the Principal-

26 AN12 Abstracts

Agent (PA) model in microeconomic theory. We showthat (1) optimal cyber-insurance contracts induced by ourmechanisms only provide partial coverage to the insureds.This ensures greater self-defense efforts on the part of thelatter to protect their computing systems, which in turnincreases overall network security, and (2) the level of de-ductible per network user contract increases in a concavemanner with the degree of the user. Our methodology isapplicable to any distributed network scenario in which aframework for cyber-insurance can be implemented.

Ranjan PalUniversity of Southern Californiarpal@usc.edu

CP18Optimal Small Wind Turbine Placement in Con-strained Spaces

Wind farms composed of small scale turbines can be eco-nomical for small groups interested in renewable energygeneration, however the placement of turbines is problem-atic. There are obstacles, effects of wind shear and waketurbulence that are challenging to address particularly ifthe available area is limited and there are other constraints.We consider a simple model of these constraints and inter-ference factors and apply steepest descent techniques tooptimize turbine placement within constrained spaces.

Vincent WinsteadMinnesota State University, MankatoMinnesota State Universityvincent.winstead@mnsu.edu

CP19Simulation of Parachute Inflation Using the FrontTracking Method

Front Tracking is a Lagrangian tool for the propagationof material interface and is known for its excellent preser-vation of interface geometry. We use the front trackingmethod on a spring system to model the dynamics evolu-tion of parachute canopies. And this mechanical structureis coupled with the incompressible Navier-Stokes solverthrough the ”Impulse Method”. We will present the sim-ulation and comparison with experiments of several typesof parachute.

Joungdong KimSUNY at Stony BrookStony Brook, NY 11794selom114@ams.sunysb.edu

Xiaolin LiDepartment of Applied Math and StatSUNY at Stony Brooklinli@ams.sunysb.edu

Yan LiSUNY at Stony BrookStony Brook, NY 11794yli@ams.sunysb.edu

CP19Drops Settling in Sharp Stratification with andWithout Marangoni Effects

We present numerical simulations of a heavy drop settling

in a two layer miscible fluid with a sharp stratification indensity and surface tension with the drop. When the sur-face tension is uniform, the drop decelerates significantlyas it encounters the lower, denser layer. Intriguingly, whenthe lower layer has greater surface tension than the upper,the drop may bounce and be prevented from crossing thetransition region. In contrast, when the lower layer haslesser surface tension, the drop may accelerate through thetransition.

Avi Shapiro, Francois BlanchetteU.C. Mercedashapiro2@ucmerced.edu, fblanchette@ucmerced.edu

CP19A Front-Tracking Method For Moving Fronts AndHyperbolic Conservation Laws

We present a new high-order method for shock captur-ing with tracked material interfaces. Tracking uses a levelset which is advected using the material interface velocityobtained from interfacial Riemann problems. Each ma-terial phase is discretized independently using a uniformCartesian grid and the embedded boundary approach tocomplex geometry. Our discretization is a high-order Go-dunov method away from the interface. Near the interfaceit is a globally conservative and consistent finite volumeapproach.

Mehdi VahabUniversity of California DavisDepartment of Applied Sciencemvahab@ucdavis.edu

Greg MillerUniversity of CaliforniaDepartment of Applied Sciencegrgmiller@ucdavis.edu

CP19A Nitsche Method for a Stokes Interface Problem

We present a finite element method for the Stokes equa-tions involving two immiscible incompressible fluids withdifferent viscosities and with surface tension. The inter-face separating the two fluids does not need to align withthe mesh. We propose a Nitsche formulation which allowsfor discontinuities along the interface with optimal a pri-ori error estimates. A stabilization procedure is includedwhich ensures that the method produces a well conditionedstiffness matrix.

Sara ZahediUppsala Universitysara.zahedi@it.uu.se

Peter HansboJonkoping Universitypeter.hansbo@jth.hj.se

Mats G. LarsonDepartment of MathematicsUmea Universitymats.larson@math.umu.se

CP20Gpu Accelerated Greedy Algorithms for Com-

AN12 Abstracts 27

pressed Sensing

Greedy algorithms for compressed sensing are efficient,suboptimal algorithms to solve the combinatorial optimiza-tion problem

min ‖x‖0 subject to y = Ax,

where ‖ ·‖0 counts the nonzero entries and A is n×N withn < N . Exploiting the computational power of graphicsprocessing units (GPU) permits testing on problems or-ders of magnitude larger than experiments in the literature.This massive computational acceleration and increase intesting capability provide numerous insights to the greedyalgorithms including when each algorithm boasts the bestperformance.

Jeffrey D. BlanchardDepartment of Mathematics and StatisticsGrinnell Collegejeff@math.grinnell.edu

Jared TannerUniversity of Edinburghjared.tanner@ed.ac.uk

CP20Sparse Support Vector Machines for Classificationon Grassmannians

We propose an approach for classifying subspaces, e.g.points on a Grassmannian embedded in Euclidean space,using sparse support vector machines (SSVMs). We con-sider a labeled set of matrices, either two-class or multi-class, and map these to points on a parameter space. Theresulting manifold is embedded in Euclidean space wherethe SSVM is applied. We present applications to both hy-perspectral and medical data sets.

Sofya Chepushtanova, MIchael KIrbyColorado State Universitychepusht@math.colostate.edu, kirby@math.colostate.edu

CP20Perceptual Grouping of Characters in AntarcticaMaps

Our aim is to create a database with information aboutthe name and location of the major geographical featuresin maps using perceptual grouping. The first step is tosegment the characters in names from the background. Thecentroids of these characters are grouped based on theirproximity and direction to other centroids. Our initial testswith simulated text accurately grouped these charactersgreater than 90% of the time.

Ravishankar N. ChityalaUniversity of Minnesotachith001@umn.edu

Sridevi PudipeddiSouth Central Collegesridevi.pudipeddi@gmail.com

CP20A Multiobjective Mesh Optimization Frameworkfor Mesh Quality Improvement and Mesh Untan-

gling

We propose a multiobjective mesh optimization frameworkfor mesh quality improvement and mesh untangling. Ourframework is able to simultaneously optimize various as-pects of the mesh such as the element shape, element size,and associated PDE interpolation error; and to untangle in-verted elements, but is not limited to these categories. Wesuccessfully apply methods within our framework to real-world applications, such as problems from hydrocephalusand shape optimization.

Jibum KimPennsylvania State Universityjzk164@psu.edu

Thap Panitanarak, Suzanne M. ShontzThe Pennsylvania State Universitytxp214@cse.psu.edu, shontz@cse.psu.edu

CP20Optical Flow Computations for Solar IrradiancePrediction

We describe our method of short-term solar irradiance fore-casting. The method is based on prediction of cloud evo-lution via optical flow computations from NASA/NOAAsatellite imagery. The future cloud configuration is deter-mined and input to Locus Energy’s irradiance estimationmodel to predict irradiance. Our forecasting model was cal-ibrated and validated against NOAA’s Surface Radiationnetwork observations; we then further enhance our predic-tion accuracy by leveraging data from PV installations andweather sensors monitored by Locus Energy.

Sergey KoltakovStanford Universitykoltakov@stanford.edu

Matthew K. Williams, Shawn KerriganLocus Energymatthew.williams@locusenergy.com,shawn@locusenergy.com

CP20Adaptive Outlier Pursuit in 1-Bit CompressiveSensing and Matrix Completion

In compressive sensing (CS), the goal is to recover signalsat reduced sample rate compared to the classic Shannon-Nyquist rate. However, the classic CS theory assumes themeasurements to be real-valued and have infinite bit pre-cision. The quantization of CS measurements has beenstudied recently and it has been shown that accurate andstable signal acquisition is possible even when each mea-surement is quantized to only one single bit. There aremany algorithms proposed for 1-bit compressive sensingand they work well when there is no noise in the measure-ments, while the performance is worsened when there area lot of sign flips. We propose a robust method for re-covering signals from 1-bit measurements using adaptiveoutlier pursuit (AOP). This method will detect the posi-tions where sign flips happen and recover the signals using“correct’ measurements. Numerical experiments show theaccuracy of sign flips detection and high performance ofsignal recovery for our algorithms compared with other al-gorithms. This AOP technique can also be applied to solvematrix completion problem when the data is damaged by

28 AN12 Abstracts

impulse noise.

Yi Yang, Ming YanUniversity of California, Los Angelesqyyf11@gmail.com, basca.yan@gmail.com

Stanley J. OsherUniversity of CaliforniaDepartment of Mathematicssjo@math.ucla.edu

CP21Effect of Permeability Anisotropy on Density-Driven Flow for CO2 Sequestration in SalineAquifers

We present a comprehensive study of the effect of perme-ability anisotropy on the onset and subsequent develop-ment of convection for CO2 sequestration in saline aquifers.Our linear stability analysis shows that anisotropy reducesthe critical time tc and the critical wavelength λc because itamplifies all perturbation modes via an exponential growthfactor that is biased towards shorter wavelength modes.Anisotropy increases parity among the modes in such a waythat λc becomes less meaningful. We have also studied thebehavior after tc using detailed numerical simulations. Weshow that anisotropy can substantially reduce the time atwhich the enhanced transport from natural convection be-comes significant. In addition, it permits higher mean CO2dissolution rates to be sustained for longer periods of time.Our results give strong indication that saline aquifers withpermeability anisotropy can provide a means for safe andpermanent storage of large amounts of CO2.

Philip ChengYale UniversityDepartment of Chemical & Environmental Engineeringphilip.cheng@yale.edu

Michael BestehornBrandenburg University of Technology CottbusInstitute for Theoretical Physics IIbes@physik.tu-cottbus.de

Abbas FiroozabadiYale Universityabbas.firoozabadi@yale.edu

CP21Universal Stability Properties for Multi-LayerHele-Shaw Flows and Its Application to Instabil-ity Control

With the motivation of understanding the effect of vari-ous injection policies currently in practice for chemical en-hanced oil recovery, we study linear stability of displace-ment processes in a Hele-Shaw cell involving injection ofan arbitrary number of fluid phases in succession. Thiswork mainly builds upon our earlier study for the three-layer case [P. Daripa, Studies on stability in three-layerHele-Shaw flows, Physics of Fluids, (20), 2008]. Stabilityresults obtained are universal in the sense that they holdregardless of number of displacing fluids. The stability re-sults have been applied here to design injection policiesthat are considerably less unstable than the pure Saffman-Taylor case. This is a joint work with my postdoc XueruDing. The research reported here has been made possibleby a grant NPRP 08-777-1-141 from the Qatar NationalResearch Fund (a member of The Qatar Foundation). The

statements made herein are solely responsibility of the au-thors.

Prabir DaripaTexas A&M UniversityDepartment of Mathematicsprabir.daripa@math.tamu.edu

CP21Internal Gravity Waves and Their Generation

Time-harmonic internal gravity waves are generated in astratified fluid by oscillating a rigid object. After removingthe time dependence, there remains a boundary value prob-lem for a hyperbolic partial differential equation. We solvethis problem when the object is a thin horizontal ellipticalplate.

Paul A. MartinDepartment of Mathematical and Computer SciencesColorado School of Minespamartin@mines.edu

Stefan Llewellyn SmithDepartment of MAEUniversity of California, San Diegosgls@ucsd.edu

CP21A Computational Framework for the Solution ofMulti-Material Fluid-Structure Interaction Prob-lems with Crack Propagation

We present a high-fidelity computational framework basedon the coupling of an embedded boundary method forCFD and XFEM for the coupled solution of nonlinearfluid-structure interaction problems with large deforma-tions and crack propagation. We illustrate this framework,highlight its features, and assess its performance with thethree-dimensional simulation of underwater implosions andpipeline explosions for which test data is available.

Kevin WangInstitute for Compuational and MathematicalEngineeringStanford University, Stanford, CAicmewang@stanford.edu

CP21An Efficient Numerical Method for Solving Cou-pled Systems of Elliptic Interface and HyperbolicPartial Differential Equations with Applications toEnhanced Oil Recovery

We will present a fast and efficient method for solving acoupled system of elliptic and hyperbolic equations aris-ing in the context of complex chemical flooding of porousmedia. The problem involves moving boundaries and dis-continuous coefficients. The mathematical model we useis based on the Buckley-Leverett model, Darcy velocityand other complex physics arising from chemicals. To bemore exact, we use finite volume method to solve the two-dimensional Riemann problem system, use the finite ele-ment method to solve the two-dimensional elliptic inter-face problem, and the level set method is used to movethe interface. The results of our numerical experimentswill be presented and discussed. This is an ongoing work.The research reported here has been made possible by a

AN12 Abstracts 29

grant NPRP 08-777-1-141 from the Qatar National Re-search Fund (a member of The Qatar Foundation). Thestatements made herein are solely responsibility of the au-thors.

Liqun Wang1301 Barthelow Drive, Apt 34B, College Station,TX,77843wliqunhmily@gmail.com

Prabir DaripaTexas A&M Universitydaripa@math.tamu.edu

CP22Supercritical And Subcritical Hopf Bifurcations Onthe Van Der Pol Nonlinear Differential Equation

The main purpose of this paper is to discuss following ob-jectives with the famous Van Der Pol Nonlinear DifferentialEquation: (i) Development of general theory and formulaefor determining Hopf Bifurcations on any non-linear Dif-ferential equations (ii) Existence of Chaos , Limit Cycles ,Supercritical and Subcritical Hopf Bifurcations of Van DerPols Oscillator and their Statistical analysis .

Tarini K. DuttaPROFESSOR OF MATHEMATICS, GAUHATIUNIVERSITY, GUWAHATI,ASSAM STATE: 781014, INDIAtkdutta2001@yahoo.co.in

CP22Mathematical Analysis of Chikungunya ModelWith Discrete Delays

The paper presents the basic model for the transmissiondynamics of chikungunya. The model, which consists ofseven mutually-exclusive compartments representing thehumans and vector dynamics, has a locally-asymptoticallystable disease-free equilibrium (DFE) whenever the associ-ated reproduction number () is less than unity. The analy-ses of the model show the existence of the phenomenon ofbackward bifurcation (where the stable DFE of the modelco-exists with a stable endemic equilibrium when the re-production number of the disease is less than unity). It isshown, that the backward bifurcation phenomenon can beremoved by substituting the associated standard incidencefunction with a mass action incidence. Analysis of the re-production number of the model shows that, the diseasewill persist, whenever > 1. Furthermore, an increase inthe length of incubation period, increases the chikungunyaburden in the community if a certain threshold quantities,denoted by ∆b and ∆v are positive. On the other hand,increasing the length of the incubation period can help re-duce disease burden if ∆b < 0 and ∆v < 0.

Salisu M. GarbaDepartment of MathematicsUniversity of PretoriaSalisu.Garba@up.ac.za

CP22Connections Between Phantom Traffic Jams, Jami-tons, and Congested Traffic Flow

In this presentation, we show that (a) a wide class of“second-order’ macroscopic traffic models (e.g. Payne-

Whitham, Zhang-Aw-Rascle) possess traveling wave so-lutions, called “jamitons’, that are analogs of detonationwaves in reacting gas dynamics; (b) the occurrence of jami-tons is equivalent to the instability of uniform traffic flow,i.e. jamitons serve as models for phantom traffic jams;and (c) the large spread of flow rates in congested trafficregimes that is observed in fundamental diagrams can beexplained with the simple 1979 Payne-Whitham model.

Benjamin SeiboldTemple Universityseibold@temple.edu

Rodolfo Ruben RosalesMassachusetts Institute of Technologyrrr@math.mit.edu

Morris FlynnUniversity of Albertamrflynn@ualberta.ca

Aslan R. KasimovDivision of Mathematical & Computer Sciences andEngineeringKing Abdullah University of Science and Technologyaslan.kasimov@kaust.edu.sa

Jean-Christophe NaveMcGill Universityjcnave@math.mit.edu

CP23Boundary Trace Inequalities

This talk will describe some simple boundary trace inequal-ities for Sobolev functions in W 1,p(Ω) with Ω a boundedregion in space with Lipschitz boundary ∂Ω and p ≤ N .The inequalities are used to provide new bounds on solu-tions of inhomogeneous Robin boundary value problems.

Giles AuchmutyDepartment of MathematicsUniversity of Houstongiles@math.uh.edu

CP23Γ-Convergence of Inhomogeneous Functionals andApplications to Dielectric Breakdown

The asymptotic behavior of inhomogeneous functionals inOrlicz-Sobolev spaces is studied via Γ-convergence. Appli-cations to the study of (first-failure) dielectric breakdownfor composites made of two isotropic phases will be dis-cussed. This is joint work with Mihai Mihailescu (Univer-sity of Craiova, Romania).

Marian BoceaLoyola University Chicagombocea@luc.edu

CP23Well-Posedness for Euler 2D in Non-Smooth Do-mains

The well-posedness of the Euler system has been of coursethe matter of many works, but a common point in all theprevious studies is that the boundary is at least C1,1. In afirst part, we will state the existence of global weak solu-

30 AN12 Abstracts

tions of the 2D incompressible Euler equations for a largeclass of non-smooth open sets. In a second part, we willgive the uniqueness if the open set is the interior or theexterior of a simply connected domain, where the bound-ary has a finite number of corners. The existence part is awork in collaboration with David Gerard-Varet.

Christophe Lacave, David Gerard-VaretInstitut Mathematiques de Jussieu.Universite Paris Diderot (Paris 7)lacave@math.jussieu.fr, gerard-varet@math.jussieu.fr

CP23Traveling Waves of an Angiogenesis Model

In this talk, we will study travel wave solutions for a classof chemotaxis system modeling the initiation of tumor an-giogenesis. The challenges of obtaining traveling wave solu-tions of such chemotaxis models lie in the high dimension-ality and the singularity. Hence the routine approaches,such as phase plane analysis, no longer work. In the talk,we shall show these challenges will be overcome by a Hope-Cole tyoe transformation, such that the transformed sys-tem can be solved by the routine approaches. The exis-tence, wave speed and stability of traveling wave solutionswill be discussed, and open questions will be presented.

Zhian WangDepartment of Applied MathematicsHong Kong Polytechnic Universitymawza@polyu.edu.hk

CP23Lattice Differential Equation Analysis of SchloeglsSecond Model for Particle Creation and Annihila-tion

Schloegls stochastic models for autocatalysis on a latticeof dimension d=2 involves: (i) spontaneous annihilation ofparticles at lattice sites; and (ii) autocatalytic creation ofparticles at vacant sites. We analyze the dynamics of in-terfaces between populated and empty regions via discretereaction-diffusion equations (dRDEs) obtained from ap-proximations to the exact master equations. These dRDEcan display propagation failure absent due to fluctuationsin the stochastic model. Higher-level approximations elu-cidate exact behavior with quantitative accuracy.

Chi-Jen WangIowa State University, Ames Laboratory-USDOEcjwang@iastate.edu

Xiaofang GuoAmes LaboratoryUSDOEDep of Physics & Astro and Dep of Math, Iowa StateUnivguoxx192@umn.edu

Da-Jiang LiuIowa State Universitydajiang@fi.ameslab.gov

Jim W. EvansAmes Laboratory USDOE and Iowa State Universityevans@ameslab.gov

CP23Uniform Estimate for Non-Uniform Elliptic Equa-

tions with Discontinuous Coefficients

Uniform estimate for non-uniform elliptic equations withdiscontinuous coefficients in heterogeneous media is con-cerned. The heterogeneous media considered here are peri-odic and they consist of a connected high permeability sub-region and a disconnected matrix block sub-region with lowpermeability. Elliptic equations with diffusion coefficientsdepending on the permeability of the media have fast diffu-sion in high permeability sub-region and have slow diffusionin low permeability sub-region, and they are non-uniformelliptic equations. Let ε denote the size ratio of the matrixblocks to the whole domain and let the permeability ratioof the matrix block sub-region to the connected high per-meability sub-region be of the order ε2. It is proved thatthe Lp norm of the gradient of the elliptic solutions in thehigh permeability sub-region are bounded uniformly in εin bounded and unbounded domains. One example alsoshows that the Lp norm of the gradient of the solutions inthe disconnected subset may not be bounded uniformly inε. It is also noted that the Lp norm of the second orderderivatives of the elliptic solutions in the high permeabilitysub-region in general are not bounded uniformly in ε.

Li-Ming YehDepartment of Applied MathematicsNational Chiao Tung University, Taiwanliming@math.nctu.edu.tw

MS0Continuous and Discrete Models for Infectious Dis-eases

In this talk, I will present a few representative papers thatI have coauthored with Carlos Castillo-Chaves and others.These include some of the earlier work on continuous mod-els for TB and influenza and more recent papers on discreteepidemic models.

Zhilan FengPurdue Universityzfeng@math.purdue.edu

MS0From Rockstar Researcher to Selfless Mentor: AnOverview of the Achievements of Carlos CastilloChavez

Carlos Castillo Chavezs record of scholarship is unparal-leled, representing some of the most important contribu-tions in the study of disease dynamics. Yet, it is a com-mitment to mentoring that has captivated his interest. Inthis brief overview, I will chart how Carlos Castillo Chaveznot only reached the pinnacle of his field, but how he thenturned that same dedication to others, becoming one of themost honored mentors in the sciences.

Melissa Castillo-GarsowYale Universitytba

MS0Modeling and Quantifying the Transmission Dy-namics and Control of Infectious Diseases

I will discuss my research experience working under the su-pervision of Carlos Castillo-Chavez from my participationin the Mathematical and Theoretical Biology Institute’sSummer Research Program to my doctoral work at Cor-

AN12 Abstracts 31

nell. In addition, I will provide an overview of some recentcollaborative projects with Carlos and others with a par-ticular focus on research on the transmission and controlof emerging and re-emerging infectious diseases.

Gerardo ChowellMathematical Modeling and AnalysisLos Alamos National Laboratorygchowell@asu.edu

MS0Insights Gained from Modeling Epidemics

I will review some of the insights gained from my col-laborations with Carlos Castillo-Chavez in creating createnew models that can anticipate the spread of a diseaseand evaluate the effectiveness of different approaches forbringing an epidemic under control. The talk will pro-vide an overview, for general audiences, of what type of in-sights these models can provide. I will describe some of themathematical advances needed to create the next genera-tion of models, and share my personal experiences workingwith Carlos to create models for controlling the spread ofHIV/AIDS, SARS, dengue fever, foot and mouth disease,Ebola, and preparing for a bioterrorist attack.

James (Mac) HymanTulane Universitymhyman@tulane.edu

MS0Influenza and Other Infectious Diseases

The complicated dynamics of influenza A exhibit fluctua-tions on multiple scales, due to the interplay of factors suchas age structure, cross-reactivity, and seasonal forcing. Toaddress this interplay, Castillo-Chavez and collaboratorsdeveloped a comprehensive mathematical framework, andanalyzed the potential for sustained oscillations. This lec-ture will review this work, set it in the context of whatcame before and after, and complement with discussion ofsome of Carlos’s other contributions to mathematical biol-ogy.

Simon LevinPrinceton University, USAslevin60@gmail.com

MS1New Directions in Algebraic Coding Theory

Abstract not available at time of publication.

Iwan DuursmaUniversity of Illinois at Urbana-ChampaignDepartment of Mathematicsduursma@math.uiuc.edu

MS1Title Not Available at Time of Publication

Abstract not available at time of publication.

Salim El RouayhebEECSUniversity of California at Berkeleysalim@eecs.berkeley.edu

MS1Title Not Available at Time of Publication

Abstract not available at time of publication.

Elena GrigorescuGeorgia Techelena@cc.gatech.edu

MS1Deep-LLL Reconsidered

Lattice reduction plays an important role both in codingtheory and cryptography. For example, it has broad appli-cations in cryptanalysis. The Deep-LLL lattice reductionalgorithm, as an improvement of classical LLL, was notstudied very well as it is outperformed by BKZ reduction.We want to argue why the concept of Deep Insertions couldimprove reduction algorithms like BKZ and provide empir-ical evidence.

Urs Wagner, Felix Fontein, Joachim RosenthalInstitut fur MathematikUniversitat Zurichurs.wagner@math.uzh.ch, felix.fontein@math.uzh.ch,rosenthal@math.uzh.ch

MS2Evasion Paths in Mobile Sensor Networks

Imagine that disc-shaped sensors wander in a planar do-main. A sensor can’t determine its location but does knowwhen it overlaps a nearby sensor. We say that an evasionpath exists in this sensor network if a moving evader canavoid detection. Using tools from topology, Vin de Silvaand Robert Ghrist can guarantee that no evasion path ex-ists in certain networks. But what about the remainingnetworks? We’ll consider examples that show the existenceof an evasion path depends not only on the sensor network’slocal connectivity data but also on its embedding.

Henry AdamsStanford Universityhenrya@math.stanford.edu

MS2Generalizing Max Flow and Min Cut: Opportuni-ties from a Topological Proof

The max-flow min-cut theorem has found recent applica-tions in image segmentation, communication, and otherforms of information processing. The classical theorem andits proof can be recast in terms of the “directed homology’of a directed graph, taking coefficients in a sheaf of con-straints. I will discuss generalizations of max-flow min-cutimplied by the topological approach, and potential appli-cations of such generalizations to real-world problems.

Sanjeevi KrishnanUniversity of Pennsylvaniasanjeevi@math.upenn.edu

MS2Sheaves and Persistence

Sheaf theory brings to persistence a rich language. Us-ing this language, I will present, through simple examples,

32 AN12 Abstracts

some ongoing work on multidimensional persistence.

Amit PatelRutgers Universityamit@akpatel.org

MS2Recent Advances and Trends in Applied AlgebraicTopology

Applied algebraic topology is a vibrant young field of re-search, with rapid ongoing development. I will give a sur-vey of recent advances and results in the field includ-ing work on coordinatization, on topological inference, ontopological simplification, and applications to signals, tocancer research, and to image analysis. I will focus, inthis, on work done by young researchers in the field.

Mikael Vejdemo JohanssonStanford Universitymvvj@st-andrews.ac.uk

MS3Stable Computation with Reproducing Kernels

Positive definite kernels and their associated reproducingkernel Hilbert spaces provide a very flexible and powerfultool for the solution of many typical problems of numericalanalysis and scientific computing such as function approx-imation, numerical integration or the numerical solutionof PDEs. I will provide a brief introduction to positivedefinite reproduc- ing kernels, mention some typical appli-cations, and then focus on stable computation with Gaus-sian kernels. The latter is motivated by the fact that, onthe one hand, interpolation with flat Gaussian kernels pro-vides a generalization of (multivariate) polynomial inter-polation with spectral convergence rates for smooth func-tions, while, on the other hand, flat Gaussian kernels leadto notoriously ill-conditioned linear systems. Our workdemonstrates that this so-called uncertainty principle canbe avoided by representing the space of functions used forthe approximation by a “better” basis. A set of Matlabroutines implementing these ideas for Gaussian kernels areavailable from http://math.iit.edu/˜mccomic/gaussqr

Greg FasshauerIllinois Institue of Technologyfasshauer@iit.edu

Michael McCourtCenter for Applied MathematicsCornell Universitymjm458@cornell.edu; mccomic@mcs.anl.gov

MS3Refinement and Remeshing in Particle Simulations

Lagrangian particle simulations are often used to studyvortex dynamics in the context of incompressible fluids.It is well-known that the simulation accuracy is sensi-tive to the particle distribution, and maintaining a properdistribution as the flow evolves is a challenging problem.I’ll discuss some techniques used to address this issue intwo applications: (1) adaptive panel refinement for vor-tex sheets, and (2) particle remeshing for the barotropicvorticity equations on a rotating sphere.

Robert KrasnyUniversity of Michigan

Department of Mathematicskrasny@umich.edu

MS3Multi-moment Vortex Methods

In this talk we develop a new, high order accurate, multi-moment vortex method (MMVM) using Hermite expan-sions to simulate 2D vorticity. The method naturally allowsthe particles to deform and become highly anisotropic asthey evolve without the added cost of computing the non-local Biot-Savart integral. Convergence for the methodis proven and examples will be provided. Time permit-ting, we will discuss the spatial accuracy and computa-tional costs of MMVM.

David T. UminskyUCLADept. of Mathematicsduminsky@math.ucla.edu

MS3A Partition of Unity Method for Divergence-freeApproximation of Vector Fields on the Sphere

Vector fields tangent to the surface of the sphere appearin many applications from the geophysical sciences. Oftenthese fields describe the velocity of some incompressiblefluid and are thus divergence-free. We present a new mesh-free, partition of unity method based on RBFs for approx-imating these types of fields that preserves the divergence-free property. The method is computationally efficient, freeof any coordinate singularities, and can be used to approx-imate surface derivatives of the field.

Grady B. WrightDepartment of MathematicsBoise State University, Boise IDgradywright@boisestate.edu

Edward J. FuselierDepartment of Mathematics and Computer ScienceHigh Point Universityefuselie@highpoint.edu

MS4Development of a Single Domain Framework toModel 3D L-Ion Intercalation Batteries using theAMP Package

Modeling of batteries involves simulation of coupled chargeand thermal transport, interfacial electrochemical reac-tions across the porous 3D structure of the electrodes (cath-odes and anodes) and electrolyte system. The resultingequations are stiffff differential algebraic systems on a sin-gle domain and require a robust solution methodology.These formulations are implemented in AMPERES code,an external package for AMP software. In the talk wedemonstrate the importance of the coupled solution proce-dure using Newton Krylov iterative solvers. Experimentsbased on various preconditioning strategies are presented.

Srikanth AlluOak Ridge National Laboratoryallus@ornl.gov

Sreekanth Pannala

AN12 Abstracts 33

Computer Science and Mathematics DivisionOak Ridge National Laboratorypannalas@ornl.gov

Partha Mukherjee, Bobby PhilipOak Ridge National Laboratorymukherjeepp@ornl.gov, philipb@ornl.gov

John TurnerOak Ridge National LaboratoryComputational Engineering and Energy Sciencesturnerja@ornl.gov

MS4The Arctic Terrestrial Simulator: Developing aFlexible Multiphysics Simulator based on Amanzi

The Arctic Terrestrial Simulator (ATS) is being developedto simulate coupled processes governing carbon releasesfrom degrading permafrost, including subsurface and over-land flow, heat transport, subsidence, and soil biogeochem-istry. A flexible simulation capability that naturally sup-ports strong and weak coupling of selected processes is re-quired. Building upon Amanzi, the ASCEM simulator, wepresent a general strategy for dynamically managing datastructures, data permissions, and process model couplingsfor the ATS.

Ethan T. Coon, Markus Berndt, J. David Moulton, ScottPainterLos Alamos National Laboratoryecoon@lanl.gov, berndt@lanl.gov, moulton@lanl.gov,spainter@lanl.gov

MS4A Multiphysics PDE Assembly Engine for Non-linear Analysis using Template-based Generic Pro-gramming Techniques

As computational algorithms, hardware, and programminglanguages have advanced over time, computational model-ing and simulation is being leveraged to understand, ana-lyze, predict, and design increasingly complex physical, bi-ological, and engineered systems. Because of this complex-ity, significant investments must be made, both in termsof manpower and programming environments, to developsimulation capabilities capable of accurately representingthe system at hand. At the same time, modern analy-sis approaches such as stability analysis, sensitivity analy-sis, optimization, and uncertainty quantification require in-creasingly sophisticated capabilities of those complex sim-ulation tools. Often simulation frameworks are not de-signed with these kinds of analysis requirements in mind,which limits the efficiency, robustness, and accuracy ofthe resulting analysis. In this work, we describe an ap-proach for building a mulitphysics assembly engine thatnatively supports requirements for many types of analysisalgorithms and solution techniques. This approach lever-ages compile-time polymorphism and generic programmingthrough C++ templates to insulate physics experts fromthe complexities associated with the analysis hierarchy andsolution techniques. The ideas presented here build onoperator overloading-based automatic differentiation tech-niques to transform a simulation code into one that is capa-ble of providing analytic derivatives. However we extendthese ideas to compute quantities that aren’t derivativessuch as polynomial chaos expansions, floating point counts,and extended precision calculations. We will show exampleuse cases including turbulent flow in a light water nuclear

reactor, and stability analysis of a magnetohydrodynamicstest problem.

Roger PawlowskiMultiphysics Simulation Technologies Dept.Sandia National Laboratoriesrppawlo@sandia.gov

Eric C. CyrScalable Algorithms DepartmentSandia National Laboratotorieseccyr@sandia.gov

John ShadidSandia National LaboratoriesAlbuquerque, NMjnshadi@sandia.gov

Eric PhippsSandia National LaboratoriesOptimization and Uncertainty Quantification Departmentetphipp@sandia.gov

MS4The Advanced Multi-Physics (AMP) Package WithAn Application to Fuel Assemblies in Nuclear Re-actors

Simulations of multiphysics systems are becoming increas-ingly important in many science application areas. In thistalk we describe the design and capabilities of the Ad-vanced Multi-Physics (AMP) package designed with multi-domain multi-physics applications in mind. AMP currentlybuilds powerful and flexible deterministic multiphysics sim-ulation algorithms from lightweight operator, solver, linearalgebra, material database, discretization, and meshing in-terfaces. In this and related talks we will describe howAMP has been used to solve coupled multi-domain multi-physics problems related to energy applications.

Bobby Philip, Kevin ClarnoOak Ridge National Laboratoryphilipb@ornl.gov, clarnokt@ornl.gov

Rahul S. SampathORNLsampathrs@ornl.gov

Mark Berrill, Srikanth AlluOak Ridge National Laboratoryberrillma@ornl.gov, allus@ornl.gov

Gary DiltsLANLgad@lanl.gov

Pallab BaraiORNLbaraip@ornl.gov

MS5Advances on the Discretizable Distance GeometryProblem

The Discretizable Distance Geometry Problem (DDGP) isa subset of the DGP which can be solved using a discretesearch occurring in continuous space. Its main applicationis to find three-dimensional arrangements of proteins using

34 AN12 Abstracts

NMR data. We will talk about our efforts that have beendirected towards adapting the DDGP to be an ever closermodel of the actual difficulties posed by the problem ofdetermining protein structures from NMR data.

Carlile LavorState University of CampinasDepartment of Applied Mathematicsclavor@ime.unicamp.br

Leo LibertiEcole Polytechniqueliberti@lix.polytechnique.fr

Nelson MaculanPrograma de Engenharia de Sistemas de ComputaoCOPPE Universidade Federal do Rio de Janeiromaculan@cos.ufrj.br

Antonio MucherinoUniversity of Rennes 1antonio.mucherino@irisa.fr

MS5Coarse Grained Normal Mode Analysis vs. RefinedGaussian Network Model for Protein Residue-Level Structural Fluctuations

We investigate several approaches to coarse grained normalmode analysis on protein residual-level structural fluctua-tions by choosing different ways of representing the residuesand the forces among them. The residue mean-square-fluctuations and their correlations with the experimentalB-factors are calculated for a large set of proteins. The ex-tracted force constants from the Hessian are surveyed, andthe statistical averages are used to build a refined Gaus-sian Network Model. Joint work with Robert Jernigan andZhijun Wu.

Jun-Koo ParkIowa State Universityjkpark@iaate.edu

MS5The Determination and Refinement of Protein En-sembles using Inter-atomic Distance Bounds

A novel approach is proposed for the determination of theensemble of structures for a protein given a set of distancebounds from NMR experiments. In this approach, simi-lar to X-ray crystallography, a protein is assumed to havean equilibrium structure with the atoms fluctuating aroundtheir equilibrium positions. Thus, the structure determina-tion problem can be formulated as an optimization prob-lem, i.e., to find the equilibrium positions and maximalpossible fluctuation radii for the atoms in the protein, sub-ject to the condition that the fluctuations should be withinthe given distance bounds. The advantages of using thisapproach are the following: (1) The mathematical prob-lem to be solved becomes more tractable, and only a singlesolution to an optimization problem is required, while inconventional approaches, multiple solutions are sought fora system of inequalities, which in general is intractable. (2)A single structure along with the estimates on the atomicfluctuations suffices to describe the structure and its fluc-tuation ranges that are underestimated in conventional ap-proaches using a finite number of structural samples. (3)A single structural model with the fluctuation radii corre-sponding to the B-factors can be obtained for the full de-

scription of an NMR structure and its dynamic properties,the same as in X-ray crystallography. The formulation ofthe optimization problem is given. The algorithm for solv-ing the problem is described. The test results on modelproteins are presented.

Atilla SitUniversity of Wisconsin - MadisonInstitute for Discoveryasit@wisc.edu

MS5An Optimal Solution to the Generalized DistanceGeometry Problem

NMR experiments on a protein yield a set of inter-atomicdistance ranges. A number of structures satisfying the dis-tance constraints, derived from distance range and bond in-formation, are then generated. This ensemble of structuresis often under represented and inaccurately represents theprotein’s structural fluctuations. In this presentation wepresent an alternative problem where its solution, derivedfrom interior point optimization, provides a single repre-sentation for a protein’s conformation and its ensemble ofpossible structures.

Zachary D. Voller, Zachary D. VollerIowa State UniversityDepartment of Mathematicszvoller@iastate.edu, zvoller@iastate.edu

Zhijun WuIowa State Universityzhijun@iastate.edu

MS6Homogenization-based Mortar Methods for PorousMedia

For an elliptic problem with a heterogeneous coefficient inmixed form, nonoverlapping mortar domain decompositionis efficient in parallel if the mortar space is small. We de-fine a new multiscale mortar space using homogenizationtheory. In the locally periodic case, we prove the methodachieves optimal order error estimates in the discretiza-tion parameters and heterogeneity period. We assess itsnumerical performance when the coefficient is not locallyperiodic.

Todd ArbogastDept of Math; C1200University of Texas, Austinarbogast@ices.utexas.edu

Hailong XiaoICESThe University of Texas at Austinxiaohl@ices.utexas.edu

MS6Multiscale Model Reduction for Flows in Hetero-geneous Porous Media

For multiscale problems, some types of coarsening of thedetailed model are usually performed before the model canbe used to simulate complex processes. In this talk, I willdescribe multiscale model reduction techniques that can beused to systematically reduce the degrees of freedoms of

AN12 Abstracts 35

fine-scale simulations and discuss applications to precondi-tioners. For parameter-dependent problems, I will describehow Reduced Basis approaches can be used offline to gen-erate reduced local problems.

Yalchin EfendievDept of MathematicsTexas A&M Universityefendiev@math.tamu.edu

MS6An Exponentially Convergent Approximation The-ory for Fields Inside Multiscale Heterogeneous Ma-terials

Large multiscale engineering systems such as airplanewings and wind turbine blades are built from fiber rein-forced composites and exhibit a cascade of substructurespread across several length scales from microns to tens ofmeters. The computational modeling of these hierarchi-cal and heterogeneous structures is a very large problemthat requires parallel computation. In this talk we ad-dress both the problems of parallelization and dimensionreduction and present an exponentially convergent approx-imation theory for multiscale problems. This is joint workwith Ivo Babuska and has appeared in Multiscale Modelingand Simulation, SIAM, (2011) 9, 373 406.

Robert P. LiptonDepartment of MathematicsLouisiana State Universitylipton@math.lsu.edu

MS6Multiscale Mortar Coupling of Multiphase Flowand Reactive Transport on Non-matching Grids

Geochemical modeling plays an important role in design-ing carbon sequestration strategies, characterizing environ-mental site contaminations, and predicting environmentalimpacts. We formulate a multiscale model for couplingmultiphase flow and reactive transport in porous media.The flow is modeled using mortar mixed finite elementsthat allow for accurate and efficient parallel domain decom-position with non-matching grids. The reactive transportequations are treated using operator splitting for decou-pling transport and reactions. Computational results arepresented.

Gergina PenchevaUniversity of Texas at Austingergina@ices.utexas.edu

Mary F. WheelerCenter for Subsurface ModelingUniversity of Texas at Austinmfw@ices.utexas.edu

Mojdeh DelshadUniversity of Texas at Austindelshad@mail.utexas.edu

MS6Modeling Flow and Coupled Transport with Ad-sorption from Pore to Core

Mathematical modeling of flow and transport in porousmedia until recently has been restricted to the scales of

observation i.e. from core scale up. However various ex-perimental techniques and discrete and continuum basedcomputational methods are now available for the study ofphenomena at porescale. Most interesting are coupled pro-cesses whose influence on the core and field scale flow andtransport is essential but for which upscaled models, espe-cially for high flow rates, are lacking. We discuss our recentresults based on experimental as well as complex syntheticgeometries.

Malgorzata PeszynskaDepartment of MathematicsOregon State Universitympesz@math.oregonstate.edu

Anna TrykozkoUniversity of Warsawaniat@icm.edu.pl

MS7Composed Solution Methods for General NonlinearEquations

The numerical solution of large-scale nonlinear systemsof equations may be performed using Newton’s method,global methods, like nonlinear Krylov methods, or localmethods, like nonlinear Gauss-Seidel. Many problems can-not be efficiently solved using Newton-like schemes. As analternative, we propose a flexible framework for the com-position of local and global methods. We demonstrate theeffectiveness and efficiency of composable nonlinear solverson problems of interest from computational biology.

Peter R. BruneMathematics and Computer Science DivisionArgonne National Laboratoriesbrune@mcs.anl.gov

Matthew G. KnepleyUniversity of Chicagoknepley@ci.uchicago.edu

Barry F. SmithArgonne National LabMCS Divisionbsmith@mcs.anl.gov

MS7Physics-based Preconditioning within ImplicitSimulations of Visco-resistive Tokamak Plasmas

Single-fluid resistive magnetohydrodynamics (MHD) is afluid description of fusion plasmas which is often usedto investigate macroscopic instabilities in tokamaks. InMHD modeling of non-spherical tokamaks it is often desir-able to compute MHD phenomena to resistive time scales,which can make explicit time stepping schemes computa-tionally intractable. Our work focuses on simulations usinga structured mesh mapped into a toroidal geometry witha shaped poloidal cross-section, and a finite volume spatialdiscretization of the PDE model. We discretize the tem-poral dimension using a fully implicit θ or BDF method,and solve the resulting nonlinear algebraic system using astandard inexact Newton-Krylov approach. The focus ofthis talk is on the construction and performance of physics-based preconditioning approaches for accelerating conver-gence of these iterative solvers. We compare precondition-ers inspired by solvers from legacy MHD codes, thoughhere they are used within a preconditioning context. We

36 AN12 Abstracts

conclude with numerical results in the context of pellet-injection fueling of tokamak plasmas.

Daniel R. ReynoldsSouthern Methodist UniversityMathematics Departmentreynolds@smu.edu

Ravi SamtaneyKAUSTravi.samtaney@kaust.edu.sa

Hilari TiedemanSouthern Methodist UniversityMathematicshtiedeman@smu.edu

MS7Anderson Acceleration of Modified Picard Itera-tion for Variably Saturated Flow

We will present our investigation of the effectiveness of theAnderson Acceleration method applied to the modified Pi-card iteration for simulations of variably saturated flow.We solve nonlinear systems using both unaccelerated andaccelerated modified Picard iteration as well as Newton’smethod. Since Picard iterations can be slow to converge,the advantage of acceleration is to provide faster conver-gence while maintaining advantages of the Picard methodover the Newton method. Results indicate that the ac-celerated method provides a robust solver with significantpotential computational advantages.

Carol S. Woodward, Aaron LottLawrence Livermore Nat’l Labwoodward6@llnl.gov, lott3@llnl.gov

Homer F. WalkerWorcester Polytechnic Institutewalker@wpi.edu

Ulrike YangLawrence Livermore Nat’l Labyang11@llnl.gov

MS7An Optimal Convergence Neighborhood Strategyfor an Implicit Timestep Solver That Converges Allthe Time

The Adaptively-Localized-Continuation-Newton (Younis,R.M. et al., 2008) method is a numerical continuationscheme that applies time-step size as its homotopy param-eter. The solver unifies implicit time-stepping with nonlin-ear iteration. A key component that dictates a trade-offbetween efficiency and robustness is the choice of Conver-gence Neighborhood about the solution path. This workanalyzes an automatically adaptive strategy for this choicein order to locally optimize the progress in time advance-ment while still guaranteeing unconditional robustness.

Rami M. YounisPostdoctoral Research FellowStanford Universityryounis@stanford.edu

MS8A Multi-numeric Method for Convection-

dominated Parabolic Problems Using an AdaptiveRegion-swapping Approach

This work couples the finite volume (FV) method withthe discontinuous Galerkin (DG) method dynamically. Foreach time-step, an efficient partition of the domain betweenthe two methods is determined in an attempt to best pre-serve the high accuracy of the DG method while also takingadvantage of the low computational cost of the FV methodwherever is possible. The implementation preserved theexpected numerical convergence rates, while yielding sub-stantially smaller linear systems. Advisor: Beatrice Riv-iere, Rice University

Joseph HuchetteRice Universityjoehuchette@gmail.com

MS8Spectral Properties of Neural Network Structures

I investigate how biologically relevant patterns of networkconnectivity affect neural activity. To encode networkstructure, I construct synaptic weight matrices and observechanges in spectra and resulting dynamics. Differences inspectra for small world, nearest neighbor, and random net-works affect prevalence of stable, periodic, and chaotic so-lutions, Lyapunov exponents, and frequencies measured byFourier series approximations. The degree of asymmetry inthe matrix affects radius, number of real eigenvalues, andtypes of chaos achieved. Advisor: Dr. Jonathan Rubin,University of Pittsburgh

Jeffrey MoultonUniversity of PittsburghJTM59@pitt.edu

MS8The Effects of Signal Delay in Gene RegulatoryNetworks

Delay can qualitatively affect the dynamics of gene regu-latory networks. It has been shown that delay can causeoscillations and increase signal-to-noise ratios. Using an-alytical techniques, stochastic modeling, model reductiontechniques, and simulations, we will study how delay affectsthe flow of information through gene regulatory networks.Advisor: William Ott, University of Houston

Sarah StanleyUniversity of Houstonsarahmailbox2@yahoo.com

MS9Analysis of Nematic Liquid Crystals with Disclina-tions

We investigate the structure of nematic liquid crystal thinfilms described by the Landau-de Gennes tensor-valued or-der parameter for energy minimizers with Dirichlet bound-ary conditions of nonzero degree. We prove that as theelasticity constant goes to zero a limiting uniaxial textureforms with disclination lines corresponding to a finite num-ber of defects, all of degree one-half or minus one-half.

Patricia BaumanPurdue Universitybauman@math.purdue.edu

AN12 Abstracts 37

Jinhae ParkSeoul National UniversitySeoul, South Koreajhpark2003@gmail.com

Daniel PhillipsDepartment of Mathematics, Purdue Universityphillips@math.purdue.edu

MS9Ferronematic Liquid Crystal Composites

The coupling effects of nematic liquid crystals to mag-netic fields are usually weak, due to the small values ofthe anisotropic diamagnetic susceptibility. In their sem-inal work, F.Brochard and P.G.de Gennes (Physique desSolides, 1970), investigated suspensions of magnetic grainsin liquid crystals. We discuss the roles and interaction be-tween theoretical and experimental research works in theensuing decades, and present a mathematical justificationof the proposed models.

Maria-Carme CaldererDeparment of MathematicsUniversity of Minnesota, USAcalde014@umn.edu

Dmitry GolovatyThe University of AkronDepartment of Theoretical and Applied Mathematicsdmitry@uakron.edu

Antonio De SimoneSISSA-International School of Advanced Studiesdesimone@sissa.it

Alexander PanchenkoWashington State Universitypanchenko@math.wsu.edu

MS9Recent Results on Nematic Elastomers

Abstract not available at time of publication.

Antonio De SimoneSISSA-International School of Advanced Studiesdesimone@sissa.it

MS9Electric-Field-Induced Instabilities inLiquid-Crystal Films

Simple models of liquid crystals characterize orientationalproperties in terms of a director fie d, which can be influ-enced by an applied electric field. The local electric field isinfluenced by the director field; so equilibria must be com-puted in a coupled way. Equilibria are stationary points ofa free energy functional, which can fail to be coercive be-cause of the nature of the director/electric-field coupling.We discuss characterizations of local stability and anoma-lous behavior in such systems.

Eugene C. GartlandKent State Universitygartland@math.kent.edu

MS9Extrinsic Curvature, and Two-dimensional Ne-matic Order

We derive two-dimensional free energies, aimed at describ-ing the alignment of nematics deposited on curved sub-strates, from the conventional three-dimensional theories ofnematic liquid crystals. Both the director and the order-tensor theories are taken into account. The so-obtainedsurface energies exhibit extra terms compared to earliermodels. These terms couple the shell geometry with thenematic order parameters. As expected, the shape of theshell plays a prominent in the equilibrium configurationsof nematics coating it.

Gaetano NapoliDipartimento di Ingegneria dell’InnovazioneUniversita del Salentogaetano.napoli@unisalento.it

MS10Characterization of Discontinuities in High-dimensional Stochastic Problems on AdaptiveSparse Grids

Stochastic collocation methods are an attractive choice tocharacterize uncertainty because of their non-intrusive na-ture. High dimensional stochastic spaces can be approxi-mated well for smooth functions with sparse grids. Therehas been a focus in extending this approach to non-smoothfunctions using adaptive sparse grids. This presentationwill present both adaptive approximation methods and er-ror estimation techniques for high dimension functions.

Rick ArchibaldComputational Mathematics GroupOak Ridge National Labratoryarchibaldrk@ornl.gov

MS10Sparse Grids for Uncertainty Quantification

This talk will discuss the use of sparse grids to approximatethe high dimensional integrals that arise when uncertaintyin problem inputs is modeled by assigning a probabilitydensity function over each range and considering the prod-uct space of all possibilities. We will consider generaliza-tions of the sparse grid approach that place more emphasison some input factors.

John BurkardtDepartment of Computational ScienceFlorida State Universityjburkardt@fsu.edu

MS10An Efficient Sparse-grid-based Method forBayesian Uncertainty Analysis

Abstract not available at time of publication.

Max GunzburgerFlorida State UniversitySchool for Computational Sciencesmgunzburger@fsu.edu

MS10A Hierarchical Adaptive Sparse Grid Stochastic

38 AN12 Abstracts

Wavelet Collocation Method for PDEs with Ran-dom Input Data

Accurate predictive simulations of complex real world ap-plications require numerical approximations to first, op-pose the curse of dimensionality and second, convergequickly in the presence of steep gradients, sharp transitions,bifurcations or finite discontinuities in high-dimensionalparameter spaces. In this talk we present a novel multidi-mensional multiresolution adaptive (MdMrA) sparse gridstochastic collocation method, that utilizes hierarchicalmultiscale piecewise Riesz basis functions constructed frominterpolating wavelets. The basis for our non-intrusivemethod forms a stable multiscale splitting and thus, opti-mal adaptation is achieved. Error estimates and numericalexamples will used to compare the efficiency of the methodwith several other techniques.

Guannan ZhangFlorida State Universitygzhang5@fsu.edu

Clayton G. WebsterOak Ridge National Laboratorywebstercg@ornl.gov

Max GunzburgerFlorida State Universitygunzburger@fsu.edu

MS11Title Not Available at Time of Publication

Abstract not available at time of publication.

Alexander BargUniversity of Marylandabarg@umd.edu

MS11Title Not Available at Time of Publication

Abstract not available at time of publication.

Simon BlackburnDepartment of MathematicsRoyal Holloway, University of Londons.blackburn@rhul.ac.uk

MS11Sheaves on Graphs

Abstract not available at time of publication.

Joel FriedmanDept. of Mathematics& Computer ScienceUniversity of British Columbiajf@math.ubc.ca

MS11New Challenges in Cryptology

Abstract not available at time of publication.

William J. MartinDepartment of Mathematical SciencesWorcester Polytechnic Institutemartin@wpi.edu

MS12Panel Discussion: Teaming Up in Tough Times

This discussion section will be provide time for questionsrelating to the collaboration and opportunities that thespeakers have addressed.

Lori A. DiachinLawrence Livermore National Laboratorydiachin2@llnl.gov

Rachel WardDepartment of MathematicsUniversity of Texas at Austinrward@math.utexas.edu

Tiffani L. WilliamsTexas A&M Universitytlw@cse.tamu.edu

MS12Some Perspectives on Teaming from the DOE Na-tional Labs

I will present my perspectives on the role of teams in thecurrent economic environment as we attempt to accomplishmore science with scarcer resources and on what has beeneffective in forming and sustaining successful teams. I willcall on my experiences in leading two multi-institutionalmathematics teams for DOEs SciDAC program and my roleas the division leader of a research organization chargedwith performing multidisciplinary research.

Lori A. DiachinLawrence Livermore National Laboratorydiachin2@llnl.gov

MS12Take Initiative, Make Contacts, and Collaborate:My Journey from Graduate Student to Professor

Being a successful mathematician involves more than justknowing the math. As in other professions, taking initia-tive and forming collaborations are crucial in a competitivejob market. These strategies can be counter-instinctualand uncomfortable in male-dominant fields such as math.I will discuss my own strategies for overcoming unease inbeing aggressive. I will also share other strategies and mis-takes that I made in transitioning from graduate studentto professor.

Rachel WardDepartment of MathematicsUniversity of Texas at Austinrward@math.utexas.edu

MS12Building Relationships in the Tree of Life

The Tree of Life is a family tree showing the evolutionaryrelationships among all of the worlds organisms. I will dis-cuss opportunities at the intersection of biology and com-puter science for constructing such an awesome represen-tation of life. However, the Tree of Lifes impact transcendsscience. It may represent the ultimate role model for build-ing connections in a sea of diversity.

Tiffani L. Williams

AN12 Abstracts 39

Texas A&M Universitytlw@cse.tamu.edu

MS13Adaptive Magnetohydrodynamics Simulationswith SAMRAI

A wide variety of plasma problems require both high res-olution and large spatial domains that present a problemfor existing models. Adaptive Mesh Refinement (AMR)provides an efficient method of obtaining both high reso-lution and a large spatial domain. AMR allows for bothhi-resolution and large spatial domain computations. Thistalk will focus on using structured AMR with a 3D plasmamodel (pixie3d). Current progress will be presented.

Mark Berrill, Luis Chacon, Bobby Philip, Zhen Wang,Manuel RodriguezOak Ridge National Laboratoryberrillma@ornl.gov, chaconl@ornl.gov, philipb@ornl.gov,wangz@ornl.gov, rodriguezrom@ornl.gov

MS13Composable Multilevel Methods for MultiphysicsSimulations

Implicit solution methods for multiphysics problems are ei-ther monolithic (treating the coupled problem directly) orsplit (solving reduced systems independently), with multi-level methods often being important for algorithmic scal-ability in both approaches. We present flexible supportdeveloped in PETSc for block preconditioners, splittingin smoothers, related multiplicative relaxation, nonlinearand matrix-free variants, and communication/bandwidthreducing techniques. We demonstrate software modular-ity without sacrificing run-time algorithmic flexibility forapplications in geodynamics and phase-field models.

Jed BrownMathematics and Computer Science DivisionArgonne National Laboratoryjedbrown@mcs.anl.gov

Mark AdamsColumbia Universitymark.adams@columbia.edu

Peter R. BruneMathematics and Computer Science DivisionArgonne National Laboratoriesbrune@mcs.anl.gov

Matthew G. KnepleyUniversity of Chicagoknepley@ci.uchicago.edu

Dave MayETH Zurichdave.may@erdw.ethz.ch

Lois Curfman McInnesArgonne National LaboratoryMathematics and Computer Science Divisioncurfman@mcs.anl.gov

Barry F. SmithArgonne National LabMCS Division

bsmith@mcs.anl.gov

MS13Tree Based Communication for Scalable MeshAdaptation in the SAMRAI Framework

SAMRAI mesh adaptation involves collective,communication-intensive operations that are challenging toscale. The critical clustering and partitioning operationsuse virtual tree networks to limit communication latencyto O(logP ) for P processes. However, ideal performanceis hindered by a number of possible causes that are dif-ficult to examine. In this work, we use newly developedtools to analyze the complex tree-based communications,with results leading to improved performance for SAMRAIapplications.

Brian GunneyLawrence Livermore National Labgunney1@llnl.gov

Abhinav Bhatele, Todd GamblinLawrence Livermore National Laboratorybhatele@llnl.gov, tgamblin@llnl.gov

MS13Building AMR into a Multiphysics Code Using theSAMRAI Framework

Supporting mature, evolving application requirements isa challenge for software frameworks. Using the SAMRAIframework, we have integrated adaptive mesh refinement(AMR) into a mature multiphysics code which is heavilyused and under continual developed. SAMRAI providesunique object-oriented support for parallel AMR mesh anddata management. We describe how SAMRAI allows de-coupling AMR operations from the application mesh anddata; SAMRAI does not own these entities, yet it manip-ulates them directly.

Richard HornungLawrence Livermore National Labhornung@llnl.gov

Robert AndersonLLNLCtr for Appl Scientific Companderson110@llnl.gov

Noah ElliottLLNLelliott22@llnl.gov

Brian GunneyLawrence Livermore National Labgunney1@llnl.gov

Michael WickettLawrence Livermore National Laboratorywickett1@llnl.gov

MS14Efficient Algorithms for Mesoscale Dynamics of In-teracting Particle Systems

We present efficient algorithms for simulating evolution ofspace-time averages of large ODE systems. Averaging pro-

40 AN12 Abstracts

duces exact PDEs but they cannot be simulated withoutsolving the underlying ODEs. We approximate these PDEsby new closed form equations that can be simulated inde-pendently of solving the underlying ODEs at a fractionof the cost. To achieve closure we use methods from thetheory of ill-posed problems. We analyze quality of theapproximation and efficiency of algorithms.

Lyudmyla BarannykUniversity of IdahoDepartment of Mathematicsbarannyk@uidaho.edu

Alexander PanchenkoWashington State Universitypanchenko@math.wsu.edu

MS14Flux Norm and Finite-dimensional Homogeniza-tion Approximation with Non-separated Scales andHigh Contrast

In joint work with Owhadi we consider the most generalcase of arbitrary L∞ coefficients, which may contain in-finitely many scales not necessarily being well-separated.We establish a finite-dimensional homogenization approxi-mation generalizing correctors in classical homogenization,and error estimates in the flux norm with an optimal errorconstant. We discuss recent results on localized multiscalebasis and work in progress on compactness of the solutionspace, and new corrector results in classical periodic ho-mogenization problem.

Leonid BerlyandPenn State UniversityEberly College of Scienceberlyand@math.psu.edu

MS14Acoustic Propagation in a Saturated Piezo-Elastic,Porous Medium

We study the problem of derivation of an effective modelof acoustic wave propagation in a two-phase, non-periodicmedium modeling a fine mixture of linear piezo-elastic solidand a viscous Newtonian, ionic bearing fluid. Bone tissue isan important example of a composite material that can bemodeled in this fashion. We develop two-scale homogeniza-tion methods for this system, and discuss also a stationaryrandom, scale-separated microstructure.

Robert P. GilbertDepartment of Mathematical SciencesUniversity of Delawaregilbert@math.udel.edu

MS14On the Integral Representation Formula (IRF) fora Two-parameter Family of Elastic Composites

This talk focuses on the derivation/implication of the IRFfor two-phase composites in which the contrasts betweentwo set of Lame coefficients can be described indepen-dently by the two parameters. This topic of research isinspired by the inverse problem of recovering microstruc-tural information from measurement of effective proper-ties of finely-structured composites (dehomogenization) inwhich IRF plays an essential role. This research is spon-

sored by ARRA-NSF-Math-Bio-0920852.

Yvonne OuUniversity of Delawaremou@math.udel.edu

MS15Evolutionary Games with Gaussian Structures

We consider a population playing two-strategy symmetricgames on a grid. A discrete Gaussian kernel rules out theinteractions and information collection between individu-als. We study how frequency and spatial structure of thepopulation change over time for Prisoner’s Dilemma gameunder four different update rules. Simulation results forthese rules show frequencies of the games for kernels withdifferent deviations. It is conjectured that, if the deviationof the kernel is large enough, bifurcation diagram of mean-field dynamics and spatial simulations agree. This resultwill be justified by showing the relation between macro-scopic and mesoscopic limits of the same microscopic rule.

Ozgur AydogmusIowa State Universityoaydogmus@iastate.edu

MS15Computation and Analysis of Evolutionary GameDynamics

Biological species (viruses, bacteria, parasites, insects,plants, or animals) replicate, mutate, compete, adapt, andevolve. In evolutionary game theory, such a process is mod-eled as a so-called evolutionary game. We describe theNash equilibrium problem for an evolutionary game anddiscuss its computational complexity. We discuss the nec-essary and sufficient conditions for the equilibrium states,and derive the methods for the computation of the optimalstrategies, including a specialized Snow-Shapley algorithm,a specialized Lemke-Howson algorithm, and an algorithmbased on the solution of a complementarity problem on asimplex. Computational results are presented. Theoreticaldifficulties and computational challenges are highlighted.

Yiping HaoDepartment of MathematicsIowa State Universityyphao@iastate.edu

MS15Within-host Dynamics of Influenza Virus Infectionwith Immune Responses

Influenza virus infection remains a public health problemworldwide. The mechanism underlying viral control duringan uncomplicated influenza virus infection is not fully un-derstood. In this talk, I will address this question by devel-oping mathematical models that include both innate andadaptive immune responses, and fitting them to experimen-tal data. This study provides a quantitative understandingof the biological factors that can explain the viral and in-terferon kinetics during a typical influenza virus infection,and may provide more information for future research ininfluenza pathogenesis, treatment, and vaccination.

Libin RongOakland Universityrong2@oakland.edu

AN12 Abstracts 41

MS15Modeling the Dynamics of Cross-infection of Leish-mania Amazonensis and Leishmania Major

Immune response during the course of Leishmania infec-tion is a classical and crucial model in immunology andpathology, as it revealed and claried a large number ofcritical and essential immunology factors such as binarypathways of CD4+ T helper cells activations, transporta-tion of pathogens by dendritic cells, and mechanisms ofmacrophage to clean the pathogens etc. Recently, a se-ries of experiments on the cross infection of Leishmaniaamazonensis and Leishmania major on C3HeB/FeJ andC57BL/6 mice [Jones et.al. 06, 11] indicates critical func-tions of B cells during the process of cleaning the pathogenand resolving the no-healing diseases caused by Leishma-nia amazonensis. Those experimental results also demon-strate interesting population dynamics that the two strainsof Leishmania interact indirectly through inducing differ-ent immune responses. Using immunobiological dynamicsapproach and game-theoretical approach, we propose andcompare two mutually different models to study the crossinfection of Leishmania amazonensis and Leishmania ma-jor based on [Jones et.al. 06, 11]. Detailed analysis andnumerical simulation are conducted based on parametersidentified from the data.

Douglas JonesDepartment of Veterinary PathologyIowa State Universityjonesdou@iastate.edu

Wen ZhouDepartment of Mathematics and Department of StatisticsIowa State Universityriczw@iastate.edu

Zhijun WuIowa State UniversityDept of Mathzhijun@iastate.edu

MS16Root Counts, Eigenvectors and Numerical Homo-topies

We will explain how solutions to polynomial systems canbe viewed as zero sets of sections of vector bundles with theresult of reducing the number of homotopy paths used in anumerical solution of the system. Specifically we will lookat the tangent bundle of projective space and associatedsystems of polynomials. We anticipate that solving thesepolynomial systems numerically amounts to a numericalmethod to compute the Jordan canonical form of a matrix.

David EklundInstitut Mittag-Lefflerdaek@math.kth.se

Chris PetersonColorado State Universitypeterson@math.colostate.edu

MS16Filtering Homotopies for Discretized BoundaryValue Problems

Discretizations of boundary value problems arising frommodels in science and engineering often yield polynomial

systems. Homotopy continuation methods allow one tocompute all solutions on a given mesh, but even a moder-ate size grid may lead to an intractably high degree system.However, generally most of the solutions are nonphysical,and so filtering techniques aim to reduce the work spent onthem. In this talk we discuss a new approach for formingfiltering homotopies over a continuous family of numeri-cal schemes, which in turn allows for more robust filteringcriteria and less reliance on ad hoc threshholds.

Tim M. MccoyUniversity of Notre Dametmccoy@nd.edu

MS16Real Algebraic Geometry in Combinatorics

The talk will give an overview of several problems in Ge-ometric Combinatorics and will describe some approachesto these problems through Real Algebraic Geometry.

Chris Peterson, Eklund DavidColorado State Universitypeterson@math.colostate.edu, daek@kth.se

Matthew KahleInstitute for Advanced Studymkahle@gmail.com

MS16Building a User Friendly Matlab Platform for Nu-merical Polynomial Algebra

Numerical polynomial algebra and numerical algebraic ge-ometry has enjoyed tremendous advancement in recentyears with many algorithms becoming standard. A Mat-lab package Apalab, initially developed several years agofor numerical polynomial algebra, is in major upgrade. Inadditional to adding algorithms/implementations, we aredesigning an intuitive interface so that casual users andearly students can engage advanced polynomial computa-tion easily. This talk will present those new developmentstoward building such a Matlab platform.

Zhonggang ZengNortheastern Illinois UniversityDepartment of Mathematicszzeng@neiu.edu

MS17Improvements in Adaptive Nonlinear Filtering inRegularization Models for Incompressilbe Flows

We will review some recent results for adaptive nonlinearfiltering in regularization models of incompressible flow.We will then discuss some improvements in how to de-fine the indicator functions. We will present a numericalmethod using these ideas, prove convergence of it to themodel, and give several test examples.

Abigail BowersDepartment of Mathematical SciencesClemson Universityabowers@clemson.edu

MS17A Least Squares Approach for the Coupled Stokes-

42 AN12 Abstracts

Darcy System

We consider a linear/nonlinear Stokes flow coupled witha porous medium flow with only flow rates specified onthe inflow and outflow boundaries in both flow domains.The coupled Stokes-Darcy system is formulated as an op-timal control problem where a common force is used as acontrol to minimize the the jump in normal velocities oftwo flows across the interface and to match the given flowrates. We analyze the optimal control problem and use aleast squares approach for which a Gauss-Newton type al-gorithm is considered. Numerical results are presented tovalidate convergence of the algorithm.

Hyesuk LeeClemson UniversityDep. of Mathematical Scienceshklee@clemson.edu

MS17Coupling Biot and Navier-Stokes Equations forModelling Fluid-poroelastic Media Interaction

The interaction between a free fluid and a deformableporous medium is found in a wide range of applications:ground-surface water flow, geomechanics or blood-vesselinteractions. We focus on the latest application. Thefluid-poroelastic structure interaction (FPSI) problem inhemodynamics couples the Navier-Stokes equations for anincompressible fluid to the Biot problem, the latter govern-ing the motion of a saturated poroelastic medium. Only alimited number of works deal with this problem. The finiteelement approximation of the FPSI problem is involved dueto the fact that both subproblems are indefinite. We intro-duce a residual-based stabilization technique for the Biotsystem, motivated by the variational multiscale approach.This technique allows the use of the same finite elementspaces for all the velocities and pressures, greatly simpli-fying the discretization and the enforcement of couplingconditions. We choose a fixed point method for the lin-earization of the Navier-Stokes/Biot coupled system. Tosolve the linear FPSI system at every fixed point iteration,we propose to use both a monolithic approach and par-titioned procedures based on domain decomposition pre-conditioners (the Dirichlet-Neumann, Robin-Robin, andRobin-Neuman ones). We compare the efficiency of all themethods on a test problem. The performance of the mono-lithic approach improves as the added-mass effect gets crit-ical and the Robin-Neumann preconditioner proves to bethe less sensitive to the added-mass effect.

Annalisa QuainiUniversity of Houstonquaini@math.uh.edu

Santiago BadiaInternational Center for Numerical Methods inEngineeringUniversitat Politecnica de Catalunya, Barcelona, Spainsbadia@cimne.upc.edu

Alfio QuarteroniEcole Pol. Fed. de LausanneAlfio.Quarteroni@epfl.ch

MS17Multiscale Deconvolution Models of Turbulence

We will prove several mathematical and physical proper-

ties for the newly developed (A. Dunca, 2011) multiscale-deconvolution models of turbulence. We prove conser-vation laws, derive a microscale, and show the existenceof global attractors. Additionally, we derive a numericalscheme for the model, and show results of preliminary testson some benchmark problems.

Leo RebholzClemson UniversityDepartment of Mathematical Sciencesrebholz@clemson.edu

Argus Adrian DuncaSpiru Haret Universitya.a.dunca.mi@spiruharet.ro

Monika NedaUniversity of Nevada Las Vegasmonika.neda@unlv.edu

Kara KohlerClemson Universitykekohle@clemson.edu

MS18Mathematical Models of Gels in Biomedical Appli-cations: Drug Delivery Devices

Abstract not available at time of publication.

Maria-Carme CaldererDeparment of MathematicsUniversity of Minnesota, USAcalde014@umn.edu

MS18Immersive Visualization and Computational Cre-ativity for Biomedicine

This talk will focus on recent advances in interactive vi-sualization in immersive virtual reality and on the emerg-ing research topic of computational creativity the devel-opment of computer tools for supporting creative humantasks, such as 3D design. Exciting recent interdisciplinaryapplications of this research to biomedicine at the Univer-sity of Minnesota will be described, including research on anew multi-touch 3D visualization environment for design-ing medical devices within virtual models of the humananatomy.

Daniel KeefeUniversity of Minnesotakeefe@cs.umn.edu

MS18Tracking Brain and CSF Evolution via LevelSet/mesh Warping Algorithm during Hydro-cephalus Treatment

Hydrocephalus is a serious neurological disorder in whichthere is an abnormal accumulation of cerebrospinal fluid(CSF) in the brain ventricles, causing brain enlargementand tissue compression. Although hydrocephalus treat-ment has been performed by surgical CSF shunt inser-tion, computational models are needed to track hydro-cephalic brain movement. Thus, we propose a combinedlevel set/mesh warping algorithm and use it to simulatethe evolution of the brain ventricles and the CSF in pedi-

AN12 Abstracts 43

atric hydrocephalic patients.

Jeonghyung Park, Suzanne M. Shontz, Corina S. DrapacaThe Pennsylvania State Universityjxp975@cse.psu.edu, shontz@cse.psu.edu, csd12@psu.edu

MS18Immunotherapy and Aging Effects in ImmuneModulated Tumor Growth

The presence of cancer in a host elicits an immune re-sponse that can be both inhibitory and stimulatory to tu-mor development. Aging decreases the effectiveness of theimmune response, which can alter immune modulation oftumor growth. We present a mathematical model basedon principles of generalized logistic growth that incorpo-rates both pro- and anti-tumor immune processes. We thenuse this model to investigate the effects of aging and im-munotherapy on tumor development.

Kathleen P. WilkieTufts University School of MedicineCenter of Cancer Systems Biologykathleen.wilkie@tufts.edu

Philip HahnfeldtTufts Universityphilip.hahnfeldt@tufts.edu

MS19Symplectic Methods for an Exactly Solvable Kol-mogorov Model of Two Interacting Species

We discuss the behavior of symplectic integration methodsfor an exactly solvable Kolmogorov predator-prey model oftwo interacting species. Using numerical experiments, weinvestigate the accuracy, conservation, and periodic orbitsof this Hamiltonian system. In light of this, we present po-tential generalizations to other population dynamics withbounded state variables. Advisor: Ari Stern, University ofCalifornia, San Diego

Katherine BallUniversity of California, San Diegokball@sdcc21.ucsd.edu

MS19CGPOP Analysis and Optimization

The CGPOP miniapp is the conjugate gradient solver fromLos Alamos National Laboratory’s Parallel Ocean Program(POP) version 2.0. It includes several algorithms with com-bination of different communication modes and task par-tition strategies. The main goal of the project is to studyand to improve the performance the methods. It involvedthe installation, execution, performance measurement andevaluation, modification and improvement to the code ofCGPOP. Students obtained better understanding on par-allel computing after working on the project. Advisors:Xiaoge Wang, Yinsheng Ji, Cheng Zhang

Hongtao Cai, Xiaoxiang Hu, Haoruo PengTsinghua University, Beijingwxiaoge@gmail.com, tba, tba

MS19Periodic Dispersion

The evolution of linearly dispersive equations with piece-wise constant initial data on periodic domains dependson the asymptotic behavior of the dispersion relation. Inparticular, dispersion relations with asymptotically poly-nomial growth lead to dispersive quantization, being (ap-proximately) quantized at rational times but fractal at ir-rational times. Similar phenomena are known as Talboteffect in optics and quantum mechanics. Numerical exper-iments and some analysis indicate that such effects persistinto the nonlinear regime. Advisor: Peter J. Olver, U Min-nesota

Gong ChenU Minnesotachenx563@umn.edu

MS19Modeling Earth’s Temperature and AtmosphericCarbon Dioxide

From ice core data, it is known that over the past 400,000years, surface temperatures and atmospheric CO2 concen-trations have oscillated with a period of approximately100,000 years. The model introduced by Budyko (1969) isa simple model for the temperature of the Earths surface,but it does not allow atmospheric CO2 to change. Here,the Budyko model is altered to allow CO2 to change, so asto explore the interactions between CO2 and temperature.Advisor: Mary Lou Zeeman

Emma CutlerBowdoin Collegeecutler@bowdoin.edu

MS20Multiscale Models for Coupled Flow and Elasticity

In this talk, a multiscale framework for fluid-structure in-teraction problem in an inelastic media is developed andanalyzed. We assume Stokes flow at the pore scale and anelasticity model for pore-level deformations. Because of thecomplexity of the interaction at the pore level, an iterativemacroscopic model is proposed. The constitutive relationsrepresenting media deformation is modeled via an iterativeprocedure. Constitutive equations are derived. Numericalresults are presented.

Yalchin EfendievDept of MathematicsTexas A&M Universityefendiev@math.tamu.edu

Peter PopovTexas A&M Universitymailto:ppopov99@gmail.com

Yulia GorbUniversity of Houstonmailto:gorb@math.uh.edu

Donald BrownTexas A&M Universitymailto:donaldbrowdr@gmail.com

44 AN12 Abstracts

MS20Advanced Discretizations for Modeling Flow andReactive Transport on Highly Distorted Unstruc-tured Grids

Abstract not available at time of publication.

Konstantin LipnikovLos Alamos National Laboratorylipnikov@lanl.gov

MS20Coupled and Hybrid Models for Methane Evolu-tion in Subsurface

We discuss challenges in computational modeling of pro-cesses of multicomponent adsorption and phase changecoupled to flow and transport processes in coalbed methaneand undersea methane hydrates. We report on our recentresults on i) implementation of solvers for PDEs with con-straints which are necessary for continuum level models, ii)handling multiscale processes in micropores using discretescale models, and iii) modeling of pore- to core- couplingsin hybrid models which bridge between continuum and dis-crete scales.

Malgorzata PeszynskaDepartment of MathematicsOregon State Universitympesz@math.oregonstate.edu

MS20Analysis of CO2-water Models

Abstract not available at time of publication.

Ralph ShowalterDepartment of MathematicsOregon State Universityshow@math.oregonstate.edu

MS20Coupling Compositional Flow, Transport, and Me-chanics in Porous Media for Modeling Carbon Se-questration in Saline Aquifers

A key goal of our work is to produce a prototypical com-putational system to accurately predict the fate of in-jected CO2 in conditions governed by multiphase flow,rock mechanics, multi-component transport, thermody-namic phase behavior, chemical reactions within both thefluid and the rock, and the coupling of all these phenomenaover multiple time and spatial scales. Even small leakagerates over long periods of time can unravel the positive ef-fects of sequestration. This effort requires high accuracyin the physical models and their corresponding numericalapproximations. For example, an error of one percent peryear in a simulation may be of little concern when deal-ing with CO2 oil recovery flooding, but such an inaccu-racy for sequestration will lead to significantly misleadingresults that could fail to produce any long-term predic-tive capability. It is important to note that very few par-allel commercial and/or research software tools exist forsimulating complex processes such as coupled multiphaseflow with chemical transport and geomechanics. Here wediscuss modeling multicomponent, multiscale, multiphaseflow and transport through porous media and through wellsand that incorporate uncertainty and history matching andinclude robust solvers. The coupled algorithms must be

able to treat different physical processes occurring simul-taneously in different parts of the domain, and for compu-tational accuracy and efficiency, should also accomodatemultiple numerical schemes. We present results demon-strating accuracy of schemes as well as applications fromthe Cranfield Mississippi demonstration site and core scaleexperiments.

Mary F. WheelerUT-Austinmfw@ices.utexas.edu

MS21Bending, Twisting, and Snapping: Mechanics andDynamics of Slender Structures

Soft materials undergo volume changes and instabilitieswhen subjected to external stimuli. These instabilities andbifurcations can lead to dynamical shape changes in themorphogenesis in growing soft tissues. In this work, wepresent the dynamic instabilities that occur by strainingan elastomer nonhomogenously with a favorable solvent.We examine how thin elastic plates undergo rapid bend-ing, twisting, and snap-buckling instabilities when swollen.

Douglas HolmesEngineering Science and Mechanics DepartmentVirginia Techdpholmes@vt.edu

Matthieu Roche, Tarun Sinha, Howard A. StoneMechanical and Aerospace EngineeringPrinceton Universitymatthieu@princeton.edu, tsinha@princeton.edu,hastone@princeton.edu

MS21An Electromechanical Model of Tubular HeartPumping in Ascidians

Recent advancements in computational fluid dynamicshave enabled researchers to efficiently explore problemssuch as insect flight and fish swimming that involve movingelastic boundaries immersed in fluids. These advances havealso made modeling the interaction between a fluid and anelastic model of an organ that includes some aspects of itsphysiology feasible. This presentation focuses on the devel-opment and implementation of coupled immersed bound-ary and electromechanical models of the tubular hearts ofAscidians.

Laura A. MillerUniversity of North Carolina - Chapel HillDepartment of Mathematicslam9@email.unc.edu

Austin Baird, Tiffany KingUniversity of North CarolinaDepartment of Mathematicsabaird@live.unc.edu, tiffankm@unc.edu

MS21Anisotropic Diffusion in Swelling Polymer Gels

When anisotropic diffusion is taken into account, specialforms of the diffusivity tensor D have to be taken intoaccount, with D = D(d) and d the unit vector identify-ing the preferential (higher diffusivity) direction of diffu-

AN12 Abstracts 45

sion. The solvent flux h = −D∇µ which drives the sol-vent balance equation, coupled with the equations of thenonlinear three-dimensional elasticity, induces mechanicalanisotropy, as evidenced in (DiMeo et al., Soft Matter 7,6068, 2011). In this work, a few numerical simulations arecarried out to investigate some significant cases.

Alessandro LucantonioUniversita degli Studi di Romaalessandro.lucantonio@gmail.com

Paola NardinocchiUniversita degli Studi di Roma ”La Sapienza”paola.nardinocchi@uniroma1.it

Luciano TeresiUniversity Roma Treteresi@uniroma3.it

MS21Nanoscale Mechanics of Natural Soft Materials

Nature requires soft tissue, e.g., elastomeric proteins orlipid layers, to be mechanically stable as they perform dif-ferent tasks. In many cases, it has not been possible toreplicate their mechanical properties in synthetic materialsdue to a lack of fundamental understanding of the mecha-nisms that the natural materials use. We present a novelinsight into the behavior of natural soft materials throughmolecular mechanics simulations.

Ishwar PuriEngineering Science and Mechanics DepartmentVirginia Techikpuri@vt.edu

Ravi KappiyoorDepartment of Engineering Science and MechanicsVirginia Techrkappiyo@vt.edu

MS22Parametric and Other Exact Solutions to EinsteinsEquations in Terms of Special Functions

In certain cosmological models the Einstein equations ofgeneral rel- ativity reduce to a differential equation whosesolutions can be found in terms of Jacobi or Weierstrasselliptic functions. In recent joint work with Floyd L.Williams we find more widespread applications of spe- cialfunctions for other cosmological models. I will give anoverview of techniques we employed in finding such specialsolutions that may be of use to a more general audience.

Jennie DAmbroiseBard Collegejdambroi@bard.edu

MS22A Method for Earthquake Cycle Simulations

We are developing a method to understand and simulatefull earthquake cycles with multiple events on geometri-cally complex faults, with rate-and-state friction and off-fault plasticity. The method advances the model over longinterseismic periods using the quasi- static equations, andthrough dynamic rupture using the elastodynamic formu-lation. To obtain an efficient and provably strictly stable

method, we use high-order summation-by- parts finite dif-ference schemes and weak enforcement of boundary condi-tions through the simultaneous approximation term.

Brittany EricksonStanford Universitybaericks@stanford.edu

MS22A Gamma-Convergence Analysis of the Quasicon-tinuum Method

Continuum mechanics models of solids have certain limita-tions as the length scale of interest approaches the atom-istic scale. A possible solution in such situations is to usea pure atomistic model. However, this approach couldbe computational prohibited as we are dealing with bil-lion of atoms. The quasicontinuum method is a computa-tional technique that reduces the atomic degrees of free-dom. In this talk, we review the quasicontinuum methodand present a Gamma-convergence analysis of it.

Malena Ines EspanolCalifornia Institute of Technologymespanol@caltech.edu

MS22Video Stabilization of Atmospheric TurbulenceDistortion

The image or the video sequence captured in a long-rangesystem, such as surveillance and astronomy, is often cor-rupted by the atmospheric turbulence degradation. Wepropose to stabilize the video sequence using Sobolev gra-dient sharpening with the temporal smoothing. One latentimage is found further utilizing the lucky-region method.With these methods, without any prior knowledge, thevideo sequence is stabilized while keeping sharp details andthe latent image shows more consistent straight edges.

Yifei LouSchool of Electrical and Computer EngineeringGeorgia Institute of Technologylouyifei@gmail.com

MS23Hom-Polytopes

Given full-dimensional polytopes P in Rp and Q in Rq, thehom-polytope Hom(P,Q) is defined to be the set of affinemaps L : Rp → Rq such that L(P ) is contained in Q. Itis not difficult to specify the facets of Hom(P,Q), but littleelse is known. We prove some categorical properties andproduce a range of examples in low dimensions. Even whenP and Q are polygons, the number of vertices of the hom-polytope depends on the geometry of P and Q, not juston m and n. We provide experimental results for pairs ofregular polygons and a structural result for generic pairsof polygons.

Tristram C. BogartSan Francisco State Universitytcbogart@gmail.com

Mark ContoisResearch in Motionmcontois@rim.com

46 AN12 Abstracts

Joseph GubeladzeSan Francisco State Universitysoso@sfsu.edu

MS23The Combinatorial Commutative Algebra of Con-formal Blocks

Vector spaces of conformal blocks are objects from confor-mal field theory which have made surprising appearancesin several moduli problems from algebraic geometry. Wediscuss the combinatorics underlying the dimension formu-las of these spaces, and answer some questions about aclassical moduli space: the moduli of rank 2 parabolic vec-tor bundles on a projective algebra curve. In particular,we will use a polyhedral description of conformal blocks toconstruct presentations for coordinate rings of these spaces.

Christopher A. ManonUC Berkeleychris.manon@math.berkeley.edu

MS23Geometry of Exceptional Divisors and theGoemans-Williamson Algorithm

By a result of Mukai we can associate to each Dynkin di-agram Ta,b,c an algebraic variety Xa,b,c whose geometry iscontrolled by the combinatorics of its (finitely many) excep-tional divisors. In this talk we ask the question of determin-ing the maximum number of pairwise intersections betweentwo disjoint sets of such divisors. We give lower and up-per bounds for this quantity and show that our bounds areasymptotically exact for the infinite families. Our resultsare a consequence of a detailed analysis of the behavior ofthe Goemans-Williamson random semidefinite approxima-tion algorithm for the maxcut problem on strongly regularmultigraphs.

Mauricio Velasco, Mauricio JuncaUniversidad de los Andesmvelasco@uniandes.edu.co, mj.junca20@uniandes.edu.co

MS23Singularities of Schubert and Richardson Varieties

This talk addresses the problem of how to analyze and dis-cuss singularities of a variety X that “naturally’ sits insidea flag manifold. Our three main examples are Schubertvarieties, Richardson varieties and Peterson varieties. Theoverarching theme is to use combinatorics and commuta-tive algebra to study the *patch ideals*, which encode lo-cal coordinates and equations of X. Thereby, we obtainformulas and conjectures about X’s invariants. We will re-port on projects with (subsets of) Erik Insko (U. Iowa),Allen Knutson (Cornell), Li Li (Oakland University) andAlexander Woo (U. Idaho).

Alexander YongUniversity of Illinois, Urbana-Champaignayong@uiuc.edu

MS24A Multiscale Method Coupling Network and Con-tinuum Models in Porous Media

In this talk, we present a numerical multiscale methodfor coupling a conservation law for mass at the contin-

uum scale with a discrete network model that describesthe pore scale flow in a porous medium. We developedsingle-phase flow algorithm and extended it to two-phaseflow, for the situations in which the saturation profile gothrough a sharp transition from fully saturated to almostunsaturated states. Our coupling method for the pressureequation uses local simulations on small sampled networkdomains at the pore scale to evaluate the continuum equa-tion and thus solve for the pressure in the domain. Wepresent numerical results for single-phase flows with non-linear flux-pressure dependence, as well as two-phase flow.

Chia-Chieh ChuUniversity of Texas at Austinccchu@math.utexas.edu

MS24Effective Properties of a Periodic Lattice of Circu-lar Inclusions

The problem of determination of effective properties (con-ductivity, permittivity, etc.) of a medium containing an ar-bitrary doubly periodic array of identical circular cylinderswithin a homogeneous matrix is considered. We constructa quasiperiodic potential and determine the average field inthe medium. The problem is then reduced to solution of aninfinite system of linear equations. The effective conduc-tivity tensor is obtained in the form of the series expansionin terms of the volume fraction of the cylinders whose co-efficients are determined exactly. Results are illustrated byexamples.

Yuri GodinUniversity of North Carolina at Charlotteygodin@uncc.edu

MS24Correctors and Field Fluctuation for the p(x)-Laplacian with Rough Exponents with Sub-LinearGrowth

A corrector theory for the strong approximation of fieldsinside composites made from two materials with differentpower law behavior is provided. The correctors are used todevelop bounds on the local singularity strength for gra-dient fields inside microstructured media. The bounds aremultiscale in nature and can be used to measure the ampli-fication of applied macroscopic fields by the microstructure.The talk will focus on the case of exponents with sublineargrowth.

Silvia JimenezWorcester Polytechnic Institutesilviajimenez@wpi.edu

MS24Inverse Born Series for the Calderon Problem

We propose a direct reconstruction method for theCalderon problem based on inversion of the Born series.We characterize the convergence, stability and approxima-tion error of the method and illustrate its use in numericalreconstructions.

Shari MoskowDrexel UniversityDepartment of Mathematicsmoskow@math.drexel.edu

AN12 Abstracts 47

MS25Efficient Computational Methods for ThermalImaging of Small Cracks in Plates

We present some fast computational methods and practicalconsiderations for identifying cracks in a two-dimensionalplate using thermal data from an infrared camera, basedon the “small volume expansions’ developed Ammari, Vo-gelius, et. al. For an applied heat flux, the plate tempera-ture is measured over its entire surface, so we have interiordata, not just on the boundary. The novelty is that thecracks we seek are near or below the single-pixel resolutionof the camera.

Kurt BryanRose-Hulman Institute of TechnologyTerre Haute, Indiana USAkurt.bryan@rose-hulman.edu

MS25Stochastic and Deterministic Inverse Solutions forCrack and Corrosion Imaging

Interesting mathematical issues arise when imaging tinycracks and hidden corrosion in engineering applications us-ing thermography. Sparse and noise pixel data “conspire’with the inverse heat (parabolic) operator to furnish an ar-ray of practical imaging challenges. This talk will exploredeterministic and stochastic approaches to ameliorate suchdifficulties and discuss the algebraic and topological con-siderations that effect posedness in the deterministic case,and informativeness within the stochastic context.

Christopher J. EarlsCornell Universitycje23@cornell.edu

MS25Application of Sparse Solutions to Underdeter-mined Problems in Imaging

The principle of parsimony has recently been demonstrateduseful in solving highly underdetermined systems of linearequations. We first review the mathematics that make suchsolutions possible and then provide several applications ofsparse (parsimonious) models in imaging. In the first wepresent results from the field of compressive sampling andshow how high-fidelity imagery can be recovered from low-fidelity measurements. We then demonstrate how to de-velop and use sparse image models for image processing.

C. C. Olson, L. N. Smith, K. P. Judd, J. WatermanNaval Research Labpele@ccs.nrl.navy.mil, pele@ccs.nrl.navy.mil,pele@ccs.nrl.navy.mil, pele@ccs.nrl.navy.mil

Jonathan NicholsNaval Research LabCode 5673pele@ccs.nrl.navy.mil

MS26Statistical Models and Methods for Anomaly De-tection in Large Graphs

Traditional statistical models and methods provide a pow-erful framework for analyzing observed data. To extend

these approaches to large graph-valued data sets, however,we must address significant theoretical and computationalchallenges. In this talk, we discuss new techniques for sta-tistical inference on large graphs, with application to thedetection of anomalous behavior in a citation database.

Nicholas ArcolanoMIT Lincoln Laboratoryarcolano@ll.mit.edu

MS26Streaming Graph Analytics for Massive Graphs

Emerging real-world graph problems include detectingcommunity structure in large social networks, improvingthe resilience of the electric power grid, and detecting andpreventing disease in human populations. The volume andrichness of data combined with its rate of change rendersmonitoring properties at scale by static recomputation in-feasible. We approach these problems with massive, fine-grained parallelism across different shared memory archi-tectures both to compute solutions and to explore the sen-sitivity of these solutions to natural bias and omissionswithin the data.

David A. BaderGeorgia Institute of Technologybader@cc.gatech.edu

David Ediger, Jason RiedyGeorgia Institute of TechnologySchool of Computational Science and Engineeringdediger@gatech.edu, jason.riedy@cc.gatech.edu

MS26Perfect Power Law Graphs: Generation, Sampling,Construction and Fitting

Power law graphs are ubiquitous and arise in the Inter-net, the Web, citation graphs, and online social networks.Deviations from the power law model do not have a largeimpact on the qualitative characterization of graphs. How-ever, the need for precise background models becomes es-sential in order to apply rigorous statistical signal process-ing techniques to detect graph anomalies. This work ex-plores the power law degree distribution that is used tomodel power law graphs. A simple heuristic for generat-ing perfect power law graphs is presented that reproducesmany observed phenomena. Using this model the samplingeffects of graph construction and edge ordering are exam-ined. Graph construction appears to be a lossy, non-linearprocess that generates many phenomena that are observedin real data (e.g., data bin scatter, low-degree tails, andhigh-degree tails). Likewise, the order that edges are gen-erated can have a strong effect on the evolution of the powerlaw slope and the overall density of the graph (i.e., densifi-cation). Applying the perfect power law model to real data(e.g., entities extracted from the Reuters Corpus) providesa self-consistent set of degree bins for measuring deviationsfrom the background. Using this scheme it is possible toidentify specific edges that are typical, surplus, or deficitusing standard signal processing techniques.

Jeremy KepnerMIT Lincoln Laboratorykepner@ll.mit.edu

48 AN12 Abstracts

MS26Fast Counting of Patterns in Graphs

The occurrence of small subgraphs is a key ingredient in un-derstanding real networks, since local interactions can re-veal a lot of information about the full graph. For instance,the number of triangles indicates how well the graph is clus-tered. However, counting such small graphs can be compu-tationally intensive, preventing adoption of such techniqueson massive graphs. We are developing sampling-based al-gorithms for counting small sugbgraphs graphs. In thistalk, we will present our latest results.

Ali Pinar, C. SeshadhriSandia National Labsapinar@sandia.gov, scomand@sandia.gov

Tamara G. KoldaSandia National Laboratoriestgkolda@sandia.gov

MS27High Order Mimetic Methods on a NonuniformMesh

Mimetic Operators satisfy a discrete analog of the diver-gence theorem and they are used to create/design conserva-tive/reliable numerical representations to continuous mod-els. We will present a methodology to construct mimeticversions of the divergence and gradient operators whichexhibit high order of accuracy at the grid interior as wellas at the boundaries. As a case of study, we will show theconstruction of fourth order operators in a one-dimensionalstaggered grid. Mimetic conditions on discrete operatorsare stated using matrix analysis and the overall high orderof accuracy determines the bandwidth parameter. Thiscontributes to a marked clarity with respect to earlier ap-proaches of construction. As test cases, we will solve 2-D el-liptic equations with full tensor coefficients arising from oilreservoir models. Additionally, applications to elastic wavepropagation under free surface and shear rupture bound-ary conditions will be given.indocument or other high-levelcommands.

Jose E. CastilloSan Diego State UniversityDepartment of Mathematicscastillo@myth.sdsu.edu

MS27Mimetic Library Toolkit

Mimetic Methods Toolkit (MTK) is an application pro-gramming interface that allows the intuitive implementa-tion of Mimetic Discretization Methods for the solutionof Partial Differential Equations. Mimetic Methods yieldnumerical solution that guarantee uniform order of accu-racy all along the modeled physical domain, while ensur-ing the satisfaction of conservative laws. Therefore, theattained numerical solutions remain physically faithful tothe underlying physics of the problem. MTK is fully de-veloped in ISO C++, thus exploiting all the well-knownadvantages of Object Oriented Applications as for exam-ple, providing the developer an intuitive perspective of thetheoretical framework of Mimetic Discretization Methods.Likewise, Object Orientation carries along the advantagesof the extensive collection of data structures manipulationcapabilities of C++, thus allowing for a clearer program-ming methodology making MTK suitable for developing

high-end scientific applications

Eduardo Sanchez, Jose CastilloSan Diego State Universityejspeiro@gmail.com, castillo@myth.sdsu.edu

MS27A Discrete Vector Calculus in Tensor Grids

The key to the success of mimetic discretization methodsis that they discretize some description of continuum me-chanics, e.g. vector calculus or differential forms. For adiscretization to be fully mimetic it must have exact dis-crete analogs of the important results from the continuumtheory. We summarize exactly which results from vectorcalculus are needed to derive energy inequalities for com-mon initial boundary value problems, which we call themimetic properties, and then produce a discrete vector cal-culus on tensor product grids in three dimensions that isfully mimetic.

Stanly L. SteinbergUniversity of New Mexicostanly@wendouree.org

Nicolas RobidouxIndependent ConsultantImage Processing and Applied Mathematicsnicolas.robidoux@gmail.com

MS27The Mimetic Spectral Element Method in theCommunity Atmosphere Model (CAM)

We describe a mimetic formulation of the spectral elementmethod and its implementation in the the Community At-mosphere Model (CAM). For the atmospheric hydrostaticprimitive equations, the mimetic properties of the methodallow for excellent conservation on the unstructured, curvi-linear meshes used by CAM. This includes local conser-vation (to machine precision) of quantities solved in con-servation form, and semi-discrete conservation (exact withexact time-discretization) of derived quantities such as en-ergy and potential vorticity.

Mark A. TaylorSandia National Laboratories, Albuquerque, NMmataylo@sandia.gov

Aime FournierNCARfournier@ucar.edu

MS28Defective Boundary Conditions for ViscoelasticFlow Problems

Abstract not available at time of publication.

Keith GalvinDepartment of Mathematical SciencesClemson Universitykjgalvi@clemson.edu

MS28An ANOVA-based Method for High-dimensional

AN12 Abstracts 49

Stochastic PDEs

The Analysis of Variance (ANOVA) expansion is often usedto reduce the cost of evaluating multivariate functions inhigh dimensions. We propose an ANOVA-based methodfor representation of multivariate functions, which does notdepend on the choice of the anchor point, and tracks allthe important parameters and important interactions, con-structing the expansion with the minimum of the neededterms. We demonstrate a real life application where ourmethod is the only usable approach.

Alexander LabovskyDepartment of Mathematical SciencesMichigan Technological Universityaelabovs@mtu.edu

Max GunzburgerFlorida State UniversitySchool for Computational Sciencesmgunzburger@fsu.edu

MS28Analysis of Long Time Stability and Errors of TwoPartitioned Methods for Uncoupling EvolutionaryGroundwater - Surface Water Flows

Abstract not available at time of publication.

Catalin S. TrencheaDepartment of MathematicsUniversity of Pittsburghtrenchea@pitt.edu

MS28An Adaptive Approach to PDE-constrained Opti-mization for Random Data Identification Problems

In this talk we will present a scalable mechanism for opti-mal identification of statistical moments or even the wholeprobability distribution of input random data, given theprobability distribution of some response of a system ofPDEs. This novel technique integrates an adjoint-baseddeterministic algorithm with the sparse grid stochastic col-location FEM. Our rigorously derived error estimates andseveral numerical examples, will be described and used tocompare the efficiency of the method with several othertechniques.

Clayton G. WebsterOak Ridge National Laboratorywebstercg@ornl.gov

Max GunzburgerFlorida State Universitygunzburg@fsu.edu

Catalin S. TrencheaDepartment of MathematicsUniversity of Pittsburghtrenchea@pitt.edu

MS29Data Assimilation in Cardiovascular Mathematics:Toward An Integration of Patient-Specific Mea-surements and Simulations

In cardiovascular sciences, images and measures provide

patient-specific knowledge that can enhance significantlythe reliability of numerical simulations by proper data as-similation procedures. We address here the variational as-similation of velocity data and images for the accurate es-timation of hemodynamics indexes of interest with botha deterministic and a Bayesian approach. The latter pro-vides a better quantification of uncertainty and confidenceregions for the quantities of interest.

Alessandro VenezianiMathCS, Emory University, Atlanta, GAale@mathcs.emory.edu

Marta D’EliaDepartment of Scientific ComputingFlorida State University, Tallahassee, FLmarti.delia@gmail.com

Alexis AposporidisEmory University, USAaapospo@emory.edu

MS29Fast Algorithms for Biophysics-based Medical Im-age Analysis

Abstract not available at time of publication.

George BirosUniversity of Texas at Austinbiros@ices. utexas.edu

MS29Patient-specific Mesh Generation for ImprovedPulmonary Embolism Prevention

Pulmonary embolism is a potentially fatal disease involv-ing the blockage of an artery of the lungs, typically by ablood clot. One treatment is via implantation of a mechan-ical device known as an inferior vena cava filter which trapslarge blood clots, preventing them from reaching the lungs.In this talk, we present a computational pipeline for gen-eration of patient-specific meshes for use in CFD studiesof blood flow for improved prevention of pulmonary em-bolism.

Shankar P. Sastry, Jibum Kim, Suzanne M. ShontzThe Pennsylvania State Universitysps210@cse.psu.edu, jzk164@cse.psu.edu,shontz@cse.psu.edu

Brent A. CravenPenn State Applied Research Laboratorybac207@psu.edu

Frank C. LynchPenn State Hershey Medical Centerflynch@hmc.psu.edu

Keefe B. Manning, Thap PanitanarakThe Pennsylvania State Universitykbm10@psu.edu, txp214@cse.psu.edu

MS29Resolving Topology Ambiguity for ComplicatedDomain

We discuss all possible topology configurations and develop

50 AN12 Abstracts

an extension of the dual contouring (DC) method whichguarantees the correct topology. We analyze all the octreeleaf cells, and categorize them into 31 topology groups bycomputing the values of their face and body saddle pointsbased on a tri-linear representation. Knowing the correctcategorization, we are able to modify the base mesh andintroduce more minimizer points to preserve the correcttopology.

Yongjie ZhangDepartment of Mechanical EngineeringCarnegie Mellon Universityjessicaz@andrew.cmu.edu

Jin QianCarnegie Mellon Universityjq@andrew.cmu.edu

MS30Results from the Early Science High Speed Com-bustion and Detonation Project

The High Speed Combustion and Detonation project usesan adaptive mesh refinement, reactive flow Navier-Stokescode augmented with the equation of state, microscopictransport, and chemical kinetics required to study thedetonation-to-deflagration transition in hydrogen. Torun on future hardware, we have implemented mixedMPI/OpenMP threading, and parellelized the adaptivemesh refinement code. Our challenge is maintaining com-putational work load balance, and managing the distribu-tion of ghost cells for communications performance.

Alexei KhokhlovThe University of ChicagoChicago, ILajk@oddjob.uchicago.edu

Charles BaconArgonne National Laboratorybacon@alcf.anl.gov

MS30Implementing Hybrid Parallelism in FLASH

FLASH is a component-based multiphysics scientific soft-ware which has been used for computations on some of thelargest HPC platforms. Simulation of turbulent nuclearcombustion, a key process in Type Ia supernovae, is oneof the target applications on the BG/Q platform at ANL.In preparation, we have introduced hybrid parallelism tothe code. We describe these modifications, and also char-acterize the performance of the modified code on our firstBG/Q racks.

Christopher DaleyFlash Center for Computational Science, Univ. of ChicagoALCF Argonne National Laboratorycdaley@flash.uchicago.edu

Vitali MorozovALCF, Argonne National Laboratorymorozov@anl.gov

Dongwook LeeFlash Center for Computational Science, Univ. of Chicagodongwook@flash.uchicago.edu

Anshu DubeyUniversity of Chicagodubey@flash.uchicago.edu

Jonathan GallagherFlash Center for Computational Science, Univ. of Chicagojbg@uchicago.edu

Don Lamb, Klaus WeideUniversity of Chicagolamb@flash.uchicago.edu, klaus@flash.uchicago.edu

MS30A Trillion Particles: Studying Large-Scale Struc-ture Formation on the BG/Q

The simulation of structure formation in the Universe sitsat the forefront of large-scale high-performance computing.I will discuss the unique algorithmic features employed onthe BG/Q in HACC, our simulation code framework forcomputational cosmology, focusing on the way in whichthe gravitational force is divided into short range and longrange components and how each component is efficientlyand scalably computed using both inter- and intra-nodeparallelism.

David Daniel, Patricia FaselLos Alamos National Laboratoryddd@lanl.gov, pkf@lanl.gov

Hal FinkelArgonne National Laboratoryhfinkel@anl.gov

Nicholas FrontiereUniversity of California, Los Angelesfrontiere@lanl.gov

Salman Habib, Katrin HeitmannArgonne National Laboratoryhabib@anl.gov, heitmann@anl.gov

Zarija LukicLawrence Berkeley National Laboratoryzarija@lbl.gov

Adrian PopeArgonne National Laboratoryapope@anl.gov

MS30Automatic Generation of the HPCC Global FFTfor BlueGene/Q

We present the automatic synthesis of the HPC Challenge’sGlobal FFT, a large 1D FFT across a whole supercomputersystem. The code was synthesized with the autotuning sys-tem Spiral. We run our optimized Global FFT benchmarkon up to 128k cores (32 racks) of ANL’s BlueGene/P “In-trepid’ and achieved 6.4 Tflop/s. Further, we discuss thenecessary changes for BlueGene/Q. Our BG/P code waspart of IBM’s winning 2010 HPC Challenge Class II sub-mission.

Franz FranchettiDepartment of Electrical and Computer EngineeringCarnegie Mellon Universityfranzf@ece.cmu.edu

AN12 Abstracts 51

MS31Shape Optimization of Plasmonic Gratings

Surface plasmons are electromagnetic fields, highly local-ized near metal- dielectric interfaces, and associated withsurface electron density oscillations. We consider a prob-lem of shape design of a metallic grating interface, so thatsurface plasmon modes are optimized. Existence and sta-bility of optimal solutions is analyzed, and a gradient-basedapproximate solution method proposed. A numerical im-plementation which is capable of continuously tracking achanging grating interface is described, and numerical ex-amples are presented.

David C. DobsonUniversity of Utahdobson@math.utah.edu

MS31Overview of Shape Optimization Problems Involv-ing Eigenvalues

Shape optimization problems involving eigenvalues arise inmany areas where one seeks to control wave phenomena,including mechanical vibration in structures, electromag-netic waves in cavities, and population dynamics. We’ll be-gin this minisymposium with an overview of the field andsurvey recent results on shape and structural eigenvalueoptimization problems. In particular, well discuss Krein’snow classic problem on the optimal density distribution ofa membrane which extremizes the k-th Dirichlet-Laplacianeigenvalue.

Braxton OstingUniversity of California, Los Angelesbraxton@math.ucla.edu

Chiu-Yen KaoThe Ohio State UniversityClaremont McKenna Collegekao@math.ohio-state.edu

MS31Asymptotic Calculation of Resonances

This work is motivated by the desire to develop a methodthat allows for easy and accurate calculation of complexresonances of a one-dimensional structures. We illustrateour approach for Schrodinger’s equation whose potentialis a low-energy well surrounded by a thick barrier. Theresonance is calculated as a perturbation of the associatedbound state when the barrier thickness is in fnite. We showthat the error of this perturbational approach is exponen-tially small in barrier thickness. A similar result has beenobtained for the case of a one-dimensional finite photonicbandgap structure with a defect. This is joint work withD. Dobson, J. Lin, S. Shipman, and M. Weinstein.

Fadil SantosaSchool of MathematicsUniversity of Minnesotasantosa@math.umn.edu

MS31Topology Optimization for Wave-PropagationProblems

The topology optimization method, originally developed

for static mechanical problems, has in recent years beenapplied to a number of different inverse problems involv-ing wave-propagation. The problem formulation makesuse of element-based design variables and includes robust-ness towards manufacturing variations. The presentationwill review the TopOpt-groups (www.topotp.dtu.dk) re-cent works within systematic design of: slow light photoniccrystal waveguides; optic and acoustic cloaking devices; aswell as structured surfaces for manipulation of visual ap-pearance.

Ole SigmundDepartment of Mechanical Engineering, Solid MechanicsNils Koppels Alle, DTUsigmund@mek.dtu.dk

MS32Mathematical Modeling of Panama Disease inCavendish Bananas Plants

The Cavendish banana has served global consumers for halfa century and has remained unaffected by most types ofPanama diseases. Currently, one type of Panama disease,fusarium oxysproum f.sp. cubense, targets the Cavendishbanana. We propose a simple mathematical system ofordinary differential equations, based on an SI epidemicmodel, describing the interactions between susceptible andinfected bananas. To lengthen survival of healthy bananasplants, infected bananas plants are removed from planta-tions. In our study, we consider various harvesting param-eter values and present preliminary numerical results.

Blake BurkettShippensburg UniversityUSAbb0580@ship.edu

Luis Melara, Alyssa BumbaughShippensburg Universitylamelara@ship.edu, acbumbaugh@ship.edu

MS32Simulation of Deformations and Shape Recoveryof Red Blood Cells Using the Lattice BoltzmanMethod

Red blood cells (RBCs) undergo substantial changes ofshape during blood flow in vivo. In the past decade, LatticeBoltzmann and Immersed Boundary methods have beenused to simulate the deformation of RBCs (e.g., Sui etal, IJMPC, 2007). We introduce a more comprehensiveversion of these models, aimed at simulating the shape re-covery of a deformed RBC. Benchmarks and preliminaryresults of the model are introduced.

John GounleyOld Dominion Universityjgounley@odu.edu

Yan PengDept of Math. & Stat.Old Dominion Universityypeng@odu.edu

MS32Modeling of the Dynamic Delamination of L-

52 AN12 Abstracts

shaped Unidirectional Laminated Composites

One of the widely used geometrically complex parts inadvanced commercial aircraft is the L-shaped composite.Due to the sharp curved geometry, interlaminar openingstresses are induced and delamination occurs under con-siderable mode-mixities in L-shaped beams. Dynamic phe-nomena during delamination initiation and propagation ofL-shaped beams are investigated using dynamic (explicit)finite element analysis in conjunction with cohesive zonemethods. The 2-D model consists of 24 plies of unidirec-tional CFRP laminate with an initial 1 mmcrack at thecenter of the laminate at the bend. Loading is appliedparallel to one of the arms quasi-statically. The loadingtype yields different traction fields and mode-mixities inthe two sides of the crack in which delamination occursunder shear stress dominated loading on one crack tip andopening stress dominated loading on the other. The speedof the delamination under shear dominated loading at oneside is 800 m/s and under normal stress dominated loadingis 50 m/s. In addition radial compressive waves at the in-terface are observed. Finally, as the thickness is changed,a different failure mode is observed in which a secondarycrack nucleates at the arm and propagates towards the cen-ter crack.

Burak GozlukluMiddle East Technical University, Turkeyburak.gozluklu@gmail.com

Demirkan CokerMETUdemir.coker@gmail.com

MS32Numerically Optimal High Order Strong StabilityPreserving Multi-step Runge-Kutta Methods

We investigate the strong stability preserving (SSP) prop-erty of multi-step Runge–Kutta (MSRK) methods with 2-6steps. Whereas explicit SSP RungeKutta methods have or-der at most four, explicit SSP MSRK methods break thisorder barrier. We present our algorithm for finding numer-ically optimal explicit MSRK methods, and methods of upto five steps and eighth order that were found using this al-gorithm. These methods have larger SSP coefficients thanany known methods of the same order of accuracy, and maybe implemented in a form with relatively modest storagerequirements. The usefulness of the MSRK methods isdemonstrated through numerical examples, including inte-gration of very high order WENO discretizations.

Zachary GrantUniversity of Massachusetts at Dartmouthzgrant@umassd.edu

Sigal GottliebDepartment of MathematicsUniversity of Massachusetts Dartmouthsgottlieb@umassd.edu

David I. KetchesonMathematical and Computer Sciences & EngineeringKing Abdullah University of Science & Technologydavid.ketcheson@kaust.edu.sa

MS32Simulating Two-Phase Flows in Fractured Reser-voirs Using a Generic Transfer Function in a Dual-

Porosity Model

Flow in carbonate reservoirs is strongly influenced by frac-tures present in the geological formations. An accuratecharacterization of fracture flow is needed to forecast oilrecovery and optimize production. We present a generaldual-porosity model. It is based on an unstructured finiteelement - finite volume technique which solves the gov-erning equations for two-phase flow fully implicitly. Masstransfer between fractures and matrix is computed witha generalized transfer function, the only known analyticsolution for Darcy law with capillarity.

Christine MaierHeriot-Watt University, UKChristine.Maier@pet.hw.ac.uk

Karen SchmidUniversitat Stuttgartkaren.schmid@iws.uni-stuttgart.de

Mohamed AhmedHeriot-Watt Universitymohamed.ahmed@pet.hw.ac.uk

Sebastian GeigerHeriot-Watt UniversityEdinburghSebastian.Geiger@pet.hw.ac.uk

MS32An Analytical Approach to Green Oxidation

Oxidation, a process in which oxygen is added to breakpollutants, often uses chemicals that can result in the pro-duction of hazardous substances. The main goal of theproject is to be able to estimate the rates of the reactionsbased on experimental observations. We have developedperturbation techniques which allowed us to derive an ap-proximate solution. It is expected that these techniqueswill yield even more far-reaching results when applied tomore realistic systems.

Diego TorrejonGeorge Mason UniversityChristine.Maier@pet.hw.ac.uk

MS33A Second Order Virtual Node Algorithm for StokesFlow Problems with Interfacial Forces and Discon-tinuous Material Properties

We present a numerical method for the solution of theStokes equations that handles interfacial discontinuitiesdue to both singular forces and discontinuous fluid proper-ties such as viscosity and density. The discretization cou-ples a Lagrangian representation of the material interfacewith an Eulerian representation of the fluid velocity andpressure. The method is efficient, easy to implement andyields discretely divergence free velocities that are second-order accurate. Numerical results indicate second orderaccuracy for the velocities and first order accuracy for thepressure in l-infinity.

Diego Cortegoso AssencioUCLAdiego.assencio@gmail.com

AN12 Abstracts 53

MS33A Fast Method for Interface and Parameter Es-timation in Linear Elliptic PDEs with PiecewiseConstant Coefficients

We present a new method for the recovery of the parame-ters and interface from an observed solution to embeddedinterface linear elliptic PDEs with piecewise constant co-efficients. Our approach uses the linear nature of theseequations to derive a function that is approximately equalto the coefficients across the entire domain. We recoverthe coefficients using split Bregman implementations ofstandard piecewise constant segmentation methods. Wedemonstrate the method on Poisson’s equation and linearelasticity.

Alejandro CantareroUCLA Mathematics DepartmentLos Angeles, CAcantarer@gmail.com

MS33Efficient Symmetric Positive Definite Second-Order Accurate Monolithic Solver for Fluid/SolidInteractions

We introduce a robust and efficient method to simu-late strongly coupled (monolithic) fluid/rigid-body inter-actions. We take a fractional step approach, where the in-termediate state variables of the fluid and of the solid aresolved independently, before their interactions are enforcedvia a projection step. Overall, the computational time tosolve the projection step is similar to the time needed tosolve the standard fluid-only projection step. Numericalresults indicate the method is second-order accurate in thel-infinity norm and demonstrate that its solutions agreequantitatively with experimental results.

Frederic GibouUniversity of California-Santa Barbarafgibou@engr.ucsb.edu

MS33A Second Order Virtual Node Method for EllipticInterface Problems with Interfaces and IrregularDomains in Three Dimensions

We present a numerical method for the variable coefficientPoisson equation in three-dimensional irregular domainswith interfacial discontinuities. The discretization embedsthe domain and interface into a uniform Cartesian gridaugmented with virtual degrees of freedom to provide ac-curate treatment of jump and boundary conditions. . Asin Bedrossian et al, this is used in a discontinuity removaltechnique that yields the standard 7-point stencil acrossthe interface and only requires a modification to the right-hand side of the linear system.

Joseph TeranUCLAjteran@math.ucla.edu

MS34The Post-Fragmentation Density Function for Bac-terial Aggregates

The post-fragmentation probability density of daughterflocs is one of the least understood aspects of modelingflocculation. A wide variety of functional forms have been

used over the years to characterize fragmentation, and fewhave had experimental data to aid in its construction. Inthis talk, we discuss the use of 3D positional data of K.pneumoniae bacterial flocs in suspension to construct aprobability density of floc volumes after a fragmentationevent. Computational results are provided which predictthat the primary fragmentation mechanism for medium tolarge flocs is erosion, as opposed to the binary fragmenta-tion mechanism (i.e. a fragmentation that results in twosimilarly-sized daughter flocs) traditionally assumed.

Erin ByrneHarvey Mudd Collegebyrne@math.hmc.edu

MS34Modelling Cell Polarity: Theory to Experiments

In order to migrate, cells recruit various proteins to theplasma membrance and spatially segregate them to forma front and back. I present two possible mechanisms forthis symmetry breaking process, and explain how cells canregulate the transition from a homogeneous, ”resting cell”,state to a spatially heterogeneous state corresponding to apolarized cell. I then focus on experimentally distinguish-ing between various proposed polarity models in crawlingcells through perturbations of cell geometry.

Alexandra JilkineUniversity of Arizonajilkine@gmail.com

MS34Epidemic Spread of Influenza Viruses: The Impactof Transient Populations on Disease Dynamics

Recent H1N1 pandemic and recent H5N1 outbreaks havebrought increased attention to the study of the role of an-imal populations as reservoirs for pathogens that couldinvade human populations. Here we study the interac-tions between transient and resident bird populations andtheir role on dispersal and persistence. A meta-populationframework based on a system of nonlinear ordinary differ-ential equations is used to study the transmission dynamicsand control of avian diseases. Epidemiological time scalesand singular perturbation methods are used to reduce thedimensionality of the model. Our results show that mix-ing of bird populations (involving residents and migratorybirds) play an important role on the patterns of diseasespread.

Karen Rios-SotoUniversity of Puerto Rico at Mayaguezkaren.rios3@upr.edu

MS34Modeling the Cofilin Pathway and Actin Dynamicsin Cell Motility Activity of Mammary Carcinomas

Polymerization of actin cytoskeleton leads to cell migra-tion, a vital part of normal physiology from embryonic de-velopment to wound healing. However, it also occurs in thepathological setting of cancer metastasis. Here I presentmathematical models of actin regulation by cofilin whichhas been identified as a critical determinant of metastasis.I will discuss results obtained from simulations and steadystate analysis and their biological implications, as well as

54 AN12 Abstracts

modeling challenges that arise.

Nessy TaniaSmith CollegeMathematics and Statistics Departmentntania@smith.edu

MS35Multiscale Simulation and Upscaling Multi-SpeciesReactive Transport from the Pore to Macro Scale

Abstract not available at time of publication.

Matthew BalhoffICESThe University of Texas at Austinbalhoff@ices.utexas.edu

MS35Multiscale Modeling and Simulation of Fluid Flowsin Deformable Porous Media

A multiscale framework for fluid-structure interactionproblems in inelastic media will be presented. Stokes flowis assumed at the pore scale with a general nonlinear elas-tic model for deformations. Due to complexity of pore-levelinteraction an iterative macroscopic model that consists ofnonlinear Darcy equations and upscaled elasticity equa-tions modeled via an iterative procedure is proposed. Nu-merical results for the case of linear elastic solid skeletonare presented for a number of model problems.

Yuliya GorbDepartment of MathematicsUniversity of Houstongorb@math.uh.edu

MS35Coupling Modeling for Compressible Fluid Flow inthe Elastic Porous Media

In this work, we consider the dynamical response of a non-linear plate with viscous damping, perturbed in both ver-tical and axial directions interacting with a Darcy flow.We first study the problem for the non-linear elastic bodywith damping coefficient. We prove existence and unique-ness of the solution for the steady state plate problem. Weinvestigate the stability of the dynamical non-linear plateproblem under some condition on the applied loads. Thenwe explore the fluid structure interaction problem with aDarcy flow in porous media. In an appropriate Sobolevnorm, we build an energy functional for the displacementfield of the plate and the gradient pressure of the fluid flow.We show that for a class of boundary conditions the energyfunctional is bounded by the flux of mass through the inletboundary.

Akif IbragimovDepartment of Mathematics and Statistics.Texas Tech Universityakif.ibraguimov@ttu.edu

E. Aulisa, Y. KayaDepartment of Mathematics and StatisticsTexas Tech Universitymailto:eugenio.aulisa@ttu.edu,mailto:yasemen.kaya@ttu.edu

MS35A Mixed Finite Element Framework for the BiotModel in Poroelasticity

Poroelasticity is the modeling of the time-dependent cou-pling between the deformation of porous materials andthe fluid flow inside. It has been well-known that stan-dard Galerkin finite element methods produce unstableand oscillatory numerical behavior of the pressure, whichis known as locking. We present a mixed finite elementformulation that has been designed to overcome locking.The formulation is based on coupling two mixed finite el-ement formulations for the flow and mechanics problems.We discuss a priori error estimates and show some numer-ical results.

Son-Young YiThe University of Texas at El Pasosyi@utep.edu

MS36Automatic Differentiation in Chebfun: Implemen-tation and Usage

The implementation of Automatic Differentation (AD) inChebfun is described. Whereas standard AD implementa-tions compute Jacobians, Chebfun works in a continuousframework so the derivatives are Frechet derivatives. Thecurrent implementation offers automatic linearity detectionand linearisation of differential operators, as well as interiorpoint and jump conditions in differential equations throughAD of functionals. Examples of AD usage in Chebfun willbe given.

Asgeir BirkissonUniversity of Oxford, Mathematical Institutebirkisson@maths.ox.ac.uk

MS36Spectral Deferred Correction in Chebfun for Time-dependent PDEs

Chebfun’s goal of providing automatic, accurate results for1D problems is challenging for time-dependent PDEs. Cur-rently Chebfun uses a built-in stiff integrator of order 1-5. Huang et al. showed that spectral deferred correctioncan be generalized to a Krylov iteration for a spectrallycomputed error, preconditioned by low-order integration.This gives an A-stable, symplectic and reversible integra-tion method capable of very high accuracy. It is readilyimplemented with Chebfun’s discretization and automaticdifferentiation capabilities.

Tobin DriscollUniversity of DelawareMathematical Sciencesdriscoll@udel.edu

MS36An Overview of Differential Equations in Chebfun

Chebfun allows users to interact with functions in Matlabas if they were vectors, giving ‘symbolic feel but numericspeed’. Chebops extend this functionality to operators andmatrices, allowing a natural and efficient means of solv-ing differential equations. In this introductory talk we’llopen the chebop hood to take a look its core components,including the adaptive collocation and domain decomposi-tion processes, and the enforcement of boundary conditions

AN12 Abstracts 55

through a new technique of rectangular projection.

Nick HaleOxford U. Mathematical Inst.hale@maths.ox.ac.uk

MS36Computation of Frequency Responses of PDEs inChebfun

We describe how frequency responses of PDEs with onespatial variable can be computed in Chebfun. Our methodrecasts the frequency response operator as a two pointboundary value problem and it has two advantages overcurrently available schemes: first, it avoids numerical insta-bilities encountered in systems with differential operatorsof high order and, second, it alleviates difficulty in imple-menting boundary conditions. We provide examples fromfluid dynamics to illustrate utility of the proposed method.

Mihailo R. Jovanovic, Binh LieuElectrical and Computer EngineeringUniversity of Minnesotamihailo@umn.edu, lieux006@umn.edu

MS37Two Layer Model for Local Tear Film Dynamics

Many tear film models utilize a single-layer approach thatrepresents only the aqueous layer, which constitutes themajority of the tear film. In such models, the layer is dom-inated by shear stresses. Some recent models have incorpo-rated surfactant effects at the liquid-air interface to modelthe effects of polar lipids there. The model presented in thistalk includes a thin lipid layer between the aqueous layerand the air, which is dominated by extensional flow. Ourresults show that the thin extensional layer significantlyperturbs the aqueous layer flow.

Nicholas GeweckeUniversity of Tennesseengewecke@math.udel.edu

Rich BraunDepartment of Mathematical SciencesUniversity of Delawarebraun@math.udel.edu

MS37Defects and Heterogeneity in Liquid Coatings

Fluid coatings occur in situations from the manufacture ofsemiconductors to the foam lacing left behind after drink-ing a pint of beer. Sometimes coating uniformity is de-sirable, but in many cases, coatings are heterogeneous,with either defects or spontaneous or deliberate pattern-ing. We examine the deposition of isolated bubbles inLandau–Levich (dip coating) flow of a pure liquid, and theself-assembly of particles in Landau–Levich flow of a sus-pension. These phenomena are explained through a com-bination of modeling, experiment, and analysis.

Justin KaoMassachusetts Institute of Technologykaoj@mit.edu

MS37Behavior of Droplets on a Thin Film

A drop of fluid on another fluid is modeled by a system offourth order nonlinear PDE derived using the lubricationapproximation. We assume the two fluids are Newtonian,incompressible, and immiscible. Relevant questions to thisproblem include: When does the drop spread over the un-derlying fluid? When does the drop touch the bottom sur-face? When does the drop break through the top interface?We explore these questions analytically, numerically, andexperimentally.

Ellen PetersonDepartment of Mathematics SciencesCarnegie Mellon Universityellenp@andrew.cmu.edu

MS37Fingering Instability Down the Outside of a Verti-cal Cylinder

We examine the fingering dynamics of a gravity-driven con-tact line of a thin viscous film traveling down the outsideof a vertical cylinder of radius R. A lubrication model isderived for the film height in the limit that H/R 1 (H isthe upstream film height). Results from a linear stabilityanalysis of the contact line are compared to experimentaldata. The influence of curvature will also be discussed.

Linda SmolkaBucknell Universitylsmolka@bucknell.edu

MS38Networks, Communities and the Ground-Truth

The Web, society, information, cells and brain can all berepresented and studied as complex networks of interac-tions. Nodes in such networks tend to organize into clustersand communities, which represent the fundamental struc-tures for understanding the organization of complex sys-tems. Even though detection of network communities is ofsignificant importance for computer science, sociology andbiology, our understanding of the community structure oflarge networks remains limited. We study a set of morethan 200 large networks with the goal to understand andidentify communities in networks. We challenge the con-ventional view of network community structure and showthat it is not exhibited by the large real-world networks.We then present a new conceptual model of network com-munity structure, which reliably captures the overall struc-ture of networks and accurately identifies the overlappingnature of network communities.

Jure LeskovecStanford Universityjure@cs.stanford.edu

MS38High-Performance Metagenomic Data Clusteringand Assembly

We present a novel de Bruijn graph-based parallel assemblyapproach for assembling metagenomic reads. The assem-bler employs a maximum-likelihood framework that han-dles the challenges posed by increased polymorphism andover-representation of conserved regions. It also providestolerance for errors due to the incomplete and fragmen-

56 AN12 Abstracts

tary nature of the reads. We also propose a two-way,multi-species, multi-dimensional Poisson mixture model-based method for representing reads from a metagenome.We use this method to cluster metagenomic reads by theirspecies of origin, and to characterize the abundance of eachspecies.

Kamesh MadduriPennsylvania State Universitymadduri@cse.psu.edu

MS38Influence Propagation on Large Graphs

Given a network of who-contacts-whom, will a contagiousvirus/product/meme take-over (cause an epidemic) or die-out quickly? What will change if nodes have partial, tem-porary or permanent immunity? What if the underly-ing network changes over time (e.g., people have differ-ent connections during the day at work, and during thenight at home)? Propagation style processes can modelwell many real-world scenarios like epidemiology and pub-lic health, information diffusion etc. We present results onunderstanding the tipping-point behavior of epidemics (en-abling among other things faster simulations), predictingwho-wins among competing viruses, and developing effec-tive algorithms for immunization and marketing for sev-eral large-scale real-world settings. Finally, we collectedand analyzed Twitter data over multiple months, to under-stand the role of external effects in how different hashtags(topics) spread. We showed fundamental differences in thedynamics of hashtags e.g. we found that hashtags of apolitical nature are primarily driven by outside influences,even though many people may be tweeting about them.

Aditya PrakashCMUbadityap@cs.cmu.edu

MS38Scaling Graph Computations at Facebook

With more than 800 million active users and 68 billionedges, scalability is at the forefront of concerns when deal-ing with the Facebook social graph. This talk will discusstwo recent advances. First, through the development of anovel graph sharding algorithm for load-balancing graphcomputations, we were able to reduce the query time of arealtime system by 50%. Second, when computing the av-erage graph distance between users on Facebook, empiricaladvances in the compression of the Facebook graph was akey step in speeding up the computation.

John UganderCornelljhu5@cornell.edu

MS39Optimization-Based Decomposition ofMultiphysics Problems with Applications

We present a new, optimization-based framework for com-putational modeling. The framework uses optimizationand control ideas to assemble and decompose multiphysicsoperators and to preserve their fundamental physical prop-erties in the discretization process. Our approach relies onthree essential steps: decomposition of the original prob-lem into subproblems for which discretizations and robustsolvers are available; integration of the subproblems into

an equivalent constrained optimization problem; and solu-tion of the resulting optimization problem either directlyas a fully coupled algebraic system, or in the null space ofthe constraints.

Pavel BochevSandia National LaboratoriesComputational Math and Algorithmspbboche@sandia.gov

Denis RidzalSandia National Laboratoriesdridzal@sandia.gov

Mitchell LuskinSchool of MathematicsUniversity of Minnesotaluskin@math.umn.edu

MS39Blended Force-based Quasicontinuum Methods

The development of consistent and stable quasicontinuummodels for multi-dimensional crystalline solids remains achallenge. For example, proving stability of the force-basedquasicontinuum (QCF) model remains an open problem.In 1D and 2D, we show that by blending atomistic andCauchy–Born continuum forces (instead of a sharp transi-tion as in the QCF method) one obtains positive-definiteblended force-based quasicontinuum models if and only ifthe width of the blending region scales as O(N1/5) atomiclattice spacings (or the width scales as O(N−4/5) in themacroscopic scale). We present computational results andanalysis.

Xingjie LiUniversity of Minnesotalixxx835@umn.edu

Mitchell LuskinSchool of MathematicsUniversity of Minnesotaluskin@umn.edu

Christoph OrtnerUniversity of Warwickc.ortner@warwick.ac.uk

MS39Energy-Based A/C Coupling for Pair Interaction

I will present a recent development in construction andanalysis of an energy-based atomistic-to-continuum cou-pling for two-body interaction (limited to zero-temperaturestatics of simple crystals).

Alexander V. ShapeevSwiss Federal Institute of Technology (Lausanne)alexander@shapeev.com

MS39Blended Energy-based Quasicontinuum Methods

We present the energy-based blended quasicontinuum(BQCE) method for coupling atomistic and continuummodels. We give error estimates for BQCE for 3D andmulti-lattice crystals, and we give optimal choices of the

AN12 Abstracts 57

approximation parameters (the blending function and fi-nite element mesh) for the problem of a localized defect sur-rounded by a perfect crystal. Our formulation of BQCE formulti-lattice crystals uses a novel continuum model whichwe also discuss. Finally, we give numerical experimentswhich confirm the predictions of our error estimates.

Brian Van KotenUniversity of Minnesotavank0068@umn.edu

Mitchell LuskinSchool of MathematicsUniversity of Minnesotaluskin@math.umn.edu

Christoph OrtnerUniversity of Warwickc.ortner@warwick.ac.uk

MS40Numerical Algebraic Geometry via Macaulay’sPerspective

F.S. Macaulay regarded theoretical solutions as prelimi-nary, a final solution to a problem is one which can actu-ally be computed. The methods he proposed in his famous1916 book are therefore computational but not all feasibleat that time. This talk will outline the speaker’s adapta-tion of Macaulay’s methods, including H-bases and inversearrays, using modern numerical linear algebra. Examplesinvolving the functorality of the global dual will be given.

Barry H. DaytonNortheastern Illinois Universityb-dayton@neiu.edu

MS40Preconditioning with H-Bases Computed UsingDual Space Operations

When solving polynomial systems using homotopy contin-uation, it is sometimes the case that we end up with alarge number of paths going to ∞. We want to precondi-tion these systems using H-bases in order to remove pathsgoing to ∞. We calculate the H-bases numerically fromoperations on the dual space. When we dualize again, werecover H-bases with the same variety as the original ideal.This process removes the extraneous pieces at ∞ with atmost an addition of ”junk” points. This eliminates pathsgoing to ∞ in the homotopy continuation run.

Steven L. IhdeColorado State Universityihde@math.colostate.edu

Daniel J. BatesColorado State UniversityDepartment of Mathematicsbates@math.colostate.edu

Jonathan HauensteinTexas A&M Universityjhauenst@math.tamu.edu

MS40Elimination of Pseudo-components in Numerical

Primary Decomposition

The goal of a numerical primary decomposition algorithmis to produce an approximation to a general point on eachcomponent of a scheme defined by an ideal of polynomialswith complex coefficients. Our approach based on homo-topy continuation and the concept of a deflated varietyproduces extraneous, the so-called pseudo-, components.This talk will outline an algorithm to detect these usingapproximate Macaulay dual space computation.

Anton LeykinSchool of MathematicsGeorgia Institute of Technologyleykin@math.gatech.edu

MS40Extended Precision Path Tracking in Parallel

To compensate for the overhead of extended precision (inparticular: of double double and quad double arithmetic),we investigated the use of multiple cores on regular pro-cessors and general purpose graphics processing units. Be-cause the cost of evaluating and differentiating polynomialsoften dominates the computational work in path tracking,we developed and implemented multithreaded algorithmson multicore processors and massively parallel algorithmsfor general purpose GPUs for multivariate polynomial eval-uation and differentiation.

Jan VerscheldeDepartment of Mathematics, Statistics and ComputerScienceUniversity of Illinois at Chicagojan@math.uic.edu

Genady YoffeDept. of Mathematics, Statistics, and CSUniversity of Illinois, Chicagogyoffe2@uic.edu

MS41A Nonconforming Finite Element Method for anAcoustic Fluid-Structure Interaction Problem

In this work, we propose and analyze a nonconformingfinite element approximation of the vibration modes ofacoustic fluid-structure interaction. The numerical schemeis based on the irrotational fluid displacement formulationwhich eliminates the occurence of spurious eigenmodes.Our method uses weakly continuous P1 vector fields for thefluid and classical piecewise linear elements for the fluid.On properly graded meshes, we show optimal order errorestimates which are validated by numerical experiments.

Susanne BrennerDepartment of MathematicsLouisiana State Universitybrenner@math.lsu.edu

Aycil CesmeliogluInstitute for Mathematics and Its Applications (IMA)aycil.cesmelioglu@ima.umn.edu

Jintao CuiInstitute for Mathematics and its ApplicationsUniversity of Minnesotajcui@ima.umn.edu

58 AN12 Abstracts

Li-yeng SungDepartment of Mathematics and CCTLouisiana State Universitysung@math.lsu.edu

MS41Fluid-fluid Calculations using the Evolve-filter-relax Regularization Strategy

Calculations for a model of two fluids coupled across ashared interface are performed by using the evolve, thenfilter and relax method, motivated by atmosphere-oceaninteraction. This method has a regularization effect andis computationally attractive since the evolution, filteringand relaxation steps can be decoupled. Different relax-ation parameters are appropriate for the two fluids. Analgorithm is described to determine these parameters au-tomatically at each time step to improve model accuracy.

Jeffrey M. ConnorsLawrence Livermore National LaboratoryCenter for Applied Scientific Computingconnors4@llnl.gov

MS41Large Eddy Simulation of the Quasi-GeostrophicEquations of Oceanic Flows

We developed an approximate deconvolution (AD) LESmodel for the two-layer quasi-geostrophic equations(QGE).The AD closure modeling approach is appealing for geo-physical flows because it needs no additional phenomeno-logical approximations to the original equations, and it canachieve high accuracy by employing repeated (computa-tionally efficient and easy to implement) filtering. We ap-plied the AD-LES model to mid-latitude two-layer squareoceanic basins, which are standard prototypes of stratifiedocean dynamics models. Compared with a high-resolutionsimulation, AD-LES yielded accurate results at signifi-cantly lower computational cost. The sensitivity of theAD-LES results with respect to changes in input parame-ters was also performed. We discovered that although theAD-LES model was robust with respect to changes in pa-rameters, changing the spatial filter made a huge difference.Two spatial filters were investigated in the AD-LES model:tridiagonal and elliptic differential. We found the tridiago-nal filter did not introduce any numerical dissipation in theAD-LES model. The differential filter, however, added asignificant amount, and our numerical results show the newAD-LES model used in with the differential filter can beemployed successfully on meshes significantly coarser thanthe Munk scale and with an eddy viscosity coefficient thatis dramatically lower than that used in the original two-layer QGE. Although we do not provide a solution to thelongstanding quest for finding a rigorous derivation of theeddy viscosity coefficients used in ocean modeling, we putforth a novel approach, serendipitously discovered in ournumerical investigation. The main strength of this newapproach is that the modeling error can be disentangledfrom the numerical discretization error and can be stud-ied separately in this framework. This could lead to morerobust and general LES models for large scale geophysicalflows.

Traian IliescuDepartment of MathematicsVirginia Techiliescu@vt.edu

MS41Uncertainly Quantification for PDEs

Abstract not available at time of publication.

Miroslav StoyanovFlorida State UniversityDepartment of Scientific Computingmkstoyanov@gmail.com

Clayton G. WebsterOak Ridge National Laboratorywebstercg@ornl.gov

MS42Improving Earthquake Ground Motion Estimateswith Blue Gene/Q

This project aims to produce the first state-wide physics-based probabilistic seismic hazard analysis (PSHA) mapfor California, a goal only feasible with petascale com-puting. The relevant phenomena span many orders ofmagnitude in spatial scale, requiring high-resolution sim-ulations. Furthermore, proper uncertainty estimation forPSHA requires simulations of large numbers of possibleevents. We will discuss the necessary optimizations to ourfinite-element simulation codes for the Blue Gene/Q ar-chiteture.

Geoffrey ElyArgonne National Laboratorygely@anl.gov

MS42Blue Gene/Q Architecture and ProgrammingModels

Managing the million-way concurrency found in the BlueGene/Q architecture requires new thinking about algo-rithms and programming models. This talk will describethe hardware architecture in detail and the connection tohybrid (i.e. multithreaded) programming models. Perfor-mance of fundamental operations will be measured usingbenchmarks derived from real applications.

Jeff R. HammondArgonne National LaboratoryLeadership Computing Facilityjhammond@alcf.anl.gov

MS42Chemical Applications of the MultiresolutionAdaptive Numerical Environment for ScientificSimulation (MADNESS)

MADNESS (multiresolution adaptive numerical environ-ment for scientific simulation) is a general numerical frame-work to solve integral and differential equations in mul-tiple dimensions. With its parallel runtime and numeri-cal methods, MADNESS has proven to be a robust plat-form for discretized problems, in particular those foundin quantum chemistry, nuclear physics, solid-state physics,atomic and molecular physics. In this work we will discussasynchronous parallelism model implemented in a multi-threaded scheme and its application to energy storage andconversion using linear-response density-functional theory.

Robert Harrison

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University of Tennessee at Knoxvillerjharrison@gmail.com

lvaro Vazquez-MayagoitiaArgonne National Laboratoryalvaro@alcf.anl.gov

MS42Accelerating and Benchmarking GAMESS onBlueGene/Q

General Atomic and Molecular Electronic Structure Sys-tem (GAMESS) is a popular ab-initio quantum chemistryprogram. The Fragment Molecular Orbital (FMO) methodimplemented in GAMESS is highly-scalable and allowsone to perform highly accurate calculations on very largemolecular systems. We will describe our experience portingand optimizing GAMESS for Blue Gene/Q. The algorithmused to multithread the integral kernels in GAMESS totake full advantage of the hardware capabilities of BlueGene/Q will be discussed in detail. Lastly, we will presentseveral benchmark results, including FMO calculations onwater clusters.

Maricris Mayes, Graham FletcherArgonne National Laboratorymmayes@alcf.anl.gov, fletcher@alcf.anl.gov

Mark GordonIowa State Universitymgordon@iastate.edu

MS43An Analytical Level Set Method for EigenvalueShape Optimization Problems

We propose an eigenvalue shape optimization methodbased on representing the boundary of the domain as thezero level set of a linear combination of eigenfunctions cor-responding to the same eigenvalue. The optimal shape isdiscovered by adjusting the shared eigenvalue and the co-efficients of the linear combination. The method works inany number of dimensions and is characterized by utmostsimplicity, arbitrarily high accuracy for a broad range ofproblems, as well as the ability to produce an exact ana-lytical solution for an approximate problem.

Pavel GrinfeldDrexel Universitypg77@drexel.edu

MS43Shape Recognition Based on Eigenvalues of theLaplacian

Recently, there has been a surge in the use of the eigenval-ues of linear operators in problems of pattern recognition.In this presentation, we discuss theoretical, numerical, andexperimental aspects of using four well known linear op-erators and their eigenvalues for shape recognition. Inparticular, the eigenvalues of the Laplacian operator un-der Dirichlet and Neumann boundary conditions, as wellas those of the clamped plate and buckling of a clampedplate are examined. Since the ratios of eigenvalues for eachof these operators are translation, rotation and scale invari-ant, four feature vectors are extracted for the purpose ofshape recognition. These feature vectors are then fed intoa basic neural network for training and measuring the per-

formance of each of the feature vectors which in turn wereall shown to be reliable features for shape recognition. Thepresentation focuses on finite difference schemes for theseoperators and summarizes key facts about their eigenval-ues that are of relevance in image recognition. (*) Jointwork with M. B. H. Rhouma and M. A. Khabou.

Lotfi HermiUniversity of ArizonaDepartment of Mathematicshermi@math.arizona.edu

MS43Shape Optimization with the Vector MaxwellEquations

An intuitive framework is presented for shape optimiza-tion with the vector Maxwell equations. Through adjointtechniques, two simulations per iteration give both theshape and topological derivatives. The method is appliedto the design of a sub-wavelength solar cell texture, result-ing in the highest reported absorption enhancement fac-tor for high-index, thin-film media. The enhancement isachieved by shaping the bandstructure and optimizing thein-coupling, possible only through non-intuitive, higher-order Fourier coefficients.

Owen D. Miller, Eli YablonovitchEECS DepartmentUniversity of California, Berkeleyomiller@berkeley.edu, eliy@eecs.berkeley.edu

MS43Characterization of Weighted Graphs using GraphLaplacians

We will discuss our recent effort on characterizing and clus-tering weighted graphs using their morphological featuresextracted by spectra of their graph Laplacians. Comparedto unweighted graphs (which we studied them previously),the graphs with weights pose a further challenge both intheory and practice. We will also discuss the eigenfunctionconcentration phenomenon on a class of simple trees wheresuch a phenomenon does not occur if unweighted.

Naoki SaitoDepartment of MathematicsUniversity of California, Davissaito@math.ucdavis.edu

MS45A Treecode Algorithm for N-body Interactionswith Disjoint Source and Target Particles

Energy and force computations are usually the bottleneckin molecular dynamics and Monte-Carlo simulations. Mostalgorithms for speeding up the N-body interactions are fora set of particles interacting with itself. We will presenta treecode algorithm that offers considerable speed up for(1) a set of particles interacting with itself as well as (2)interactions between a disjoint pair of source and targetparticles while achieving high accuracy.

Henry A. BoatengDepartment of MathematicsUniversity of Michiganboateng@umich.edu

Robert Krasny

60 AN12 Abstracts

University of MichiganDepartment of Mathematicskrasny@umich.edu

MS45Multi-frequency It-erative Integral Equations Method for the ShapeReconstruction of an Acoustically Sound-soft Ob-stacle Using Backscattering

We present a method of solving the problem of obtaininga reconstruction of a planar acoustically sound-soft obsta-cle from the measured far-field pattern generated by planewaves with a fixed incidence and varying frequencies. Wesolve iteratively the problem for each frequency, from thelowest to the highest, using as an initial guess the solutiongiven by the previous frequency. We present numerical re-sults showing the benefits of our approach.

Carlos C. BorgesWorcester Polytechnic Instituteceduardo@wpi.edu

MS45A Novel Multiscale Model of Glioblastoma Multi-forme (gbm)

Glioblastoma multiforme (GBM) is the most malignant,invasive, and lethal form of brain cancer; the median sur-vival time of patients diagnosed with GBM is 15 months.We develop an adaptive, multiscale mathematical and nu-merical model to study the development of GBM. We use acontinuum (partial differential equation) model to describethe changes in the concentrations of important chemicalsand proteins, such as glucose, oxygen, TGFα, PLCγ , andan agent-based model for the tumor cells. In the develop-ment of a tumor, distinct regions evolve. There is eventu-ally a necrotic core filled with dead cells surrounded by aregion of quiescent (inactive) cells. The quiescent region isrimmed by proliferating and/or migrating cells. While onemay acceptably describe the quiescent or necrotic regionsof the tumor with a continuum model which would rep-resent activities on a macroscale, such a model would notcapture the important details in the invasive regions wherethe cells are actively migrating and dividing. A fully mi-croscale model would represent each cell as an individualentity but since a fully grown tumor has 1012 cells, thisapproach is too computationally expensive. We developa numerical model on adaptive quadtree grids that allowsfor multiresolution. A phenotypic function determines thephenotype population in each grid block as a function ofthe concentration of chemicals and proteins there, and cueschanges in the grid resolution periodically to accuratelycapture the tumor structure.

Gerardo HernandezMathWorksWorcester Polytechnic Institutegeherco@wpi.edu

MS45Improving Hurricane Storm Surge Forecasting us-ing Data Assimilation Methods

Uncertainty is inherent in numerical forecast models as wellas in measurements of model solutions. Given both a modeland measurements, advanced data assimilation methodscan be used to improve state estimates of nonlinear prob-

lems. One such method, the singular evolutive interpolatedKalman (SEIK) filter, has been applied to the AdvancedCirculation (ADCIRC) storm surge model. Here ADCIRCalong with data produced from a detailed hindcast studyis used to improve hurricane storm surge forecasts.

Talea MayoUniversity of Texas at Austintalea@ices.utexas.edu

Troy ButlerInstitute for Computational Engineering and SciencesThe University of Texas at Austintbutler@ices.utexas.edu

Muhammad AltafKing Abdullah University of Science and Technologymuhammad.altaf@kaust.edu.sa

Clint DawsonInstitute for Computational Engineering and SciencesUniversity of Texas at Austinclint@ices.utexas.edu

Ibrahim HoteitKing Abdullah University of Science and Technology(KAUST)ibrahim.hoteit@kaust.edu.sa

Xiaodong LuoKing Abdullah University of Science and Technologyxiaodong.luo@kaust.edu.sa

MS46Orbits of Projective Point Configurations

Given an r×n matrix, thought of as representing n pointsin projective (r−1)-space, we consider the closure of the or-bit of all projectively equivalent matrices. I will discuss theequations cutting out this variety, its finely graded Hilbertseries, and their relation to the matroid of the point con-figuration.

Alex FinkNorth Carolina State Universityarfink@ncsu.edu

Andrew BergetUniversity of California, Davisberget@math.ucdavis.edu

MS46Finiteness Theorems and Algorithms for Polyno-mial Equations in an Infinite Number of Variables

We discuss the theory of symmetric Groebner bases, a con-cept allowing one to prove Noetherianity results for sym-metric ideals in polynomial rings with an infinite number ofvariables. We also explain applications of these objects toother fields such as algebraic statistics, and we present analgorithm for computing with them on a computer. Someof this is joint work with Matthias Aschenbrener and SethSullivant.

Christopher HillarUniversity of California, Berkeleychillar@msri.org

AN12 Abstracts 61

MS46Stable Intersections of Ttropical Varieties

Taking the stable intersection of a list of tropical hyper-surfaces is a purely combinatorial operation. The stableintersection can also be obtained by generically perturb-ing the coefficients of the defining equations and takingthe tropical variety of the ideal they generate. This ob-servation leads to a new proof of Bernstein’s theorem. Wediscuss how some combinatorial properties of stable inter-sections can be proven either purely combinatorially or bederived from tropical varieties of ideals.

Anders JensenUniversitat des Saarlandesjensen@imf.au.dk

Josephine YuSchool of MathematicsGeorgia Institute of Technologyjosephine.yu@math.gatech.edu

MS46Computer-aided Design Algebra and Combina-torics

Computer Aided Design (CAD) software allows a userto specify a finite number of rigid bodies and pair-wise coincidence, angular, and distance (cad) constraintsamong them. It is important to know when such a “body-and-cad” framework is rigid or when the bodies may moverelative to one another while maintaining the given con-straints. A body-and-cad framework may be specified byan edge-colored multigraph. I will discuss a combinatorialcharacterization of the rigidity of a body-and-cad frame-work in which 20 of the 21 possible 3D constraints mayappear. For our analysis we build on algebro-geometricmethods developed by White and Whiteley to study therigidity of systems consisting of a finite collection of bodiesconnected by fixed-length bars using flexible joints.

Audrey Lee-St.John, Jessica SidmanMount Holyoke Collegeastjohn@mtholyoke.edu, jsidman@mtholyoke.edu

MS47A Global Holmgren Theorem for Hyperbolic PDE

A global uniqueness theorem for solutions to hyperbolicdifferential equations with analytic coefficients in a space-time cylinder Q = (0, T ) × Ω is established. Zero Cauchydata on a part of the lateral C1-boundary will force ev-ery solution to a homogeneous hyperbolic PDE or systemto vanish at half time T/2 provided that T > T0. Theminimal time T0 depends on the geometry of the slownesssurface of the hyperbolic operator. This theorem is an ex-tension of an earlier result by Walter Littman from 2000.Furthermore, it is shown that this global uniqueness resultholds for hyperbolic operators with C1-coefficients as longas they satisfy the conclusion of Holmgren’s Theorem.

Matthias EllerGeorgetwon UniversityDepartment of Mathematicsmme4@georgetown.edu

MS47Conservation Laws in Mathematical Biology

In this talk I will consider conservation laws for a systemof hyperbolic equations, in which the coefficients are non-linear and nonlocal functions of unknown variables. I willexplain how each such system arises as a mathematicalmodel of a biological process, and address the mathemat-ical results and, in some cases, open problems associatedwith the model equations. The examples are taken fromthe the areas of public health (drug resistance strains ofbacteria), immune cell (Th cell differentiation), movementof molecules along axon, cancer, and wound healing

Avner FriedmanDepartment of Mathematics, Ohio State Universityafriedman@math.osu.edu

MS47Controllability and Regularity of Some 1-d ElasticSystems with Internal Point Masses

In the case of a wave equation with an internal point mass,it is known that exact controllability holds on an asymmet-ric space, where the regularity is higher on one side of themass. We consider several variations of this problem, in-cluding the SCOLE beam model, but with an interior rigidbody and thermoelastic systems with internal masses.

Scott HansenIowa State UniversityDepartment of Mathematicsshansen@iastate.edu

MS47Some Absolutely Continuos Schrodinger OperatorsWith Oscillating Potentials

In this talk we report on the principle of limiting absorptionfor a family of Schrodinger operators of the form

−∆+ c sin b|x|α/|x|β .

More specifically, we formulate conditions on the param-eters c, b, α, β and interval I which ensure that the PLAholds for such an operator over the interval I. Note thatalthough this potential is spherically symmetric, the valid-ity of the PLA for the seperated operator does not implythe PLA for the original operator. Our principal referenceis the forthcoing paper of Golennia and Jecko, A New LookAt Mourre’s Commutator Theory.

Peter RejtoSchool of MathematicsUniversity of Minnesotarejto@math.umn.edu

MS48Modeling Evaporation and Transport in PorousMedia. Comparing Models Using Different Depen-dent Variables

Fick’s law for molecular diffusion can be used to describehow water vapor is transported through a gas mixture. Thegeneral forms of Fick’s law can be written using gradientsof either mass concentration, mole fraction, or chemicalpotential of the water vapor as dependent variables. Us-ing concentration as a dependent variable is more naturalfor the modeling process (as it appears naturally in the

62 AN12 Abstracts

conservation of mass equations), but can yield unnaturalboundary conditions and nonlinear equations. Using chem-ical potential is less natural for modeling but yields govern-ing equations that are more mathematically tractable andboundary conditions that are more natural. In this talk weconsider evaporation and diffusion of water vapor. Depend-ing on the choice of dependent variable we derive differentsets of governing equations for the transport of water va-por. A careful derivation and analysis of each model will bepresented for water evaporation and diffusion in a simplecapillary tube, and comparisons of evaporation rates willbe made between the models. Consequences for macroscalemodeling will be discussed.

Lynn S. BennethumUniversity of Colorado DenverLynn.Bennethum@cudenver.edu

MS48Title Not Available at Time of Publication

Abstract not available at time of publication.

Clint DawsonInstitute for Computational Engineering and SciencesUniversity of Texas at Austinclint@ices.utexas.edu

MS48Numerical Methods for Shallow Water Models

In this talk we will introduce and discuss numerical schemesfor the shallow water equations. These equations arewidely used in many scientific applications related to mod-eling of water flows in rivers, lakes and coastal areas. Fur-thermore, many real world engineering applications requirethe use of triangular meshes due to the complicated struc-ture of the computational domains of the problems beinginvestigated. Therefore the development of robust and ac-curate numerical methods for the simulation of shallowwater models is important and challenging problem. Inour talk we will discuss the recently developed numericalschemes for such models. We will demonstrate the perfor-mance of the proposed methods in a number of numericalexamples.

Yekaterina Epshteyndepartment of mathematicsuniversity of utahepshteyn@math.utah.edu

MS48A Comparison of Finite Element Methods forStrongly Density Dependent Flows

Saltwater intrusion is a frequent issue in coastal freshwa-ter aquifers. We develop a Discontinuous Galerkin (DG)formulation for these saltwater flow and transport prob-lems. The transport scheme must handle sharp frontswhile the flow scheme requries high accuracy. DG methodshave potential advantages over continuous Galerkin modelsfor such problems. We discretize the flow with local DGand the transport with Non-symmetric, Interior PenaltyGalerkin. We present the formulation and comparisons forsaltwater intrusion benchmarks.

Chris KeesU.S. Army Engineer Research and Development CenterCoastal and Hydraulics Laboratory

christopher.e.kees@usace.army.mil

Matthew FarthingUS Army Engineer Research and Development Centerqmatthew.w.farthing@usace.army.mil

Clint DawsonInstitute for Computational Engineering and SciencesUniversity of Texas at Austinclint@ices.utexas.edu

Timothy PovichDepartment of Mathematical SciencesUnited States Military Academy at West Pointblockedmailto:timothy.povich@us.army.mil

MS49Delaying Wetting Failure In Coating Flows ViaMeniscus Confinement

Wetting failure brought about by air entrainment remainsone of the biggest obstacles to faster operation of numer-ous processes that deposit coatings of thin liquid films.Improving upon the coating speeds used in current tech-nologies requires a better understanding of how system pa-rameters influence wetting failure. We use both experi-ment and modeling to determine the effect of one suchparameter—meniscus confinement—on the initiation of dy-namic wetting failure. Our experimental apparatus con-sists of a scraped steel roll that rotates into a bath of glyc-erol, and confinement is imposed via a gap formed betweena coating die and the roll surface. Comparison of the datafrom confined and unconfined systems—obtained via flowvisualization—shows a clear increase in the relative criticalspeed as the meniscus becomes more confined. A hydrody-namic model for wetting failure is developed and analyzedwith (i) lubrication theory and (ii) a two-dimensional finiteelement method (FEM). Both approaches do a remarkablejob of matching the observed confinement trend, but onlythe two-dimensional model yields accurate estimates of theabsolute values of the critical speeds due to the highlytwo-dimensional nature of the stress field in the displac-ing liquid. The overall success of the hydrodynamic modelsuggests a wetting failure mechanism primarily related toviscous bending of the meniscus.

Satish KumarChemical Engineering and Materials ScienceUniversity of Minnesotakumar030@umn.edu

Eric VandreUniversity of Minnesotavand0640@umn.edu

Marcio CarvalhoPUC-Riomsc@puc-rio.br

MS49Tear Film Dynamics on an Eye Shaped Domain

We consider a tear film dynamics model on a 2-D eyeshaped domain with specification of the flux normal tothe boundary. The domain is fixed in time, but we cy-cle the time dependence of the flux boundary condition.This treatment is a drastic simplification of what occurs invivo. Model simulations are conducted in the OVERTURE

AN12 Abstracts 63

computational frame work. Results are compared with ex-isting tear film models with both 1-D and 2-D domains aswell as clinical measured data.

Longfei Li, Richard BraunUniversity of DelawareDepartment of Mathematical Scienceslongfei@math.udel.edu, braun@math.udel.edu

MS49Tear Film Dynamics with Surfactant Transport andOsmolarity

We consider a model problem for the breakup up of the tearfilm including surface tension, Marangoni stresses, insol-uble surfactant transport, evaporation, osmolarity trans-port, osmosis and wetting of corneal surface. Surface-concentration evaporation mimics the tear film lipid. Inmany, the Marangoni effect seems to eliminate a localizedarea of increased evaporation while the osmolarity increasesbecause of evaporation.

Javed SiddiquePenn State Yorkjis15@psu.edu

Richard BraunUniversity of DelawareDepartment of Mathematical Sciencesbraun@math.udel.edu

MS49Effective Slip for An Upper Convected MaxwellFluid

We consider an upper convected Maxwell fluid with sol-vent and diffusion undergoing shear flow at a solid wall.We show that even for this simple model, stress diffusionmay lead to plug flow and sharp boundary layers near thesolid wall. We discuss this for a simple channel flow con-figuration and generalize the results to lubrication modelsof a thin film flowing over a solid substrate. For this freeboundary problem a distinguished limit can be identified.The lubrication models are found to correspond in part topreviously known lubrication models with a slip boundarycondition.

Barbara WagnerInstitute of MathematicsTechnische Universitat Berlinbwagner@math.tu-berlin.de

Pamela CookDept of Mathematical SciencesU of Delawarecook@math.udel.edu

Richard BraunUniversity of DelawareDepartment of Mathematical Sciencesbraun@math.udel.edu

Andreas MuenchOCIAM Mathematical InstituteUniversity of Oxfordmuench@maths.ox.ac.uk

MS50Exploiting Saliency in Compressive and AdaptiveSensing

Recent developments in compressive and adaptive sensinghave demonstrated the tremendous improvements in sens-ing resource efficiency that can be achieved by exploitingsparsity in high-dimensional inference tasks. In this talkwe describe how compressive sensing techniques can be ex-tended to exploit saliency. We discuss our recent workquantifying the effectiveness of a compressive sensing strat-egy that accurately identifies salient features from compres-sive measurements, and we demonstrate the performanceof this technique in a two-stage active compressive imagingapproach to automated surveillance.

Jarvis HauptUniversity of Minnesotajdhaupt@umn.edu

MS50Sharp Recovery Bounds for Convex Deconvolution,With Applications

This work investigates the limits of a convex optimizationprocedure for the deconvolution of structured signals. Thegeometry of the convex program leads to a precise, yet in-tuitive, characterization of successful deconvolution. Cou-pling this geometric picture with a random model revealssharp thresholds for success, and failure, of the deconvolu-tion procedure. These generic results are applicable to awide variety of problems. This work considers deconvolv-ing two sparse vectors, analyzes a spread-spectrum codingscheme for impulsive noise, and shows when it is possibleto deconvolve a low-rank matrix corrupted with a specialtype of noise. As an additional benefit, this analysis re-covers, and extends, known weak and strong thresholds forthe basis pursuit problem.

Michael McCoyCaltechmccoy@caltech.edu

Joel A. TroppCaltech CMSjtropp@cms.caltech.edu

MS50Fast Global Convergence of Gradient Methods forHigh-dimensional Statistical Recovery

Many statistical M-estimators are based on convex opti-mization problems formed by the combination of a data-dependent loss function with a norm-based regularizer.We analyze the convergence rates of projected gradientmethods for solving such problems, working within a high-dimensional framework that allows the data dimension dto grow with (and possibly exceed) the sample size n.This high-dimensional structure precludes the usual globalassumptions—namely, strong convexity and smoothnessconditions—that underlie much of classical optimizationanalysis. We define appropriately restricted versions ofthese conditions, and show that they are satisfied with highprobability for various statistical models. Under these con-ditions, our theory guarantees that projected gradient de-scent has a globally geometric rate of convergence up tothe statistical precision of the model, meaning the typi-cal distance between the true unknown parameter θ∗ andan optimal solution θ. This result is substantially sharper

64 AN12 Abstracts

than previous convergence results, which yielded sublin-ear convergence, or linear convergence only up to the noiselevel. Our analysis applies to a wide range of M-estimatorsand statistical models, including sparse linear regressionusing Lasso (1-regularized regression); group Lasso forblock sparsity; log-linear models with regularization; low-rank matrix recovery using nuclear norm regularization;and matrix decomposition. This is based on joint workwith Alekh Agarwal and Martin Wainwright.

Sahand NegahbanMITsahandn@mit.edu

MS50Robust Image Recovery via Total Variation Mini-mization

Discrete images, consisting of slowly-varying pixel valuesexcept across edges, have sparse or compressible represen-tations with respect to the discrete gradient. Despite beinga primary motivation for compressed sensing, stability re-sults for total-variation minimization do not follow directlyfrom the standard ”l1” theory of compressed sensing. Inthis talk, we present near-optimal reconstruction guaran-tees for total-variation minimization and discuss severalrelated open problems.

Rachel WardDepartment of MathematicsUniversity of Texas at Austinrward@math.utexas.edu

Deanna NeedellDepartment of MathematicsClaremont McKenna Collegedneedell@cmc.edu

MS51Version 2.0 of the Parallel Boost Graph Library:Message-Driven Solutions to Data-Driven Prob-lems

Data-driven applications, such as graph analytics, areunique in that the computational structure of the appli-cations is entirely dependent on the input data. This factmakes static analysis difficult and necessitates dynamic,lightweight, execution-time solutions. Version 2.0 of theParallel Boost Graph Library (PBGL) demonstrates oneapproach to building a modular, scalable, and perhapsmost importantly, performance portable set of graph ker-nels. The PBGL 2.0 uses the AM++ active messaging li-brary (an implementation of the Active Pebbles program-ming and execution model) to provide portable, generic,thread-safe messaging support on a variety of platforms.On top of AM++, PBGL 2.0 provides a variety of graphtypes, auxiliary data structures, and algorithmic kernelssuitable for both shared- and distributed-memory paral-lelism (e.g. threads and processes) with the potential forstraightforward extension to various types of accelerators.

Nick EdmondsOpen Systems LaboratoryIndiana Universityngedmond@cs.indiana.edu

MS51Massive Graphs: The Way Forward

Large graph analytics have become an increasingly impor-tant in a wide variety of application areas such as inter-net search, bioinformatics, social media, and cybersecu-rity. Massive graphs push the state of the art in both bigcompute and big data. This presentation will collect andpresent the outstanding questions in this field that havebeen raised over the course of the mini-symposium.

John R. GilbertDept of Computer ScienceUniversity of California, Santa Barbaragilbert@cs.ucsb.edu

MS51Extended Sparse Matrices as Tools for Graph Com-putation

Sparse matrices frame a powerful graph computation ar-chitecture. Extensions such as complex elemental types,runtime filtering and arbitrary semiring operations greatlyexpand the utility of sparse matrices for graph analytics.Implementations must also match available hardware to beuseful. Individual shared-memory machines, distributed-memory clusters and cloud HPC systems all raise uniquechallenges, but significant commonality remains amongthem. This talk will cover how we address these challengesin our Knowledge Discovery Toolbox.

Adam LugowskiUC Santa Barbaraalugowski@cs.ucsb.edu

MS51Graph Analytics for Subject-Matter Experts: Bal-ancing Standards, Simplicity, and Complexity

Subject-matter experts needing to analyze large graphsideally want the abilities to incorporate data from dis-parate sources, perform simple analyses to find data need-ing deeper analysis, and execute complex analyses on thatdata, all via clear, reliable, and widely-available interfaces.Knowledge Discovery Toolkit (KDT) enables complex anal-yses on very large data (beyond what will reside in thememory of a single cluster node) through procedural inter-faces, though it does not (yet) ingest numerous data for-mats. Emerging semantic-web technologies are starting todeliver the promise of straightforward fusing of disparatedata sources through standard interfaces and ontologies,yet the current SPARQL 1.1 language does not supportthe calculation of complex graph metrics, such as between-ness centrality. This talk will cover our work to mergethe ease-of-use of the semantic-web technologies with thecomplex analytics of KDT.

Steve ReinhardtCray, Inc.spr@cray.com

MS52Pointwise Estimates for Stokes Equation

In this talk I will describe new stability results of the fi-nite element solution for the Stokes system in W 1

∞ normon general convex polyhedral domain. In contrast to pre-viously known results, W 2

r regularity for r > 3, which doesnot hold for a general convex polyhedral domains, is not

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required. I will briefly describe the main ideas of the proofthat uses recently available sharp Holder pointwise esti-mates of the corresponding Greens matrix together withnovel local energy error estimates, which do not involve anerror of the pressure in a weaker norm.

Dmitriy LeykekhmanDepartment of MathematicsUniversity of Connecticutdmitriy.leykekhman@uconn.edu

MS52Conforming and Divergence Free Stokes Elements

We present a family of conforming finite elements for theStokes problem on triangular meshes. We show that theelements satisfy the inf-sup condition and converge opti-mally. Moreover, the pressure space is exactly the diver-gence of the velocity space. Therefore the discretely diver-gence free functions are divergence free pointwise. We alsoshow how the elements are related to a class of C1 elementsthrough the use of a discrete de Rham complex.

Michael J. NeilanLouisiana State UniversityMathematics and Center for Computation andTechnologyneilan@pitt.edu

Johnny GuzmanBrown Universityjohnny guzman@brown.edu

MS52Transparent Boundary Conditions and the GapCondition for Stokes Elements

In the context of a Finite Element discretization of theStokes equation, a gap property is the possibility of uni-formly approximating velocities with discrete zero diver-gence by exactly solenoidal fields. This property seems tobe rare among non-divergence-free stable Finite Elementspaces for the Stokes equation. We will discuss it for someexamples and we will prove that it implies the discrete wellposedness of the simplest FEM-BEM coupled schemes forStokes.

Francisco J. SayasDepartment of Mathematical SciencesUniversity of Delawarefjsayas@math.udel.edu

Johnny GuzmanBrown Universityjohnny guzman@brown.edu

Salim Meddahi, Virginia SelgasUniversity of Oviedo, Spainsalim@uniovi.edu, selgasvirginia@uniovi.es

MS53Optimal Bilaplacian Eigenvalues

We consider the shape optimization for the clamped plateand buckling plate eigenvalue problems. We develop a nu-merical method using Hadamard’s shape derivative and theMethod of Fundamental Solutions as forward solver whichallows to propose numerical candidates to be minimizers of

the first ten eigenvalues of both problems.

Pedro R. S. AntunesGroup of Mathematical PhysicsUniversity of Lisbonprsantunes@gmail.com

MS53Principal Eigenvalue Minimization for an EllipticProblem with Indefinite Weight

An efficient rearrangement algorithm based on Rayleighquotient and rearrangement is introduced to the minimiza-tion of the positive principal eigenvalue under the con-straint that the absolute value of the weight is boundedand the total weight is a fixed negative constant. Bio-logically, this minimization problem is motivated by thequestion of determining the optimal spatial arrangementof favorable and unfavorable regions for a species to sur-vive. The optimal results are explored both theoreticallyand numerically.

Michael HintermullerHumboldt-University of Berlinhint@math.hu-berlin.de

Chiu-Yen KaoThe Ohio State UniversityClaremont McKenna Collegekao@math.ohio-state.edu

Antoine LaurainHumboldt-University of Berlinlaurain@math.hu-berlin.de

MS53Microcavity Optimization via the Frequency-averaged Local Density of States

Applications such as lasers and nonlinear devices requireoptical microcavities with long lifetimes Q and small modalvolumes V . We formulate and solve a full 3d optimizationscheme, over all possible 2d-lithography patterns in a thindielectric film. The key to our formulation is a frequency-averaged local density of states, where the frequency aver-aging corresponds to the desired bandwidth, evaluated bya novel technique: solving a single scattering problem at acomplex frequency.

Xiangdong Liang, Steven JohnsonMITxdliang@math.mit.edu, stevenj@math.mit.edu

MS55Tracing the Progression of Retinitis Pigmentosa viaPhotoreceptor Interactions

Retinitis pigmentosa (RP) is a group of inherited degener-ative eye diseases characterized by mutations in the geneticstructure of the photoreceptors that leads to the prematuredeath of the photoreceptors. We trace the progression ofRP to complete blindness through each subtype via bifur-cation theory. We show that the evolution of RP requiresthe failure of multiple components and that a delicate bal-ance between nutrients and the rates of shedding and re-newal is needed to halt its progression.

Erika T. Camacho

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Arizona State UniversityDivision of Mathematics and Natural Scienceserika.camacho@asu.edu

MS55Oscillation Criteria for Nonlinear Dynamic Equa-tions

In this talk we consider the second-order linear delay dy-namic equation

(p(t)y∆(t)

)∆+ q(t)y(τ (t)) = 0

on a time scale T . By employing the Riccati transfor-mation technique, we establish some sufficient conditionswhich ensure that every solution oscillates. The obtainedresults unify the oscillation of second-order delay differen-tial and difference equations. We illustrate our results withexamples.

Raegan HigginsTexas Tech UniversityDepartment of Mathematics and Statisticsraegan.higgins@ttu.edu

MS55Order of Events and Optimal Control in DiscreteTime Biological Models

The order of events in models with discrete time is crucial.Two examples illustrate the effect of the order of eventson optimal control of models with discrete time. One ex-ample involves augmentation of an endangered species andthe other example is a harvesting problem for an integrod-ifference population model.

Suzanne M. LenhartUniversity of TennesseeDepartment of Mathematicslenhart@math.utk.edu

MS55A Mathematical Modeling Approach to the Rever-sal of Type 2 Diabetes and β-Cell Compensation

Mathematically we explore fat accumulation and β-cellfunction in the progression of Type 2 diabetes (T2D). Ex-tending previous models we consider a link between adi-pose tissue and insulin sensitivity. Incorporating fat anddirect effects of both insulin and β-cell sensitivity, the lat-ter embodies a logistic response. Qualitative descriptionon glucose-insulin-β-cell, and fat dynamics with bifurca-tion analysis address irreversibility of T2D and β-cell fail-ure which yield insight on clinical interventions targeted tocertain stages of T2D.

Anarina MurilloAMLSS-Mathematical, Computation & ModelingSciences CenterArizona State Universityanarina.murillo@asu.edu

MS56Jet Flows in Active Nematic Fluids

We have investigated the organisation, order and flow in-duced in an active fluid, consisting of an isotropic fluid con-taining elongated swimming organisms. Using an adapted

form of the Ericksen-Leslie theory of liquid crystals, wehave found instabilities from the trivial no-flow solution,which lead to kink-like flow profiles and flow-aligned orien-tational structures. There are also other, jet-like, solutionswhich are often higher energy solutions but are, at leastlocally, stable.

Nigel MottramDepartment of Mathematics and StatisticsUniversity of Strathclydenigel.mottram@strath.ac.uk

MS56Analysis of Smectic C* Films with Defects

We analyze a model for the elastic energy of planer c-director patterns in a smectic film. Because of boundaryconditions and polar fields topological defects form in thesepatterns. We use a Ginzburg Landau model that allows thedirector field to have variable length and to vanish at thedefect cores. We prove that if the models G-L parameteris small then low energy states develop degree +(-) one de-fects that tend to a minimal energy configuration with alimiting far field texture. Our main contribution is that weare able to treat the case of unequal splay and bend elastic-ity constants. Earlier analytic work for the G-L functionalhad been limited to the equal constant case.

Daniel PhillipsDepartment of Mathematics, Purdue Universityphillips@math.purdue.edu

Sean Colbert-KellyPurdue Universityscolbert@math.purdue.edu

MS56Shear Flow in Smectic A Liquid Crystals

The onset of a dynamic instability in the shear flow of pla-nar aligned smectic A liquid crystals will be discussed. Os-cillatory shear will also be examined and the results will belinked to the onset of an analogous dynamic instability forlipid bilayers induced by forced oscillations. Mathematicalmodelling equivalences will be highlighted and key criticalcontrol parameters will be identified for the occurrence ofinstabilities.

Iain W. StewartUniversity of Strathclydei.w.stewart@strath.ac.uk

MS56Anisotropic Wave Propagation in Nematic LiquidCrystals

As early as 1972, Mullen, Luthi and Stephen [1] showedexperimentally that the director alignment of a nematicliquid crystal induces an anisotropic propagation of acous-tic waves. By contrast, Selinger and co-workers [2] havestudied a liquid crystal cell where the nematic moleculescan be realigned by an ultrasonic wave, leading to a changein the optical transmission through the cell. The existingmodels for this acousto-optic effect [2,3] propose a free en-ergy that depends on the density gradient thus describingthe nematic liquid crystal as a compressible second gradefluid. In the presentation I will show how the introductionin the stress tensor of the simple anisotropic term n⊗n, n

AN12 Abstracts 67

being the director field, easily reproduces the experimen-tal anisotropic behaviour of the sound speed, thus provid-ing a simpler first-grade model for the acousto-optic effect.It is worth noticing that Ericksen already considered thisterm in his seminal papers but subsequently it has beenneglected. This term is non-hyperelastic. However, weshow that it can be interpreted as the linear approximationof a new interaction term in the free energy for the NLCmedium which couples the director field with the elasticproperties of the fluid. Some noticeable consequences ofthis choice are then discussed.[1] M.E. Mullen, B. Luthi and M.J. Stephen, ”Sound ve-locity in a nematic liquid crystal”, Phys. Rev. Lett. 28,799-801 (1972).[2] J.V. Selinger, M.S. Spector, V.A. Greanya, B.T. Wes-lowski, D.K. Shenoy, and R. Shashidhar, ”Acoustic realign-ment of nematic liquid crystals”, Phys. Rev. E 66, 051708(2002).[3] E.G. Virga, ”Variational theory for nematoacoustics”,Phys. Rev. E 80, 031705 (2009).

Antonio Di CarloDipartimento di StruttureUniversita Roma Treadc@uniroma3.it

Paolo BiscariDipartimento di MatematicaPolitecnico di Milanopaolo.biscari@polimi.it

Stefano TurziPolitecnico di Milanostefano.turzi@polimi.it

MS57Quasistatic Nonlinear Viscoelasticity and GradientFlows

We consider the equation of motion for one-dimensionalnonlinear viscoelasticity of strain-rate type under the as-sumption that the stored-energy function is λ-convex, al-lowing for solid phase transformations. We show how thisproblem can be formulated as a gradient flow, leading to ex-istence and uniqueness of solutions. By approximating gen-eral initial data by those in which the deformation gradienttakes only finitely many values, we show that the defor-mation gradient is instantaneously bounded and boundedaway from zero. Finally, we discuss the open problem ofshowing that every solution converges to an equilibrium so-lution as time t→∞, proving by means of a new argumentthat this occurs in some previously unsolved cases.

John BallOxford Centre for Nonlinear PDE Mathematical InstituteOxfordball@maths.ox.ac.uk

Yasemin SengulOzyegin University, Istanbulyasemin.sengul@ozyegin.edu.tr

MS57Energy Scaling Laws for Conically ConstrainedThin Elastic Sheets

In this talk, we discuss recent work on energy scaling lawsfor thin elastic sheets subject to a boundary displacementcondition consistent with a conical deformation. Under

the constraint that the center of the sheet deform onlyslightly, we derive upper and lower bounds for the elasticenergy which agree, up to a factor, with the energy of theassociated conical deformation smoothed out near its tip.For a restricted class of boundary deformations, we showthat similar energy scaling laws hold without a constrainton the deformation at the sheets center.

Jeremy BrandmanCourant Institute of Mathematical SciencesNew York Univeristybrandman@cims.nyu.edu

Robert V. KohnCourant Institute of Mathematical SciencesNew York Universitykohn@cims.nyu.edu

Hoai-Minh NguyenDepartment of MathematicsUniversity of Minnesotahmnguyen@math.umn.edu

MS57Pattern Formation in Compressed Elastic Films onCompliant Substrates: An Explanation of the Her-ringbone Structure

We consider the buckling of a thin elastic film bonded toa thick compliant substrate, when the (compressive) misfitis relatively large. Previous experimental and numericalstudies suggest that a herringbone pattern minimizes thetotal energy (the membrane and bending energy of the film,plus the elastic energy of the substrate). We verify this, by(i) identifying the scaling law achieved by the herringbonepattern, and (ii) proving that no structure can achieve abetter scaling law.

Robert V. KohnCourant Institute of Mathematical SciencesNew York Universitykohn@cims.nyu.edu

Hoai-Minh NguyenDepartment of MathematicsUniversity of Minnesotahmnguyen@math.umn.edu

MS57On the Inability of Continuum Theory to Predictthe Elastic Energy of a Strained Alloy Film

An explicit calculation of a ball and spring model showsthat while continuum theory can predict the average dis-placement field for an alloyed system it cannot correctlydetermine the elastic energy. Implications of this resultwill be discussed. This is joint work with Christian Ratschand Arvind Baskaran.

Peter SmerekaDepartment of MathematicsUniversity of Michiganpsmereka@umich.edu

Christian RatscUCLAcratch@ipam.ucla.edu

68 AN12 Abstracts

Arvind BaskaranInstitute for Pure and Applied Mathematics, UCLAUniversity of California, Irvinebaskaran@umich.edu

MS58Aposteriori Analysis of Multirate and MultiscaleEvolution Systems

We consider analysis of numerical methods for multiscaleand multirate evolution models that present significantlydifferent temporal and spatial scales within the compo-nents of the model. We interpret the multirate method as amultiscale operator decomposition method and use this toconduct both an apriori and a hybrid apriori–aposteriori er-ror analysis. We formulate an iterative multirate Galerkinfinite element method then employ adjoint operators andvariational analysis. We consider analyses of both ODEsand PDEs.

Jehanzeb H. ChaudhryColorado State UniversityDepartment of Mathematicsjehanzeb.hameed@gmail.com

Don EstepColorado State Universityestep@stat.colostate.edu

Victor E. GintingDepartment of MathematicsUniversity of Wyomingvginting@uwyo.edu

Simon TavenerColorado State Universitytavener@math.colostate.edu

MS58Quantification of Operator Splitting Effects in Fi-nite Volume Calculations of Advection-diffusion

Some issues are presented involving splitting effects nearboundaries in operator-split finite volume calculations foradvection-diffusion. In applications, it is desirable to un-derstand the errors and sources of errors in calculations,such as splitting effects, which may be difficult to deter-mine. One approach is presented for a posteriori error esti-mation to calculate the error in a quantity of interest (QoI)and investigate the effect of the splitting on the computedQoI value.

Jeffrey M. ConnorsLawrence Livermore National LaboratoryCenter for Applied Scientific Computingconnors4@llnl.gov

Jeffrey W. BanksLawrence Livermore National Laboratorybanks20@llnl.gov

Jeffrey A. HittingerCenter for Applied Scientific ComputingLawrence Livermore National Laboratoryhittinger1@llnl.gov

Carol S. WoodwardLawrence Livermore Nat’l Lab

woodward6@llnl.gov

MS58Consistency and Stability Considerations forImplicit-explicit Additive Splittings

Stability and consistency properties of operator splittingtime-marching are challenging to characterize and inter-pret due to the coupling effects, which lead to complex in-teractions among operators. In additive splittings the righthand side can be represented as a sum of terms that typ-ically have different properties, such as stiff and nonstiff,and require integrators with different stability properties.We focus on multistage additive implicit-explicit (IMEX)splittings and present new IMEX schemes.

Emil M. ConstantinescuArgonne National LaboratoryMathematics and Computer Science Divisionemconsta@mcs.anl.gov

MS58Coupling for a Virtual Nuclear Reactor

Abstract not available at time of publication.

John TurnerOak Ridge National LaboratoryComputational Engineering and Energy Sciencesturnerja@ornl.gov

MS59A Problem of Boundary Controllability for a Plate

The boundary controllability problem, here discussed,might be described by a two-dimensional space equationmodeling, at the same time t, different physical phenom-ena in a composite solid made of different materials. Thesephenomena may be governed, at the same time t, for ex-ample, by the heat equation and Schrodinger equation intwo separate regions. Interface transmission conditions areimposed.

Orazio ArenaUniversita di FirenzeFlorence, Italyarena@unifi.it

MS59Mathematical Challenges Arising from the Ques-tions of Controllability for Linked Elastic Struc-tures

A tremendous challenge in the study of control and sta-bilization of dynamic elastic systems is the ability to rig-orously address whether linked dynamic structures can becontrolled using boundary feedback alone. When a struc-ture is composed of a number of interconnected elastic el-ements or is modelled by a system of coupled partial dif-ferential equations, the behavior becomes much harder toboth predict and to control. This talk focuses on a num-ber of issues that arise when attempting to control thesecomplex systems.

Mary Ann HornVanderbilt University & National Science Foundationmary.ann.horn@vanderbilt.edu

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MS59Limitations on Control and Stabilization of CertainHybrid Systems

Hybrid systems are often modeled as continuous parame-ter systems modeled by partial differential equations cou-pled to point masses. It is natural to attempt to establishexact controllability and/or uniform exponential stabiliz-ability of the overall system using controls applied to thesepoint masses. We show, using extensions of the notion ofthe operator trace, that the discrete mass property of suchpoints of control application impose definite limitations onachievement of these goals.

David RussellDepartment of MathematicsVirginia Techdlr@math.vt.edu

MS59Ensemble Dynamics and Bred Vectors

Abstract not available at time of publication.

George SellSchool of MathematicsUniversity of Minnesotasell@math.umn.edu

MS60Heated Tear Film in One Dimension with a MovingBoundary

We consider model problems for the tear film over multipleblink cycles with evaporation and with heat transfer fromwith a model domain for the eye. The nonlinear PDEfor film thickness is coupled with heat transfer under thefilm; simultaneous solution on a moving domain is via aspectral method. The numerical results reveal a similarityto quantitative in vivo observations of the film dynamicsand the surface temperature of the film.

Quan DengDepartment of Mathematical SciencesUniversity of Delawaredengquan@udel.edu

MS60Fingering Instability of Evaporating Thin Films

The fingering instability of a volatile, viscous liquid flowingdown an inclined, heated surface is investigated. A lubrica-tion type approach is used to develop a three-dimensionalmodel of the flow, and numerical simulations are conductedbased on the model. Liquids of various wetting propertiesare considered. Evaporation is found to have a stabiliz-ing influence on the flow, with the strength of evaporationneeded to completely suppress the instability increasingwith increasing apparent contact angle.

Jill KlentzmanUniversity of Arizonajklentzm@email.arizona.edu

Vladimir AjaevSouthern Methodist Universityajaev@smu.edu

Tatiana Gambaryan-Roisman, Peter StephanTechnische Universitaet Darmstadtgtatiana@ttd.tu-darmstadt.de,pstephan@ttd.tu-darmstadt.de

MS60A Multiple Scales Approach to Evaporation in-duced Marangoni Convection

In this talk, we consider the stability of a thin liquid layerof a binary mixture of a volatile (solvent) and a non-volatile(polymer) species. Evaporation depletes the solvent nearthe liquid surface, which can lead to Benard-Marangoni-type convection. Due to evaporation, the base state is timedependent, thus impeding the use of normal modes. How-ever, the evaporation is slow on the diffusive time scale, andthis is exploited via a systematic multiple scales expansion.

Andreas MuenchOCIAM Mathematical InstituteUniversity of Oxfordmuench@maths.ox.ac.uk

Matthew HennessyMathematical InstituteUniversity of Oxfordmatthew.hennessy@maths.ox.ac.uk

MS60Asymptotics of a Thermally Driven Thin Film

A flow driven up an inclined plane by thermal Marangonistresses is modeled using the lubrication approximation inone dimension, yielding a fourth order nonlinear PDE. Twoqualitatively distinct solutions to the steady-state ODEarise when additional localized heating is introduced. Solu-tion type is determined by the magnitude of this localizedheating. Solution behavior as a function of this heatingparameter is explored using asymptotic analysis and vali-dated through comparison with numerical simulations.

Harrison Potter, Thomas P. WitelskiDuke UniversityDepartment of Mathematicshdp2@math.duke.edu, witelski@math.duke.edu

MS61Application of Graph Scaffolding in Approximatingthe Chromatic Number

We introduce the concept of graph scaffolding, through itsapplication in finding the chormatic number of large-scalenetworks. Graph scaffolding is a a generalized frameworkfor working with combinatorial optimization problems thatfirst exploits theoretical results to compute exact or near-exact solutions on well-defined portions of the graphthescaffoldand then leverages the answer on the scaffold toconstruct a high-quality solution to the overall problem.We demonstrate through empirical and theoretical resultshow by using chordal graphs as a scaffold, the chormaticnumber of a given graph can be closely approximated.

Sanjukta BhowmickDepartment of Computer ScienceUniversity of Nebraska, Omahasbhowmick@unomaha.edu

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MS61Sparsification Techniques for Metaphor Compre-hension

Comprehension of metaphors occurs at the highest level oflanguage proficiency. Metaphor comprehension is compu-tationally challenging as well. The basic technique involvesbuilding semantic spaces for words using relevant corpora.Given large scale corpora such as English Wikipedia, spar-sification becomes a necessity. In this presentation, we willdetail some of the sparsification techniques we have usedfor metaphor comprehension.

Mahantesh HalappanavarPacific Northwest National Laboratorymahantesh.halappanavar@pnnl.gov

MS61Graph Sparsification Methods in Cybersecurity

In cybersecurity and related problem domains we oftenmust deal with very large graphs. For example, considertraffic on a large computer network, a multigraph withupwards of hundreds of thousands of nodes. In order toaccomplish tasks like connected component identification,path finding, and subgraph isomorphism in these large net-work graphs we are turning to graph sparsification. We willdescribe the sparsification techniques we are using and givean analysis of their performance.

Emilie HoganPacific Nortwest National Labemilie.hogan@pnnl.gov

John Johnson, Mahantesh HalappanavarPacific Northwest National Laboratoryjohn.johnson@pnnl.gov,mahantesh.halappanavar@pnnl.gov

MS61Sparse Graph Realization from a Metric Space

We present an approach for constructing a locality graphfor set of points in a given metric space, without the needfor an underlying geometry on the space. In addition, thegraph of all calculated distances is sparse, making our ap-proach appropriate for very high-dimensional data.

Chad ScherrerPacific Northwest National Laboratorychad.scherrer@pnnl.gov

MS62On Local Refinement via T-splines

We study properties of Analysis Suitable (AS) T-splineswhich are needed to use T-splines within an adaptive pro-cedure in Isogeometric Analysis. We set up a priori and aposteriori error analysis; we study the use of AS T-splinesto solve mixed problems and, more in general, non-coercivedifferential problems.

Annalisa BuffaI.M.A.T.I. - C.N.R.Pavia, Italyannalisa@imati.cnr.it

MS62Challenges in Isogeometric Analysis (IGA)

IGA replaces traditional Finite Elements by watertightstructures of 3-variate NURBS. The introduction ofNURBS in FEA allows accurate representation of CAD-shapes in FEA. However, efficient technology for establish-ing watertight IGA-models from CAD-models has to bedeveloped, local refinement of IGA-models has to be im-proved, and direct GPU-based visualization of IGA-modelshas to be developed. IGA potentially simplifies analysis ofas-is models as the path from measurement through CADto analysis is shortened.

Tor DokkenSINTEF ICT, Department of Applied MathematicsOslo, Norwaytor.dokken@sintef.no

MS62Isogeometric Analysis for Shape Optimization

One of the attractive features of isogeometric analysis isthe exact representation of the geometry. The geometryis furthermore given by a relative low number of controlpoints and this makes isogeometric analysis an ideal basisfor shape optimisation. I will describe some of the resultswe have obtained and also some of the problems we haveencountered. One of these problems is that the geometryof the shape is given by the boundary alone. And, it is theparametrisation of the boundary which is changed by theoptimisation procedure. But isogeometric analysis requiresa parametrisation of the whole domain. So in every opti-misation cycle we need to extend a parametrisation of theboundary of a domain to the whole domain. It has to befast in order not to slow the optimisation down but it alsohas to be robust and give a parametrisation of high qual-ity. These are conflicting requirements so we propose thefollowing approach. During the optimisation a fast linearmethod is used, but if the parametrisation becomes singu-lar or close to singular then the optimisation is stopped andthe parametrisation is improved using a nonlinear method.The optimisation then continues using a linear method.

Jens GravesenTechnical University of Denmarkj.gravesen@mat.dtu.dk

MS62Locally Refined B-splines

We will address local refinement of a tensor product gridspecified as a sequence of inserted line segments parallelto the knot lines. We obtain a quadrilateral grid withT-junctions in the parameter domain, and a collection oftensor product B-splines on this mesh here named an LR-mesh. The approach applies equally well in dimensionshigher than two. Moreover, in the two dimensional casethis collection of B-splines spans the full spline space onthe LR-mesh.

Tom LycheUniversity of OsloDepartment of Informatics and CMAtom@ifi.uio.no

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MS63The Challenges of Robustness in High Dimensions

We consider the problem of dealing with (potentially ma-liciously) corrupted points in the high dimensional regime.We show that even for basic problems like regression andPCA, existing techniques from robust statistics fail dra-matically. We develop new techniques designed for robust-ness in the high dimensional regime.

Constantine CaramanisThe University of Texas at Austincaramanis@mail.utexas.edu

MS63Compressive Principal Component Pursuit

We consider the problem of recovering target matrix that isa superposition of low-rank and sparse components, froma small set of linear measurements. This problem arisesin compressed sensing of videos and hyperspectral images,as well as in the analysis of transformation invariant low-rank matrix recovery. We analyze the performance of thenatural convex heuristic for solving this problem, underthe assumption that measurements are chosen uniformlyat random. We prove that this heuristic exactly recoverslow-rank and sparse terms, provided the number of obser-vations exceeds the number of intrinsic degrees of freedomby a polylogarithmic factor. Our analysis introduces sev-eral ideas that may be of independent interest for the moregeneral problem of compressed sensing of superpositions ofstructured signals.

Yi MaDepartment of Electrical and Computer EngineeringUniversity of Illinois at Urbana-Champaignyima@uiuc.edu

John WrightDepartment of Electrical EngineeringColumbia Universityjohnwright@ee.columbia.edu

MS63Robust Locally Linear Analysis with Applicationsto Image Denoising and Blind Inpainting

I will talk about the problems of denoising images cor-rupted by impulsive noise and blind inpainting (i.e., in-painting when the deteriorated region is unknown). Ourbasic approach is to model the set of patches of pixels in animage as a union of low-dimensional subspaces, corruptedby sparse but perhaps large magnitude noise. For this pur-pose, we develop a robust and iterative method for singlesubspace modeling and extend it to an iterative algorithmfor modeling multiple subspaces. I will also cover the con-vergence for the algorithm and demonstrate state of theart performance of our method for both imaging problems.

Yi WangSchool of MathematicsUniversity of Minnesotawangx857@umn.edu

Arthur SzlamDepartment of MathematicsNYUaszlam@courant.nyu.edu

Gilad LermanSchool of MathematicsUniversity of Minnesotalerman@umn.edu

MS63A Novel M-Estimator for Robust PCA

We formulate a convex minimization to robustly recover asubspace from a contaminated data set, partially sampledaround it, and propose a fast iterative algorithm to achievethe corresponding minimum. We establish exact recoveryby this minimizer, quantify the effect of noise and regular-ization, explain how to take advantage of a known intrinsicdimension and establish linear convergence of the iterativealgorithm. We compare our method with many other al-gorithms for Robust PCA on synthetic and real data setsand demonstrate state-of-the-art speed and accuracy.

Teng ZhangInstitute for Mathematics and its ApplicationsUniversity of Minnesotazhang620@umn.edu

Gilad LermanSchool of MathematicsUniversity of Minnesotalerman@umn.edu

MS64Relaxation Results for Nematic Elastomers

We compute the relaxation of a free-energy functionalwhich describes the order-strain interaction in incompress-ible nematic elastomers in the regime of small strains.Adopting the uniaxial order tensor theory (Frank model)to describe the liquid crystal order, we prove that the min-ima of the relaxation exhibit an effective biaxial nematictexture (that of the de Gennes theory). The relaxed energydensity satisfies a solenoidal quasiconvexification formula.(ARMA 197 N.3, 2010).

Pierluigi CesanaMechanical Engineering Departmentcesana@caltech.edu

MS64Title Not Available at Time of Publication

Abstract not available at time of publication.

Greg ForestDepartment of MathematicsUniversity of North Carolina, Chapel Hillforest@unc.edu

MS64A Ginzburg-Landau-type Model for Liquid Crys-tals

We will discuss some results regarding the Landau-DeGennes energy, often used to model liquid crystals, withinthe framework developed by Bethuel, Brezis and Heleinfor the Ginzburg-Landau energy of superconductivity. Ouraim is to describe the singularities allowed by this model.

Dmitry GolovatyThe University of Akron

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Department of Theoretical and Applied Mathematicsdmitry@uakron.edu

Alberto MonteroDepartamento de MatematicaPontificia Universidad Catolica de Chileamontero@mat.puc.cl

MS64Hypertractions and Hyperstresses in Second Gra-dient Continua

A complete and coherent theory of second gradient con-tinua has not yet been fully developed. Hyperstresses andedge interactions are some of the key features which needto be better understood. We shall review some of the mainproblems and recent results in this field.

Maurizio VianelloMathematics DepartmentPolitecnico di Milanomaurizio.vianello@polimi.it

MS65Nucleation and Motion of Crystals in a Binary So-lution

Abstract not available at time of publication.

Dmitry GolovatyThe University of AkronDepartment of Theoretical and Applied Mathematicsdmitry@uakron.edu

MS65Pseudo-spectral Simulations of Models for Regu-larized Dynamic Models in Nonlinear Elasticity

We discuss results of computations of two dimensional vis-coelastic models which arise as simplifications of modelsfor phase transformations. These models in include dy-namical scalar Aviles-Giga and Kohn-Muller models. Wealso discuss the resulting nature of energy minimizing solu-tions that are obtained from numerical simulations of thesemodels. Finally, we show that some similar results can beobtained in vectorial two dimensional models for marten-sitic phase transformations.

Benson K. MuiteDepartment of MathematicsUniversity of Michiganmuite@umich.edu

MS65Wrinkling of a Floating Elastic Film: Energy andPattern

In this talk, I discuss the floating film problem in whicha rectangle elastic film floats on the surface of a pool ofliquid and is compressed along two opposing sides. I firstpresent the energy scaling law and then show how to useit to explain the cascade pattern at the edges of the twoother sides of the film observed experimentally.

Hoai-Minh NguyenSchool of MathematicsUnviersity of Minnestoahmnguyen@umn.edu

Robert V. KohnCourant Institute of Mathematical SciencesNew York Universitykohn@cims.nyu.edu

MS65Conical Singularities in Thin Elastic Sheets

When one slightly pushes a thin elastic sheet into a hol-low cylinder, the resulting configuration of the sheet is aso-called d-cone. D-cones have drawn some attention inthe physics community in the last two decades or so, seee.g. Cerda et al., Nature 401, 46 (1999). In this talk, weexamine the scaling of the elastic energy with the sheetthickness h in a rigorous setting and give a lower boundthat is optimal in the leading order of h.

Heiner OlbermannHausdorff Center for Mathematics & Institute for Appl.Math.University of Bonnheiner.olbermann@hcm.uni-bonn.de

Stefan MullerUniversity of Bonnstefan.mueller@hcm.uni-bonn.de

MS66Searching for Exceptional Mechanisms with FiberProducts

Given a family of mechanisms and its parameterized sys-tem of equations, techniques from Numerical Algebraic Ge-ometry can be used to find mechanisms with greater thanexpected motion. The parameters of such mechanisms canbe found using the fiber product technique of Sommeseand Wampler to uncover irreducible sets that are obscuredwithin a larger algebraic set. Applications to particularfamilies of mechanisms and adaptations for dealing withlarge sets of defining equations will be discussed.

Daniel J. BatesColorado State UniversityDepartment of Mathematicsbates@math.colostate.edu

Eric HansonDepartment of MathematicsColorado State Universityhanson@math.colostate.edu

Jonathan HauensteinTexas A&M Universityjhauenst@math.tamu.edu

Charles WamplerGeneral Motors Research Laboratories, EnterpriseSystems Lab30500 Mound Road, Warren, MI 48090-9055, USAcharles.w.wampler@gm.com

MS66Quasi Steady State Solution and Bifurcation for aCell Cycle Model

We consider a free boundary problem for a system ofpartial differential equations, which arises in a model oftissue growth. For the steady state system, it depends

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on a positive parameter β, which describes the signalsfrom the microenvironment. Upon discretizing this model,we obtain a family of polynomial systems parameterizedby β. We numerically find that there exists a radially-symmetric stationary solution with tumor free boundaryr = R for any given positive number R. By homo-topy tracking with respect to the parameter β, there ex-ist branches of symmetry-breaking stationary solutions.Moreover, we proposed a numerical algorithm based onCrandall-Rabinowitz theorem to numerically verify the bi-furcation points. By continuously changing µ using a ho-motopy, we are able to compute nonradial symmetric solu-tions. We additionally discuss optimal control on β.

Wenrui HaoDept. of Applied and Comp. Mathematics and StatisticsUniversity of Notre Damewhao@nd.edu

Andrew Sommese, Bei HuDept. of Applied & Computational Mathematics &StatisticsUniversity of Notre Damesommese@nd.edu, b1hu@nd.edu

MS66Real Solutions to Polynomial Systems Arising inMechanism Design

Parameterized polynomial systems naturally arise in manyapplications, including mechanism design. This talk willexplore using techniques from numerical algebraic geome-try to attempt to compute parameters for which the poly-nomial system has an extremal number of real solutions.An example from mechanism design will be used to demon-strate the approach where there exists a set of parametersfor which the corresponding system has no real solutionsand a set of parameters for which the corresponding systemhas all solutions real.

Jonathan Hauenstein, Zachary GriffinTexas A&M Universityjhauenst@math.tamu.edu, zacgriffin21@neo.tamu.edu

MS66Cell Decomposition of Real Surfaces Defined byMechanism Motions

This talk will describe the application of numerical alge-braic geometry to decompose a real algebraic surface intoa cell structure. A general technique for almost smoothalgebraic surfaces will be reviewed and then applied to sev-eral mechanisms. An interesting case is the study of one-degree-of-freedom mechanisms with one free design param-eter, such as a link length. The cell decomposition findscritical values of the parameter where the topology of themotion curve changes.

Charles WamplerGeneral MotorsR&D Centercharles.w.wampler(at)gm.com

MS67Multilevel Algorithms for Stokes Type Systems

We analyze multilevel algorithms for symmetric saddlepoint systems. We combine inexact Uzawa algorithms at

the continuous level with Uzawa and gradient type algo-rithms at the discrete level. The algorithms are based onthe existence of multilevel sequences of nested approxima-tion spaces that do not have to satisfy a discrete LBB sta-bility condition. The main idea is to maintain an accuraterepresentation of the residuals at each step of the inexactUzawa algorithm at the continuous level. The residual rep-resentations at each step are approximated by projections.Iteration on a fixed level corresponds to standard Uzawa orGradient method for solving symmetric saddle point sys-tems. Whenever a sufficient condition for the accuracy ofthe representation for the main residual (of the first equa-tion) fails to be satisfied, the representation is projectedon the next larger space. We emphasize on the gradientmethod which has the advantages of automatically select-ing the relaxation parameter, lowering the number of iter-ations on each level, and improving on running time andon global error reduction. Numerical results are presentedfor the Stokes system.

Constantin BacutaUniversity of DelawareDepartment of Mathematicsbacuta@math.udel.edu

Lu ShuUniversity of DelawareMathematical Sciencesshu@math.udel.edu

MS67HDG Methods for the Vorticity-Velocity-PressureFormulation of the Stokes Problem

In this talk we discuss the hybridizable discontinuousGalerkin (HDG) method for solving the vorticity-velocity-pressure formulation of the three-dimensional Stokes equa-tions of incompressible fluid flow. The idea of the a priorierror analysis consists in estimating a projection of the er-rors that is tailored to the very structure of the numericaltraces of the method. We show that the approximatedvorticity and pressure, which are polynomials of degree k,converge with order k + 1/2 in L2-norm for any k ≥ 0.Moreover, the approximated velocity converges with orderk + 1.

Jintao CuiInstitute for Mathematics and its ApplicationsUniversity of Minnesotajcui@ima.umn.edu

Bernardo CockburnSchool of MathematicsUniversity of Minnesotacockburn@math.umn.edu

MS67An Alternative Multigrid Method for Incompress-ible Flow

A multigrid method for H(div)-conforming DG discretiza-tions of the Stokes problem is presented. It is basedon an overlapping domain decomposition smoother. Thesmoother operates in thedivergence free subspace and thusdoes not require to be embedded into a block precondi-tioner for the saddle point problem. It is proven that themethod is a uniform preconditioner.Its efficiency is docu-

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mented with numerical examples.

Youli MaoTexas A&MDepartment of Mathematicsyoulimao@math.tamu.edu

Guido KanschatDepartment of MathematicsTexas A&M Universitykanschat@tamu.edu

MS67Flow in Pebble Bed Geometries

Flow in complex geometries intermediate between freeflows and porous media flows occurs in pebble bed reactorsand in optimization of turbine placement in wind farms.The Brinkman models have consistently shown that forsimplified settings accurate prediction of essential flow fea-tures depends on the impossible problem of meshing thepores. In this paper we investigate new model to under-stand the flow and its properties in these geometries.

Aziz TakhirovUniversity of Pittsburghazt7@pitt.edu

MS68The Importance of the Inner-problem in Compu-tational Models of Dynamic Brittle Fracture andwhy Peridynamics Works

I discuss the importance of capturing the “inner-problem’in modeling dynamic fracture. The mechanism for crackbranching proposed by experimentalists suggests that whenthe S.I.F. becomes sufficiently high, voids grow into micro-cracks ahead of the crack tip. I argue that computationalmodels which are not able to represent the evolution ofthese microcracks, will not be able to correctly predict dy-namic brittle fracture. Peridynamics, a nonlocal extensionof classical mechanics, accounts implicitly for microcracksby the way in which nonlocal damage evolves in this theory.

Florin BobaruUniversity of Nebraska-Lincolnfbobaru2@unl.edu

MS68Peridynamic Energy Balance and Damage

Our presentation reviews the recently proposed nonlocalenergy balance for peridynamic solids. Appropriate ex-pressions for the first and second laws of thermodynamicsare given, including a justification using the principles ofnon-equilibrium statistical mechanics. The first law expres-sion explicitly includes nonlocal interactions in a term thatrepresents the stress power in peridynamic theory. Thesecond law enables restrictions to be placed on constitu-tive relations and is demonstrated to be a generalization ofthe Coleman-Noll procedure. An application to damage ispresented.

Richard B. LehoucqSandia National Laboratoriesrblehou@sandia.gov

MS68The Peridynamic J-integral

In fracture mechanics, the J-integral characterizes the en-ergy balance for a growing crack. In the nonlocal peri-dynamic version of the J-integral, the rate of work doneon the contour is replaced by a volume integral of workdone on the bonds that connect the inside to the outsideof the contour. The peridynamic J-integral converges tothe standard version in the limit of small horizon. Nu-merical examples compare values in the peridynamic andstandard theories.

Stewart SillingSandia National Laboratoriessasilli@sandia.gov

Florin BobaruUniversity of Nebraska-Lincolnfbobaru2@unl.edu

Wenke HuUniversity of Nebraska - Lincolnhuwenke hbu@hotmail.com

MS68The Effect of Surface Tension on the Stress Fieldnear a Curvilinear Crack

In this talk, an approach to modeling fracture incorpo-rating interfacial mechanics is applied to the exampleof a curvilinear plane strain crack. The classical Neu-mann boundary condition is augmented with curvature-dependent surface tension. It is shown that the consideredmodel eliminates the integrable crack-tip stress and strainsingularities of order 1/2 present in the classical linear frac-ture mechanics solutions, and also leads to the sharp crackopening that is consistent with empirical observations.

Anna ZemlyanovaDepartment of MathematicsTexas A&M Universityazem@math.tamu.edu

Jay R. WaltonDepartment of MathematicsTexas A&Mjwalton@math.tamu.edu

MS70Cocircuits of Linear Matroids

We present a set covering problem (SCP) formulation ofthe matroid cogirth problem. Addressing the matroid co-girth problem can lead to significantly enhancing the de-sign process of sensor networks. The solution to the ma-troid cogirth problem provides the degree of redundancyof the corresponding sensor network, and allows for theevaluation of the quality of the network. We provide com-putational results to validate a branch-and-cut algorithmthat addresses the SCP formulation.

John David ArellanoComputational and Applied MathematicsRice Universityjda2@rice.edu

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MS70Recent Advances in Optimization Methods for Im-age Processing

Nonlinear image reconstruction based upon sparse repre-sentations of images has received widespread attention re-cently with the advent of compressed sensing. This emerg-ing theory indicates that, when feasible, judicious selectionof the type of distortion induced by measurement systemsmay dramatically improve our ability to perform recon-struction. In this talk, we discuss some recent advances inlarge-scale optimization methods for solving these sparsesignal recovery problems.

Roummel F. MarciaUniversity of California, Mercedrmarcia@ucmerced.edu

MS70Approximate Murphy-Golub-Wathen Precondi-tioning for KKT Matrices

Karush-Kuhn-Tucker matrices arise from first order nec-essary conditions for nonlinear optimization. Murphy,Golub, andWathen proposed a preconditioner having threedistinct eigenvalues, giving exact GMRES convergence inthree iterations. This ideal preconditioner involves the in-verse of a large submatrix, but when computed inexactly,GMRES will no longer converge in three steps. How willthis compromise slow convergence? Recent results on thestability of GMRES give rigorous bounds on the numberof iterations. Numerical computations verify these resultsfor problems from optimization and fluid dynamics.

Josef SifuentesNew York UniversityCourant Institutesifuentes@cims.nyu.edu

MS70Recent Results on the Smallest Enclosing BallProblem and the Smallest Intersecting Ball Prob-lem

In the 19th century, J.J. Sylvester introduced the smallestenclosing circle problem: find a circle of smallest radius en-closing a given set of finite points on the plane. We extendthe problem and find a ball with the smallest radius thatencloses a finite number of nonempty closed sets. Similarly,we study the smallest intersecting ball problem. Necessaryand sufficient optimality conditions will be presented, aswell, as numerical results. Applications exist in the field offacility location.

Cristina VillalobosUniversity of Texas-Pan Americanmcvilla@utpa.edu

MS71Markovian Projection of Stochastic Processes

We give conditions under which the flow of marginal distri-butions of a discontinuous semimartingale can be matchedby a Markov process whose infinitesimal generator can beexpressed in terms of its local characteristics, generaliz-ing a result of Gyongy (1986) to the discontinuous case.Our construction preserves the martingale property and al-lows to derive a partial integro-differential equation for theone-dimensional distribution of discontinuous semimartin-

gales, extending the Kolmogorov forward equation (FokkerPlanck equation) to a non-Markovian setting.

Amel BentataUniversite Pierre & Marie Curie, Franceamel.bentata@gmail.com

Rama ContCNRS (France) & Columbia UniversityRama.Cont@gmail.com

MS71Functional Ito Calculus and PDEs on FunctionSpaces

The Functional Ito Calculus (Dupire 2009 ; Cont & Fournie2010) is a calculus for non-anticipative functionals on thespace of right-continuous paths, which extends the Ito cal-culus to path-dependent functionals of stochastic processes(Cont & Fournie 2011). This calculus, applied to function-als of a martingale, leads to a new class of PDEs on thespace of continuous functions, which share various prop-erties with parabolic PDEs in finite dimensions : compar-ison principle, maximum principle, functional Feynman-Kac formula. In particular, we characterize Brownian mar-tingales as weak solutions of a functional heat equation.

Rama ContCNRS (France) & Columbia UniversityRama.Cont@gmail.com

MS71Viscosity Solutions of Path Dependent PDEs

We propose a notion of viscosity solutions for path depen-dent parabolic PDEs. This can also be viewed as viscositysolutions of non-Markovian control problems, and thus ex-tends the well known nonlinear Feynman-Kac formula tonon-Markovian case. We shall prove the existence, unique-ness, stability, and comparison principle for the viscositysolutions. The key ingredient of our approach is a func-tional Itos calculus recently introduced by Dupire and fur-ther developed by Cont-Fournie.

Ibrahim EkrenDepartment of MathematicsUniversity of Southern Californiaekren@usc.edu

Christian KellerUSCkellerch@usc.edu

Nizar TouziEcole Polytechniquenizar.touzi@polytechnique.edu

Jianfeng ZhangUniversity of Southern Californiajianfenz@usc.edu

MS71Control of Non-Markovian Stochastic DifferentialEquations

We study stochastic differential equations (SDEs) whosedrift and diffusion coefficients are path-dependent and con-trolled. We construct a value process on the canonical path

76 AN12 Abstracts

space, considered simultaneously under a family of singu-lar measures, rather than the usual family of processes in-dexed by the controls. This value process is characterizedby a second order backward SDE, which can be seen as anon-Markovian analogue of the Hamilton-Jacobi-Bellmanpartial differential equation.

Marcel NutzDepartment of MathematicsColumbia Universitymnutz@math.columbia.edu

MS72Adaptive Split-operator Methods for ModelingFlow and Transport Phenomena in Porous MediumSystems

Split-operator methods facilitate computation of large cou-pled problems. However, these methods introduce splittingerror, which is typically either ignored or controlled heuris-tically. In this work, we develop algorithms to control thesplitting error by dynamically adapting the temporal split-ting step based upon error estimators. The methods yieldrobust and efficient solutions with error control for non-linear reaction problems and can be extended to Navier-Stokes and multiphase problems. These algorithms havewidespread applicability in environmental modeling.

Sarah GasdaCenter for Integrated Petroleum Research, Uni Researchsarah.gasda@uni.no

Matthew FarthingUS Army Engineer Research and Development Centerqmatthew.w.farthing@usace.army.mil

Christopher KeesUS Army Engineer Research and Development Centerchristopher.e.kees@usace.army.mil

Cass MillerEnvironmental Sciences and Engineering DepartmentUniversity of North Carolinacasey miller@unc.edu

MS72An IMEX Method for the Euler Equations ThatPosses Strong Non-Linear Heat Conduction andStiff Source Terms (Radiation Hydrodynamics)

We present a truly second order time accurate self-consistent IMEX (IMplicit/EXplicit) method for solvingthe Euler equations that posses strong nonlinear heat con-duction and very stiff source terms (Radiation hydrody-namics). IMEX methodology is suggested when deal-ing with physical systems that consist of multiple physicsor fluid dynamics problems that exhibit multiple timescales such as advection-diffusion, reaction-diffusion, oradvection-diffusion-reaction. It can be challenging to pro-vide fully converged and second order time accurate nu-merical results to these kinds of coupled systems. Orderreductions in time accuracy are often reported due to in-consistent operators splitting. Our JFNK (Jacobian-FreeNewton Krylov)-based IMEX method splits the operatorsin a self-consistent way in which all-non-linearities are con-verged and second order time accuracy of different physicalterms is preserved. We have applied this strategy to a Ra-diation Hydrodynamics model (at diffusion approximationlimit) that posses multi-scale terms and demonstrated sec-

ond order time accuracy.

Samet Y. KadiogluIdaho National Laboratorysamet.kadioglu@inl.gov

Dana KnollLos Alamos National Laboratorynol@lanl.gov

MS72Operator Splitting Integration Factor Methods forComplex Biological Systems

For reaction-diffusion-advection equations, the stiffnessfrom the reaction and diffusion terms often requires very re-stricted time step size, while the nonlinear advection termmay lead to a sharp gradient in localized spatial regions.It is challenging to design numerical methods that can ef-ficiently handle both difficulties. For reactiondiffusion sys-tems with both stiff reaction and diffusion terms, implicitintegration factor (IIF) method and its higher dimensionalanalog compact IIF (cIIF) serve as an efficient class of time-stepping methods, and their second order version is linearlyunconditionally stable. Here we use splitting methods toincorporate different numerical methods to handle differ-ent terms of the equations. In particular, we apply theIIF-cIIF method to the stiff reaction and diffusion termsand the WENO method to the advection term in two dif-ferent splitting sequences. Calculation of local truncationerror and direct numerical simulations for both splittingapproaches show the second order accuracy of the splittingmethod, and linear stability analysis and direct compari-son with other approaches reveals excellent efficiency andstability properties. Applications of the splitting approachto several biological systems demonstrate that the overallmethod is accurate and efficient.

Qing NieUniversity of California at Irvineqnie@math.uci.edu

MS72Reduced Description of Reactive Flows with Tab-ulation of Chemistry

Reduced description with chemistry tabulation can effec-tively reduce the simulation time of reactive flows by solv-ing the evolution equations only for represented species.With operator splitting, chemical reactions are separatedinto a reaction fractional step. The effect of chemical re-actions on the reduced composition is addressed throughspecies reconstruction and the evaluation of reaction map-ping in the full composition space. ISAT is employed tospeed chemistry calculation by tabulating information ofthe reduced system.

Zhuyin RenUniversity of ConnecticutDepartment of Mechanical Engineeringzhuyin.ren@engr.uconn.edu

MS73Multiscale Engineering for Heterogeneous Mediaand Structures

In this talk, we present multiscale materials design successstories and discuss some technical barriers to using multi-

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scale simulation for rapid materials design and qualifica-tion. A paradigm for computational multiscale modelingand simulation will be discussed which, when integratedinto the structural design loop, will significantly expand thedesign space and enable increased efficiency, performance,and affordability by delivering materials and structures op-timized across all engineered scales for their mission.

Timothy D. BreitzmanAir Force Research Laboratorytimothy.breitzman@wpafb.af.mil

MS73Development of Computational Algorithms for Ma-terials Simulation and Design

Supported first by NSF-ITR then by the NSF-IUCRC cen-ter for computational materials design, we have workedon a number of mathematical and algorithmic issues thatare related to efficient and multiscale simulation of vari-ous physical processes such as nucleation and coarseningduring phase transformations. In this talk, we will dis-cuss some of our recent works, including the developmentof algorithms for predicting critical nuclei morphology inanisotropic elastic solids, the study of coarsening kineticsof a mixture with disparate mobility and the uncertaintyquantification and statistical assessment of database usedfor material property optimization.

Qiang DuPenn State UniversityDepartment of Mathematicsqdu@math.psu.edu

Jingyan ZhangDepartment of Mathematics, Penn State Universityj zhang@math.psu.edu

Lei ZhangDepartment of MathUniversity of California, Irvine,zhangl4@uci.edu

Long-qing ChenDepartment of Materials Science and EngineeringPennsylvania State Universitylqc3@psu.edu

Zikui LiuDepartment of Materials Science and EngineeringPenn State Universitydr.liu@psu.edu

MS73The Role of SIAM As An Advocate for the Math-ematical Science Community

This presentation will describe the efforts of SIAM to ad-vocate for the interests of the mathematical sciences com-munity with policy makers and funding agencies, includingthe activities of the SIAM Committee for Science Policy.The presentation will also detail ways in which the SIAMmembership can participate in this effort.

Reinhard LaubenbacherVirginia BioinformaticsInstitutereinhard@vbi.vt.edu

MS73Materials Genome: An Opportunity for AppliedMathematics and Computational Science

The recent Materials Genome Initiative seeks to acceleratethe process between materials discovery and their indus-trial application. In this talk we highlight problems wherecomputational science and mathematics can play a role inmaterials innovation and development.

Robert P. LiptonDepartment of MathematicsLouisiana State Universitylipton@math.lsu.edu

MS74Staggered Discontinuous Galerkin Method forWave Transmission Between Dielectric and Meta-materials

Some electromagnetic materials exhibit, in a given fre-quency range, effective dielectric permittivity and/or mag-netic permeability which are negative. In the literature,they are called negative index materials, left-handed ma-terials or meta-materials. We propose a staggered discon-tinuous Galerkin method to solve a wave transmission be-tween a classical dielectric material and a meta-material.Convergence of the numerical method is proven, with thehelp of explicit inf-sup operators, and numerical examplesare provided to show the efficiency of the method.

Eric ChungThe Chinese University of Hong KongDepartment of Mathematicstschung@math.cuhk.edu.hk

MS74HDG Methods for Wave Propogation

We describe the devising and analysis of the so-called hy-bridizable discontinuous Galerkin method for the acousticequation in the time-continuous domain. The method pro-vides optimal approximations for the velocity, the gradi-ent and the original scalar unknown. A superconvergenceproperty of the velocity allows us to obtain a new approxi-mation to the original scalar unknown converging with oneadditional order.

Bernardo CockburnSchool of MathematicsUniversity of Minnesotacockburn@math.umn.edu

MS74Eulerian Gaussian-beams in the Viscosity Sensefor Multidimensional Schrodinger Equation in theSemi-classical Regime

We design an Eulerian Gaussian-beam method for theSchrodinger equation in the semi-classical regime, wherethe Planck constant is small. The method is constructedfrom a leading-order WKBJ ansatz for the quantum wavefunction, where the phase and the amplitude satisfy aneikonal and a transport equation respectively. The trans-port equation is weakly coupled to the eikonal equation inthe sense that one must first solve the eikonal equation toprovide related coefficients for the transport equation. Weuse a high-order numerical scheme to evolve the set of equa-tions to get a highly efficient and accurate approximation

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of the Schrodinger equation in multidimensions.

Susana SernaDepartment of MathematicsUniversitat Autonoma de Barcelonaserna@mat.uab.es

MS74Is a Curved Flight Path in SAR Better than aStraight One?

We study the simplified model of Synthetic Aperture Radarimaging: recovery of singularities of a function in the planeby knowing integrals along circles centered at a given curve(the flight path). If the curve is a straight line, the symme-try about it cannot be resolved. It has been suggested thata curved flight path might be better to break the symmetry.We show that in some sense (local measurements), a curvedpath is not better but a closed (and of course, curved) pathoffers some advantages. Our approach is based on wavepropagation methods and provides constructive algorithmsfor reconstruction in some cases. This is a joint work withGunther Uhlmann.

Plamen StefanovPurdue Universitystefanov@math.purdue.edu

MS75Investigating through Optimal Control of ParabolicPDEs: Does Movement Toward a Better ResourceBenefit a Population?

We investigate optimal control of the convective coefficientin parabolic parabolic partial differential equation, mod-eling a population with nonlinear growth. This work ismotivated by the question: Does movement toward a bet-ter resource environment benefit a population? Results onexistence, uniqueness, and characterization of the optimalcontrol will be presented along with numerical illustrations.This work is in collaboration with Tuoc Phan and HeatherFinotti.

Suzanne M. LenhartUniversity of TennesseeDepartment of Mathematicslenhart@math.utk.edu

MS75Stabilization of Wave Equations with WentzellBoundary Conditions

I will discuss uniform feedback stabilization of wave equa-tions subject to second-order boundary conditions. Bothdynamic (Wentzell) and static (higher derivatives in spaceonly) boundary conditions will be considered. It will beshown how a combination of a partially localized bound-ary feedback and a partially localized collar feedback leadsto uniform energy decay rates. The analysis combinesweighted energy methods for observability of Neumann-type wave problems and differential-geometric techniquesfor proving stability of waves on compact manifolds.

Marcelo CavalcantiUniversidade Estadual de MaringaBrazilmmcavalcanti@uem.br

Irena M. Lasiecka

University of Virginiail2v@virginia.edu

Daniel ToundykovUniversity of Nebraska-Lincolndtoundykov2@unl.edu

MS75Asymptotic Behavior in a 2-allele Genetic Modelwith Population Control

The standard model for the evolution of the densities ofthe three genotypes aa, aA, and AA is ∂ρaa/∂t −∆ρaa =r[2ρaa + ρaA]2/2[ρaa + ρaA + ρAA] − τaaρaa ∂ρaA/∂t −∆ρaA = 2r[2ρaa+ρaA][2ρAA+ρaA]/2[ρaa+ρaA+ρAA]−τaaρaa ∂ρAA/∂t−∆ρAA = r[2ρAA + ρaA]2/2[ρaa + ρaA +ρAA] − τAAρaa,where the parameters are constants. It has recently beenshown by Souplet and Winkler that in the heterozygoteintermediate case τaa ≥ τaA ≥ τAA, τaa > τAA the genefraction u := [2ρaa + ρaA]/2[ρaa + ρaA + ρAA] convergesto 0. However, the proof in the biologically interesting casedepends on the fact that ρAA converges to infinity, which,as the authors pointed out, makes the model unrealistic.We produce a large class models of the above form with thebirth rate r replaced by a density-dependent function andno terms dropped which have the property that when thepopulation lives in a bounded domain with impenetrableboundary and its initial conditions satisfy some reasonableconditions, then as the time approaches infinity, the popu-lation densities converge uniformly to those of a constantequilibrium in which the allele a is absent.

Hans WeinbergerSchool of MathematicsUniversity of Minnesotahfw@math.umn.edu

MS75Quasi-Stationary Limit and Landau-Lifshitz Equa-tions Without Exchange Energy

In this paper we study a dynamic model of Landau-Lifshitzequations in ferromagnetism that do not include exchangeenergy. The weak solution to such an equation is obtainedas the quasi-stationary limit of a simple coupled Maxwellsystem when dielectric permittivity approaches zero. Wepresent a new direct proof of this quasi-stationary limitresult and also establish a finite-time local L2-stability re-sult and thus the uniqueness for the weak solutions withbounded initial data.

Baisheng Yan, Wei DengDepartment of MathematicsMichigan State Universityyan@math.msu.edu, dengwei@msu.edu

MS76Quadratic Sum of Squares Relaxations

We consider the question of minimizing a quadratic ob-jective function over a real variety described by quadraticequations. This problem is NP-hard in general. We givenecessary and sufficient conditions in terms of Lagrangemultipliers under which the first sum of squares relaxationis exact, assuming attainment of both the SOS relaxationand the original objective. We apply the theorem when theobjective is squared Euclidean distance to a point, where

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we see that these methods can effectively tackle image re-construction problems in computer vision which motivatedthis work.

Chris AholtUniversity of Washingtonaholtc@uw.edu

MS76Positive Gorenstein Ideals

I will explain how positive Gorenstein ideals arise naturallyfrom the dual cone to the cone of sums of squares. Thestructure of these ideals provides a new tool for addressingquestions of nonnegative polynomials and sums of squares.I will present applications in algebraic geometry, analysisand optimization. In particular there is a simple proof ofHilbert’s result on representation of ternary forms as sumsof squares of rational functions.

Greg BlekhermanUniversity of California, San Diegogreg@math.gatech.edu

MS76Algebraic Structure in Optimization

Solving polynomial optimization problems is known to be ahard task in general. In order to turn the recently emergedrelaxation paradigms into efficient tools for these optimiza-tion questions it is necessary to exploit further structurewhenever presented in the problem structure. In this talkwe will focus on the situation of optimization problems thatare given by symmetric polynomials in order to highlightseveral approaches to take advantage of symmetry. Thetechniques presented in the talk will also give a better un-derstanding of the cones of symmetric sums of squares andsymmetric non negative forms and the symmetric mean in-equalities associated to these. In particular, we will showthat in degree four, symmetric mean inequalities are char-acterized by sum of squares decomposition.

Cordian B. RienerUniversity of Konstanz, Germanyriener@math.uni-frankfurt.de

MS76Regularization Methods for SDP Relaxations inLarge Scale Polynomial Optimization

In this talk, we discuss how to solve semidefinite pro-gramming relaxations for large scale polynomial optimiza-tion. When interior-point methods are used, only small ormoderately large problems could be solved. Here we useregularization methods on semidefinite programming withblock structures, and significant bigger problems could besolved on a regular computer, which is almost impossibleby interior point methods. The performance is tested onvarious numerical examples. Some numerical issues arealso discussed.

Li WangUniversity of California, San DIegoliw022@math.ucsd.edu

Jiawang NieUniversity of California, San Diegonjw@ucsd.edu

MS77A Continuous Multilevel Solver for the Vertex Sep-arator Problem

Given an undirected graph G, the vertex separator prob-lem is to find the smallest number of nodes whose removaldisconnects the graph into disjoint subsets A and B, whereA and B are subject to size constraints. We will show howthis problem can be formulated as a continuous quadraticprogram. We use the QP as a local processor in a multi-level scheme for solving large scale instances of the prob-lem. Computational results will be presented.

James T. Hungerford, William W. HagerUniversity of FloridaDepartment of Mathematicsfreerad@ufl.edu, hager@ufl.edu

Ilya SafroArgonne National Laboratorysafro@mcs.anl.gov

MS77An Exact Algorithm for Graph Partitioning basedon Quadratic Programming

Abstract not available at time of publication.

Dzung PhanIBMphandu@us.ibm.com

MS77Exact Combinatorial Branch-and-bound for GraphBisection

We present a novel exact algorithm for the minimum graphbisection problem, whose goal is to partition a graphinto two equally-sized cells while minimizing the numberof edges between them. Our algorithm is based on thebranch-and-bound framework and, unlike most previousapproaches, it is fully combinatorial. We present strongerlower bounds, improved branching rules, and a new de-composition technique that contracts entire regions of thegraph without losing optimality guarantees. In practice,our algorithm works particularly well on instances with rel-atively small minimum bisections, solving large real-worldgraphs (with tens of thousands to millions of vertices) tooptimality.

Daniel Delling, Andrew GoldbergMicrosoft Research Silicon Valleydadellin@microsoft.com, goldberg@microsoft.com

Ilya RazenshteynLomonosov Moscow State Universityilyaraz@gmail.com

Renato F. WerneckMicrosoft Corporationrenatow@microsoft.com

MS77Multi-Level Edge Separator Using a HybridCombinatorial-Quadratic Programming Approach

The graph partitioning problem arises in a variety of sci-entific and engineering domains such as VLSI design, com-

80 AN12 Abstracts

puter networking, parallel computing, and sparse directmethods. In this talk, we discuss the edge separator graphpartitioning problem and present an algorithm which com-bines aspects of multi-level combinatorial methods with aquadratic programming formulation. We discuss a novelstrategies for both graph coarsening and refinement withthe goal of producing high quality cut sets.

Nuri YeralanUniversity of Floridanuriatuf@gmail.com

Timothy A. DavisUniversity of FloridaComputer and Information Science and EngineeringDrTimothyAldenDavis@gmail.com

MS78The Geometry of Interpolation Error Estimates forIsogeometric Analysis

Barycentric coordinates provide a basis for linear finiteelements, and underlie the definition of higher-order ba-sis functions for shape and isogeometric analysis, i.e. theBezier triangle in computer aided-design, together with in-terpolation and shading techniques in computer graphicsand optimal convergence rates in isogeometric analysis.The versatility of this construction has led to barycen-tric coordinates for more general shapes; the resultingfunctions are called generalized barycentric coordinates(GBCs). GBCs while unique over triangles, have mul-tiple definitions for convex polygons with four or moresides, namely Harmonic (H), Wachspress(W), Sibson (S)and Mean Value (MV) coordinates. Interpolation prop-erties of H, W, S and MV have a complex dependenceon polygonal geometry. W exhibits the subtleties of ge-ometrical dependence: if the polygon contains interior an-gles near 180 degrees, gradients of the coordinates becomevery large. S and MV avoid this problem. In this talk weprove that given certain conditions on the geometry of thepolygon, each of H, W, S and MV can obtain optimal in-terpolation convergence estimates, and hence suitable forisogeometric analysis.

Chandrajit BajajComputer Science, ICES, CVCThe University of Texas - Austinbajaj@cs.utexas.edu

Alex RandThe University of Texas - Austinarand@ices.utexas.edu

Andrew GilletteUniversity of California, San DiegoDepartment of Mathematicsakgillette@mail.ucsd.edu

MS78Analysis Aware Representations, Parameteriza-tions, and Models

Isogeometric Analysis (IA) has been proposed as a method-ology for bridging the gap between Computer Aided De-sign (CAD) and Finite Element Analysis (FEA). In orderto support design and full 3D IA, new ab initio designmethods must create suitable representations and approxi-mation techniques must include parameterization method-ologies for volumes. This presentation discusses some of

the challenges in moving from current representations anddatafitting techniques towards this goal and demonstratesinitial results and analyses.

Elaine CohenUniversity of Utahcohen@cs.utah.edu

MS78Applications of Isogeometric Analysis at Boeing

Isogeometric analysis at Boeing has a surprisingly long his-tory. Univariate applications using B-splines as finite ele-ments have existed since the late 1980s, with numerousapplications. The essence of isogeometric analysis – usinga fixed parameter space to formulate a family of problems– was employed in an aeroelastic tool in the late 1990s.That application entailed solving boundary integral equa-tions for a family of surfaces, requiring a form of bivariateisogeometric analysis. We will explore those and futureBoeing applications of this exciting technology.

Michael A. EptonBoeingepton@redwood.rt.cs.boeing.com

Thomas A. GrandineApplied MathematicsThe Boeing Companythomas.a.grandine@boeing.com

MS78Solid T-spline Construction from Boundary Repre-sentations

We present a novel method to construct solid rational T-splines for complex genus-zero geometry from boundaries.We first build a parametric mapping between the triangu-lation and a unit cube. After that we adaptively subdividethe cube using an octree subdivision, pillow the subdivi-sion result one layer on the boundary, and use templates tohandle extraordinary nodes. The obtained solid T-splineis C2-continuous except for the local region around eachextraordinary node.

Yongjie ZhangDepartment of Mechanical EngineeringCarnegie Mellon Universityjessicaz@andrew.cmu.edu

MS79Posterior Rates of Contraction for Sparse BayesianModels

Sparse inverse covariance matrix modeling is an importanttool for learning relationships among different variables ina Gaussian graph. Most existing algorithms are based on1 regularization, with the regularization parameters tunedvia cross-validation. In this talk, a Bayesian formulation ofthe problem is proposed, where the regularization parame-ters are inferred adaptively and cross-validation is avoided.Variational Bayes (VB) is used for the model inference. Re-sults on simulated and real datasets validate the proposedapproach. In addition, a graph extension algorithm is pro-posed to include a new variable in an existing graph, whichcan be used when separate testing data are available.

Larry CarinElectrical & Computer Engineering

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Duke Universitylcarin@ee.duke.edu

MS79Clustering and Embedding of High-DimensionalMulti-Manifold Data using Sparse Representation

In many problems across different areas of science and en-gineering, we are dealing with massive collections of high-dimensional data. Having thousands and millions of di-mensions, the data often lie in or close to low-dimensionalstructures, called manifolds. Separating the data into theunderlying low-dimensional models and finding compactrepresentations for them is one of the most fundamentalproblems in the high-dimensional data analysis. We ad-dress the problem of clustering and embedding of the dataon multiple manifolds using sparse representation tech-niques. We use the collection of the data points as a self-expressive dictionary in which each point can be efficientlyrepresented as a sparse combination of a few other pointsfrom the same manifold with appropriate weights that en-code locality information. We propose a convex optimiza-tion program whose solution is used in a spectral graph the-ory framework to infer the clustering and embedding of thedata. When the manifolds correspond to low-dimensionalsubspaces, we show that under appropriate conditions onthe principal angles between the subspaces and the distri-bution of the data, the solution of the proposed convexprogram recovers the desired solution. We demonstratethe effectiveness of the proposed algorithm through exper-iments on several real-world problems.

Ehsan ElhamifarDepartment of Electrical and Computer EngineeringJohns Hopkins Universityehsan@cis.jhu.edu

Rene VidalDepartment of Biomedical EngineeringJohns Hopkins Universityrvidal@cis.jhu.edu

MS79Poisson Tensor Factorization for Sparse CountData

In data mining and analysis, we often encounter data thatis indexed by three or more indices. Tensor factorizationscan be used for such ”multidimensional” data and havealready found application in a variety of fields, includinghigh-dimensional function approximations, signal process-ing, chemometrics, multi-attribute graph analysis, imagerecognition, and more. We consider the problem of ten-sor factorizations for sparse count data. For example, wemight have a collection of email messages and arrange themby sender, receiver, and date; the data is sparse becausenot all potential senders and receivers communicate andeven those that do communicate do not necessarily do soevery day. Typically, we would fit a tensor factorizationmodel to data by minimizing the least squares differencebetween the data and the tensor factorization model. Sta-tistically speaking, we have assumed that the random vari-ation is best described by a Gaussian distribution. Wepropose, however, that the random variation may be bet-ter described via a Poisson distribution because the countobservations (especially the zeros) are more naturally ex-plained. Under this Poisson assumption, we can fit a modelto observed data using the negative log-likelihood score,also known as Kullback-Leibler divergence. We discuss an

alternating optimization approach and propose solving thesubproblem using a majorization-minimization approachthat yields multiplicative updates. In fact, the methodwe propose is a generalization of the Lee-Seung multiplica-tive updates but has the advantage of being faster andalso having provable convergence even for solutions on theboundary (i.e., with zeros in the factorization). Moreover,we show how to prevent the algorithm from converging tonon-stationary points (i.e., fixing the problem of gettingstuck at undesirable zero values). We will show severalexamples to demonstrate the utility of the approach.

Tamara G. KoldaSandia National Laboratoriestgkolda@sandia.gov

Eric ChiHuman Genetics DepartmentUCLAecchi@ucla.edu

MS79Performance Limits of Non-local Means

In this talk I describe a novel theoretical characterizationof the performance of non-local means (NLM) for noise re-moval. NLM has proven effective in a variety of empiricalstudies, but little is understood fundamentally about howit performs relative to classical methods based on waveletsor how various parameters (e.g., patch size) should be cho-sen. For cartoon images and images which may containthin features and regular textures, the error decay ratesof NLM are derived and compared with those of linear fil-tering, oracle estimators, variable-bandwidth kernel meth-ods, Yaroslavskys filter and wavelet thresholding estima-tors. The trade-off between global and local search formatching patches is examined, and the bias reduction asso-ciated with the local polynomial regression version of NLMis analyzed. The theoretical results are validated via simu-lations for 2D images corrupted by additive white Gaussiannoise. This is joint work with Ery Arias-Castro and JosephSalmon.

Ery Arias-CastroUCSDeariasca@ucsd.edu

Joseph SalmonDuke Universityjs415@duke.edu

Rebecca WillettElectrical and Computer EngineeringDuke Universitywillett@duke.edu

MS80Local Pointwise a posteriori Gradient ErrorBounds for the Stokes Equations

We consider the standard Taylor-Hood finite elementmethod for the stationary Stokes system on polyhedraldomains. We prove local a posteriori error estimates forthe maximum error in the gradient of the velocity field.Because the gradient of the velocity field blows up nearre-entrant corners and edges, such local error control isnecessary when pointwise control of the gradient error isdesirable. Computational examples confirm the utility of

82 AN12 Abstracts

our estimates in adaptive codes.

Alan DemlowUniversity of KentuckyDepartment of Mathematicsdemlow@ms.uky.edu

Stig LarssonDepartment of Mathematical Sciences ChalmersUniversityof Technology and University of Gothenburgstig@chalmers.se

MS80Mixed Finite Elements for the Coupling of FluidFlow with Porous Media Flow

In this talk we a introduce mixed finite element method forthe coupling of fluid flow with porous media flow. Flowsare governed by the Stokes and Darcy equations, respec-tively, and the corresponding transmission conditions aregiven by mass conservation, balance of normal forces, andthe Beavers-Joseph-Saffman law. We consider mixed for-mulations in both the Stokes domain and the Darcy re-gion, which yields the introduction of the traces of theporous media pressure and the fluid velocity as suitableLagrange multipliers. Then, considering generic finite ele-ment spaces with some technical conditions, we apply theBabuska-Brezzi theory together with a classical result onprojection methods for Fredholm operators of index zeroto show stability, convergence, and a priori error estimatesfor the associated Galerkin scheme. Finally, we generalizethe previous results and introduce a mixed finite elementmethod for the coupling of fluid flow with nonlinear porousmedia flow.

Gabriel N. GaticaDIM and CI2MAUniversidad de Concepcionggatica@ing-mat.udec.cl

Ricardo OyarzuaUniversidad de Concepcionroyarzua@math.ubc.ca

Francisco J. SayasDept. Mathematical SciencesUniversity of Delawarefjsayas@math.udel.edu

MS80A Space-Time Hybridizable DiscontinuousGalerkin (HDG) Method for Incompressible Flowson Deforming Domains

We present the first space-time HDG finite element methodfor the incompressible Navier-Stokes and Oseen equations.Major advantages of a space-time formulation are its ex-cellent capabilities of dealing with moving and deformingdomains and grids and its ability to achieve higher-orderaccurate approximations in both time and space by simplyincreasing the order of polynomial approximation in thespace-time elements.

Sander RhebergenUniversity of MinnesotaSchool of Mathematicssrheberg@umn.edu

Bernardo CockburnSchool of MathematicsUniversity of Minnesotacockburn@math.umn.edu

MS81Math modeling as the core of Applied Math under-graduate Curricula

Abstract not available at time of publication.

Jeffrey HumpherysBrigham Young Universityjeffh@math.byu.edu

MS82Manycore-portable Multidimensional Arrays forFinite Element Computations

Performance-portability to multicore-CPU and manycore-accelerator (e.g., GPGPU) devices is a significant chal-lenge due to device-specific programming models and per-formance characteristics. The Kokkos multidimensionalarray library uses C++ template meta-programming toprovide performance-portable multidimensional array datastructures and data parallel algorithm dispatch capabil-ities (e.g., parallel-for and parallel-reduce). These datastructures and dispatch capabilities are demonstrated bycompiling and executing the same finite element mini-application codes on NUMA multicore-CPU (Intel andAMD) and GPGPU manycore-accelerator (NVIDIA) de-vices.

H. Carter Edwards, Daniel SunderlandSandia National Laboratorieshcedwar@sandia.gov, dsunder@sandia.gov

MS82Asynchronous, Performance-portable KrylovMethods on Accelerators

In this presentation we discuss our efforts to use theTrilinos/Kokkos multi-dimensional array package to writeportable generic code implementing the GMRES iterativemethod. Performance results from several distinct plat-forms are presented.

Kurtis L. NusbaumUIUCklnusbaum@gmail.com

MS82Auto-Tuned Hybrid Asynchronous Krylov Itera-tive Eigensolvers on Petascale Supercomputers

Asynchronous hybrid parallel Krylov co-methods, suchas the Multiple Explicitly Restart Arnoldi Method(MERAM), are well adapted for Petascale supercomput-ing. Each ERAM may exploit all parallelism of a largenumber of processors and asynchronously exchange Ritzelements with the other concurrent methods. Each ERAMmay have a dedicated restart strategy to accelerate theconvergence to different eigensubspaces. We study the or-chestration of different strategies with respect to severaldistributions along the ERAM methods. We propose tooverview these strategies and to evaluate experimentallytheir efficiencies on a Petascale computer. As a conclusion,we propose an algorithm to auto-tune these strategies and

AN12 Abstracts 83

we discuss the first results.

Jerome DuboisCEA-DENjerome.dubois@cea.fr

Serge G. PetitonCNRS/LIFL and INRIAserge.petiton@lifl.fr

Christophe CalvinCEA-Saclay/DEN/DANS/DM2S/SERMA/LLPRchristophe.calvin@cea.fr

France BoillodCNRS/LIFLfrance.boillod-cerneux@cea.fr

MS82Retrofitting a Production Sparse Linear AlgebraLibrary for Accelerators

The Trilinos Epetra package provides most of the cur-rent production quality matrix and vector services forother Trilinos packages. Although new packages haveemerged (Tpetra and Kokkos) to fundamentally addressthe next generation of computing needs, especially sup-port for emerging architectures, there is merit in providingsome support for new architectures in Epetra. In this talkwe discuss efforts to retrofit Epetra with support for accel-erators, highlighting design constraints and benefits of theeffort.

Benjamin SeefeldtSt John’s Universitybdseefeldt@csbsju.edu

MS83Spatio-temporal Dynamics of 2009 A/H1N1 In-fluenza

We provide a quantitative description of the age-specificand regional 2009 A/H1N1 pandemic incidence patterns inMexico and Peru. We analyze the geographic spread ofthe pandemic waves and their association with the winterschool closing periods, demographic factors, and absolutehumidity. Our results indicate substantial regional varia-tion in pandemic pattern and highlight the importance ofschool cycles on the transmission dynamics of pandemicinfluenza.

Gerardo ChowellMathematical Modeling and AnalysisLos Alamos National Laboratorygchowell@asu.edu

MS83Game Theory and Vaccination with a Network Epi-demiology Approach

Abstract not available at time of publication.

Ariel Cintron-AriasDepartment of Mathematics and StatisticsEast Tennessee State Universitycintronarias@mail.etsu.edu

MS83The Implications of Different Probability DensityFunctions for Disease Stages from Sir Epidemiolog-ical Models on the Effectiveness of Public HealthInterventions

Quantifying the uncertainty attributed to the assumedprobability density functions for disease stages from SIRepidemiological models is crucial. Hence, the lack of itmight leads to i) limited statements with respect to thenet effectiveness of intervention strategies or ii) proposingthe implementation of inadequate or non-optimal interven-tion strategies and thus, these might increase the risks ofhigh mortality and morbidity and misguide public healthpolicy and decision makers. We illustrated that these as-sumptions quantitatively matter greatly.

Emmanuel J. Morales-ButlerSchool of Human Evolution and Social ChangeArizona State Universityemmanuel.m.b@gmail.com

MS83Modeling the Effect of Hospital Acquired Infec-tions in the Outcomes of Neurosurgical Patients

Abstract not available at time of publication.

Miriam NunoDepartment of NeurosurgeryCedars Sinai Medical Centermiriamucla@gmail.com

MS84Title Not Available at Time of Publication

Abstract not available at time of publication.

Eray AydilChemical Engineering and Materials ScienceUniversity of Minnesotaaydil@umn.edu

MS84Atomic Properties Database Development andMining for Materials Genome Applications

Exploiting correlations between materials macroscopicproperties and atomic properties of their constituents isat the heart of materials informatics whose main goal is tosignificantly reduce the time to unravel materials with de-sirable properties. We have initiated a series of studies toexplore such correlations by using data mining techniques.This talk will summarize these studies and address specif-ically the questions: How to build the needed databasesand how to use them effectively?

Da GaoDepartment of Computer Science and EngineeringUniversity of Minnesotadagao2008@gmail.com

Yousef SaadDepartment of Computer ScienceUniversity of Minnesotasaad@cs.umn.edu

James R. Chelikowsky

84 AN12 Abstracts

Institute for Computational Engineering and SciencesUniversity of Texas at Austinjrc@ices.utexas.edu

MS84Renewable Polymers for a Sustainable Future

Polymers are essential to myriad technologies we encounterevery day. Over the past century an immense and highlyintegrated knowledge base has evolved that guides the ma-nipulation of petroleum feedstocks, the design of polymer-ization catalysts, and the resulting structure - propertyrelationships in a small set of relatively simple homopoly-mers. Yet the production and disposal of these prod-ucts presents inescapable environmental challenges that arecostly to correct at a minimum and unsustainable in thelong term. In response to a global mandate for sustain-ability, the development of alternatives based on renew-able feedstocks such as carbohydrates, plant oils, and ter-penes is of central importance. Realizing the tremendousmarket potential for bio-based materials hinges on creatingnew fundamental chemistry-based foundations upon whichan industry can be established. Many known sustainablehomopolymers have inadequate property profiles to meetthe application requirements of modern polymeric mate-rials. Researchers in the Center for Sustainable Polymers(CSP) at the University of Minnesota (UMN) are estab-lishing a comprehensive knowledge base that enables theefficient and economical conversion of natural and abun-dant molecules into tomorrows advanced polymeric mate-rials. Members of the CSP blend efforts in polymer design,monomer synthesis, polymerization catalysis, architectureand morphology control, and polymer property optimiza-tion to establish the basic scientific tenants for innovativerenewable resource polymer technologies. A key and uni-fying concept in the CSP is that multiple renewable com-ponents, properly integrated into a single material, willyield tunable properties not achievable with either simplehomopolymers or blends, which have dominated the renew-able polymer industry to date.

William B. TolmanDepartment of ChemistryUniversity of Minnesotawtolman@umn.edu

MS84Mesoscale Description of Defected Materials

A mesoscale description is necessary for a quantitative de-scription of defected materials, including microstructureevolution. Not only they naturally incorporate defect solu-tions, but they also permit numerical computation on thediffusive time scales that are appropriate for overdampeddefect motion. We describe the general methods involvedin the derivation and validation of such models, and applythem to grain boundary motion and pinning.

Jorge VinalsSchool of Physics and AstronomyUniversity of Minnesotavinals@umn.edu

MS85Coverage Statistics for Sequence Census Methods

I will illustrate how to view fragments produced in ahigh-throughput sequencing experiment as a set of dis-

crete points in the plane. This collection of points formsa two-dimensional spatial Poisson process, which yields anull model for random fragment coverage. After givingan overview of this model, I will show how the successivejumps of the depth coverage function can be encoded asa random tree. This discrete, probabilistic theory can po-tentially be of use in a wide variety of sequence censusmethods. Two specific applications will be presented: analgorithm for finding protein binding sites using ChIP-Seqdata and a statistical test to address fragment bias in RNA-Seq data.

Valerie HowerUniversity of California, Berkeleyvhower@math.miami.edu

MS85Some New Combinatorial Problems from RNA

In the Fall of 2011, I taught a graduate-level topics courseon Combinatorial Computational Biology of RNA. Therewere eleven grad students in the class, and they had diversebackgrounds and research areas. Our goal was to learnsome of the mathematical results and techniques from thepast decade and to pinpoint future research problems. Inthose regards, it was quite successful. I will summarizesome of the main themes of the area as well as outline somenew ideas and directions that a few graduate students fromthe class are currently pursuing in their research.

Matthew MacauleyMathematical SciencesClemson Universitymacaule@clemson.edu

MS85Non-parametric Species Delimitation Based onBranching Rates

Many probabilistic tests have been developed to delimitspecies based on the coalescent model. These computa-tional efforts rely primarily on parametric models that tryto account for known variance found in genetic processes.Unfortunately, this variance is difficult to model precisely.Using non-parametric tests, we develop a method to de-lineate species by estimating the time species change fromgrowth (e.g., Yule models) to a coalescence process with-out constraining the processes to a particular model. Usingsimulated gene trees from a known species tree, we com-pare our non-parametric method to established parametricmethods.

Edward RoualdesStatisticsUniversity of Kentuckyedward.roualdes@uky.edu

MS85Reverse Engineering of Regulatory Networks UsingAlgebraic Geometry

Discrete models have been used successfully in modeling bi-ological processes such as gene regulatory networks. Whencertain regulation mechanisms are unknown it is impor-tant to be able to identify the best model with the avail-able data. In this context, reverse engineering of finitedynamical systems from partial information is an impor-tant problem. In this talk we will present a framework andalgorithm to reverse engineer the possible wiring diagrams

AN12 Abstracts 85

of a finite dynamical system from data. The algorithmconsists on using an ideal of polynomials to encode all pos-sible wiring diagrams, and choose those that are minimalusing the primary decomposition. We will also show thatthese results can be applied to reverse engineer continuousdynamical systems.

Alan Veliz CubaMathematicsUniversity of Nebraska- Lincolnaveliz-cuba2@unl.edu

MS86Acceleration of a Multiple Scattering High Fre-quency Iterative Method

A recent high frequency analysis of the Neumann seriesin the context of multiple scattering configurations showsthat the rate of convergence converges to 1 when the dis-tance separating scatterers converge to 0. This impairs theKrylov-subspace based iterative method that was designedespecially to deal with this kind of problems. We proposea preconditioner based on the Kirchhoff approximation toimprove this iterative solver.

Yassine BoubendirDepartment of Mathematical Sciencesboubendi@njit.edu

MS86A Fast Iterative Method for Solving the EikonalEquation on Triangular and Tetrahedral Domainsusing GPUs

In this talk we presents an efficient, fine-grained parallel al-gorithm for solving the Eikonal equation on unstructuredtriangular and tetrahedral meshes. The Eikonal equa-tion, and the broader class of Hamilton-Jacobi equationsto which it belongs, have a wide range of applications fromgeometric optics and seismology to biological modeling andanalysis of geometry and images. The ability to solve suchequations accurately and efficiently provides new capabili-ties for constructing solutions on large grids, exploring andvisualizing parameter spaces, and for solving inverse prob-lems that rely on such equations in the forward model.Efficient solvers on state-of-the-art, parallel architecturesrequire new algorithms that are not, in many cases, opti-mal, but are better suited to synchronous updates of thesolution and constrained memory access patterns. In thistalk we address some particular challenges associated with2D and 3D unstructured meshes, in order to extend the fastiterative method to solve the Eikonal equation efficiently ontwo-dimensional triangular and three-dimensional tetrahe-dral domains on parallel architectures, including graphicsprocessors. We propose a new local update scheme whichprovides solutions of first-order accuracy on both serial andparallel architectures, and extend that scheme to the caseof inhomogeneous, anisotropic speed functions. We alsopropose two novel update schemes and their correspondingdata structures for efficient irregular data mapping to par-allel, SIMD processors. We provide detailed descriptionsof the implementations on a single CPU, a multicore CPUwith shared memory, and SIMD architectures, with com-parative results against state-of-the-art Eikonal solvers.

Mike KirbyUniversity of UtahSchool of Computingkirby@cs.utah.edu

MS86High Frequency Wave Propagation with Geomet-rical Optics and Beyond

We propose a new method by combining the geometri-cal optics and Huygens-Kirchhoff identities to numericallysolve the Helmholtz equation with single point-source con-dition in high frequency regime. Data compression withChebyshev expansions and random sampling based pseu-doskeleton approximations are applied to make the wave-field reconstruction efficient. The new approach is efficientand has no pollution effects. And it can reconstruct wave-fields for a set of source points and a band of high frequen-cies.

Songting Luo, Jianliang QianDepartment of MathematicsMichigan State Universityluos@math.msu.edu, qian@math.msu.edu

MS86Efficient Computation of the Semi-Classical Limitof the Schroedinger Equation

An efficient method for simulating the Schroedinger equa-tion near the semiclassical limit is presented. It uses atransformation based on Gaussian wave packets and yieldsa Schroedinger type equation ammenable to computationin the semi-classical limit. The number of grid pointsneeded is small enough that computations in dimensionsof up to 4 or 5 are feasible without the use of any ba-sis thinning procedures. This is joint work with GiovanniRusso.

Peter SmerekaDepartment of MathematicsUniversity of Michiganpsmereka@umich.edu

MS87Discretization of Integral Operators on Compli-cated Surfaces

I will describe an efficient method for the numerical eval-uation of the singular integrals which arise in the dis-cretization of weakly singular integral operators on sur-faces. Standard techniques for evaluating these integrals,while adequate in simple cases, become prohibitively ex-pensive when applied to integral operators given on com-plicated surfaces. The scheme I will describe, by contrast,is largely insensitive to the geometry of the underlying sur-face.

James BremerUC Davisbremer@math.ucdavis.edu

MS87Integral Equation Methods for Unsteady StokesFlow in Two Dimensions

We present an integral equation formulation for the un-steady Stokes equations in two dimensions. This problemis of interest in its own right, as a model for slow viscousflow, but perhaps more importantly, as an ingredient inthe solution of the full, incompressible Navier-Stokes equa-tions. Using the unsteady Green’s function, the velocityevolves analytically as a divergence-free vector field. Thisavoids the need for either the solution of coupled field equa-

86 AN12 Abstracts

tions (as in fully implicit PDE-based marching schemes) orthe projection of the velocity field onto a divergence freefield at each time step (as in operator splitting methods).In addition to discussing the analytic properties of the op-erators that arise in the integral formulation, we describea family of high-order accurate numerical schemes and il-lustrate their performance with several examples.

Shidong JiangDepartment of Mathematical SciencesNew Jersey Institute of Technologyshidong.jiang@njit.edu

MS87Boundary Integral Methods for Inextensible Vesi-cle Dynamics in Two Dimensions

A boundary integral method for simulating inextensiblevesicles in a 2D viscous fluid was developed by Veerapa-neni et. al. Recent extensions include developing precondi-tioners, implementing a near-singular integration strategy,allowing for vesicles with different bending moduli, andincoporating the Fast Multipole Method. The goal is todevelop a robust method to simulate high concentrationsof vesicles.

Bryan D. QuaifeInstitute for Computational Engineering and SciencesUniversity of Texas at Austinquaife@ices.utexas.edu

George BirosUniversity of Texas at Austinbiros@ices.utexas.edu

MS87Fast, High-order Accurate Methods for EvaluatingLayer Heat Potentials

We will describe a new fast algorithm for evolving the ”his-tory part” of the heat potentials. It overcomes some ofthe limitations of previous fast algorithms and lowers thecomplexity constants. We will also discuss a new recur-sive product integration to overcome the ”geometricallyinduced stiffness” of the heat potentials. The new schemeis arbitrary-order accurate and in particular, we presentresults that exhibit 16th order convergence for evaluat-ing layer potentials on time-dependent boundaries. Thisis joint work with Lesle Greengard, Shidong Jiang andGeorge Biros.

Shravan VeerapaneniCourant InstituteNew York Universityshravan@umich.edu

MS88Modeling Tear Films, Contact Lenses and Evapo-ration

We explore thin film models for the tear film on a humaneye in the presence of a porous contact lens. We are in-terested in pre-lens and post-lens tear film dynamics. Ourmodel assumes that the contact lens remains wetted uponevaporation of the pre-lens tear film and allows for contin-ued evaporation from an exposed contact lens. Treatmentof the post-lens film as a squeeze layer is also discussed.

Daniel M. Anderson

Department of Mathematical SciencesGeorge Mason Universitydanders1@gmu.edu

Matt GerhartGeorge Mason Universitymgerhart@masonlive.gmu.edu

MS88A Comparison of Numerical Methods for Modelsof Thin Liquid Films

Together, experiments, analytical solutions and numericalsimulations have advanced our fundamental understandingof the motion of thin liquid films. The models involve par-tial differential equations that are tractable by several nu-merical approaches; there is no agreed-upon best scheme.Many mathematicians write their own code for numericalsimulations. Open source code is uncommon. I will re-view pros and cons of a variety of numerical approaches tothin films problems and discuss possibilities for open sourcecode.

Rachel LevyHarvey Mudd Collegelevy@math.hmc.edu

MS88Settling of a Contact Lens

When a contact lens is placed in the eye, it is fit onto thecornea by the action of the blink. The upper lid appliesa normal force on the lens deforming it and squeezing thetear film out between the lens and cornea. To better un-derstand the fit performance, we model coupled fluid andsolid mechanics of the settling of a soft contact lens duringa blink.

Kara L. MakiInstitute for Mathematics and its ApplicationsUniversity of Minnesotakmaki@rit.edu

David S. RossRochester Institute of Technologydsrsma@rit.edu

MS88New Models of Two-phase Flow in Porous Media

Plane waves for two phase flow in a porous medium aremodeled by the one-dimensional Buckley-Leverett equa-tion, a scalar conservation law. We analyze stability ofsharp planar interfaces to two-dimensional perturbations,which involves a system of partial differential equations.Linear stability analysis results in a criterion that distin-guishes between stable and unstable interfaces. Numericalsimulations of the full nonlinear system of equations, in-cluding dissipation and dispersion, illustrate the analyticalresults.

Michael ShearerMathematicsNC State Universityshearer@ncsu.edu

Kim SpaydNC State University

AN12 Abstracts 87

krspayd2@ncsu.edu

Zhengzheng HuDepartment of MathematicsNorth carolina State Universityzhu4@ncsu.edu

MS89Approximation on Non-Cartesian Lattices

For applications such as visualization in higher dimensionsnon-Cartesian uniform lattices outperform the Cartesianlattice. I will present a generic framework that extendspopular approximation methods, such as B-splines, fromthe Cartesian lattice to uniform non-Cartesian lattices.

Mahsa MirzargarUniversity of Floridasmahsa@cise.ufl.edu

MS89Box-Splines on Crystallographic Lattices

The talk characterizes families of symmetric box-splinesthat are natural analogues of tensor-product B-splines, butthat are shift-invariant on other crystallographic latticesthat appear in nature, such as the BCC and FCC latticesand their generalizations. In particular, the talk summa-rizes the basic properties for computational use: the poly-nomial degree, the continuity, the linear independence ofshifts on the lattice and optimal quasi-interpolants for fastapproximation of fields.

Jorg PetersUniversity of Floridajorg@cise.ufl.edu

Minho KimSchool of Computer ScienceUniversity of Seoulminhokim@uos.ac.kr

MS89Patterns in Free Form Architecture and DiscreteDifferential Geometry

Contemporary architecture generates a stunning variety ofnew designs and patterns which are based on freeform ge-ometry. These patterns are often closely related to theactual fabrication, for example in panel layouts and sup-porting structures. In this talk, the speaker will address themathematical concepts behind some recent developments,which are closely linked to discrete differential geometryand concern circle patterns, geodesic patterns and patternsformed by support structures and shading systems.

Helmut PottmannKing Abdullah University of Sciencehelmut.pottmann@kaust.edu.sa

MS89Shape Space Exploration of Constrained Meshes

In geometry processing, meshes are often specified by a col-lection of non-linear constraints, typically associated withmesh faces or edges. Exploring the corresponding shapespace, i.e., the possible meshes sharing the same combi-

natorics while satisfying the constraints, are widely be-lieved to be challenging. In this talk, I will present ageneral method to locally characterize any shape space ofmeshes implicitly prescribed by a collection of non-linearconstraints and how to navigate the desirable subspaces.

Yongliang Yang, Yijun YangKing Abdullah University of Science and Technologyyongliang.yang@kaust.edu.sa, yijun.yang@kaust.edu.sa

Helmut PottmannKing Abdullah University of Sciencehelmut.pottmann@kaust.edu.sa

Niloy MitraKing Abdullah University of Science and Technologyniloy.mitra@kaust.edu.sa

MS90Learning to Classify HSI

We present a sparse modeling framework for sub-pixel map-ping that mitigates the effects of noise, spectral variability,and spectral mixing by learning material dictionaries, anda spatialspectral coherence regularizer. Experiments withsynthetic and real data demonstrate the suitability of themethod. This technique retains high-performance classifi-cation accuracy when dealing with reconstructed data fromundersampled images. Finally, we apply this technique forHSI-LiDAR fusion. Work in collaboration with ZhengmingXing, John Greer, Edward Bosch, and Lawrence Carin.

Guillermo SapiroUniversity of MinnesotaDept Electrical & Computer Engineeringguille@umn.edu

Alexey CastrodadNGA and the University of Minnesotaalexey.castrodad@nga.mil

MS90Classification of Hyperspectral Images by Varia-tional Methods

Hyperspectral classification methods have often focused onthe wealth of spectral information available in each pixel.However, the incorporation of spatial information can alsogreatly aid in object identification. We will discuss theadaptation of variational segmentation methods, primarilydesigned for grayscale and color imagery, to the segmenta-tion of hyperspectral data. We also show that multi-phasesegmentation finds a natural extension into the high di-mensions of hyperspectral data.

Alex ChenSAMSI/University of North Carolina at Chapel Hillachen@samsi.info

MS90Social Network Clustering of High DimensionalSparse Data

Data mining is the mathematics, methodologies and proce-dures used to extract knowledge from large datasets. Spec-tral embedding uses eigenfunctions of a Laplace operator(or related graph affinity matrix) for extracting the under-lying global structure of a dataset. This talk will give an in-

88 AN12 Abstracts

troduction to spectral embeddings. Applications presentedwill include clustering LA street gang members based onsparse observations of where and who they are seen with.

Blake HunterUCLA Mathematics Departmentblakehunter@math.ucla.edu

Yves van GennipUCLAyvgennip@math.ucla.edu

MS90Robust Computation of Linear Models

Consider a dataset of vector-valued observations that con-sists of a modest number of noisy inliers, which are ex-plained well by a low-dimensional subspace, along with alarge number of outliers, which have no linear structure.We describe a convex optimization problem that can re-liably fit a low-dimensional model to this type of data.When the inliers are contained in a low-dimensional sub-space we provide a rigorous theory that describes when thisoptimization can recover the subspace exactly. We also for-mulate an efficient algorithm for solving this optimizationproblem and demonstrate its effectiveness with numericalexperiments.

Gilad LermanSchool of MathematicsUniversity of Minnesotalerman@umn.edu

Michael McCoyCaltechmccoy@caltech.edu

Joel TroppCMSCaltechjtropp@cms.caltech.edu

Teng ZhangInstitute for Mathematics and its ApplicationsUniversity of Minnesotazhang620@umn.edu

MS91Determinants of Successful Cancer Therapy withCytokine-expressing Oncolytic Viruses

Oncolytic viruses selectively infect and destroy tumorswhile largely sparing healthy cells. Many of today’s mostpromising oncolytic viruses express cytokines which inducean immune attack against the tumor. Here, we systemat-ically develop deterministic mathematical models describ-ing the therapeutic mechanism. For model validation, weleverage in vivo measurements illustrating the antitumoreffects of several cytokine-armed oncolytic adenoviruses inmelanoma cells. We present our modeling approach andpreliminary findings regarding the mathematical basis fortumor elimination.

Joseph J. CrivelliCornell UniversitySchool of Medicinejjc2004@med.cornell.edu

Peter S KimSchool of Mathematics and StatisticsUniversity of Sydneyp.kim@maths.usyd.edu.au

Joanna R WaresDepartment of Math and Computer ScienceUniversity of Richmondjwares@richmond.edu

MS91The Role of Biomechanics in the Early Develop-ment of Breast Cancer: A Hybrid Model

We investigated the role of microenvironment in an earlydevelopment of Ductal carcinoma in situ (DCIS) and theinvasion process in later stages. DCIS is an early stage non-invasive breast cancer that originates in the epithelial liningof the milk ducts, but it can evolve into comedo DCIS andultimately the most common type of breast cancer, inva-sive ductal carcinoma. Understanding the progression andhow to effectively intervene in it presents a major scientificchallenge. The extracellular matrix (ECM) surroundinga DCIS tumor contains several types of cells and severaltypes of growth factors that are known to individually af-fect tumor growth. However, the complex biochemical andmechanical interactions of stromal cells with tumor cellsis poorly understood. The model can predict how per-turbations of the local biochemical and mechanical stateinfluence tumor evolution via cross-talk between a tumorand stromal cells such as fibroblasts. We first focus onthe EGF-TGFbeta signaling pathways and show how cellgrowth and proliferation can be affected by up- or down-regulation of components in these pathways. We present ahybrid model for the interaction of cells with the tumor mi-croenvironment (TME), in which epithelial cells (ECs) aremodeled individually while the ECM is treated as a con-tinuum, and show how these interactions affect the earlydevelopment of tumors. We then present an invasion modelwhere stromal cells play a significant role in triggering theinvasion process. Our results shed light on the interactionsbetween growth factors, mechanical properties of the ECM,and feedback signaling loops between stromal and tumorcells, and suggest how epigenetic changes in transformedcells affect tumor progression in the early and late stage ofbreast cancer.

Yangjin KimUniversity of Michigan, USAahyouhappy@konkuk.ac.kr

Hans G. OthmerUniversity of MinnesotaDepartment of Mathematicsothmer@math.umn.edu

MS91Modeling Preventative Breast Cancer Vaccines us-ing an Agent-based Approach

A next generation approach to breast cancer treatment fo-cuses on developing preventative vaccinations to stimulatea person’s immune system to attack incipient tumors beforeclinical detection. Relevant cell interactions would takeplace on the scale of several thousands of cancer cells. Tounderstand dynamics at this small scale, we develop anagent-based model of anti-tumor immune responses thataccounts for cell size, cell crowding near the microtumor,

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and the possibility of stochastic tumor elimination.

Peter S. KimUniversity of UtahDepartment of Mathematicspkim@maths.usyd.edu.au

Peter LeeCity of Hope Cancer Centerplee@coh.org

MS91Traveling Waves in a Model of Tumor Angiogenesis

In this talk, we will discuss traveling wave solutions for achemotaxis model with logarithmic sensitivity, which de-scribes the initiation of angiogenesis. The challenges ofanalyzing traveling wave solutions of such type of chemo-taxis model lie in the high dimensionality and the singu-larity. Hence the routine approaches, such as phase planeanalysis, no longer work. In the talk, we shall show thesechallenges can be resolved by variable transformations,suchthat the transformed system can be solved by the regularapproaches. The existence, wave speed and stability oftraveling wave solutions will be discussed and open ques-tions will be presented.

Zhian WangDepartment of Applied MathematicsHong Kong Polytechnic Universitymawza@polyu.edu.hk

MS92The Extended Combinatorial Inverse EigenvalueProblem

Let S(G) be the set of all real symmetric n × n matricescorresponding to a graph G on n vertices. We investigatethe problemGiven G, a vertex v of G, and 2n − 1 realnumbers

λ1 ≥ µ1 ≥ λ2 ≥ µ2 ≥ · · · ≥ λn−1 ≥ µn−1 ≥ λn,

is there a matrix A ∈ S(G) such that λ1, λ2, ..., λn are theeigenvalues of A and µ1, . . . , µn−1 are the eigenvalues ofA(v)?A complete solution can be found for a few graphson n vertices.

Wayne BarrettBrigham Young Universitywayne@math.byu.edu

John Sinkovic, Curtis Nelson, Nicole Malloy, WilliamSexton, Robert Yang, Anne LazenbyDepartment of MathematicsBrigham Young Universityjohnsinkovic@gmail.com, curtisgn@gmail.com,nicolea.malloy@gmail.com, wnsexton@gmail.com, talent-edbread@hotmail.com, alazenberry@gmail.com

MS92Zero Forcing, Minimum Rank, and Applications toControl of Quantum Systems

We study the dynamics of systems on networks from a lin-ear algebraic perspective. Under appropriate conditions,there is a connection between the quantum (Lie theoretic)property of controllability and the linear systems (Kalman)

controllability condition. We investigate how the graphtheoretic concept of a zero forcing set impacts the control-lability property. In particular, we prove that if a set of ver-tices is a zero forcing set, the associated dynamical systemis controllable. Joint work with Burgarth, DAlessandro,Severini, Young.

Leslie HogbenIowa State University,American Institute of Mathematicshogben@aimath.org

MS92Lower Bounds for Minimum Semidefinite Rank

The minimum semidefinite rank (msr) of a graph is theminimum rank among positive semidefinite matrices withthe given graph. The OS-number is a useful lower boundfor msr, which arises by considering ordered vertex setswith some connectivity properties. In this talk we presenttwo new interpretations of the OS-number. We first showthat OS-number is also equal to the maximum number ofvertices which can be orthogonally removed from a graphunder certain nondegeneracy conditions. Our second in-terpretation of the OS-number is as the maximum possi-ble rank of chordal supergraphs who exhibit a notion ofconnectivity we call isolation-preserving. These interpre-tations not only give insight into the OS-number, but alsoallow us to prove some new results. For example we showthat msr(G) = |G| − 2 if and only if OS(G) = |G| − 2.

Sivaram NarayanDepartment of MathematicsCentral Michigan Universitynaray1sk@cmich.edu

MS92Positive Semidefinite Zero Forcing

The positive semidefinite zero forcing number of a graph,Z+(G), is a variant of the (standard) zero forcing numberof a graph, Z(G), which uses the same definition with adifferent color change rule. The positive semidefinite zeroforcing number was introduced as an upper bound for pos-itive semidefinite maximum nullity. This talk will discussproperties of Z+(G) and positive semidefinite zero forcingsets. Joint work with Ekstrand, Erickson, Hall, Hay, Hog-ben, Johnson, Kingsley, Osborne, Peters, Roat, Ross, Row,Warnberg.

Michael YoungIowa State Universitymyoung@iastate,edu

MS93Assessing Beliefs and Content Knowledge in FirstSemester Biocalculus

Many colleges and universities struggle with finding waysto meet the quantitative needs of their biology and lifescience majors. Here I will share my experiences in thedevelopment and implementation of a first semester cal-culus course for biology majors. I will discuss assessmentof student beliefs and attitudes about mathematics pre-and post-biocalculus, their performance as compared tostudents in traditional calculus, and the similarities anddifferences in their styles of learning mathematics.

Hannah L. Callender

90 AN12 Abstracts

Institute for Mathematics and its ApplicationsUniversity of Minnesotacallende@up.edu

MS93Calculus II for Biology Students

Abstract not available at time of publication.

David GammackMarymount Universitydgammack@marymount.edu

MS93Introducing Quantitative Thinking into an Intro-ductory Biology Curriculum

Introducing quantitative thinking in introductory biologyclasses presents challenges from students and instructors.To address these, we have identified quantitative conceptsthat support introductory biology concepts; designed tu-torials and exercises placing them in biological contexts;designed an instrument to assess the effectiveness of thisapproach; and piloted the approach in a small section ofintroductory biology. This work is supported by a grant tothe University of Arizona from the Howard Hughes MedicalInstitute (52006942).

Susan HesterUniversity of Arizonasdhester@email.arizona.edu

Lisa Elfring, Lisa NagyArizona State UniversityMolecular and Cellular Biologyelfring@email.arizona.edu, lnagy@email.arizona.edu

MS93A New Quantitative Modeling Course for First-year Biology Students

In the last few decades biological and medical fields haveundergone a profound transformation into data-driven,quantitative sciences. The standard calculus courses whichtraditionally constitute the quantitative training for biol-ogy majors do not adequately prepare students for theseneeds. A new course developed at the University ofChicago takes the place of the last course in the requiredcalculus sequence. It combines mathematical modeling,computational implementation, and basic statistics, all ap-plied to specific biological and medical problems. I willpresent the results of assessments, both of student learningand of their evaluations of the course effectiveness.

Dmitry A. KondrashovUniversity of Chicagodkon@uchicago.edu

MS94Multi-precision Inner/outer Solvers via GenericProgramming Libraries

Multi-precision and mixed-precision techniques combineinefficient high-precision types with efficient low-precisiontypes in order to provide fast and high-precision solvers andpreconditioners. Traditional approaches typically utilize ahigh precision solver preconditioned using a lower precisionsolve, but modern generic programming techniques allow

researchers and pracitioners a rich set of possibilities, in-cluding deep recursive solves and mixed-precision primi-tives. We demonstrate hybrid-parallel multi-precision iter-ative linear and eigenvalue solvers using the generic pro-gramming library support in Trilinos.

Christopher G. BakerOak Ridge National Laboratorybakercg@ornl.gov

MS94Design and Development of Sustainable Librariesfor Numerical Computation on Many Core Archi-tectures

The new supercomputers have millions of cores intercon-nected hierarchically by high-speed networks. The hierar-chic and massive parallelism present in these architecturesimply that the numerical libraries have to be defined ac-cording to an adequate design model and the existing oneswould have to be adapted to this design. In this talk, wepresent a model for numerical library allowing reusabilityand sustainability. Some experiments on large scale many-core platforms validating the approach will be presented.

Nahid EmadUniversity of Versailles, PRiSM LaboratoryNahid.Emad@prism.uvsq.fr

Makarem DandounaUniversity of Versaillesmakarem.dandouna@prism.uvsq.fr

MS94Incorporation of Multicore FEM Integration Rou-tines into Scientific Libraries

We have developed a system for integration of the finiteelement residual and Jacobian arising from a given weakform. This system is based upon the Ignition code gen-eration package and ideas from the FEniCS project, andgenerates code targeting GPUs. Since this is merely a partof the overall PETSc library framework, we discuss the de-sign decisions made in order to incorporate these routineswith a minimum of user input, generation of debuggablecode, and smooth integration into the PETSc build pro-cess.

Matthew G. KnepleyUniversity of Chicagoknepley@ci.uchicago.edu

Andy TerrelTexas Advanced Computing CenterUniversity of Texasaterrel@tacc.utexas.edu

MS94Cray Scientific Library for Accelerators

We will present Cray Scientific Libray for accelerators de-signed for Cray XK family. This library provides thesame interface of the original BLAS and LAPACK thatcan be executed on accelerators and CPUs together. Forthe performance enhancement, we have applied an auto-adaptation mechanism to select the best implementationfor different problem size, type of host memory allocation

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and data location. These features deliver immediate speedup for existing applications with relatively light coding ef-forts.

Keita Teranishi, Adrian TateCray Inc.keita@cray.com, adrian@cray.com

MS95Resilience of Small Social Networks with MultipleRelations

The ability of a network to retain a given property underperturbation of its structure is referred to as resilience. Wefocus on the resilience of small social networks with multi-ple types of relations. Here, we describe the multirelationalstructure as a partially ordered semigroup, represented byits Hasse diagram. We discuss qualitative differences be-tween networks with connected and disconnected Hasse di-agrams, and we illustrate the resilience formulation with anumber of empirical examples.

Taniecea ArceneauxMathematicsPrinceton UniversityTAArceneaux@gmail.com

MS95Matroidal Branchwidth

Abstract not available at time of publication.

Illya HicksTexas A&M Universityivhicks@rice.edu

MS95Price Optimization under the Nested Logit ModelWith Multiple No-Purchase Options

We consider a pricing problem under the Nested LogitModel in which nests represent agencies acting as amal-gamators of product offerings from several firms, ratherthan being wholly controlled by a single firm. We considera revenue maximization problem from the perspective of asingle firm utilizing n channels and show that the optimalrevenue can be obtained by an iterative procedure whichadjusts prices sequentially over each nest.

William Z. RayfieldOperations Research and Information EngineeringCornell Universitywzr2@cornell.edu

Paat RusmevichientongMarshall School of BusinessUniversity of Southern Californiapaat.rusmevichientong@usc.edu

MS95Optimal Toll Design: A Lower Bound Frameworkfor the Traveling Salesman Problem

We propose a framework of lower bounds for the asymmet-ric traveling salesman problem based on approximating thedynamic programming formulation, and give an economicinterpretation wherein the salesman must pay tolls as hetravels between cities. We then introduce an exact reformu-

lation that generates a family of successively tighter lowerbounds, all solvable in polynomial time, and compare thesenew bounds to the well-known Held-Karp bound.

Alejandro TorielloIndustrial and Systems EngineeringUniversity of Southern Californiatoriello@usc.edu

MS96Eulerian Approaches for Transmission TraveltimeTomography with Discontinuous Slowness

We propose an Eulerian approach for transmission trav-eltime tomography with discontinuous slowness. The ap-proach is to minimize the mismatch between the measure-ments and the Eulerian solutions of the eikonal equation.To accurately incorporate the contributions from discon-tinuity in the slowness, we propose a level-set formula-tion to describe the discontinuity in the velocity model.This results in a shape recovery problem. In the first partof the talk, we match only the first arrivals from pointsources. Even though the algorithm is computationally ef-ficient, such approach discards all information from laterarrivals. In the second part of the talk, we consider us-ing multivalued Eulerian traveltime solutions. We proposea novel algorithm to compute such multivalued solutionsof the eikonal equation without doing any computation inthe phase space. Preliminary numerical results will also begiven.

Wenbin LiDepartment of Mathematics,Hong Kong University of Science and Technologylwb@ust.hk

MS96Simulation of Light Waves in Large Scale PhotonicCrystal Devices

Photonic crystals (PhCs) are periodic structures with a pe-riod on the scale of the wavelength of light. Devices can becreated in a PhC by introducing various types of defectsand they are usually connected by waveguides that serve asinput and output ports. A large scale PhC device may havea length scale that is much larger than the wavelength. Wepresent some techniques for simulating lightwaves in PhCdevices. These techniques can take advantage of the exis-tence of many identical unit cells, the partial periodicity ofthe structure and the locality of some nonlinear processes,etc.

Ya Yan LuCity University of Hong KongDept of Mathematicsmayylu@cityu.edu.hk

MS96Unformization of WKB Solutions via WignerTransform

We propose a renormalization process of a two phase WKBsolution, which is based on an appropriate surgery of localuniform asymptotic approximations of the Wigner trans-form of the WKB solution. We explain in details how thisprocess provides the correct spatial variation and frequencyscales of the wave field on the caustics where WKB methodfails. The detailed analysis is presented in the case of a fun-damental problem, that is the semiclassical Airy equation,

92 AN12 Abstracts

which arises from the model problem of acoustic propaga-tion in a layer with linear variation of the sound speed.

George MakrakisDepartment of Applied MathematicsUniversity of Cretemakrakg@iacm.forth.gr

MS96Randomized Structured Direct Solvers for SeismicProblems

We consider the solution of 2D and 3D inhomogeneousacoustic wave equation in the frequency domain, by solv-ing Helmholtz equations via a new set of structured ma-trix methods. Randomized techniques are used to facilitatethe structured matrix operations. The advantages of suchsolvers include: 1. For a single frequency, all solution stepsshare a common Helmholtz operator, which can be quicklyfactorized so as to solve linear systems with multiple right-hand sides, each in nearly linear time and storage. Wetake advantage of certain hidden rank structures in theoperators. 2. For different frequencies, the same adjacencypattern is used, so that only one step of matrix ordering isneeded. 3. The factorizations are relatively insensitive tothe frequencies. We try to justify such insensitivity. Theefficiency and accuracy are demonstrated by various impor-tant numerical examples, such as 2D (BP2004 & BP2007TTI) and 3D (SEAM) models. This is joint work withMaarten V. de Hoop, Xiaoye S. Li, and Shen Wang.

Jianlin XiaDepartment of MathematicsPurdue Universityxiaj@math.purdue.edu

MS97Fast Computation of Eigenfrequencies of PlanarDomains via the Spectrum of the Neumann-to-Dirichlet Map

We present a new method for the spectrum and eigenfunc-tions of a planar star-shaped Dirichlet domain. It is ‘fast’since it is computes a cluster of eigenfunctions (number-ing of order the square-root of the eigenvalue) with theeffort usually taken to find a single one. For a domain 400wavelengths across, and relative error 10−10, the resultingspeed-up is ∼ 103. Its error analysis is rigorous, and itachieves higher-order accuracy than the ‘scaling method’.I will also discuss a new technique for evaluation of poten-tial fields close to their source curves.

Alexander H. BarnettMathematics DepartmentDartmouth Collegeahb@math.dartmouth.edu

Andrew HassellAustralian National Universityandrew.hassell@anu.edu.au

MS97A Fast Direct Solver for Non-oscillatory IntegralEquations

We present a fast direct solver for non-oscillatory integralequations via multilevel matrix compression and sparsematrix embedding. For boundary integral equations in 2D,

the solver has optimal O(N ) complexity, where N is thesystem size; in 3D, it incurs an O(N/∈) precomputationcost, followed by O(N logN ) solves. Numerical experi-ments suggest the utility of our method as a direct solver,a generalized fast multipole method, and as a precondi-tioner for complex problems.

Kenneth L. HoCourant Instituteho@courant.nyu.edu

Leslie GreengardCourant InstituteNew York Universitygreengard@courant.nyu.edu

MS97Fast Methods for Boundary Integral Equations onthe Sphere

Models describing physical or biological phenomena con-strained to evolve on subsurfaces of compact manifolds canbe reformulated in terms of integral equations. Examplesof such models include point vortices moving on the sur-face of the earth, or polar-driven chemotactic migrationon cell membranes during mitosis. The use of integralequation strategies in this context is fairly new, and re-quires a careful examination of the relevant parametricesfor the elliptic operator of concern. In this talk we firstdescribe reformulations of a boundary value problem forthe Laplace-Beltrami operator in terms of layer potentials.We then describe a class of fast methods based on the fastmultipole method.

Nilima NigamDept. of MathematicsSimon Fraser Universitynigam@math.sfu.ca

Mary-Catherine KropinskiSimon Fraser Universitymkropins@math.sfu.ca

MS97Mathematical and Numerical Aspects of the Adap-tive Fast Multipole Poisson-Boltzmann Solver

We present recent progress on the development of the adap-tive fast multipole Poisson-Boltzmann solver. We brieflyreview previous efforts on integral equation reformulation,mesh generation and discretization, and new versions of thefast multipole methods. We introduce our recent progresson parallelization based on the dynamic prioritization tech-nique for large-scale problems and on-going work on time-marching schemes for long-time simulations.

Jingfang HuangDepartment of MathematicsUniversity of North Carolina, Chapel Hillhuang@amath.unc.edu

Bo ZhangDuke Universityzhangb@cs.duke.edu

Xiaolin ChengOak Ridge National Laboratorychengx@ornl.gov

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Benzhuo LuInstitute of Computational Mathematics, Chinabzlu@lsec.cc.ac.cn

Nikos PitsianisDepartment of Electrical and Computer EngineeringAristotle Universitynikos.p.pitsianis@duke.edu

Xiaobai SunDepartment of Computer ScienceDuke Universityxiaobai@cs.duke.edu

J. Andrew McCammonHoward Hughes Medical InstituteUniversity of California, San Diegojmccammo@ucsd.edu

MS98Undergraduate Research on the Fast Track: FromNothing to Publication in Eight Weeks

Since Summer 2010, we have been hosting the REU Site:Interdisciplinary Program in High Performance Comput-ing. It introduces undergraduate students to scientific, sta-tistical, and parallel computing with MPI and conducts re-search with application scientists from industry, academia,and government agencies in only eight weeks. We will shareour experiences of how to make this program work throughteam work and by involving several layers of support fromgraduate students to faculty, with lessons that are usefulfor anyone interested in running an REU Site.

Matthias K. GobbertUniversity of Maryland, Baltimore CountyDepartment of Mathematics and Statisticsgobbert@umbc.edu

Nagaraj NeerchalDepartment of Mathematics and StatisticsUniversity of Maryland, Baltimore Countynagaraj@umbc.edu

MS98Building An Applied and Computational Math De-gree Program from the Ground Up

We are developing a new undergraduate degree programin applied and computational mathematics, scheduled tocommence Fall 2013. Each year, this major will admit a co-hort of up to 40 students into a two-year lock-step curricu-lum commencing at the beginning of their junior year andcontinuing through to graduation. This carefully plannededucational experience will provide students with a tightlyintegrated combination of coursework and computer labs,together with a capstone project and close mentoring.

Jeffrey HumpherysBrigham Young Universityjeffh@math.byu.edu

MS98Models for Undergraduate Research, Best Prac-tices, and Questions

This talk will highlight some successful models that fac-ulty have used to foster undergraduate research, some best

practices that have emerged, and some questions that re-main.

Jennifer PearlDivision of Mathematical SciencesNational Science Foundationjslimowi@nsf.gov

MS98Multidisciplinary Undergraduate Researchin Computational Mathematics and Nonlinear Dy-namics of Biological, Bio-inspired and EngineeringSystems

In this talk, we will describe a multidisciplinary under-graduate research program in computational mathematicsand nonlinear dynamics of biological, bio-inspired and en-gineering systems that has not only helped to enhance on-going interaction among communities of people includingstudents, educators and academicians, but also serve as acatalyst to help reinforce and drive reform across the insti-tution.

Padmanabhan SeshaiyerGeorge Mason Universitypseshaiy@gmu.edu

MS99Mapping the Connectome with Convex AlgebraicGeometry

The human brain connectome project seeks to provide acomplete map of neural connectivity. Just as the humangenome represents a triumph of marrying technology (highthroughput sequencers) with theory (dynamic program-ming for sequence alignment), the human connectome isthe result of a similar union. The technology is that ofdiffusion magnetic resonance imaging while the requisitetheory, we shall argue, comes from a combination of har-monic analysis and convex algebraic geometry.

Lek-Heng LimUniversity of Chicagolekheng@galton.uchicago.edu

Thomas SchultzMax Planck Institute for Intelligent Systemstschultz@tuebingen.mpg.de

MS99Klein’s Idea and Identities for Powers of Polynomi-als

In his famous book on the icosahedron, Felix Klein con-sidered the identification of a point on the unit sphere u,with the linear form x− vy, where v is the image of u un-der the Riemann map. If you start with the vertices of anice polytope inscribed in the sphere, and take quadraticforms corresponding to products of linear forms associatedwith antipodal pairs of vertices, you get interesting setsof quadratic forms. For example, the octahedron corre-sponds to xy, x2 − y2, x2 + y2 (the Pythagorean parame-terization), the cube to four quadratic forms whose 5-thpowers are dependent and the icosahedron to six quadraticforms whose 14-th powers are dependent. We’ll give moreexamples and try to explain this phenomenon.

Bruce ReznickUniversity of Illinois, Urbana-Champaign

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reznick@math.uiuc.edu

MS99Linearization Functors on Real Convex Sets

We prove that linearizing certain families of polynomialoptimization problems leads to new functorial operationsin real convex sets. We show that under some conditionsthese operations can be computed or approximated in waysamenable to efficient computation. These operations areconvex analogues of Hom functors, tensor products, sym-metric powers, exterior powers and general Schur functorson vector spaces and lead to novel constructions even forpolyhedra.

Mauricio VelascoUniversidad de los Andesmvelasco@uniandes.edu.co

MS99A Sums of Squares Relaxation for HyperbolicityCones

Hyperbolic programming a useful generalization ofsemidefinite programming. Here we will investigate therelationship between them. Using derivative cones, I willgive an inner approximation of a hyperbolicity cone usingsums of squares. In particular, this will give an inner ap-proximation of the hyperbolicity cone by the feasible set ofan SDP. As a bonus, this relaxation is exact for hyperbolicpolynomials already coming from an SDP.

Cynthia VinzantUniversity of California, Berkeleyvinzant@umich.edu

Daniel PlaumannUniversity of Konstanz, Germanydandaniel.plaumann@uni-konstanz.de

MS100Spline Operators for Subdivision and Differentia-tion

The discrete derivatives of a Bezier curve are known to con-verge to the continuous derivative under subdivision. Soafter a sufficient number of subdivisions one can obtain a‘good’ approximation of the derivative. Here a tight errorbound for this approximation is derived and the numberof subdivisions required for a prescribed error tolerance iscalculated. This is done considering the subdivision algo-rithm as an operator acting on the control points of thecurve.

Hugh CassidyUniversity of Connecticuthugh.cassidy@huskymail.uconn.edu

MS100The Case Against Interactivity in Geometric De-sign

Interactive geometric design tools are now a firmly en-trenched means of building geometric models suitable forproduct definition and engineering analysis. Such toolshave seemingly been a boon to mechanical engineering andproduct design worldwide, and it is hard to imagine a mod-

ern design shop in which such tools don’t play a vital role.

Thomas A. GrandineApplied MathematicsThe Boeing Companythomas.a.grandine@boeing.com

MS100Knot Theorems and Counterexamples for Splines

For piecewise linear approximation of spline curves, it iswell-known that repeated subdivision produces a controlpolygon that converges to the spline under the Hausdorffmetric. Little has been shown about the relationship oftopological properties between the control polygon and itsspline curve. We i) provide sufficient conditions for sub-division to yield a control polygon ambient isotopic to thecurve, and ii) show examples of topological differences be-tween a spline and its control polygon.

Thomas PetersUniversity of Connecticuttpeters@cse.uconn.edu

MS100Volume Rendering Verification Using Discretiza-tion Errors Analysis

Much recent research has been dedicated to direct volumerendering (DVR). In disciplines such as image-based med-ical diagnosis or material science, images generated usingDVR require high accuracy and precision. Unfortunately,little research has been dedicated to assess volume ren-dering correctness. We propose a technique for volumerendering verification based on an analysis of the volumerendering integral. We apply order-of-accuracy and con-vergence analysis - well-established verification techniques- to volume rendering implementations, and derive the the-oretical foundations of our verification approach.

Tiago Etiene QueirozNew York Universitytiago.etiene@gmail.com

MS101Non-modal Amplification of Disturbances in Chan-nel Flows of Viscoelastic Fluids: A Possible Routeto Elastic Turbulence?

Abstract not available at time of publication.

Satish KumarChemical Engineering and Materials ScienceUniversity of Minnesotakumar030@umn.edu

MS101Title Not Available at Time of Publication

Abstract not available at time of publication.

Thomas PenceMichigan State UniversityDepartment of Mechanical Engineeringpence@egr.msu.edu

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MS101Regularized Two-phase Models for Gels

Abstract not available at time of publication.

Longhua ZhaoUniversity of Minnesotalzhao@math.umn.edu

MS1022-Matching Covered Loopy Graphs

A 1, 2-factor is a spanning subgraph consisting of pair-wise vertex disjoint edges and cycles. Tutte has character-ized graphs which have a 1, 2-factor. We investigate min-imal 2-matching covered graphs, i.e. graphs in which everyedge is in some 1, 2-factor and removal of any edge yieldsa graph without this property. We will discuss some classesof minimally 2-matching covered loopy graphs (graphs inwhich vertices may have a loop), where loops are cycle oflength one.

Adam BerlinerDepartment of MathematicsSt. Olaf Collegeberliner@stolaf.edu

Richard A. BrualdiUniversity of WisconsinDepartment of Mathematicsbrualdi@math.wisc.edu

MS102Spectrally Arbitrary Patterns over Finite Fields

A zero-nonzero pattern is a square matrix where each entryis either a zero or a star. A realization of a zero-nonzeropattern over a specified field is a matrix where each of thestars is replaced by a nonzero entry from the field. A pat-tern is said to be a Spectrally Arbitrary Pattern over thespecified field if for every monic polynomial(with degreecorresponding to the size of the matrix) with coefficientsfrom the field, there exists a realization whose character-istic polynomial is the given polynomial. We will look atthe interplay between pattern structure and field stucturein determining whether or not a pattern turns out to bespectrally arbitrary over a given field.

Judith J. McDonaldWashington State UniversityDepartment of Mathematicsjmcdonald@math.wsu.edu

MS102Minor Monotone Floors and Ceilings of Graph Pa-rameters

A graph parameter is minor monotone if it preserves theminor relation. We consider the transformation of real-valued graph parameters into related minor monotonegraph parameters using two different methods. The mi-nor monotone floor of well-ordered graph parameter p isdefined by p = minp(H)|G H with a similar def-inition for the minor monotone ceiling. We consider theminor-monotone floor and ceiling of a number of graphparameters, with particular attention given to parametersthat relate to the zero-forcing number. Results dealing

with the Hadwiger conjecture are also considered.

Thomas MilliganDepartment of Mathematics and StatisticsUniversity of Central Oklahomatmilligan1@uco.edu

MS102A Colin de Verdiere-type Invariant and odd-K4-and odd-K2

3 -free Signed Graphs

A signed graph is a pair (G,Σ) where G is an undi-rected graph (we allow parallel edges, but no loops) andΣ ⊆ E(G). A cycle C of G is called odd if C has anodd number of edges in common with Σ. A signed graph iscalled bipartite if it has no odd cycles. We have introducedν(G,Σ), which generalizes the Colin de Verdiere invariantν(G). The invariant ν characterizes bipartite signed graphsas those signed graphs (G,Σ) with ν(G,Σ) ≤ 1, and signedgraphs with no odd-K4- and no odd-K2

3 -minor as thosesigned graphs (G,Σ) with ν(G,Σ) ≤ 2. In this talk we willdiscuss these results. Joint work with Marina Arav, FrankHall, and Zhongshan Li.

Hein van der HolstDepartment of MathematicsGeorgia State Universityhvanderholst@gsu.edu

MS103Dynamic Density Functional Theory (DDFT)Model for Freezing of a Pair Potential Fluid: TheEffect of Fluid Flow

The Classical Density Functional Theory (CDFT) and thePhase Field Crystal (PFC) models have proven to be goodapproaches to model crystal growth from a fluid phase.These models capture atomic level details including defectsand grain boundaries. However these approaches usuallyinvolve a phenomenological gradient descent based timeevolution. and do not take the convection of the fluid phase(fluid flow) into consideration. In this work we start withthe Revised Enskog Theory (RET) (an effective kinetic the-ory) as the definition of time evolution. Then exploitingthe connection to CDFT of freezing, we develop evolutionequations for the macroscopic density and flow fields. Theover damped limit provides us a DDFT model for time evo-lution of the density field. Some studies of this model andresults on crystal growth from fluid phase will be discussed.

Arvind BaskaranInstitute for Pure and Applied Mathematics, UCLAUniversity of California, Irvinebaskaran@umich.edu

Aparna BaskaranBrandeis UniversityDepartment of Physicsaparna@brandeis.edu

John LowengrubDepartment of MathematicsUniversity of California at Irvinelowengrb@math.uci.edu

MS103Liquid Crystal Phase Transitions in Elastic Net-

96 AN12 Abstracts

works

We develop a modelling approach to anisotropic, nonlinearelasticity using ideas from the liquid crystal theory. Weconsider highly compressible elastic networks with embed-ded rigid units. The work is motivated by the structureand functionality of actin and collagen networks found ininter-connective tissue. We analyze the phase transitionbehavior of these systems under compression and shear,and found a range of nematic phases and a soft-elasticityregime, according to geometric properties of the network.

Maria-Carme CaldererDeparment of MathematicsUniversity of Minnesota, USAcalde014@umn.edu

Chong LuoOxford Universityluochong@gmail.com

MS103A General Framework for High Accuracy Solutionsto Energy Gradient Flows from Material ScienceModels

Abstract not available at time of publication.

Brian R. WettonUniversity of British ColumbiaDepartment of Mathematicswetton@math.ubc.ca

MS103Energy Stable Scheme for Phase Field Models

Abstract not available at time of publication.

Zhengfu XuMichigan Technological UniversityDept. of Mathematical Scienceszhengfux@mtu.edu

MS104Nucleation Events in Soft Condensed Matter Usingthe String Method

Within the self-consistent field theory, we develop an “on-the-fly’ string method to compute nucleation events in soft-condensed matter systems. Several applications of themethod are given, including: membrane pore formationand rupture, particle translocation, and the budding ofa micelle from a rod-like micelle. Where applicable, themethod is compared against classical nucleation theory.

Daniel AppeloDivision of Engineering and Applied ScienceCalifornia Institute of Technologyappelo@math.unm.edu

Christina TingBiochemistry and Molecular BiophysicsCalifornia Institute of Technologyclting@caltech.edu

Zhen-Gang WangCaltechzgw@cheme.caltech.edu

MS104Failure of Random Materials: Asymptotic Analysisand Importance Sampling

We study the problem of estimating small failure probabili-ties for elastic random material which is described by a onedimensional stochastic elliptic partial differential equationwith certain external force and boundary conditions. Gaus-sian random function is used to model the spatial variationof the material property parameters. The failure event ofthe bulk material is simply characterized by the exceedingof certain thresholds for the max stress or load in any spa-tial location. With the large deviation heuristics, we pro-vide a intuitive description of the most probable realizationof the random material parameters which could lead to thecritical situation of material failure in engineering. An ef-ficient Monte Carlo method to compute such probabilitiesis presented.

Jingchen Liudepartment of statisticsColumbia Universityjcliu@stat.columbia.edu

Xiang ZhouDivision of Applied MathematicsBrown Universityxiang zhou@brown.edu

MS104Sampling Transition States Using Gentlest AscentDynamics

The dynamics of complex systems often involve thermallyactivated barrier-crossing events that allow the system tomove from one basin of attraction on the energy surfaceto another. Such events are ubiquitous, but difficult tosimulate using conventional simulation tools like moleculardynamics. We present an extension of the gentlest ascentdynamics (GAD) under which the system evolves in a man-ner opposite to that of the steepest descent method.

Amit SamantaProgram in Applied and Computational MathematicsPrinceton University, Princetonasamanta@math.princeton.edu

Weinan EPrinceton UnivesityDepartment of Mathematicsweinan@math.princeton.edu

MS104Some Interacting Particle Methods for SamplingComplex Energy Landscapes

This talk will survey my efforts with coworkers to developand analyze Monte Carlo sampling algorithms for complex(usually high dimensional) probability distributions. Thesesampling problems are typically di?cult because they havemultiple high probability regions separated by low proba-bility regions and/or they are badly scaled in the sense thatthere are strong unknown relationships between variables.The dimensionality and complexity of the problems neces-sitate a Monte Carlo approach (as opposed to numericalquadrature) but standard MC schemes converge extremelyslowly in the presence of barriers or bad scalings. Newmethods designed to address these issues directly have thepotential to significantly accelerate the solution of impor-

AN12 Abstracts 97

tant problems in many areas of science. I’ll discuss somevery preliminary work on geophysical and chemical appli-cations.

Jonathan WeareUniversity of ChicagoDepartment of Mathematicsweare@math.uchicago.edu

MS105Parametric Steering for Autotuning NumericalKernels and Scientific Codes in Multicore Environ-ments

Our goal is to find a way to represent the correlationbetween different performance tuning parameters, auto-tuning techniques and understand their relevance for im-plementing different numerical kernels in multicore envi-ronments. Our goals are to find some trends in perfor-mance driving parameters and form a criteria for the case-based selection of kernels at runtime.

Leroy A. DrummondComputational Research DivisionLawrence Berkeley National LaboratoryLADrummond@lbl.gov

Serge G. PetitonCNRS/LIFL and INRIAserge.petiton@lifl.fr

Christophe CalvinCommissariat l’Energie Atomiquecalvinchristophe.calvin@cea.fr

MS105Promise Chaining for Automatic Kernel Fusion andAvoiding Data Movement on Accelerators

Performance optimizations for discrete compute accelera-tors (like GPUs) cut across computational kernels. Forexample, launching a single kernel is expensive, which mo-tivates ”fusing” multiple kernels. Moving data from the ac-celerator to the CPU is slow, which forces programmers totrack data placement. Cross-kernel optimizations clutterinterfaces, confuse algorithm developers, and hinder evolu-tion of kernel optimizations. We propose a programmingmodel that uses dataflow and promise chaining to hide dataplacement and fuse kernels automatically.

Mark HoemmenSandia National Laboratoriesmhoemme@sandia.gov

MS105Adaptation of ppOpen-AT To Numerical Kernelson Explicit Method

ppOpen-AT is an auto-tuning (AT) language for code op-timization in 5 kinds of crucial numerical methods pro-vided by ppOpen-HPC project. In this presentation, wepresent preliminary result by adapting ppOpen-AT to anumerical kernel derived by explicit method on Finite Dif-ference Method. We have developed a new AT functionon ppOpen-AT for its code optimization; loop fusion andloop split. Performance evaluation is performed by usingthe T2K Open Supercomputer (U.Tokyo) and HITACHI

SR16000/M1.

Takahiro Katagiri, Satoshi Itoh, Satoshi OhshimaThe University of Tokyokatagiri@kata-lab.itc.u-tokyo.ac.jp, sito@cc.u-tokyo.ac.jp,satoshi ohshima (ohshima@cc.u-tokyo.ac.jp

MS105ppOpen-HPC: Open Source Infrastructure for De-velopment and Execution of Large-Scale ScientificApplications with Automatic Tuning

ppOpen-HPC is an open source infrastructure for devel-opment and execution of optimized and reliable simula-tion codes with capabilities of automatic tuning (AT) onpost-peta (pp) scale parallel computers using heteroge-neous computing nodes which consist of multicore CPUsand co-processors. ppOpen-HPC consists of various typesof libraries, which covers various types of procedures forscientific computations. In this talk, current status ofppOpen-HPC and results of recent developments are de-scribed.

Kengo NakajimaThe University of TokyoInformation Technology Centernakajima@cc.u-tokyo.ac.jp

Masaki SatohAtmospheric and Ocean Research InstituteThe University of Tokyosatoh@aori.u-tokyo.ac.jp

Takashi FurumuraEarthquake Research InstituteUniversity of Tokyofurumura@eri.u-tokyo.ac.jp

Hiroshi OkudaResearch into Artifacts, Center for Engineering (RACE)The University of Tokyookuda@race.u-tokyo.ac.jp

Takeshi IwashitaAcademic Center for Computing and Media StudiesKyoto Universityiwashita@media.kyoto-u.ac.jp

Hide SakaguchiJapan Agency for Marine-Earth Science and Technologysakaguchih@jamstec.go.jp

MS106Self-assembly of Islands during the Initial Stages ofFilm Growth: Sizes and Spatial Arrangements

Atoms deposited on a flat surface at the onset of filmgrowth diffuse and aggregate into islands (whose locationsimpact subsequent multilayer film morphologies). The sizedistribution and spatial arrangement of islands reflect thestochastic nature of the self-assembly process. Mean-fieldtreatments fail to describe this behavior prompting devel-opment of alternative formalisms. We describe recent anal-ysis for the distribution of capture zones, where the surfaceis tessellated so that one capture zone surrounds each is-land.

Jim W. Evans

98 AN12 Abstracts

Ames Laboratory USDOE and Iowa State Universityevans@ameslab.gov

MS106On the Dynamics of Crystal Facets in MaterialsSurface Relaxation

Below the roughening temperature, crystal surfaces relaxthrough the motion of line defects (steps); and developmacroscopically flat surface regions (facets). A challeng-ing problem is to reconcile step motion, which is describedby discrete schemes, with a viable continuum theory, basedon variational principles and Partial Differential Equations,near facets. In this talk, I will discuss recent progress informulating and analyzing an evaporation step model thatis fully consistent with a continuum thermodynamics ap-proach.

Dionisios MargetisUniversity of Maryland, College Parkdio@math.umd.edu

Kanna NakamuraDepartment of MathematicsUniversity of Maryland, College Parknakamura@math.umd.edu

MS106Strain Dependence of Microscopic Parameters andits Effect on Ordering during Epitaxial Growth

Strain is often the driving force behind self-organization ofquantum dots and other nanoscale structures. I presenta DFT analysis of the effect of strain on key microscopicgrowth parameters. I then illustrate in growth simulationsthat employ the level-set technique how such strain depen-dence affects growth. This approach includes a variable(and strain dependent) potential energy surface for adatomdiffusion, and an additional step-edge barrier via a mixedRobin boundary condition.

Christian RatschUCLADepartment of Mathematicscratsch@math.ucla.edu

MS106Kinetic Monte Carlo Simulation of HeteroepitaxialGrowth: Wetting Layers, Quantum Dots, Capping,and NanoRings

A KMC algorithm efficiently accounting for elastic strainis developed for heteroepitaxial growth. It exploits the ob-servation that adatoms are essentially decoupled from theelastic field. The film is therefore decomposed into weaklyand strongly bonded portions. The first evolves indepen-dent of the elastic field which is updated infrequently. Weshow that faceted quantum dots form from layer-by-layernucleation of pre-pryamids. Capping simulations provideinsights into dot erosion and ring formation. Joint withT.P. Schulze.

Peter SmerekaDepartment of MathematicsUniversity of Michiganpsmereka@umich.edu

MS107Numerical Solution of An Inverse Diffraction Grat-ing Problem

In this talk, we consider the diffraction of a time-harmonicplane wave incident on a perfectly reflecting periodic sur-face. A continuation method on the wavenumber will beproposed for the inverse diffraction grating problem, whichreconstructs the grating profile from measured reflectedwaves on a constant height away from the structure. Nu-merical examples will be presented to show the validity andefficiency of the proposed method.

Gang BaoMichigan State Universitybao@math.msu.edu

Peijun LiDepartment of MathematicsPurdue Universitylipeijun@math.purdue.edu

Haijun WuDepartment of MathematicsNanjing Universityhjw@nju.edu.cn

MS107Resoance of 1D Phototic Crystal with Finite Ex-tent

Abstract not available at time of publication.

Junshan LinUniversity of Minnesotalinxa011@ima.umn.edu

Fadil SantosaInstitute for Mathematics and its ApplicationsUniversity of Minnesotasantosa@ima.umn.edu

MS107Numerical Methods for the Complex HelmholtzEquation and Scattering from a Lossy Inclusion

I will discuss a new method for solving the Helmholtz equa-tion in lossy materials that is based on the variationalprinciples developed by Milton, Seppecher, and Bouchitte.This method results in a system of equations which can bereduced to a symmetric positive-definite system, and canbe solved using conjugate gradient and Cholesky factoriza-tion. Also, I will discuss the application of this methodto the problem of scattering from an inclusion filled withlossy material, which requires the application of a trans-parent boundary condition.

Russell B. RichinsMichigan State Universityrichins@math.msu.edu

MS107Mathematical Analysis in Quantifying MechanicalProperties for Nano-Materials

Nanotechnology deals with structures sized between 1 to100 nanometer and involves investigating and designingmaterials or devices within that scale. Due to its small

AN12 Abstracts 99

size, it is difficult to quantify the mechanical propertiesof nanomaterials which significantly rely on measurementtechniques, conditions and environment. In this talk, wepropose a novel model based on Euler-Bernoulli equationwith a stochastic source term accounting for the effect ofinitial bending, surface roughness and white noise duringthe measurement. The forward problem is demonstratedto have a unique and explicit path-wise solution. Further-more, the inverse problem consists of identifying the elasticmodulus of nanobelt and reconstructing the random sourcestructure, i.e., the mean and the variance. Based on theexplicit formula of the direct problem, the inverse problemcan be reduced into a first kind of Fredholm type integralequation. Two kinds of regularization techniques are in-troduced to obtain stable solutions. Numerical examplesare presented to illustrate the validity and effectiveness ofthe proposed methods.

Xiang XuMichigan State Universityxuxiang@math.msu.edu

MS107Phase Retrieval for Diffractive Imaging

Abstract not available at time of publication.

Chao YangLawrence Berkeley National LabCYang@lbl.gov

MS108Climate Transitions in a Conceptual Model withMultiple Time Scales

Techniques from dynamical systems are used to analyzea multiple timescale conceptual model incorporating tem-perature, glacial motion, and the carbon cycle. Withinthis framework, we examine how both ice-albedo andgreenhouse gas feedback effects can cause a wide vari-ety of glacial oscillations, including variations between ice-covered and ice-free states.

Anna BarryMathematicsBoston Universityannab@math.bu.edu

MS108A Dynamical Systems Perspective on Period Tran-sitions in Glacial Cycles

About one million years ago, the Earth’s glacial cycleschanged character, increasing in amplitude and movingfrom a period of about 40 thousand years to a period ofabout 100 thousand years. Various theories attempting toexplain this transition can be expressed as dynamical sys-tems phenomena.

Richard McGeheeUniversity of Minnesotamcgehee@math.umn.edu

MS108Abrupt and Gradual Transitions from the DeepPast

Gaining information about ancient Earth climates is not

an easy task. Then, once data is acquired, what insightscan be gained? In this talk, we consider the observationsand scientific hypothesis around two historic transitionsin Earth’s history. Approximately 650 million years ago,Earth is likely to have been completely covered in ice inwhat is called ”Snowball Earth”. Additionally we’ll con-sider an abrupt transition (PETM) when atmospheric car-bon sky rocketed nearly 55 million years ago.

Samantha OestreicherUniversity of MinnesotaSchool of Mathematicsoestr042@umn.edu

MS108Climate Tipping Points: Overview and Outlook

I will provide some overview of investigations of potentialtipping elements in Earths climate, highlighting challengesof developing early warning signs for impending criticaltransitions. Drawing on material covered in our “virtualseminar” on this topic, I will survey mathematical mech-anisms for tipping, some of which depart from classicalbifurcation theory. Parts of the discussion will be framedin terms of case studies associated with conceptual modelsof (1) Arctic sea-ice retreat, and (2) desertification.

Mary SilberNorthwestern UniversityDept. of Engineering Sciences and Applied Mathematicsm-silber@northwestern.edu

MS109Optimality of the Neighbor Joining Algorithm andFaces of the Balanced Minimum Evolution Poly-tope

Balanced minimum evolution (BME) is a statistically con-sistent distance-based method to reconstruct a phyloge-netic tree from an alignment of molecular data. In 2000,Pauplin showed that the BME method is equivalent to op-timizing a linear functional over the BME polytope, theconvex hull of the BME vectors obtained from Pauplinsformula applied to all binary trees. The BME method isrelated to the popular Neighbor Joining (NJ) algorithm,now known to be a greedy optimization of the BME prin-ciple. In this talk I will elucidate some of the structureof the BME polytope and strengthen the connection be-tween the BME method and NJ Algorithm. I will showthat any subtree-prune-regraft move from a binary tree toanother binary tree corresponds to an edge of the BMEpolytope. Moreover, I will describe an entire family offaces parametrized by disjoint clades. Finally, given a phy-logenetic tree T, I will show that the BME cone and everyNJ cone of T have intersection of positive measure.

David HawsUniversity of Kentuckydchaws@gmail.com

MS109WNT Signaling in Melanoma Cells

Experimental evidence suggests that retinoic acid deacti-vates canonical WNT signaling in early stage melanomacells, thereby affecting cell division. More agressivemelanoma cell lines are not responsive to retinoic acid. Thequestion then arises how such a switch in signaling could beaffected in these unresponsive cell lines. This talk will dis-

100 AN12 Abstracts

cuss a time- and state-discrete mathematical model of thetwo pathways and its use in identifying potential effectorsof a switching mechanism.

Reinhard LaubenbacherVirginia BioinformaticsInstitutereinhard@vbi.vt.edu

MS109A Differential Algebra Method for Finding Identi-fiable Parameter Combinations of Nonlinear ODEModels

Parameter identifiability analysis for dynamic system ODEmodels concerns finding which unknown parameters can bequantified from given input-output data. If all the param-eters of a model have a finite number of solutions, then themodel is said to be identifiable. However, many models areunidentifiable, i.e. the parameters can take on an infinitenumber of values and yet yield identical input-output data.This problem has been especially apparent in Systems Bi-ology. In this talk, we examine unidentifiable models and adifferential algebra method for finding globally identifiableparameter combinations using Groebner Bases. We alsodiscuss computational difficulties in finding these identifi-able parameter combinations and explore possible improve-ments to our algorithm.

Nicolette MeshkatDepartment of MathematicsSanta Clara Universitynicolette.meshkat@gmail.com

MS109Disentangling Phylogenetic Mixture Models

Mixture models are used to model the heterogeneity inher-ent in evolutionary processes. A mixture model is specifiedby a collection of trees (possibly with repetitions). I willdiscuss ongoing work on the identifiability of phylogeneticmixture models. The best results in this area require a mixof techniques from algebraic geometry and discrete math-ematics.

Seth SullivantNorth Carolina State Universitysmsulli2@ncsu.edu

MS110Exploiting Sparsity in Derivative Computation

Jacobian and Hessians matrices that arise in large-scalecomputations are typically sparse. We discuss combinato-rial algorithms and software we have developed for makingthe computation of such matrices using Automatic Differ-entiation efficient in terms runtime and memory usage. Weillustrate the advantages the methods afford using a nu-merical optimization problem in chemical engineering asan example.

Assefaw H. GebremedhinPurdue Universityagebreme@purdue.edu

MS110Automating Sparse Gradient Computations in Op-

timization of Partially Separable Functions

Optimization problems often exhibit partial separability(PS). A function f is partially separable if f can be rep-resented in the form f(x) =

∑m

i=1 fi(x) where fi dependson pi n variables. The sparsity of the Jacobian (andHessian) of f can be exploited by computing the sparseJacobians of the elemental functions first. We present PSsupport in ADIC2 by using the ColPack coloring toolkitand demonstrate it with a TAO optimization example.

Boyana Norris, Sri Hari K. NarayananArgonne National Laboratorynorris@mcs.anl.gov, snarayan@mcs.anl.gov

Todd MunsonArgonne National LaboratoryMathematics and Computer Science Divisiontmunson@mcs.anl.gov

Assefaw H. GebremedhinPurdue Universityagebreme@purdue.edu

MS110An Efficient Overloaded Method for ComputingAnalytic Derivatives of Mathematical Functions inMATLAB

An operator-overloaded method is presented that gener-ates analytic derivatives of mathematical functions definedby MATLAB computer code. The method implements for-ward more automatic differentiation in a manner that pro-duces a source code that contains the derivative of the orig-inal function. Because a new source code is produced, themethod can be applied recursively to generate derivativesof any order. A description of the method is given and itseffectiveness is demonstrated on three examples.

Michael PattersonAerospace EngineeringUniversity of Floridampatterson@ufl.edu

Matthew WeinsteinDepartment of Mechanical and Aerospace EngineeringUniversity of Floridamweinstein@ufl.edu

Anil RaoMechanical and Aerospace EngineeringUniversity of Floridaanilvrao@ufl.edu

MS110Computing Higher-order Derivatives: Approaches,Tools and Uses

The approximation errors of finite difference schemes forcomputing higher-order derivatives make their use in prac-tical applications unattractive. Except for cases where an-alytical derivatives are available, only algorithmic differen-tiation (AD) can provide derivatives of an arbitrarily highorder with machine precision. The talk will cover the ba-sic approaches used in the AD context for computing suchderivatives, cover the most relevant AD tool implementa-tions, and the computational complexity. It will brieflyhighlight current developments addressing heterogeneous

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computing hardware. The talk will conclude with exampleuses of higher-order derivatives and practical tool applica-tions from ODE solvers, model reductions, path continua-tion methods, and others.

Jean UtkeArgonne National Laboratoryutke@mcs.anl.gov

MS111Weather, Uncertainty, Supercomputing, and Can-cer: Research Experiences for Math Majors at Ari-zona State University

This talk describes innovative programs that involve math-ematically talented students at the sophomore through se-nior level. Interdisciplinary group projects and relatedcourses in modern applications of mathematics, includingensemble forecasting, biomedical models, state estimation,finance, and high-performance computing, are offered to11 to 16 juniors each year (with beneficial impacts on thegraduate program as well). I will also discuss efforts todevelop a 21st Century undergraduate mathematics cur-riculum.

Eric J. KostelichArizona State UniversityDepartment of Mathematicskostelich@asu.edu

MS111Experiences in Running the STAGE Program

’Smooth Transition for Advancement to Graduate Edu-cation’ (STAGE), is a multi-year NSF-funded eight-weeksummer research experience for underrepresented minorityundergraduate students which intends to immerse the par-ticipants, mainly from the HBCUs, in an intensive train-ing program that includes (a) crash courses,(b) guided re-search, and (c) professional developments. This talk isbased on the rewarding experience of managing STAGEin 2011 which can help other researchers in running simi-lar programs nationwide.

Nabendu PalMathematics DepartmentUniversity of Louisiana at Lafayettenxp3695@louisiana.edu

MS111Excel-lent Experiences: Computational ResearchInternships

Professors can help undergraduates excel through obtain-ing meaningful CSE research internships. Such internshipscan enhance students’ professional and personal lives andcan add new dimensions to a school’s program. Withstudents’ inexperience, active involvement by professors isusually a crucial. Using numerous ”success stories,” thistalk explores how advisors can help students obtain andbenefit from computational research experiences.

Angela B. ShifletChair of Computer Science and Director ofComputational Sci.Wofford Collegeshifletab@wofford.edu

MS111Undergraduate CSE Programs in the U.S.

In this talk, a brief survey of some of the different modelsof undergraduate computational science and engineeringprograms will be presented. This will highlight some cur-rent best practices that can be extended to applied mathe-matics in general. relevant activities of SIAM’s EducationCommittee will also be presented including possibilities foroutreach into the K-12 community.

Peter R. TurnerClarkson UniversitySchool of Arts & Sciencespturner@clarkson.edu

MS112Addressing the Materials Genome Initiativethrough the AFLOWLIB.ORG Consortium: Ther-moelectric Properties of Sintered Compounds withHigh-throughput Ab-initio Calculations

In this presentation we will describe the aflowlib.org con-sortium and give some examples of its use including scintil-lator, thermoelectrics and topological insulators research.

Stefano CurtaroloDuke Universitystefano@duke.edu

MS112Data Mining Applications for Knowledge Discov-ery in Materials Science: Promises and Challenges

Extensive materials databases are available for new knowl-edge discovery. However, in spite of considerable advancesin data mining techniques, materials scientists still lackpractical data mining tools to manage and transform thedata into actionable knowledge. We have initiated a seriesof computational experiments with various materials datain an attempt to create such tools. An overview of promisesas well as challenges of such studies will be presented.

Da GaoDepartment of Computer Science and EngineeringUniversity of Minnesotadagao2008@gmail.com

Yousef SaadDepartment of Computer ScienceUniversity of Minnesotasaad@cs.umn.edu

James R. ChelikowskyInstitute for Computational Engineering and SciencesUniversity of Texas at Austinjrc@ices.utexas.edu

MS112Informatics for the Materials Genome: a Minimal-ist Perspective

The recently announced Materials Genome Initiative raisesa fundamental question of whether materials can in facthave a ”gene”. Implied in the term of ”genome” is theidea for the need for large quantities of data. This talkventures to show, however, that we in fact need to seek

102 AN12 Abstracts

the minimal amount of data . Applications of statisticalinference integrated into a variety of data mining tools formaterials design are presented.

Krishna RajanIowa State UniversityDepartment of Materials Science and Engineeringkrajan@iastate.edu

MS112USPEX: Evolutionary Crystal Structure Predic-tion as a Tool in Materials Design

The evolutionary methodology USPEX for crystal struc-ture prediction [1] provides, with high reliability and ef-ficiency, the stable and low-energy metastable structuresof a given compound at given P-T-conditions. Theory ofenergy landscapes of solids [2] gives tools that greatly en-hance structure prediction. The following results will bediscussed: 1. Theoretical and experimental evidence for anew stable high-pressure phase of boron, γ-B [3], showingsuperhardness and charge transfer between boron. 2. Newhigh-pressure phase, a transparent insulator, was found forsodium [4]. 3. High-pressure phases of group IV hydridesmethane CH4 [5], silane SiH4 [6], germane GeH4 [7] andstannane SnH4 [8]. We found much more stable phasesof SiH4 and SnH4 than previous random-sampling predic-tions, and unusual structure of the superconducting phaseof GeH4 with high Tc= 64. CH4 decomposes into diamondand hydrogen within interiors of giant planets; this processis important for understanding the energy balance of Nep-tune. Our method has been extended to enable efficientprediction of the structure of nanoparticles and surface re-constructions, which opens doors for many geochemical ap-plications, as well as predictive studies of nanomaterialsand catalysis. References [1] Oganov A.R., Glass C.W.,J.Chem.Phys. 124, 244704 (2006) [2] Oganov A.R., ValleM., J.Chem.Phys. 130, 104504 (2009) [3] Oganov A.R.,Chen J., Gatti C., et al., Nature 457, 863 (2009) [4] MaY., Eremets M.I., Oganov A.R., et al., Nature 458, 182(2009) [5] Gao G., Oganov A.R., et al., J.Chem.Phys. 133,144508 (2010). [6] Martinez-Canales M., Oganov A.R., etal., Phys.Rev.Lett. 102, 087005 (2009) [7] Gao G., OganovA.R., et al., Phys.Rev.Lett. 101, 107002 (2008). [8] GaoG., Oganov A.R., et al. (2010). Proc.Natl.Acad.Sci. 107,1317 (2010).

Qiang ZhuState University of New York, Stony Brookalecfans@gmail.com

MS113Efficient Spectral-Galerkin Methods for High-orderEquations and Systems of Coupled Elliptic Equa-tions with Applications to Phase-field Models

Abstract not available at time of publication.

Feng ChenPurdue University, West Lafayettechen221@math.purdue.edu

Jie ShenDept. of MathematicsPurdue Universityshen7@purdue.edu

MS113Computational Issues for Multi-physics, Multi-Phase Equations

Abstract not available at time of publication.

Andrew ChrisliebDept. of MathematicsMichigan State Universitychristlieb@math.msu.edu

Keith PromislowMichigan State Universitykpromisl@math.msu.edu

MS113Using GPUs to Compute Solutions to the Func-tionalized Cahn-Hilliard Equation

We present a nonlinear semi-implicit numerical scheme forcomputing solutions to the evolution equation,

ut = ∆(ε2∆−W ′(u) + ε2η)(ε2∆u−W ′(u)), (4)

that describes pore network formation in a functionalizedpolymer/solvent system as described by the Functional-ized Cahn-Hilliard Model. The physical process is definedby multiple time-scales: short time phase separation, longtime network growth, and slow evolution to steady state.This requires very long simulations, so our scheme is de-signed to be unconditionally gradient stable allowing foradaptivity in the time stepping while preserving the dis-crete energy law. The gradient stability derives from thesemi-implicit splitting of the chemical potential into con-tractive and expansive components. We present a noveliteration for solving the nonlinear equation with a Fourierspectral method, and numerical results are shown with a10x speedup using Graphics Processing Units (GPUs).

Jaylan S. Jones, Andrew Christlieb, Keith PromislowMichigan State Universityjaylanjones@gmail.com, christlieb@math.msu.edu,kpromisl@math.msu.edu

MS113Variational Multiscale Models for BiomolecularSystems

A major feature of biological science in the 21st Centurywill be its transition from a phenomenological and de-scriptive discipline to a quantitative and predictive one.I will discuss the use of differential geometry theory of sur-faces for coupling microscopic and macroscopic scales on anequal footing. Based on the variational principle, we derivethe coupled Poisson-Boltzmann, Nernst-Planck (or Kohn-Sham), Laplace-Beltrami and Navier-Stokes equations forthe structure, dynamics and transport of ion-channel sys-tems. As a consistency check, our models reproduce ap-propriate solvation models at equilibrium. Moreover, ourmodel predictions are intensively validated by experimen-tal measurements. Mathematical challenges include thewell-posedness and numerical analysis of coupled partialdifferential equations (PDEs) under physical and biologi-cal constraints, lack of maximum-minimum principle, effec-tiveness of the multiscale approximation, and the modelingof more complex biomolecular phenomena.

Guowei WeiDepartment of MathematicsMichigan State University

AN12 Abstracts 103

wei@math.msu.edu

MS114A Dynamic Model of Polyelectrolyte Gels

Abstract not available at time of publication.

Yoichiro MoriSchool of MathematicsUniversity of Minnesotaymori@umn.edu

MS114Models with Increasing Complexity for Hydro-gel/enzyme Feedback Oscillations

Abstract not available at time of publication.

Ronald SiegelUniversity of MinnesotaDepartment of Pharmaceutics and BiomedicalEngineeringsiege017@umn.edu

MS114Computations of Moving and Deforming Objectsin Biological Flows

Abstract not available at time of publication.

Lingxing YaoUniversity of Minnesotalyao@math.umn.edu

Aaron L. FogelsonUniversity of Utahfogelson@math.utah.edu

MS115Noise-induced Transitions of Barotropic Flow overTopography

We study the noise-induced transitions in a climate systemmodeled by the barotropic quasi-geostropic equations withtopography. The stochastic dynamic is constrained on aconstant energy surface and it exhibits metastable behav-ior: The system is likely to stay trapped for a long timenear one state until it switches to another. The metastablestates are characterized by the strength of the zonal flow.We compute the maximum likely-hood transition pathsand the transition rates between the metastable states us-ing the string method. We first study a truncated one-mode ODE model, then generalize the results to the fullPDE model. This is a joint work with Xu Yang and EricVanden-Eijnden.

Weiqing RenCourant Institute of Mathamatical Sciencesmatrw@nus.edu.sg

MS115Analysis of Parallel Replica Dynamics

Parallel replica dynamics was first proposed by A.F. Voteras a numerical tool for accelerating molecular dynamicssimulations characterized by a sequence of infrequent, butrapid, transitions from one state to another. An example

would be the migration of a defect through a crystal. Par-allel replica dynamics accelerates this by simulating manyreplicas simultaneously, concatenating the simulation timespent of the ensemble, as thought it were a single long tra-jectory. This leads to several numerical analysis questions:Is parallel replica dynamics doing what we think it is? Forwhat systems will it be useful? How do we implement itefficiently? In this talk, I will thoroughly describe the algo-rithm and report on progress towards rigorous justification.Open questions will also be highlighted.

Gideon SimpsonUniversity of Torontogsimpson@umn.edu

Mitchell LuskinSchool of MathematicsUniversity of Minnesotaluskin@umn.edu

MS115Escape from An Attractor: Importance Samplingand Rest Point

We discuss asymptotically optimal importance samplingschemes for the estimation of finite time exit probabilityof small noise diffusions that involve escape from an equi-librium point. The appearance of the rest point compli-cates the prefactor of the second momentum of the ordi-nary state-dependent importance sampling estimator. Ouranalysis points out a useful and efficient scheme to obtain anice prefactor by using the linear quadratic regulator nearthe rest point.

Xiang ZhouDivision of Applied MathematicsBrown Universityxiang zhou@brown.edu

Paul Dupuis, Konstantinos SpiliopoulosDivision of Applied MathBrown Universitypaul dupuis ¡dupuis@dam.brown.edu¿,konstantinos spiliopoulos@brown.edu

MS116The Adaptive Finite Element Simulations for theElectronic Structures

Abstract not available at time of publication.

Guanghui HuMichigan State Universityghhu@math.msu.edu

MS116Multiscale Modeling and Model Computation forScanning Near-Field Optical Microscopy

Abstract not available at time of publication.

Songting LuoDepartment of MathematicsMichigan State Universityluos@math.msu.edu

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MS116Scattering and Resonances of Thin High ContrastDielectrics

Abstract not available at time of publication.

Shari MoskowDrexel UniversityDepartment of Mathematicsmoskow@math.drexel.edu

MS116Some Reconstruction Algorithms in QuantiativePhotoacoustic Tomography

In quantitative photoacoustic tomography (qPAT) we aimat reconstructing physical parameters of biological tissuesfrom “measured’ data of absorbed radiation inside the tis-sues. Mathematically, qPAT problems can be regarded asinverse problems related to some elliptic partial differentialequations. We present in this talk some new reconstruc-tion strategies for inverse problems in qPAT with differenttypes of available data.

Kui RenUniversity of Texas at Austinren@math.utexas.edu

MS117Liszt: A Domain Specific Language for Partial Dif-ferential Equations

Liszt is a domain specific language to simplify solving par-tial differential equations (PDE) on parallel computers andgraphics processing units (GPU). Liszt is a high level lan-guage that contains constructs specific to PDE solvers suchas finite-volume or finite-element methods on unstructuredgrids. Topological objects like mesh, cell, face, edge andvertex are part of the language. Knowledge of the meshconnectivity allows the compiler to automatically reasonabout data dependency and schedule communication (eg,MPI calls). As a result Liszt code does not contain anyexplicit parallel instruction, such as inter-node communi-cation, aside from the use of parallel for loops to iterateover mesh objects. A Liszt code is very portable. Thesource to source compiler can take the same code as in-put and produce MPI code for clusters, openMP code formulticore processors, and CUDA code for GPUs. The per-formance of Liszt matches or in some cases exceeds handtuned code.

Eric F. DarveStanford UniversityMechanical Engineering Departmentdarve@stanford.edu

Zach DevitoStanford Universityzdevito@stanford.edu

Niels Joubert, Pat HanrahanStanfordnjoubert@stanford.edu, hanrahan@cs.stanford.edu

MS117Linear Solvers at Extreme Scale: Challenges and

Opportunities

The emergence of scalable manycore computing systemspresents fundamental challenges and opportunities for lin-ear equation solvers. In this talk we discuss the role of pro-cessor and memory architecture, system faults and problemsize in guiding linear solver algorithms research and devel-opment. In particular, we discuss new opportunities formaking linear solvers faster, more robust and resilient tosystem faults.

Michael A. HerouxSandia National Laboratoriesmaherou@sandia.gov

MS117A Heterogenous Scale-bridging Kinetic Solver forEmerging Architectures

The advent of modern parallel architectures, and thepromise of exascale computing resources, brings new chal-lenges to computational science. Dependably taking ad-vantage of billion-way parallelism and distinct levels ofparallelism will stress solver algorithms. We are develop-ing a broadly applicable scale-bridging solver algorithm tohelp meet some of this challenge. Development of simi-lar moment-based acceleration methods can be found ina variety of application areas such as neutron transport,thermal radiation (photon) transport, kinetic plasma sim-ulation. We will provide algorithm fundamentals and openresearch questions. We will provide some indication of al-gorithm performance on emerging architectures.

Dana KnollLos Alamos National Laboratorynol@lanl.gov

C.N. Newman, H. Park, R. RauenzahnLANLcnewman@lanl.gov, hkpark@lanl.gov, rick@lanl.gov

L. Chacon, G. ChenORNLchaconl@ornl.gov, gcc@ornl.gov

W. TaitanoUNMwilliamtaitano1208@hotmail.com

Jeffrey A. WillertNorth Carolina State Universityjawiller@ncsu.edu

MS117Co-Design and You

In this talk I will give a high-level, general discussion ofthe DOE ASCR Exascale Co-Design Centers and the role ofapplied mathematics in extreme-scale scientific computing.

Karen I. PaoOffice of ScienceUS Department of Energykaren.pao@science.doe.gov

PP1A Gpu Implementation of Von Mises-Fisher Distri-bution Algorithm for Polymer Conformation Anal-

AN12 Abstracts 105

ysis

The statistical representation of polymer conformations isvery important because it is impossible to track all relevantmicroscopic variables for each polymer in a polymer-ladensolution due to the huge number of degrees of freedom. Inour study we consider one of the most descriptive kineticmodels of polymer, Kramers’ bead-rod model, where theprobability density function models the angle of each rodwith respect to the fixed coordinate axes. Towards thisgoal we apply von Mises-Fisher distribution for a polymerconformation distribution. The hard and soft assignmentmethods of clustering of the Expectation-Maximization al-gorithm are used to cluster the mixture model which havebeen implemented in parallel using CPU and GPU basedplatforms. We demonstrate that the GPU-accelerated ver-sion of the clustering algorithm is significantly faster thanthe CPU version.

Bakytzhan KallemovCenter for Energy ResearchNazarbayev University, Astanabkkallemov@ucdavis.edu

Aidos AbzhanovNazarbayev UniversityAstanaaabzhanov@nu.edu.kz

PP1Pollutants Transport Simulation in AtmosphericBoundary Layer Using Stabilized Finite ElementFormulations

This work deals with a numerical method based on theGalerkin Least Square scheme for a two-dimensional modelof pollutant dispersion in the atmosphere. The model,which is described through a diffusion-convection equation,accounts for pollutant emission from the soil and from anelevated source. It also accounts for diurnal changes in theatmospheric stability conditions via parametric models forturbulent diffusion and wind speed. Numerical results areobtained and compared with results available in the liter-ature.

Roseane A. AlbaniPEM/COPPE- Universidade Federal do Rio de Janeiroroseane@mecsol.ufrj.br

Antonio CruzPEM/COPPE/UFRJaguicruz@mecanica.ufrj.br

Eduardo carmoPEN/COPPE/UFRJegdcarmo@hotmail.com

Fernando DudaPEM/COPPE/UFRJfpduda@yahoo.com.br

PP1Advanced Optimization Techniques for Entropy-Based Closures in Slab Geometry

Entropy-based moment closures are a parallelizable simu-lation technique with attractive theoretical properties forreducing the state-space of the kinetic equation, but thedefining optimization problem is arbitrarily poorly condi-

tioned for moments of highly anisotropic distributions. Weresolve this difficulty by adaptively selecting the polyno-mial basis defining the moments, and when the optimiza-tion problem cannot be solved in finite precision, we find aphysically similar solvable problem.

Graham AlldredgeUniversity of Maryland, USAgwa@umd.edu

Cory HauckOak Ridge National Laboratoryhauckc@ornl.gov

Andre TitsUniversity of Maryland at College Parkandre@umd.edu

Dianne P. O’LearyUniversity of Maryland, College ParkDepartment of Computer Scienceoleary@cs.umd.edu

PP1Alternate Powers in Serrin’s Swirling Vortex Solu-tions

We consider a modification of the fluid flow model for aswirling vortex developed by J. Serrin, where velocity de-creases as the reciprocal of the distance from the vortexaxis. Recent studies, based on radar data of selected se-vere weather events, indicate that the angular momentumin a tornado may not be constant with the radius, and thussuggest a different scaling of the velocity/radial distancedependence. Motivated by this suggestion, we considerSerrin’s approach with the assumption that the velocitydecreases as the reciprocal of the distance from the vortexaxis to the power b with a general b > 0. This leads to aboundary-value problem for a system of nonlinear differ-ential equations. We analyze this problem for particularcases, both with nonzero and zero viscosity, discuss thequestion of existence of solutions, and use numerical tech-niques to describe those solutions that we cannot obtainanalytically.

Doug DokkenUniversity of St. Thomasdpdokken@stthomas.edu

Pavel BelikMathematics DepartmentAugsburg Collegebelik@augsburg.edu

Kurt Scholz, Misha ShvartsmanUniversity of St. Thomask9scholz@stthomas.edu, mmshvartsman@stthomas.edu

PP1High Order Numerical Method for the Nearly Sin-gular Integration of the Stokes Kernel

Simulating Stokesian particulate flows using integral equa-tions requires the resolution of nearly singular integrals(evaluation of the fluid variables near the surface of a parti-cle), which are inaccurate using standard quadrature rules.We propose a method to resolve this numerical difficulty.We partition the space around a particle into two different

106 AN12 Abstracts

zones: we use quadrature in the far zone and we interpo-late in the nearly singular zone. We present results in twodimensions.

Walid Ben RomdhaneInstitute for Computational Engineering and SciencesUniversity of Texas at Austinwalid.benromdhane@gmail.com

George BirosUniversity of Texas at Austinbiros@ices.utexas.edu

Bryan D. QuaifeInstitute for Computational Engineering and SciencesUniversity of Texas at Austinquaife@ices.utexas.edu

PP1An Axisymmetric Boundary Element Method forModeling Biphasic Articular Cartilage Mechanics

In comparing the stress, strain, and deformation of healthyand osteoarthritic cartilage under an applied load, differ-ences in parameter values can give insight into the na-ture and progression of osteoarthritis. An axisymmetricLaplace-domain boundary element method is presented forsolving the boundary integral equations modeling the re-sponse of biphasic cartilage tissue under mechanical load-ing, which involve fundamental solutions of the governingPDEs. Simulation of confined compression stress relax-ation of a biphasic cartilage cell is shown.

Brandy A. BenedictMerrimack Collegebenedictb@merrimack.edu

PP1Predicting Bifurcations in Dynamical Systems

Nonlinear dynamical systems, which include models of theEarths climate, financial markets and complex ecosystems,often undergo abrupt transitions that lead to radically dif-ferent behavior. The ability to predict such qualitativeand potentially disruptive changes is an important problemwith far-reaching implications. For a nonlinear dynamicalsystem with multiple parameters, we combine Conley in-dex theory with machine learning techniques to accuratelypredict global bifurcations.

Jesse BerwaldDepartment of MathematicsCollege of William and Maryjjberwald@wm.edu

Tomas GedeonMontana State UniversityDepartment of Mathematicsgedeon@math.montana.edu

Kelly SpendloveDepartment of Mathematical SciencesMontana State Universitykelly.spendlove@msu.montana.edu

PP1AWM - Time Asymptotic of Non-Darcy Flows with

Total Boundary Flux

We study a time asymptotic of the non-linear Forchheimerflows in porous media with given total flux and constraintson the pres- sure trace on the boundary. We prove thatif total flux stabilizes then the difference between pressureaverage inside domain and on the boundary stabilizes aswell. The refined comparison of fully transient and cer-tain time-invariant pressure was performed. These resultscan be applied in reservoir engineering and other problemsmodeled by diffusive equations.

Lidia BloshanskayaTexas Tech UniversityDepartment of Mathematics and Statisticslidia.bloshanskaya@ttu.edu

PP1Faraday Waves on Surfactant-Covered Thin Films

Liquid layers under vertical vibration give rise to a surfacewave pattern known as Faraday waves. In this work, theeffects of surfactants on Faraday waves are explored underthe assumption that the depth of the liquid layer is small.Owing to the importance of inertial effects, the standard lu-brication approximation is not suitable and extended thinfilm type approximation must be used. Numerical simu-lations and linearized analysis of this modified model arepresented.

Lake BookmanNorth Carolina State Universityldbookma@ncsu.edu

Michael ShearerMathematicsNC State Universityshearer@ncsu.edu

Karen Daniels, Stephen StricklandNorth Carolina State Universitykdaniel@ncsu.edu, slstric2@ncsu.edu

PP1Multi-Frequency IterativeIntegral Equations Method for the Shape Recon-struction of An Acoustically Sound-Soft Obstaclein the Presence of Multiple Scatterers

We present a method to solve the problem of obtaininga reconstruction of a planar acoustically sound-soft obsta-cle from the measured far-field pattern generated by planewaves with a fixed incidence and varying frequencies. Wesolve iteratively the problem for each frequency, from thelowest to the highest, using as initial guess the solutiongiven by the previous frequency. We present numerical re-sults showing the benefits of our approach.

Carlos C. BorgesWorcester Polytechnic Instituteceduardo@wpi.edu

Marcus SarkisWorcester Polytechnic InstituteInstituto de Matematica Pura e Aplicada (Brazil)msarkis@wpi.edu

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PP1Particle Methods for Geophysical Flows on theSphere

We develop a fluid dynamics solver for spherical domainswith a focus on applications related to the “dynami-cal cores” of global circulation models. We use a tree-structured Lagrangian grid and intermittent interpolationof the Lagrangian flow map to avoid inaccuracies caused bymesh distortion without introducing significant mass error.Interpolation is carried out using integral convolution witha regularized delta kernel. Fluid equations are solved usingGreen’s function integral solutions for the velocity streamfunction and potential.

Peter A. BoslerUniversity of Michiganpbosler@umich.edu

Robert KrasnyUniversity of MichiganDepartment of Mathematicskrasny@umich.edu

Christiane JablonowskiUniversity of MichiganAnn Arbor MI 48109-2143cjablono@umich.edu

PP1Software Development for a Three DimensionalGravity Inversion and Application to Study of theBorder Ranges Fault System, South Central Alaska

Our research involves the testing of several plausible den-sity models of structure along the Border Ranges FaultSystem in South-Central Alaska by developing a novel, 3Dinversion software package. The inversion utilizes gravitydata constrained with geophysical, borehole, and surfacegeological information to produce a density solution. Thenovel inversion approach involves directly modeling knowngeology, initially free-air corrected data, and revising ”apriori” uncertainties on the geologic model to allow com-parisons to alternative interpretations.

Rolando Cardenas, Diane DoserUniversity of Texas at El Pasoroncardenas3@gmail.com, doser@utep.edu

Mark BakerGeomedia R&Dbakergrd@cs.com

PP1Numerical Solution of Integral Equations in Solid-ification and Laser Melting

We consider the evolution of the liquid-solid interface ina freezing or laser-induced melting process. Using theGreen’s representation theorem for the heat equation andthe Stefan condition we obtain a system of nonlinearintegro-differential equations in space and time. The in-tegral equations are discretized with the Nystrom methodwhich leads to an efficient time stepping scheme to deter-mine the position and velocity of the interface with givenmaterial properties.

Elizabeth CaseSouthern Methodist University

ekaram@smu.edu

Johannes TauschSouthern Methodist UniversityDepartment of Mathematicstausch@mail.smu.edu

PP1Stochastic Approximated-Gradient OptimizationMethods for Oilfield Well Placement

Well placement is critical to optimal hydrocarbon resourcemanagement. This work compares the performance ofEnsemble-based Optimization (EnOpt) and Fixed-GainSPSA (FSP) for optimal well placement. These algorithmsbelong to the broad class of stochastic approximated-gradient methods and offer several practical benefits:They combine the advantages of both gradient-based andstochastic optimization algorithms without the correspond-ing computation effort, do not require access to simulatorcode and the gradient approximation is independent of theproblem dimensions.

Yuqing Chang, Deepak DevegowdaMewbourne School of Petroleum and GeologicalEngineeringUniversity of Oklahomayuqing.chang@ou.edu, deepak.devegowda@ou.edu

PP1Spatio-Temporal Calcium Smoothing in DendriticTrees

To understand how animals learn it is necessary to studychanges in the strength of synaptic connections betweenneurons. It is thought that synaptic plasticity underlieslearning and memory at a cellular level. Therefore themechanisms of synaptic plasticity have been a key ques-tion in neuroscience. However, current imaging techniquesare limited in their ability to capture the electric proper-ties of a neuron at the fine scales necessary to address thisproblem. We use fast, random access, fluorescent multiphoton microscopy to indirectly measure calcium concen-tration from different locations on a cell. The recordings oflight intensity of the probe molecules (fluorophore) is spa-tially sparse and have low signal to noise ratio. Therefore,we propose two methods to infer the underlying calciumsignal across the entire dendritic tree from such record-ings. The first method is a simple least squares estimate,which recovers the signal at isolated spatial locations, fol-lowed by spatial interpolation using splines. The secondmethod uses Bayesian inference to smooth signal. Bothalgorithms have the ability to infer the underlying calciumsignal up to some affine transformation. Each approachhas advantages and disadvantages in complexity and com-puting time. However, we show how the recovered tracesfrom each algorithm can provide insight into the mecha-nisms that underlie synaptic plasticity

Rebecca Chen, Kresimir JosicUniversity of HoustonDepartment of Mathematicsrlchen@math.uh.edu, josic@math.uh.edu

Peter SaggauBaylor College of MedicineNeuroscience Departmentpeter@cns.bcm.edu

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Keith KelleherDepartment of Biology and BiochemistryUniversity of Hostonkeith.kelleher@gmail.com

Liam PaninskiStatistics DepartmentColumbia Universityliam@stat.columbia.edu

Eftychios PnevmatikakisColumbia UniversityStatistics Departmenteftychios@stat.columbia.edu

PP1AWM - Tumor Growth in Complex, Evolving Ge-ometries: A Diffuse Domain Approach

In this poster, we present a new diffuse domain methodfor simulating tumor growth in complex, evolving geome-tries, taking into account homotype adhesion between tu-mor cells and heterotype adhesion between the cells andthe basement membrane. We develop an adaptive energy-stable nonlinear multigrid method to solve the governingequations efficiently. Two and three dimensional simula-tions are performed. This provides a model for ductal car-cinoma in situ.

Ying ChenUniversity of California, Irvineyingc@uci.edu

John LowengrubDepartment of MathematicsUniversity of California at Irvinelowengrb@math.uci.edu

PP1Singular Limits of Geophysical Fluid Dynamics inSpherical and Bounded Domains

We study 2D geophysical fluid models in physically rel-evant, fast rotating domains. The initial data are un-prepared. The first model is the rotating shallow wa-ter equations with solid-wall boundary conditions. Weprove convergence rates of a singular limit problem as theRossby number goes to zero. The second model is incom-pressible Euler equations on a fast rotating sphere. Thetime-averages of solutions are shown to be approximatelylongitude-independent zonal flows, which is due to the non-flat geometry.

Bin Cheng(SoMSS) School of Mathematical and Statistical SciencesArizona State Universitybin.cheng@asu.edu

PP1Crossover Design for Studying Obstructive SleepApnea

The physiological response to sleep apnea was determinedfrom beat to beat blood pressure in 16 healthy subjects bya series of breath hold maneuvers. The experiments weredone for both sitting and supine posture of the subject. Forfinding the difference in breath hold related physiologicalchanges during different protocols and posture, crossover

design is carried out on the area under blood pressure wave-form during breath holds and the results will be presented.

Hyung Wook ChunUniversity of Texas at Arlingtonhyungwook.chun@mavs.uta.edu

PP1Modeling and Simulating Flow-Induced Fluctua-tions in Polymer Solutions

Polymer solutions under flow exhibit anisotropically ampli-fied concentration fluctuations due to stress/concentrationcoupling. The full model incorporates a two-fluid approachwith polymer stress described by the Rolie-Poly equationstogether with thermal noise, introduced consistently by ap-plication of the fluctuation-dissipation theorem. Pertur-bations of the resulting Langevin equations about homo-geneous, in particular extensional, flow are examined. Amethod of characteristics solver is developed and the pre-dictions are compared with experiments on a polystyrenesolution in extensional flow.

Michael Cromer, Michael Villet, Glenn FredricksonUniversity of California, Santa Barbaracromer@mrl.ucsb.edu, villet@mrl.ucsb.edu,ghf@mrl.ucsb.edu

Gary LealDepartment of Chemical EngineeringUniversity of California, Santa Barbaralgl20@engineering.ucsb.edu

PP1AWM - Curve Matching Using Discrete IntegralInvariants

As a result of its use in medical imaging, aerial photog-raphy, and handwriting recognition, curve matching is asignificant problem in the field of image analysis. Previ-ous works propose integral invariants as a robust solutionfor the curve matching problem. However, these invariantsrely on a parametric equation fit to the curve and in manyreal world applications, this fit requires a fair amount ofcomputational work. We generate discrete invariants thatrequire only an ordered set of points. We apply our dis-crete invariants to the fields of image recognition and ob-ject assembly. In this poster, we present examples of curvematching used for handwriting recognition and puzzle com-pletion.

Susan CrookNorth Carolina State Universitysbcrook@ncsu.edu

PP1A Finite-Element Mmoc Groundwater Model forGpu’s on the Cloud

We use finite-elements with a modified method of charac-teristics to model a reaction-diffusion problem with advec-tion. Our application of interest is in the area of Ground-water flow with contaminant transport where biofilms arepresent. The linear system of equations developed from thePDEs governing this physical model are solved on a clusterof GPUs accessed over the Cloud.

Mark C. CurranUniversity of St Thomas

AN12 Abstracts 109

St. Paul, MNmjcurran99@gmail.com

PP1AWM - Polyhedral Combinatorics For Phyloge-netic Trees

Tree agglomeration methods such as Neighbor-Joining andUPGMA continue to play a significant role in phylogeneticresearch. Polyhedral combinatorics offers a robust toolkitfor analyzing the natural subdivision of Euclidean spaceinduced by classifying the input vectors according to treetopologies returned by an agglomerative algorithm. Wegive a closed form for the extreme rays of UPGMA coneson n taxa via the partition lattice Πn. We also study thecones induced by the NJ algorithm.

Ruth E. Davidson, Seth SullivantNorth Carolina State Universityredavids@ncsu.edu, smsulli2@ncsu.edu

PP1Stochastic Heterogeneous Multiscale Modeling ofSingle Phase Flow in a Porous Media

Risk assessment for carbon sequestration applications re-quires detailed analysis of multiphase flow through porousmedia. We present a stochastic Heterogeneous MultiscaleMethod (HMM) with iterative coupling to model the dis-tributions of macroscopic pressure based upon statistical-based random pore-throat size probability density. We an-alyzed its impact in a one dimensional macroscopic model,coupled to a two dimensional microscale network model.We further propose a domain decomposition strategy witha highly efficient implementation for large scale simula-tions.

Paul M. DelgadoUTEPpmdelgado2@utep.edu

PP1Probabilistic Divide-and-Conquer: a New Methodfor Exact Sampling with Integer Partitions as anExample

For us, the random objects S whose simulation might ben-efit from a divide-and-conquer approach are those that canbe described as S = (A,B), where there is some abil-ity to simulate A and B separately. Specifically, we re-quire that A ∈ A, B ∈ B, and that there is a functionh : A× B → ′,∞, so that for a ∈ A, ∈ B, h(a, b) is theindicator that “a and b fit together to form an acceptables.’ Furthermore, we require that A and B be indepen-dent, and that the desired S be equal in distribution to( (A,B)|h(A,B) = 1). This description, independent ob-jects conditional on some event, may seem restrictive, butvery broad classes — combinatorial assemblies, multisets,and selections — fit into this setup.

Stephen DesalvoUniversity of Southern Californiasdesalvo@usc.edu

PP1Numerical Methods for Delay Differential Equa-

tions with Applications to Biology

In this poster we present a numerical method for delay dif-ferential equations with application to some biology prob-lems. Two different applications are presented. The firstone is R.V Culshaw and S. Ruan s DDE model of cell-free viral spread of human immunodeficiency virus ( HIV )in a well-mixed compartment such as the bloodstream. Adiscrete time delay was introduced to describe take into ac-count the time between infection of a CD4+ T-cell and theemission of viral particles at the cellular level. We presentan analytic stability analysis of the endemically infectedequilibrium. we then present a numerical analysis of thestability and bifurcation process of the same equilibriumusing numerical tools. The second application is the DDEmodel proposed by Barlett and Wangersky. Their modelis a Non-Kolmogorov-Type predator prey model with twodiscrete times delay. We again present an analytic and anumerical analysis of the stability and bifurcation processof the steady state solutions. Numerical simulations arepresented to illustrate the results.

Ibrahim O. Diakite, Benito Chen-CharpentierDepartment of MathematicsUniversity of Texas at Arlingtonibrahim.diakite@mavs.uta.edu, bmchen@uta.edu

PP1A Predictive Model for Geographic Statistical Data

Any planar map may be transformed into a graph. If weconsider each country to be represented by a vertex (ornode), if they are adjacent they will be joined by an edge.To consider how trends migrate across boundaries, we ob-tain relevant measures of the statistic we want to consider;namely, the index of prevalence, and the index of incidence.We define a cycle by a given unit of time, usually a year.We then propose various alternate equations whereby, byparametrizing various variables, such as population size,birth rate, death rate, and rate of immigration/emigration,we calculate a new index of prevalence/index of incidence,for the next cycle. For a given data set, each statistic weconsider may propagate by a different equation, and/or adifferent set of parameters; this will be determined empiri-cally. What we are proposing is, technically, to model howa discrete stochastic process propagates geographically, ac-cording to geographical proximity. Very often, statisticsthat depend on geographical proximity are tabulated byvariables that are not; i.e., alphabetically. Such a predic-tive model would be relevant in areas such as public health;and/or crime mapping, for law enforcement purposes. Wepresent an application using a GIS (geographic informationsystem).

Jorge Diaz-CastroUniversity of P.R. School of LawUniversity of P.R. at Rio Piedrastranscripciones@mail.com

PP1Investigations of Cai’s Power Law for Strong Tor-nados

We investigate the consequences of power laws and selfsimilarity in mesocyclones and tornados as presented in thework of H. Cai. We give a model for tornado genesis andmaintenance using the 3-dimensional vortex gas theory ofChorin. High energy vortices with negative temperature inthe sense of Onsager play an important role in the model.

110 AN12 Abstracts

We speculate that the high temperature vortices formationis related to the helicity they inherit as they form or tilt intothe vertical. We also exploit the notion of self similarityto give justification for power laws corresponding to weakand strong tornados given by Cai. Doing a nested gridsimulation using ARPS we find results consistent with Cai’sscaling.

Doug DokkenUniversity of St. Thomasdpdokken@stthomas.edu

Pavel BelikMathematics DepartmentAugsburg Collegebelik@augsburg.edu

Kurt Scholz, Misha ShvartsmanUniversity of St. Thomask9scholz@stthomas.edu, mmshvartsman@stthomas.edu

PP1Convergence in Mallows-Wasserstein Distance ofRandomly Indexed Partial Sums and UpperBounds for the Ruin Probabilities

Abstract: Classical risk processes are modelled with a Pois-son arrival process along with light-tailed claim variables.However, some real data measurements may not be com-patible with the assumption of the finiteness of the sec-ond moment. In this case, heavy-tailed rewards may ariseas a suitable approach. By considering a heavy-tailed re-newal reward dependent process and by making use ofthe Mallows-Wasserstein distance, we study the asymptoticproperties of the resulting randomly indexed partial sumsand obtain upper bounds for ruin probabilities. Applica-tions to data traffic in cumulative broadband networks aswell as buffer overflow probabilities are also presented.

Chang C. DoreaUniversidade de Brasiliachangdorea@unb.br

PP1Statistical Methods for Detecting Fraudulent Pre-scriptions

In the medical field, fraud, waste, and abuse are prevalent.A large percentage of medical expenditures are for pro-cedures later deemed unnecessary. In order to cut downthis rate, this project focuses on detecting unneeded pre-scriptions by comparing insurance claims against normalbehavior patterns. The prescriptions are sorted by similarmedical claims and analyzed within these groups. Abnor-mal transactions are then detected and flagged for humanreview.

Jessica DoudBrigham Young Universityjess.doud@gmail.com

PP1Unsupervised Methods to Detect Health CareWaste

Detecting fraud is a big part of credit card management.We are trying to apply similar methods to detect waste inhealth care. A good portion of health care procedures and

drugs are unnecessary. We use data that contain healthinsurance claims to attempt to detect the unnecessary pro-cedures and drugs. It isnt explicitly obvious from the datawhich claims are wasteful, so we must use unsupervisedmethods. These methods include developing a measure-ment of similarity between different procedures.

Ben EhlertBrigham Young Universityben@ehlert.org

PP1Three-Dimensional High-Resolution Simulation ofConvective Mixing

Dissolution by convective mixing is an essential trappingmechanism during CO2 sequestration. The injected CO2mixes with brine and creates mixture denser than bothinitial fluids, leading to a Rayleigh-Benard type instabil-ity, which greatly accelerates the dissolution process.While2D analyses on this phenomenon have elucidated variousaspects of this mechanism, full 3D studies are scarce. Wepresent high-resolution, 3D simulations of convective dis-solution, and discuss the validity of quantitative resultsderived from lower-dimensional models.

Xiaojing FuMITrubyfu@mit.edu

Luis Cueto-FelguerosoMITCivil and Environmental Engineeringlcueto@mit.edu

Ruben JuanesMITtba

PP1Fast Algorithms for Inverse Problems of Reaction-Diffusion-Advection Equations

We present a method for the solution of an inverse prob-lem with parabolic PDE constraints. The constraint is areaction-diffusion-advection equation. We discuss two nu-merical methods to solve the associated least squares in-verse problem, one based on a direct solve and one based ona randomized SVD. Numerical tests are performed to showthe effectiveness of the methods for different cases, that isto compare the speed of calculations and the accuracy ofthe predicted data.

Amir GholaminejadPhD Student, Institute for Computational Engineeringand Sciences, University of Texas at Austina.gholaminejad@gmail.com

George BirosUniversity of Texas at Austinbiros@ices.utexas.edu

PP1A Fast Algorithm to Solve Slow IncompressibleSteady Flows

We present a high order fast algorithm to solve the bound-ary value problems associated with the inhomogeneous Bi-

AN12 Abstracts 111

harmonic equation in the interior of a unit disk of the com-plex plane using uniform and non-uniform grid. The fastalgorithm is based on the representation of the solution interms of Green functions, uniform and non-uniform fastFourier transforms and some recursive relation derived inthe Fourier space. Performance of this algorithm on non-uniform mesh and with singular source terms are some ofthe attractive features of this algorithms. This algorithmhas been implemented, validated and applied to solve sev-eral interesting applied problems from fluid mechanics andelectrostatics.

Aditi GhoshTexas A&M Universityamathematics@gmail.com

PP1Analysis of Interfaces for the Nonlinear Diffusion-Convection Equations

The problem of determining the short-time behavior for in-terfaces of nonlinear diffusion equations, known as a Baren-blatt problem, was first formulated in the 1950s. A fullsolution of the Barenblatt problem for the related prob-lem of reaction-diffusion was given in 2000 [Abdulla andKing, SIAM J. Math. Anal.] but the problem remainsopen for the diffusion-convection case. In this work wefirst identify the regions in the parameter space relevantfor the expanding, shrinking and stationary interfaces. Wefully characterize the case when diffusion dominates overthe convection. We prove explicit asymptotic formulae forthe expanding interface and local solution. The methodsused are maximum principle for the weak solutions, com-parison theorems and scaling techniques. We also analyzeself-similar solutions and travelling waves in the borderlinecase.

Jonathan Goldfarb, Nathan MertinsFlorida Institute of Technologyjgoldfar@my.fit.edu, nmertins2008@my.fit.edu

PP1Identifying Fraud with Bayesian Networks

Detecting fraud, waste, and abuse in healthcare is an im-portant topic. Our approach aims to identify anomalies inmedical insurance claims data by combining a prior fraudlikelihood rating with Bayesian network classification. Wecalculate the probability of an insurance claim with thehelp of a Bayesian network and compare this probabilitywith the probabilities of other claims. By assuming thatmost insurance claims are legitimate, we can use this com-parison to tag low probability claims for further investiga-tion.

Ryan GroutBrigham Young Universityrgrout@byu.net

PP1Minimizing Rational Functions by Exact JacobianSDP Relaxation Applicable to Finite Real Singu-larities

This paper consider the minimization of rational functionswith or without polynomial constraints. We reformulatethis problem as polynomial optimization by homogeniza-tion. We give some conditions under each of which weshow the equivalence of these two optimizations. As a

special case, these two optimizations are always equiva-lent when there are no constraints. We also investigate therelations between the achievabilities of their optima. Theexact Jacobian SDP relaxation proposed by Jiawang Nieis employed to solve the polynomial optimization obtainedby homogenization. We also prove that the assumption ofthe smoothness in Nie’s paper under which the JacobianSDP relaxation is exact can be weakened as the finitenessof real singularities. Some numerical examples are given inthe end to illustrate the efficiency of our method.

Feng GuoUniversity of California, San Diegofguo@mmrc.iss.ac.cn

Li WangUniversity of California, San DIegoliw022@math.ucsd.edu

Guangming ZhouDepartment of Mathematics and Computational Science,Xiangtan Universityzhougm@xtu.edu.cn

PP1Statistics of Solar Cycle-La Nina Connection: Cor-relation of Two Autocorrelated Time Series.

Both the 11-year solar cycle and the El Nino-Southern Os-cillation (ENSO) phenomena are quasi-periodic, with pe-riods of 9-11 years and 3-4 years, respectively. There havebeen claims that the two are correlated, with the Sun at itspeak in Sunspot number presumably forcing a cold eventin the equatorial Pacific. However both phenomena arealso highly auto-correlated. Caution should be exercisedwhen testing for statistical significance of the correlationof two autocorrelated time series. Even if the two timeseries are independent, the solar peak years can coincidewith cold-ENSO by chance, and then persist for many cy-cles due to their autocorrelation, before drifting apart. Wedemonstrate that this is indeed the case using the QuinnEl Nino Index going back to 1525, which is a chronicle ofobservation of El Nino related events, and Sunspot Num-ber (SSN) series, which goes back to 1750. Appropriatestatistical tests are suggested that can test for correlationtaking into account autocorrelation and are applicable tothe shorter instrumental records. There is so far no solarpeak-La Nina connection found that is statistically signifi-cant at 95% confidence level.

Eddie HaamHarvard Universitykehaam@gmail.com

Ka-Kit TungUniversity of Washingtontung@amath.washington.edu

PP1Topic Analysis and Grouping of Insurance Claims

Latent Semantic Analysis and Latent Dirichlet Allocationare fairly new tools for document and topic analysis. Withsome simple modifications, these tools can be used forgrouping clusters of medical insurance claims to get someinteresting results. This process of grouping claims is alsohelpful in building models for disease progression. Ourgoal with these tools is to better predict future medical

112 AN12 Abstracts

costs given a patient’s claim history.

Danielle Hanks, Mason VictorsBrigham Young Universitydaniellehanks@gmail.com, mason.victors@gmail.com

PP1Computation and Analysis of Evolutionary GameDynamics

Biological species (viruses, bacteria, parasites, insects,plants, or animals) replicate, mutate, compete, adapt, andevolve. In evolutionary game theory, such a process is mod-eled as a so-called evolutionary game. We describe theNash equilibrium problem for an evolutionary game anddiscuss its computational complexity. We discuss the nec-essary and sufficient conditions for the equilibrium states,and derive the methods for the computation of the optimalstrategies, including a specialized Snow-Shapley algorithm,a specialized Lemke-Howson algorithm, and an algorithmbased on the solution of a complementarity problem on asimplex. Computational results are presented. Theoreticaldifficulties and computational challenges are highlighted.

Yiping HaoDepartment of MathematicsIowa State Universityyphao@iastate.edu

Wen ZhouDepartment of Mathematics and Department of StatisticsIowa State Universityriczw@iastate.edu

Zhijun WuIowa State Universityzhijun@iastate.edu

PP1Explicit Update Scheme for Inverse Elliptic Prob-lems

We introduce an efficient method to recover piecewise con-stant coefficients occurring in elliptic PDEs as well as theinterface where these coefficients have jump discontinuities.We use an output least squares approach with level set andaugmented Lagrangian methods. Our formulation incorpo-rates the inherent nature of the piecewise constant coeffi-cients, which allows us to obtain an explicit update formulafor them. Numerical examples of Poisson’s equation andlinear elasticity are given.

Jan HegemannUniversity of MuensterUniversity of California, Los Angelesj.hegemann@uni-muenster.de

Alejandro CantareroUCLAcantarer@math.ucla.edu

Casey RichardsonJohns Hopkins Universityclr@cis.jhu.edu

Joseph TeranUCLAjteran@math.ucla.edu

PP1AWM - Inferring Gang Affiliation for ViolentEvents with Incomplete Data

Data sets are often plagued with portions of incompletedata. In this case, the data are assumed to be associatedwith one of N self-exciting point processes that lie on anetwork. The time and geographical location for all eventsare known, however the process affiliation is not known forsome events. This work proposes an iterative method witha directly calculable score function assigning weights forprocess affiliation and approximating the process parame-ters.

Rachel HegemannUniversity of California, Los Angelesrachel.a.hegemann@gmail.com

PP1A Bayesian Approach to Uncertainty Quantifica-tion for Stochastic Epidemic Models

We present a method to quantify the uncertainty in predic-tions made by stochastic models of epidemics. For thesetypes of simulations random events cause important fac-tors, such as epidemic size and duration, to vary over awide range of values. This makes it difficult for policy mak-ers to base decisions on these types of epidemic models. Inthis research we use Bayesian techniques to construct dis-tributions for important epidemic quantities from sampleruns of the simulation. Once a distribution is found foran output quantity of interest the quality of the model’spredictions can be evaluated. We propose a measure toquantify the effectiveness of a stochastic epidemic modelspredictive ability using these distributions.

Kyle S. Hickmann, Mac HymanTulane Universitykhickma@tulane.edu, mhyman@tulane.edu

PP1A Family of Euler-Maclaurin Formulae for N-PointGaussian Quadrature

The Euler-Maclaurin Formula is a powerful and well-knownresult from classical numerical analysis relating discretesums to integrals. One way to establish this equationis by utilizing periodic Bernoulli Polynomials, which canbe derived using a generating function, and performing astraight-forward integration by parts. The obtained for-mula relates the standard trapezoid rule (or the zero-pointGauss Method) of numerical integration to a series of termsinvolving the Bernoulli Numbers, the derivatives of thefunction at the endpoints and an error term. My aim inthis presentation is to show one can derive an analogousformula based on the midpoint (1-point Gauss Method),2-point Gauss method, and, in turn, a general family ofEuler-Maclaurin formulae for N-Point Gaussian-LegendreQuadrature.

Andrew M. HofstrandHunter College–City University of New Yorkhofmaster4740@hotmail.com

PP1A Slow Pushed Front in a Lotka-Volterra Compe-tition Model

We study invasion speeds in the Lotka-Volterra competi-

AN12 Abstracts 113

tion model when the rate of diffusion of one species is small.Our main result is the construction of the selected frontand a rigorous asymptotic approximation of its propaga-tion speed, valid to second order. From a perspective oflinear versus nonlinear speed selection, this front providesan interesting example as the propagation speed is slowerthan the linear spreading speed. However, our front sharesmany characteristics with pushed fronts that arise when theinfluence of nonlinearity leads to faster than linear speedsof propagation. We show that this is a result of the linearspreading speed arising as a simple pole of the resolventinstead of as a branch pole. Using the pointwise Green’sfunction, we show that this pole poses no a priori obsta-cle to marginal stability of the nonlinear traveling front,thus explaining how nonlinear systems can exhibit slowerspreading that their linearization in a robust fashion.

Matt HolzerSchool of MathematicsUniversity of Minnesotamdholzer@umn.edu

Arnd ScheelUniversity of Minnesotascheel@umn.edu

PP1Convergence of a Gauss Pseudospectral Method forOptimal Control

A convergence theory is established for approximations ofcontinuous-time optimal control problems using a Gausspseudospectral method. Specifically, it is shown that,under assumptions of coercivity and smoothness, theGauss pseudospectral method has a local minimizer thatconverges in the sup-norm to a local minimizer of thecontinuous-time optimal control problem. The convergencetheory is summarized and examples are provided that agreewith the theoretical results.

Hongyan Hou, William HagerDepartment of MathematicsUniversity of Floridahhongyan@ufl.edu, hager@ufl.edu

Anil RaoMechanical and Aerospace EngineeringUniversity of Floridaanilvrao@ufl.edu

PP1A Fast Spectral Algorithm for the Quantum Boltz-mann Collision Operator

Numerically solving the quantum Boltzmann equation(Nordheim-Uehling-Uhlenbeck equation) is challenging dueto the multidimensional structure of the collision integral.Comparing to its classical counterpart, the main difficultycomes from the cubic interaction term. We propose a fastspectral algorithm based on a special decomposition of thecollision kernel. Numerical results in 2-D and 3-D for boththe Bose gas and the Fermi gas are presented to illustratethe accuracy and efficiency of the method.

Jingwei HuThe University of Texas at Austinhu@ices.utexas.edu

Lexing Ying

University of TexasDepartment of Mathematicslexing@math.utexas.edu

PP1AWM Variance Reduction for Monte Carlo Simu-lation for European Call Options Under the Cou-pled Additive-Multiplicative Noise Model

We propose a variance reduction method for Monte Carlocomputation of option prices in the context of the Cou-pled Additive-Multiplicative Noise model. Four differentschemes are applied for the simulation. The methods selectcontrol variates which are martingales in order to reducethe variance of unbiased option price estimators. Numer-ical results for European call options are presented to il-lustrate the effectiveness and robustness of this martingalecontrol variate method.

Wanwan HuangFlorida State Universitybsbhuang8527@hotmail.com

Brian EwaldDepartment of MathematicsFlorida State Universityewald@math.fsu.edu

PP1Device Modeling for Organic Solar Cells

Organic solar cells (OSCs) have great potential to play animportant role in addressing our future energy needs. Adrift-diffusion model is developed to describe the dynamicsof excitons and free charge carriers in OSC. Our model pre-dicts the performance of OSC devices by calculating theirquantum efficiency and current-voltage curves, as well asmany other important physical quantities, such as electricfield, and the carrier concentration.

Lunmei Huang, Robert KrasnyUniversity of MichiganDepartment of Mathematicslunmeih@umich.edu, krasny@umich.edu

Kyle RenshawDepartment of Physics, University of Michigankrenshaw@umich.edu

Stephen ForrestDepartment of Physics, Department of ElectricalEngineeringstevefor@umich.edu

PP1Shortest Path for High-Dimensional Data Repre-sentation

We show that the power-weighted shortest path lengththrough random points reflects metric deformation affectedby the probability density function. Such metric defor-mations adapt the data structure of the random samplefor machine learning purposes. We reason how the power-weighted shortest path length achieves asymptotic consis-tency in data clustering and connects to classical single-linkage clustering. Furthermore, the deformation metricframework will be proposed to encompass and connect

114 AN12 Abstracts

spectral methods and shortest paths.

Sung Jin HwangUniversity of Michiganssjh@umich.edu

Steven DamelinGeorgia Southern Universitysteve.damelin@gmail.com

Alfred HeroUniversity of Michiganhero@umich.edu

PP1Analysis of Optimal Mortgage Termination Underthe Cox-Ingersoll-Ross Model

We consider mortgage contracts where the borrower hasthe option to pay the outstanding balance at any time.In theory, the decision to terminate depends on the yieldcurve. Assuming the Cox-Ingersoll-Ross model for inter-est rates, the problem can be formulated as a variationalinequality or an equivalent free boundary problem. Exis-tence and uniqueness of a solution as well as regularity ofthe free boundary will be presented.

Christopher S. JonesUniversity of Pittsburghcsj3@pitt.edu

PP1Computing Characteristic Classes in Algebraic Ge-ometry

Characteristic classes, i.e., Chern and Segre classes of va-rieties are important invariants in algebraic geometry. Wepresent a method to compute them which works eithersymbolically using Grobner bases or numerically using ho-motopy continuation methods for polynomial equation sys-tems. It has been implemented using Macaulay2 andBertini.

Christine JostStockholm Universityjost@math.su.se

David EklundInstitut Mittag-Lefflerdaek@math.kth.se

Chris PetersonColorado State Universitypeterson@math.colostate.edu

PP1Minimizing Communication in Sparse Matrix-Vector Multiplication Using a Novel Representa-tion

We consider the problem of multiplying a sparse matrixA ∈ Rn×n with a dense matrix X ∈ Rn× with the aim ofincreasing register reuse. A new block compressed formatthat is shown to have less loads compared with compressedsparse row and block compressed sparse row formats, isproposed. The format stores blocks as bitmaps and is lesssensitive to the non–zero structure (in comparison withblocked formats). A C++ based algorithm that decodes

blocks in O(\‡) time, where nzb is the number of non–zeros in a block, is developed. Performance comparisonswith Intel MKL sparse BLAS and with standard CSR andBSR implementations are presented.

Ramaseshan KannanUniversity of Manchester, UK and Arup Ltd. UKrkannan@maths.man.ac.uk

PP1AWM - A Stochastic Delay Model for Pricing

In the business world, in addition to equity, corporatebonds are also a main source of funds for many com-panies. However, depending on the ability of the man-agers or other reason, it can happen that a company facesbankruptcy. When a company becomes insolvent, the stockvalue decreases to zero and the equity-holders lose theirinvestments. Naturally, debt-holders would like to makesure that their investments are secured. In order to sup-port companies in this situation and encourage new in-vestments, some government agencies provide loan guar-antees. In this presentation, we give a formula for theprice of an option used for the pricing of corporate default-able bonds satisfying a stochastic delay differential equa-tion (SDDE). Assuming that the company value satisfies aSDDE as above, we evaluate government loan guaranteesfor companies in financial distress.

Elisabeth KemajouSouthern Illinois University Carbondaleisakema@aol.com

PP1Deforming Cylindrical Hypersurfaces in Hyper-bolic Space by Their Harmonic Mean Curvature

We show that under harmonic mean curvature flow cylin-drically symmetric hypersurfaces about a closed geodesic inhyperbolic space contract to the geodesic and the shape ofthe evolving hypersurface becomes like a round cylinder.A novel approach is developed to distinguish the radialand angular principal curvatures of the evolving hypersur-face by their qualitative behavior using parabolic maximumprinciple. The evolution equation is a fully nonlinear de-generate parabolic PDE.

Chris KimUniversity of Minnesotacmkim@umn.edu

Robert GulliverUniversity of MinnesotaSchool of Mathematicsgulliver@math.umn.edu

PP1Deforming Cylindrical Hypersurfaces in Hyper-bolic Space by their Harmonic Mean Curvature

We show that under harmonic mean curvature flow rota-tionally symmetric hypersurfaces about a closed geodesic inhyperbolic space contract to the geodesic and the shape ofthe evolving hypersurface becomes like a round cylinder.A novel approach is developed to distinguish the radialand angular principal curvatures of the evolving hypersur-face by their qualitative behavior using parabolic maxi-mum principle. The evolution equation is a fully nonlinear

AN12 Abstracts 115

parabolic PDE.

Christopher KimCornell Universitycmkim@umn.edu

Robert GulliverUniversity of MinnesotaSchool of Mathematicsgulliver@math.umn.edu

PP1Mechanism of Default Contagion with Graph Rep-resentations

We consider a mechanism of contagion of default followingdefault of Greek banks, in which creditor banks in Euro-pean countries give proportional haircuts to their creditors,in a sequence of stages. Net liabilities are represented bysimple weighted directed graphs and bilateral liabilities bymultigraphs. We compare with current data. This includeswork by undergraduate student Shuangshi Han, with fac-ulty sponsor Katherine Kime.

Katherine KimeUniversity of Nebraska at KearneyDepartment of Mathematics and Statisticskimek@unk.edu

Shuangshi HanUniversity of Nebraska KearneyLanzhou University of Finance and Economics (P.R.China)shuangshihan@gmail.com

PP1A Delay-Differential Equation Approach to Deter-mine Insulin Sensitivity

After initial research by Bergman et al. (1985) using math-ematical models to determine insulin sensitivity in diabet-ics, the insulin sensitivity question has largely been ignoredin preference of directly modeling the glucose/insulin dy-namics in the human body. These models have greatlyincreased in their complexity and ability to explain clin-ically observed data. This research aims to reopen theinsulin sensitivity question using the more sophisticatedtechniques that have recently been applied to this field.

Stephen M. KisslerUniversity of Colorado Boulderstephen.kissler@colorado.edu

PP1Linear Response Closure Approximation for Mul-tiscale Systems

Many physical processes involve multiscale dynamics, char-acterized by time and space scale separation with a largeset of rapidly evolving variables and a smaller set of slowlyevolving variables. We present a method to obtain a closedsystem for the slow variables, requiring only a simple cal-culation of statistics of the fast variables and use of thefluctuation-dissipation theorem. We apply this method toa two-scale model with linear coupling.

Marc KjerlandUniversity of Illinois at Chicago

kjerland@math.uic.edu

Rafail AbramovDepartment of Mathematics, Statistics and ComputerScienceUniversity of Illinois at Chicagoabramov@math.uic.edu

PP1Accuracy-Enhancing Moving Grid Method forStratified Flow Calculations

We present the moving grid method an r-adaptive dis-cretization of the underlying system of PDEs. This gridadaptivity allows to dynamically increase resolution in theareas of interest (an interface or a rapid flow variation)while keeping the size of computational mesh unchanged.The method was tested on several stratified flow configu-rations with sharp density discontinuities and consistentlyoutperformed its static-grid counterpart. Scalability andparallel performance of our solver on a supercomputer willbe discussed.

Sergey KoltakovStanford Universitykoltakov@stanford.edu

Oliver FringerEnvironmental Fluid Mechanics LaboratoryStanford Universityfringer@stanford.edu

PP1Reduced Order Modeling for Dynamic EarthquakeSimulations

Motivated by the devastating earthquake and tsunami lastyear in Japan, we explore the use of reduced order modelsfor subduction zone, megathrust earthquake simulations.The technique we employ uses a few parallel, full physicssimulations to build a surrogate model which can be sam-pled to explore the parameter space. The quantities ofinterest are the total slip on the fault, slip at the trenchaxis (where the fault meets the seafloor), and seafloor de-formation.

Jeremy E. KozdonStanford UniversityGeophysicsjkozdon@stanford.edu

Paul ConstantineStanford UniversityMechanical Engineeringpaul.constantine@stanford.edu

PP1A POD Study for a Coupled Burgers Equation

We study the coupled Burgers Equation that share similari-ties with the Boussinesq equations that are commonly usedin thermal-fluid dynamics. A training set” of FE solutionsis generated and a POD model reduction scheme is applied.However, the actual dynamics of the system can vary fromthe dynamics that are contained in the training set. Hence,we investigate the dependence of the reduced order modelon the input parameters(especially the Reynolds number).

116 AN12 Abstracts

Boris KraemerVirginia Techbokr@vt.edu

John A. BurnsVirginia TechInterdisciplinary Center for Applied Mathematicsjaburns@vt.edu

PP1Approximating the Singularities of a Function byMeans of Its Fourier-Jacobi Coefficients: An En-hanced Power Method

We modify the method suggested earlier by us and over-come its main deficiency. The method enables the approx-imation of the locations of jump discontinuities of a func-tion, one by one, by means of ratios of so called higher orderFourier-Jacobi coefficients of the function. It is shown thatthe location of singularity of a piecewise constant functionwith one discontinuity is recovered exactly and the loca-tions of singularities of a piecewise constant function withmultiple discontinuities are recovered with exponential ac-curacy. Unlike the previous one, the modified method isrobust, since its success is independent of whether or nota location of the discontinuity coincides with a root of aJacobi polynomial. In addition, some numerical examplesare presented.

George KvernadzeWeber State Universitygkvernadze@weber.edu

PP1Computational Docking of Molecular Wires to theReaction Center of Rhodobacter Sphaeroides

Given the worldwide interest in renewable energy, scien-tists have been exploring the possibility of using bacterialphotosynthetic reaction centers to build a new generationof highly efficient photovoltaic devices. To build such de-vices, molecular wires (MWs) that serve as good conduc-tors to transport electrons from and to the reaction cen-ters are needed. The MWs must dock at specific bindingsites within the reaction centers. We explore computa-tional models of docking MWs to the reaction centers.

Byong Y. KwonGeorge Mason Universitybkwon1@masonlive.gmu.edu

PP1Mixed Methods of Viscoelastic Wave Propagation

We present new mixed finite element methods for wavepropagation in viscoelastic solids. We use recently devel-oped mixed finite elements for elasticity with weak sym-metry of stress for which we have proved optimal a priorierror estimates. We present numerical results which sup-port our error analysis and demonstrate the performanceof the methods on problems of practical interest.

Jeonghun LeeUniversity of Minnesotaleex2454@umn.edu

PP1Vector-Valued Parametric Kernel-Based Interpola-tion for Two-Dimensional Facial Animations

This paper explores a scattered-data, interpolation-basedapproach, which uses a vector-valued parametric interpo-lation method for creating tween frames. Using the blend-shapes method, a 27-frame, two-dimensional, facial anima-tion was generated. Key-frames 1, 3, and 27 were then usedto produce similar animations with the following inter-polation methods: Gaussian RBF,Inverse multiquadratic,C2 Mate rn, Multiquadratic, and the Distance Function.All methods were then compared and performance adjust-ments made.

Barrett A. LeslieIllinios Institute of Technologybleslie@iit.edu

PP1A Neuronal Network Model of Drosophila Anten-nal Lobe

We construct a conductance based neuronal network modelof the Drosophila antennal lobe with the aim of proposingpossible interactions within the antennal lobe that accountfor the variety of projection neuron activity observed inexperimental data. Computational studies using olfactoryreceptor neuron inputs that mimic experimental recordingsdemonstrate the possible roles of excitatory local neuronsin spreading excitation among glomeruli and in recruitinginhibition.

Dori LuliArizona State Universitydori.luli@su.edu

Sharon M. CrookDept of Mathematics and Statistics & School of LifeSciencesArizona State Universitysharon.crook@asu.edu

PP1SmartGrid Pricing and Consumer Privacy Con-straints

The widespread adoption of SmartGrid technologiespromises to radically change the way electricity is deliveredand priced, in part by enabling the collection of fine-graineddata on customer power consumption. Unfortunately, thisusage data can be linked by adversaries to other behav-iors, seriously threatening consumer privacy. We exploreschemes for maintaining privacy, investigate tradeoffs be-tween privacy and fairness, and model the game that arisesbetween providers and strategic, privacy-conscious electric-ity consumers.

Shaudi Mahdavi HosseiniUniversity of Pennsylvaniashaudi@seas.upenn.edu

PP1Massively ParallelAdaptive Fast Multipole Method for Volume Po-tentials

FMM is traditionally used to solve N-body problems with

AN12 Abstracts 117

point sources. Here, we present a FMM based solver forvolume potentials in 3D, using piecewise polynomials andadaptive octree to represent source distribution and outputpotential. We use OpenMP and MPI for shared and dis-tributed memory parallelism, and BLAS, FFTW and SSEoptimizations are used to get high FLOP rates. We presentconvergence results for various kernels and show scalabilityto over 100,000 processor cores.

Dhairya MalhotraInstitute of Computational Engineering and SciencesThe University of Texas at Austindmalhotra@ices.utexas.edu

George BirosUniversity of Texas at Austinbiros@ices.utexas.edu

PP1A Network-Patch Model for the Transmission andEmergence of Mosquito-Borne Pathogens

We derive a network-patch model for the spread ofmosquito-borne diseases that couples to agent-based spa-tial epidemic models. The new model accounts for environ-mental factors, such as rainfall and temperature, and forvariations in mosquito-related parameters, including theemergence rates and incubation period of the pathogen. Itconsiders spatial heterogeneity in vector populations with-out modeling individual mosquitoes, thus reducing compu-tational expense while maintaining accuracy. Our simula-tions quantify the importance of heterogeneity in predict-ing the spread of vector-borne diseases.

Carrie A. Manore, James HymanTulane Universitycmanore@tulane.edu, mhyman@tulane.edu

Christopher MoresLouisiana State Universitycmores@lsu.edu

Sarah DelValle, Susan MniszewskiLos Alamos National Laboratorysdelvall@lanl.gov, smm@lanl.gov

Kyle S. HickmannTulane Universitykhickma@tulane.edu

Rebecca ChristoffersonLouisiana State Universityrcarri1@lsu.edu

Helen WearingUniversity of New Mexicohwearing@math.unm.edu

Reid PriedhorskyLos Alamos National Laboratoryreidpr@lanl.gov

PP1High-Order Nodal Formulation of the Mimetic Fi-nite Difference Method for Elliptic Problems

The high-order nodal formulation of the Mimetic FiniteDifference Method for two-dimensional elliptic problems

is based on a consistency condition that reproduces ex-actly the integration by parts formula for polynomials ofdegree higher than one. This formulation requires differentkinds of degrees of freedom, like moments of polynomialsor normal derivatives at edges. Optimal convergence rate isproved in a mesh-dependentH1 norm for meshes with verygeneral shaped elements and experimental results confirmthis behavior. This presentation is based on joint workswith L. Beirao da Veiga and K. Lipnikov.

Gianmarco ManziniLos Alamos National Laboratorygm.manzini@gmail.com

PP1Meshfree Quadratures for Planar Regions

Radial Basis Function (RBF) methods have gained signif-icant attention in the last decade as robust and highlyaccurate alternatives to classical polynomial methods forfunction approximation. Here, we present a novel quadra-ture scheme to approximate integrals in smooth planar re-gions using RBFs. Preliminary numerical results show thescheme to be spectrally (exponentially) convergent and ro-bust with respect to node location.

Jordan M. MartelUniversity of Colorado at BoulderDepartment of Applied Mathematicsjordan.martel@colorado.edu

PP1Numerical Modeling of Flow Over Flexible Vegeta-tion

Understanding the interaction of currents, waves, andstorm surge with coastal vegetation is important for coastaland environmental engineering. The existence of vegeta-tion greatly affects flow resistance, but modeling vegetationat small scales is challenging. In particular, plant flexibil-ity is often an important factor in the resistance charac-teristics. We numerically model the interaction of complexflow fields with flexible vegetation, utilizing the immersedboundary method and stabilized finite element methods onhighly-resolved computational meshes.

Steven A. MattisThe Institute for Computational Engineering and SciencesUniversity of Texas at Austinsteven@ices.utexas.edu

Clint DawsonInstitute for Computational Engineering and SciencesUniversity of Texas at Austinclint@ices.utexas.edu

Christopher KeesUS Army Engineer Research and Development Centerchristopher.e.kees@usace.army.mil

Matthew FarthingUS Army Engineer Research and Development Centerqmatthew.w.farthing@usace.army.mil

PP1Systems of Conservation Laws for Thermodynam-ically Consistent Adsorption with Subscale Diffu-

118 AN12 Abstracts

sion

Multicomponent adsorption is typically described by asystem of conservation laws in which the nonlinear fluxterms come from explicit functional relationships calledisotherms. Unfortunately the most popular extendedLangmuir isotherm is thermodynamically inconsistent. Wediscuss analysis and numerical approximation of multicom-ponent adsorption system where the thermodynamicallyconsistent isotherms are given only implicitly. Addition-ally, we consider subscale diffusion coupled to the transportand the associated nonlocal in time effects which smoothout the solutions.

Francis P. Medina, Malgorzata PeszysnkaOregon State Universitymedinaf@math.oregonstate.edu,mpesz@math.oregonstate.edu

PP1Multiscale Seismic Imaging

Imaging the Earth’s interior requires estimation of mechan-ical parameters (velocities and densities) that describe aregion of the subsurface. Numerical solution of the waveequation involves discretization and a choice of a particularscale of interest. The Earth contains interesting features atmany scales (from the millimeter to the kilometer scale).We describe an algorithm for solving the wave equationin which sub-wavelength heterogeneities are captured andincorporated into the macro-scale solution.

Susan E. MinkoffUniversity of Maryland, Baltimore CountyDept of Mathematics and Statisticssminkoff@umbc.edu

PP1Pandemic Influenza:Best Strategies to MinimizeTransmission Despite Parameter Uncertainty

When under the threat of Pandemic Influenza countriesdecide to take certain measures in order to contain thetransmission of the virus. Given that the parameters of thetransmission might not be accurate, the scenarios mightbe far from reality. We employed the robust optimizationframework to determine the most efficient strategies thatmitigate the adverse effects of Pandemic Influenza.

Romarie MoralesArizona State Universityromarie.morales@asu.edu

PP1The Case for Exponential Time Differencing forNeuronal Network Simulations

Exponential time differencing (ETD) has been used forHodgkin-Huxley-like ODEs by several authors, and is thedefault integrator in the popular neuronal simulation pack-age GENESIS. We show that the effectiveness of ETD forHodgkin-Huxley-like ODEs comes from the fact that it pre-vents overshoot during the very fast rising phase of theaction potential, allowing simulations that sacrifice accu-rate resolution of action potentials without significant lossof overall accuracy. We also propose a second-order ETDscheme.

Alexander Nectow

Rockefeller UniversityLaboratory of Molecular Geneticsanectow@rockefeller.edu

Christoph BorgersTufts Universitychristoph.borgers@tufts.edu

PP1Highly Accurate 3D Nearly Singular Integration

Boundary integral methods often give rise to nearly sin-gular integrals in which the integrand is very steep at apoint. Standard integration techniques on such integralssuffer from low accuracy. We develop a highly accuratemethod for 3D surface integrals with near singularities.The method involves isolation and smoothing of the nearsingularity with two changes of variables. Stokes flow isused as a test case.

Mike NicholasCarthage Collegemnicholas@carthage.edu

PP1Application of Fractional Calculus to Domain WallMotion

The equation of motion carrying the domain wall motioninside a ferromagnetic material has been solved fractionallyusing Laplace transform technique for a fractional deriva-tive of the damping term. The solution reduces to the wellknown result of the simple harmonic oscillator when alpha=0 and to the damping result when alpha =1 where thedamping term is proportional to the viscosity of the sus-pension. Results for different values of alpha and dampingratio are drawn and discussed under special initial condi-tions.

Abdalla A. Obeidat, Wesam Al-Sharoa, Manal Al-AliJordan University of Science and Technologyaobeidat@just.edu.jo, wesamalsharoa@yahoo.com, etu-nal@hotmail.com

PP1Applying Stochasticity to Models of Rotavirus Dis-ease and Vaccination

Despite significant advances in water quality and hygienearound the world, rotavirus diarhhea continues to be themain cause of severe gastroenteritis across the globe. Atwo-strain continuous-time Markov chain model of ro-tavirus infection is formulated. This model considers natu-ral immunity from subsequent infections and the effects ofvaccination are analyzed. Although, the disease can not becompletely eradicated without perfect vaccination, differ-ent scenarios for the reduction of morbidity and mortalityare evaluated and compared.

Omayra OrtegaArizona State Universityomayra.ortega@asu.edu

PP1Cost Benefit Analysis of Vector Control Strategiesfor Dengue in Bangkok

We use the data from Queen Sirkit National Institute of

AN12 Abstracts 119

Child Health (QSNICH) from 1973-1999 to estimate thetrue prevalence of Dengue disease in Bangkok, Thailandusing Monte Carlo Markov Chain Simulations. We presentpreliminary results of a cost benefit analysis on three vectorcontrol strategies: Larvicide and Adult control, Blockingtransmission and Reducing mosquito biting.

Abhishek PandeyClemson Universityabhishe@g.clemson.edu

Anuj MubayiNortheastern Illinois Universityanujmubayi@yahoo.com

Jan MedlockOregon State Universityjan.medlock@oregonstate.edu

PP1The Behaviour of a Thin Ridge Or Rivulet of Fluid

Two problems involving a thin ridge or rivulet of fluid arediscussed. Firstly, a ridge on an inclined planar substratesubject to an external airflow directed tangentially to thesubstrate is considered; in particular, the effect of increas-ing the strength of the airflow is analysed. Secondly, thegravity-driven draining of a rivulet of fixed width arounda large horizontal cylinder is considered; qualitatively dif-ferent behaviour is exhibited depending on whether therivulet is “narrow’ or “wide.’

Colin Paterson, Stephen Wilson, Brian DuffyUniversity of Strathclydecolin.paterson@strath.ac.uk, s.k.wilson@strath.ac.uk,b.r.duffy@strath.ac.uk

PP1Use of the String Method to Find Minimal EnergyPaths of Droplets on Superhydrophobic Surfaces

Interest in superhydrophobic surfaces has increased due toa number of interesting advances in science and engineer-ing. Here we use a diffuse interface model for dropletson topographically and chemically patterned surfaces inthe regime where gravity is negligible. We then applythe constrained string method to examine the transition ofdroplets between different metastable/stable states. Thestring method finds the minimal energy paths (MEPs)which correspond to the most probable transition pathwaysbetween the metastable/stable states in the configurationspace. In the case of a hydrophobic surface with postsof variable height and separation, we determine the MEPcorresponding to the transition between the Cassie-Baxterand Wenzel states. Additionally, we realize critical dropletmorphologies along the MEP associated with saddle pointsof the free-energy potential and the energy barrier of thefree energy. We analyze and compare the MEPs and free-energy barriers for a variety of surface geometries, dropletssizes, and static contact angles ranging from partial wettingto complete wetting. We also introduce an unbiased doublewell potential in the diffuse interace model by introducinga chemical potential that is fixed for a given simulation.We find that the energy barrier shifts toward the Wenzelstate along the MEP as the height of the pillars increasesin the topographically patterned case while a shorter en-ergy barrier exists and is more centered along the MEPfor pillars of shorter height. More importantly, we demon-strate the string method as a useful tool in the study of

droplets on superhydrophobic surfaces by presenting a nu-merical study that finds MEPs in configuration space, crit-ical droplet morphologies and free-energy barriers whichin turn give us a greater understanding of the free-energylandscape.

Kellen PetersenCourant Institute of Mathematical SciencesNew York Universitykellen@cims.nyu.edu

PP1Exact Chirped Soliton Solutions for 1D Gross-Pitaevskii Equation with Time-Dependent Param-eters

The Gross-Pitaevskii equation describing the dynamics of aBose-Einstein condensates at absolute zero temperature, isa generalized form of the Nonlinear Schroedinger equation.In this work, the exact one bright soliton solution of 1DGP equation with time-dependent parameters is directlyobtained by using the well known Hirota method under thesame conditions as Ref (10). In addition the two-solitonsolution is also constructed effectively.

Zhenyun QinFudan universityzyqin@fudan.edu.cn

Gui MuQujing Normal Universityactuary2010@163.com

PP1Small Steady Self-Similar Inviscid Flow

We consider solutions of the 2-d compressible Euler equa-tions that are steady and self-similar. Examples arise nat-urally at interaction points in genuinely multi-dimensionalflow, and we are able to classify all possible solutions thatare L∞-close to a constant supersonic background. As aspecial case we prove that solutions of 1-d Riemann prob-lems are unique in the class of small L∞ functions, andmore generally that all solutions are necessarily BV .

Joseph P. Roberts, Volker W. EllingUniversity of Michiganjoeprob@umich.edu, velling@umich.edu

PP1Computing An Approximation to the HelmholtzEquation with a High Contrast Thin ScattererPresent

In this poster, we present new computations stemmingfrom the work of Moskow, Santosa, and Zhang [S. Moskow,F. Santosa, J. Zhang. An Approximate Method for Scat-tering by Thin Structures. SIAM J. Appl. Math. 66, pp.187-205]. We compute solutions to the Helmholtz equationwith a high contrast thin scatterer present where the di-aelectic constant is discontinuous. We then compare theaccuracy of a leading term approximation under such con-ditions.

Scott RomeDrexel UniversityDepartment of Mathematicsromescott@gmail.com

120 AN12 Abstracts

PP1Snakes and Ladders: Stability of Fronts and Pulses

The subject of this poster are localized patches composed ofspatially periodic structures. These patterns often exhibitsnaking: in parameter space, the localized states lie on avertical sine-shaped bifurcation curve so that the width ofthe underlying periodic pattern increases as one moves upalong the bifurcation curve. The issue addressed here is thestability of these structures as a function of the bifurcationparameter.

Bjorn SandstedeBrown Universitybjorn sandstede@brown.edu

PP1AWM Physiologically-Based Pharmacokinetic(pbpk) Modeling of Metabolic Pathways of Bro-mochloromethane in Rats.

An updated PBPK model for bromochloromethane is gen-erated and applied to two different metabolic hypotheses:1) a two-pathway model using CYP2E1 and glutathionetransferase enzymes, and 2) a two-binding site model wheremetabolism occurs only with CYP2E1. Our computer sim-ulations show that both hypotheses describe the experi-mental data in a similar manner. In addition, we explorethe sensitivity of different parameters for each model usingour obtained optimized values and explore their applica-tions to risk assessment.

Megan SawyerNorth Carolina State Universitymesawyer@ncsu.edu

PP1On the Spectral Stability of Soltion Solutions of theVector Nonlinear Schrodinger Equation

We consider a system of coupled cubic nonlinearSchrodinger (NLS) equations

i∂ψj

∂t= −∂

2ψj

∂x2+

n∑

k=1

αjk|ψk|2ψj j = 1, 2, . . . , n

where αjk = αkj are real. The stability of solitary wavesolutions is examined numerically using Hill’s method (De-coninck, B. and J. N. Kutz. J. Comput. Phys., 219: 296-321, 2006). Our results extend the analysis of Nguyen(Commun. Math. Sci., 9: 997-1012, 2001.) to incorpo-rate solitons with nontrivial phase profile.

Natalie SheilsDepartment of Applied MathematicsUniversity of Washingtonnsheils@amath.washington.edu

Bernard DeconinckUniversity of Washingtonbernard@amath.washington.edu

Nghiem Nguyen, Rushun TianUtah State Universitynghiem.nguyen@usu.edu, rushun.tian@aggiemail.usu.edu

PP1Detecting And Using Stable Communities For

Modularity Maximization

Community detection through modularity maximization,is an important objective in large-scale network analysis.However, the value of the modularity and consequently thecommunity membership is affected by vertex ordering ofthe network. We define a stable community as an invari-ant group of vertices that are always assigned to the samecommunity. We present an algorithm to identify stablecommunities and show that combining stable communitiesas a preprocessing step leads to higher modularity. .

Sriram Srinivasan, Sanjukta BhowmickDepartment of Computer ScienceUniversity of Nebraska, Omahasriramsrinivas@unomaha.edu,sanjukta.bhowmick1@gmail.com

PP1Quantized Vortex Dynamics in Complex Ginzburg-Landau Equation in Bounded Domain

In this presentation, I will present efficient and accuratenumerical methods for studying the quantized vortex dy-namics and their interaction of the two-dimensional (2D)complex Ginzburg-Landau equation (CGLE) with a dimen-sionless parameter ε > 0 in bounded domains under eitherDirichlet or homogeneous Neumann boundary condition. Iwill begin with a review of various reduced dynamical lawsfor time evolution of quantized vortex centers and showhow to solve these nonlinear ordinary differential equa-tions numerically. Then, I will present some results on thequantized vortex interaction under various different initialsetup, and identify the cases where the reduced dynamicallaws agree qualitatively and/or quantitatively as well asfail to agree with those from CGLE. Some other interest-ing phenomena will also be presented.

Qinglin TangNational University of SingaporeSingaporetqltql2010@gmail.com

PP1Statistical Test and Simulation for Multi-ScaleComputation of 2D Polymer Model

Multi-scale computation is an accurate and highly efficientcomputing method involving simulation and analysis of in-formation at different resolutions. Due to its common ap-plications, many mathematicians expect to ameliorate thelevel of accuracy and efficiency to an even higher level. Onepotential way is to analyze the statistics of data, and en-hance the algorithm by knowing the trend of data. Herewe discuss the statistical methods involving in 2D polymermodel.

Sunli TangRensselaer Polytechnic InstituteDepartment of Mathematical Sciencestangs4@rpi.edu

PP1An Analytical Approach to Green Oxidation

In this poster, we study the problem of suicidal inactivationof oxidation catalysts. We formulate a system of differen-tial equations that models chemical reactions and analyzeits numerical and analytical properties. Noticing its sim-

AN12 Abstracts 121

ilarity with Michaelis-Menten system, we have been ableto develop quasi-state approximation that together withperturbation techniques has allowed us to derive an ap-proximate solution. The main goal is to estimate the ratesof the reactions for deeper understanding of the system.

Diego TorrejonGeorge Mason Universitydtorrejo@masonlive.gmu.edu

PP1Conditional Stochastic Simulations and Error Esti-mates for Flow and Transport in Porous Media

We use stochastic parameterizations to describe the prop-erties of the coefficients of flow and transport model; thenwe use stochastic collocation or Monte Carlo simulationsto solve the system of PDEs. The novelty is that we areable to include prior data for which conditional parame-terizations are obtained. We provide comparison with un-constrained simulations. Additionally, we derive error esti-mates for the quantities of interest in the coupled system.

Veronika S. VasylkivskaDepartment of MathematicsOregon State Universityvasylkiv@math.oregonstate.edu

Mina E. OssianderMath DeptOregon State Universityossiand@math.oregonstate.edu

Malgorzata PeszynskaDepartment of MathematicsOregon State Universitympesz@math.oregonstate.edu

PP1A Method of Lines Approach to Solving Pdes onSurfaces

Partial differential equations (PDEs) posed on surfacesappear often in mathematical modelling. The ClosestPoint Method is a numerical technique for solving thesetypes of equations, by embedding the surface in a higher-dimensional space. We present a new way to formulatean embedding equation which leads to a simple method oflines approach. We also include a variety of computationalexamples.

Ingrid Von GlehnUniversity of Oxfordingrid.vonglehn@maths.ox.ac.uk

Colin MacdonaldOxford Universitymacdonald@maths.ox.ac.uk

PP1Proper Orthogonal Decomposition Reduced OrderModels For Complex Flows

Reduced-order models are frequently used in the simula-tion of complex flows to overcome the high computationalcost of direct numerical simulations, especially for three di-mensional nonlinear problems. Proper orthogonal decom-

position is one of the most commonly used methods to gen-erate reduced-order models for turbulent flows dominatedby coherent structures. To balance the low computationalcost required by a reduced-order model and the complexityof the targeted turbulent flows, appropriate closure model-ing strategies need to be employed. In this paper, we willpresent several new nonlinear closure methods for properorthogonal decomposition reduced-order models. We willalso present numerical results for the new models used inrealistic applications such as energy efficient building de-sign and control, and climate modeling.

Zhu Wang, Traian IliescuDepartment of MathematicsVirginia Techwangzhu@vt.edu, iliescu@vt.edu

Jeff BorggaardVirginia TechDepartment of Mathematicsjborggaard@vt.edu

Imran AkhtarVirginia Techakhtar@vt.edu

PP1Computing Positive Semidefinite Minimum Rankfor Small Graphs

The positive semidefinite minimum rank (mr+) of a sim-ple graph G is the smallest possible rank over all posi-tive semidefinite real symmetric matrices whose ijth ( inot equal to j) entry is nonzero whenever ij is an edge,and zero otherwise. We programmed an implementationof known bounds in the open-source mathematical softwareSage. The program, along with orthogonal representations,establishes mr+ for all graphs of order 7 or less.

Nathan Warnberg, Steven OsborneIowa State Universitywarnberg@iastate.edu, sosborne@iastate.edu

PP1Improving Hidden Markov Models that use Classi-fied Observations

A Hidden Markov Model looks at observations generatedby a ”hidden” Markov process. When the observed datais complex, it must first be classified before it can be usedin such a model. We use classification methods borrowedfrom natural language processing to prepare observationdata to train a Hidden Markov Model. As an example weconsider grouping clients based on health insurance claims.

Matthew Webb, Danielle Hanks, Mason Victors, JaredWebbBrigham Young Universitymawebb@math.byu.edu, daniellehanks@gmail.com, ma-son.victors@gmail.com, webb@math.byu.edu

PP1Improving Certainty Using Informed Markov Mod-els

Hidden Markov Models are a powerful tool for analysiswhen a Markov Process is not directly observable. How-ever, in a complicated model the sequence of observable

122 AN12 Abstracts

states with maximum likelihood may have a probabilityvery near to zero. We examine how these probabilities areaffected as we add information to the model, either via thehidden Markov process, or through the observation proba-bility matrix.

Jared WebbBrigham Young Universitywebb@math.byu.edu

PP1Diversification Effect of Distributed Solar EnergyUpon Energy Generation Volatility

High levels of volatility are a significant impediment to theintegration of solar energy into the electric grid. Combiningthe output of geographically distributed solar systems re-sults in a diversification effect that reduces the aggregatedvolatility. This diversification effect has been previouslyproposed, but it has undergone limited validation undercontrolled conditions. We have quantified and validatedthis diversification effect across a large fleet of distributedsolar installations in the field using highly granular data.

Matthew K. Williams, Shawn Kerrigan, Alex Thornton,Sergey KoltakovLocus Energymatthew.williams@locusenergy.com,shawn@locusenergy.com, alex.thornton@locusenergy.com,sergey.koltakov@locusenergy.com

PP1Restructuring the Ppm Gas Dynamics Algorithmfor Many-Core Cpu Devicces

The latest CPU devices contain a large number of cores(over 50 on Intels new MIC processors) that all must worktogether in order to achieve the best performance. Tech-niques and tools for restructuring fluid dynamical com-putations to allow all the cores on a single CPU chip towork cooperatively on data that they share in the proces-sor caches will be described, using the PPM gas dynamicsalgorithm as an example.

Paul R. WoodwardLaboratory for Computational Science and EngineeringUniversity of Minnesotapaul@lcse.umn.edu

Jagan Jayaraj, Pei-Hung LinUniversity of Minnesotajaganj@cs.umn.edu, phlin@cs.umn.edu

PP1A Radial Basis Function Partition of Unity Methodfor Transport on the Sphere

The transport process dominates geophysical fluid motionson all scales making the numerical solution of the transportproblem fundamentally important for the overall accuracyof any flow solver. We present a new high-order, computa-tionally efficient method for this problem that uses radialbasis functions in a partition of unity framework. Resultsof the method are presented for several well-known testcases that probe the suitability of numerical methods formodeling transport in spherical geometries.

Grady B. Wright, Kevin AitonDepartment of Mathematics

Boise State University, Boise IDgradywright@boisestate.edu, kevinaiton@u.boisestate.edu

PP1Grain Boundaries in Turing Patterns

Our main results show the existence of grain boundaries,describe their shapes, and exhibit bifurcations where grainboundaries split into pairs of concave and convex disclina-tions. Our work is split into two parts. In the first part, weshow that universally, for any pattern-forming system nearonset, that is, for small-amplitude patterns, the shape ofgrain boundaries is determined by a system of coupled or-dinary differential equations. Those equations are obtainedby recently developed reduction theorems for ill-posed el-liptic partial differential equations. The key observation isthat those reduced equations are universal once put in nor-mal form, that is, after a suitable change of coordinates.They contain only very few parameters and their solutionscan be fully analyzed despite the fact that the dimension ofthe system of equations is at least 12, and tends to infinitywhen the angle between rolls becomes small.

Qiliang WuUniversity of Minnesotawuxxx410@umn.edu

Arnd ScheelUniversity of MinnesotaSchool of Mathematicsscheel@math.umn.edu

PP1Parallel Cardiac Image Segmentation with RandomProjection Tree

Due to noise, artifacts and high accuracy requirement,medical image segmentation is always a challenging prob-lem. We proposed a data-driven approach, which classifiedeach pixel based on the similarity along the low dimen-sional parameterization of the feature space. In particu-lar, our framework discovers the intrinsic structure of highdimensional wavelet features using a random projectiontree structure, which is built on top of MPI and OpenMPfor massive dataset, and shows excellent scalability andspeedup.

Bo XiaoSchool of Computational Science and EngineeringGeorgia Institute of Technologyboxiao@gatech.edu

Geroge BirosThe Institute for Computational Engineering and SciencesUniversity of Texas at Austinbiros@ices.utexas.edu

PP1Local Convergence of Newton-Type Methods forDegenerate Eigenvalues of Nonlinear AlgebraicEigenvalue Problems

We analyze the local convergence rates of several Newton-type methods for the computation of a semi-simple or de-fective eigenvalue of general nonlinear algebraic eigenvalueproblems of the form T (λ)v = 0. We show that the con-vergence for semi-simple eigenvalues is similar to that forsimple ones. For defective eigenvalues, Newton-type meth-

AN12 Abstracts 123

ods converge only linearly. A class of accelerated methodsis proposed and shown to exhibit quadratic convergence.

Fei XueTemple Universityfxue@temple.edu

Daniel B. SzyldTemple UniversityDepartment of Mathematicsszyld@temple.edu

PP1Computation of Harmonic Forms of the VectorLaplacian

The vector Laplacian arises in electromagnetics and otherapplications, and an important role is played by its nullspace, the space of harmonic forms. I present an algorithmto compute a basis of this space. The algorithm combinesmixed finite elements for discretization, algorithms fromcomputational geometry to analyze the topology, and avariation of the power method suitable for multiple eigen-values. I also consider various ways to approximate localizethe harmonic basis functions.

Bo YangSchool of Mathematics, University of Minnesotayangbo@math.umn.edu

PP1AWM - A New Approach to Understanding theDynamics of the Formation of Magnetic Domains

Traditionally, ferromagnetism is studied using the Isingmodel, which is exactly solvable in one or two dimensionsand of limited use in the infinite- dimensional mean fieldcase. While preserving the classic energy arguments, ourmodel uses techniques previously applied to sociophysics toallow for arbitrary coupling between particles. By predict-ing the dynamics of the approach to magnetic equilibrium,we hope to improve the understanding of phase transitionsin materials of various lattice structures.

Haley YapleNorthwestern Universityhaleyyaple@u.northwestern.edu

PP1Partially Parallel Magnetic Resonance Image Re-construction Using Bregmanized Operator Split-ting with Variable Stepsize

This paper proposes a Bregman operator splitting algo-rithm with variable stepsize (BOSVS) for solving nons-mooth and nonlinear optimization problems of the formminuφ(∇u)+1/2‖Au−f‖22, where φ is a nonsmooth func-tion. This algorithm uses a line search to achieve betterefficiency. The stepsize rule starts with a Barzilai-Borwein(BB) step, and increases the nominal step until a termi-nation condition is satisfied. Theoretically, this algorithmconverges globally to the optimal solution of the optimiza-tion problem. Numerically, we get significantly better re-sults compared to original BOS algorithm with fixed step-size and SBB algorithm with BB stepsize. Experimentalresults in partially parallel magnetic resonance image re-construction displays that BOSVS algorithm gives greater

stability, accuracy and speed.

Maryam YashtiniUniversity of FloridaMathematics Departmentmyashtini@ufl.edu

William Hager, Yumni ChenDepartment of MathematicsUniversity of Floridahager@ufl.edu, yun@math.ufl.edu

Xiaojing YeSchool of MathematicsGeorgia Techxye33@math.gatech.edu

PP1Stochastic Simulation and Power-Law Relaxationof Highly Entangled Wormlike Micellar Solutions

Wormlike micelles, long flexible self-assembled aggregatesof surfactant molecules, form entangled networks in solu-tion. These mixtures exhibit two relaxation mechanisms,reptation and reversible breaking. Experiments in concen-tration regimes in which the worms are highly entangledshow power law stress relaxation instead of the exponentialrelaxation predicted by most traditional models (Johnson-Segalman, Giesekus, VCM). In this poster, we present flowpredictions, using stochastic simulations, to understand themechanisms of the power-law relaxation regime.

Yun ZengDepartment of Mathematical Sciences, University ofDelawareNewark, DE 19716, USAzengyun@math.udel.edu

Pamela CookDept of Mathematical SciencesU of Delawarecook@math.udel.edu

Lin ZhouDepartment of Mathematics, New York City College ofTechnology, Brooklyn, NY 11201, USAlzhou@citytech.cuny.edu

PP1AWM - Min-Max Game Theory Problem for theFluid-Structure Interaction Model: An Applica-tion to the Medicine Effect on Blood Flow in Hu-man Body

The min-max game theory problem for the fluid-structureinteraction model is considered. We apply the model toa biological scenario, where the medicine and the bacte-ria/viruses become two players counteracting on the bloodflow and blood cells inside the human body. The motionsof the blood flow and blood cells are described by Navier-Stokes equation and elastic equation respectively. Our goalis to find the optimal dose of the medicine for the patientthat can kill worst possible bacteria/viruses in his body.

Jing ZhangUniversity of Virginiajz4f@virginia.edu

124 AN12 Abstracts

PP1How to Compute Transition States/saddle Points?

Exploring complex energy landscape is a challenging issuein many applications. Besides locating equilibrium states,it is often also important to identify transition states givenby saddle points. In this talk, we will discuss existingand new algorithms for the computation of such transi-tion states with a focus on the newly developed ShrinkingDimer Dynamics and present some related mathematicaltheory on stability and convergence. We will consider anumber of applications including the study of frustrationsof interacting particles and nucleation in solid state phasetransformations.

Jiangyan ZhangDepartment of MathematicsPenn State Universityj zhang@math.psu.edu

Qiang DuPenn State UniversityDepartment of Mathematicsqdu@math.psu.edu

PP1Multi-Layer and Multi-Resolution Large Popula-tion Stochastic Games

Game theory has been used to understand and design com-plex systems with many interacting independent decision-making agents in changing environments. In this work, westudy a class of large population stochastic games withmulti-layer (ML) and multi-resolution (MR) structures.We first look at ML games in which the players have hy-brid dynamics where the continuous dynamics model theinteractions at the physical layer of the system, and thediscrete dynamics model the behavior at the cyber layer.In the second part of the work, we study MR games whereplayers face competitions within their group as well as in-teract with members outside their groups through globalparameters such as price, temperature, etc. We adopt amean-field approach to characterize the mean-field Nashequilibria of ML and MR games. We apply the frameworkand results to study complex systems such as moleculartransport and demand response in the smart grid.

Quanyan Zhu, Tamer BasarUniversity of Illinois at Urbana-Champaignzhu31@illinois.edu, basar1@illinois.edu

PP1Dynamics and Noise Minimization of Femto-Second Similariton Pulses in a Fiber Laser withZero Average Disperion

Various experimental designs have recently been proposedfor ultra-short pulse mode-locked fiber lasers with applica-tions to optical clocks, time and frequency transfer, gener-ation of arbitrary optical waveforms, and frequency-combspectroscopy. We will present simulation results (indepen-dently confirmed by laboratory experiments) demonstrat-ing the existence of self-similar femto-second pulses nearzero average dispersion in a laser with a Ytterbium fiber,and show that timing jitter is minimized when the averagedispersion is close to zero.

John W. ZweckUniversity of Maryland Baltimore County

Mathematics and Statisticszweck@umbc.edu

Curtis R. MenyukUMBCBaltimore, MDmenyuk@umbc.edu

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126 FM12 Abstracts

IC1Optimal Execution in a General One-Sided LimitOrder Book

We construct an optimal execution strategy for the pur-chase of a large number of shares of a financial asset overa fixed interval of time. Purchases of the asset have a non-linear impact on price, and this is moderated over time byresilience in the limit-order book that determines the price.The limit-order book is permitted to have arbitrary shape.The form of the optimal execution strategy is to make aninitial lump purchase and then purchase continuously forsome period of time during which the rate of purchase isset to match the order book resiliency. At the end of thisperiod, another lump purchase is made, and following thatthere is again a period of purchasing continuously at a rateset to match the order book resiliency. At the end of thissecond period, there is a final lump purchase. Any of thelump purchases could be of size zero. A simple condition isprovided that guarantees that the intermediate lump pur-chase is of size zero. This is joint work with GennadyShaikhet and Silviu Predoiu.

Steven E. ShreveCarnegie Mellon UniversityDept of Mathematical Sciencesshreve@cmu.edu

IC2Stable Diffusions With Rank-based Interactions,and Models of Large Equity Markets

We introduce and study ergodic diffusion processes inter-acting through their ranks. These interactions give rise toinvariant measures which are in broad agreement with sta-bility properties observed in large equity markets over longtime-periods. The models we develop assign growth ratesand variances that depend on both the name (identity)and the rank (according to capitalization) of each individ-ual asset. Such models are able realistically to capturecritical features of the observed stability of capital distri-bution over the past century, all the while being simpleenough to allow for rather detailed analytical study. Themethodologies used in this study touch upon the questionof triple points for systems of interacting diffusions; in par-ticular, some choices of parameters may permit triple (orhigher-order) collisions to occur. We show, however, thatsuch multiple collisions have no effect on any of the sta-bility properties of the resulting system. This is accom-plished through a detailed analysis of collision local times.The models have connections with the analysis of Queue-ing Networks in heavy traffic, and with competing par-ticle systems in Statistical Mechanics (e.g., Sherrington-Kirkpatrick model for spin-glasses). Their hydrodynamic-limit behavior is governed by generalized porous mediumequations with convection, whereas limits of a differentkind display phase transitions and are governed by Poisson-Dirichlet laws.

Ioannis KaratzasColumbia Universityik@math.columbia.edu

IC3Simulation Schemes for Stopped Lvy Processes

Jump processes, and Lvy processes in particular, are noto-riously difficult to simulate. The task becomes even harderif the process is stopped when it crosses a certain boundary,

which happens in applications to barrier option pricing orstructural credit risk models. In this talk, I will presentnovel adaptive discretization schemes for the simulation ofstopped Lvy processes, which are several orders of magni-tude faster than the traditional approaches based on uni-form discretization, and provide an explicit control of thebias. The schemes are based on sharp asymptotic estimatesfor the exit probability and work by recursively adding dis-cretization dates in the parts of the trajectory which areclose to the boundary, until a specified error tolerance ismet.

Peter TankovUniversite Paris-Diderot (Paris 7)tankov@math.univ-paris-diderot.fr

IC4Talk Title TBA - Avellaneda

Abstract not available at time of publication.

Marco AvellanedaCourant InstituteNew York Universityavellaneda@courant.nyu.edu

IC5Optimal Order Placement in Limit Order Books

Abstract not available at time of publication.

Xin GuoUniversity of California, Berkeleyxinguo@ieor.berkeley.edu

IC6Quantitative Absence of Arbitrage and EquivalentChanges of Measure

It is well known that absence of arbitrage is a highly desir-able feature in mathematical models of financial markets.In its pure form (whether as NFLVR or as the existence ofa variant of an equivalent martingale measure R), it is qual-itative and therefore robust towards equivalent changes ofthe underlying reference probability (the ”real-world” mea-sure P). But what happens if we look at more quantitativeversions of absence of arbitrage, where we impose for in-stance some integrability on the density dR/dP? To whichextent is such a property robust towards changes of P? Wediscuss these questions and present some recent results.The talk is based on joint work with Tahir Choulli (Uni-versity of Alberta, Edmonton).

Martin SchweizerETH MathZurich, Switzerlandmartin.schweizer@math.ethz.ch

SP1AWM-SIAM Sonia Kovalevsky Lecture : The Roleof Characteristics in Conservation Laws

Sonya Kovalevsky, in the celebrated Cauchy-Kovalevskytheorem, made clear the significance of characteristics inpartial differential equations. In the field of hyperbolicconservation laws, characteristic curves (in one space di-mension) and surfaces (in higher dimensions) dominate thebehavior of solutions. Some examples of systems exhibit

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interesting, one might even say pathological, characteristicbehavior. This talk will focus on ways that characteristicsin systems of conservation laws give information about thesystems being modeled.

Barbara Lee KeyfitzThe Ohio State UniversityDepartment of Mathematicsbkeyfitz@math.ohio-state.edu

SP2The John Von Neumann Lecture: Liquid Crystalsfor Mathematicians

Liquid crystals form an important class of soft matter sys-tems with properties intermediate between solid crystalsand isotropic fluids. They are the working substance of liq-uid crystal displays, which form the basis of a huge multi-national industry. The lecture will describe these fascinat-ing materials, and what different branches of mathematics,such as partial differential equations, the calculus of vari-ations, multiscale analysis, scientific computation, dynam-ical systems, algebra and topology, can say about them.

John BallOxford Centre for Nonlinear PDE Mathematical InstituteOxfordball@maths.ox.ac.uk

SP3Past President’s Address: Reflections on SIAM,Publishing, and the Opportunities Before Us

Upon taking up the post of president I had, of course, for-mulated my priorities for SIAM. This talk provides a goodoccasion to revisit some of those. One area turned outto play a vastly larger role than I would have anticipated,namely mathematical publishing and many issues associ-ated with it, ethical, technological, economic, political, andscientific. The future of scholarly publishing is far fromclear, but one thing seems certain: big changes are neededand will be coming. We, as mathematicians, are majorstakeholders. We should also be major agents in guidingthese changes. I will present some of my observations andthoughts as we confront the opportunities before us.

Douglas N. ArnoldSchool of MathematicsUniversity of Minnesotaarnold@umn.edu

SP4W. T. and Idalia Reid Prize Lecture: Large Alge-braic Properties of Riccati Equations.

In the eighties there was considerable interest in the alge-braic properties of the following Riccati equation

A∗X +XA−XBB∗X + C∗C = 0, (1)

where A,B,C ∈ A, a Banach algebra with identity, andthe involution operation ∗. Conditions are sought to ensurethat the above equation has a solution in A. The resultswere disappointing and the problem was forgotten untilthis century when engineers studied the class of spatiallydistributed systems. One application was to control forma-tions of vehicles where the algebraic property was essential.This case involves matrices A,B,C with components in a

scalar Banach algebra. Positive results are obtained forboth commutative and noncommutative algebras.

Ruth CurtainUniversity of Groningen, Netherlandsr.f.curtain@math.rug.nl

SP5I.E. Block Community Lecture: Creating Reality:the Mathematics Behind Visual Effects

Abstract to follow.

Robert BridsonUniversity of British Columbiarebridson@gmail.com

SP6SIAG/FME Junior Scientist Prize: Market-BasedAapproach to Modeling Derivatives Prices

Most of the existing quantitative methods in Finance relyon the assumptions of the underlying mathematical mod-els. The problem of choosing the appropriate model as-sumptions is one of the cornerstones of modern FinancialEngineering. I am interested in developing modeling frame-works that facilitate the use of historical observations whenmaking the choice of model assumptions. It turns out that,in the markets with a large family of liquid derivative con-tracts, it is rather hard to construct a model that exploitsthe information contained in the historical prices of thesederivatives. In fact, constructing such models requires theuse of the so-called Market-Based Approach. The idea ofthis approach is to treat the liquid derivatives as genericfinancial assets and prescribe the joint evolution of theirprices in such a way that any future arbitrage-free combi-nation of prices is possible. In this presentation, I will out-line the main difficulties associated with the construction ofmarket-based models and will present a general methodol-ogy that bypasses these difficulties. Finally, I will illustratethe theory by describing (both mathematically and numer-ically) a family of market-based models for the Europeancall options of multiple strikes and maturities.

Sergey NadtochiyOxford UniversityOxford-Man Institutesergey.nadtochiy@oxford-man.ox.ac.uk

JP1Systemic Risk

What is systemic risk, how do we model it, how to we an-alyze it, and what are the implications of the analysis? Iwill address these issues both in a larger historical contextand within current research mathematical finance. The keyproperty of systems subject to systemic risk is their inter-connectivity and the way individual risk can become over-all, systemic risk when it is diversified by inter-connectivity.I will discuss theoretical issues that come up with mean-field and other models and will also show results of numer-ical simulations.

George C. PapanicolaouStanford UniversityDepartment of Mathematicspapanico@math.stanford.edu

128 FM12 Abstracts

CP1Pricing Interest Rate Derivatives in a MultifactorHjm Model with Time Dependent Volatility

We investigate the partial differential equation (PDE) forpricing interest rate derivatives in a multi-factor CheyetteModel, that involves time-dependent volatility functionswith a special structure. The high dimensional parabolicPDE that results is solved numerically via a sparse gridapproach, that turns out to be both accurate and efficient.The results are compared to the analytical solution forbonds and caplets and also the Monte Carlo simulationsolution for Bermudan Swaptions.

Ingo BeynaFrankfurt School of Finance & Managementingo.beyna@web.de

Carl ChiarellaProfessor, School of Finance and Economics, University ofTechnology, Sidney, Broadway NSW 2007, Australiacarl.chiarella@uts.edu.au

Boda KangUniversity of Technology Sydneyboda.kang@uts.edu.au

CP1A Paradigm Shift in Interest-Rate Modeling

This research starts with a solution for modeling non-negative interest rates in an incomplete bond market. Itis the stochastic-splines model, in which instantaneous for-ward rates are almost surely finite and approximately log-normal under both the real-world and the risk-adjustedmeasures. A unique term structure of convenience yieldfor the default-free bond market is introduced for thefirst time to compensate idiosyncratic risk. Addressingon the market completeness issue, the stochastic-volatilitystochastic-splines model is presented whereby bond conve-nience yield vanishes. Under this framework, the marketprice of volatility risk can be computed endogenously. Var-ious applications are given.

Peter LinJohns Hopkins Universitypeter.lin@jhu.edu

CP1Pricing Swaptions under Multifactor Gaussian HjmModels

Several approximations have been proposed in the liter-ature for the pricing of European-style swaptions undermultifactor term structure models. However, none of themprovides an estimate for the inherent approximation er-ror. Until now, only the Edgeworth expansion techniqueof Collin-Dufresne and Goldstein (2002) is able to char-acterize the order of the approximation error. Under amultifactor HJM Gaussian framework, this paper proposesa new approximation for European-style swaptions, whichis able to bound the magnitude of the approximation er-ror and is based on the conditioning approach initiated byCurran (1994) and Rogers and Shi (1995). All the pro-posed pricing bounds will arise as a simple by-product ofthe Nielsen and Sandmann (2002) setup, and will be shownto provide a better accuracy-efficiency trade-off than all the

approximations already proposed in the literature.

Joao Pedro V. NunesISCTE-IUL Business Schooljoao.nunes@iscte.pt

Pedro PrazeresSociedade Gestora dos Fundos de Pensoes do Banco dePortugalpedro.prazeres@sgfpbp.pt

CP1Pricing and Hedging the Smile with Sabr: Evi-dence from the Interest Rate Caps Market

This is the first comprehensive study of the SABR(Stochastic Alpha-Beta-Rho) model (Hagan et. al (2002))on the pricing and hedging of interest rate caps. We imple-ment several versions of the SABR interest rate model andanalyze their respective pricing and hedging performanceusing two years of daily data with seven different strikesand ten different tenors on each trading day. In-sampleand out-of-sample tests show that in addition to havingstochastic volatility for the forward rate, it is essential torecalibrate daily either the vol of vol or the correlation be-tween forward rate and its volatility, although recalibrat-ing both further improves pricing performance. The fullystochastic version of the SABR model exhibits excellentpricing accuracy and more importantly, captures the dy-namics of the volatility smile over time very well. Thisis further demonstrated through examining delta hedgingperformance based on the SABR model. Our hedgingresult indicates that the SABR model produces accuratehedge ratios that outperform those implied by the Blackmodel.

Tao L. WuIllinois Institute of Technologytw33 99@yahoo.com

CP2Swing Options in Commodity Markets: A Modelwith Multidimensional Jump Diffusions

The objective of this talk is to study the optimal exercisepolicy of a swing option in the electricity markets. We for-mulate a model in terms of a stochastic control problemin continuous time, subjected to a total volume constraint.The underlying price process is a linear function depend-ing on a multidimensional Levy diffusion. The results areillustrated with examples.

Marcus ErikssonPh.D Studentmkerikss@math.uio.no

Jukka LempaCentre of Mathematics for ApplicationsUniversity of Oslojukka.lempa@cma.uio.no

Trygve NilssenSchool of ManagementUniversity of Agdertrygve.k.nilssen@uia.no

CP2Decomposing the Risk from Investing in Foreign

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Commodities

Several papers show that FX rates and commodity pricesare interlinked. When investing in commodities traded ina foreign currency, the investor faces both price risk andFX risk. We investigate how exchange-traded contracts onWTI crude oil and EUR/USD correlate. We propose andestimate a model that accounts for the stochastic correla-tion between the two. This can be used to price and riskmanage foreign commodity positions, e.g., quanto optionsor oil-linked gas contracts.

Nina LangeCopenhagen Business Schoolnl.fi@cbs.dk

CP2A Real-Time Pricing Model for Electricity Con-sumption

Input your abstract, including TeX commands, here. TheCalifornia electric company, i.e., PGE (Pacific Gas andElectric Co.,), has recently announced its intentions tocharge small businesses in the state with dynamic pricesfor electricity consumption. In this regard, we study areal-time electricity pricing model in the paper and com-pare it with two static pricing models. We show that real-time pricing outplays static pricing when it comes to jointlymaximizing provider and consumer welfare.

Ranjan PalUniversity of Southern Californiarpal@usc.edu

CP2A Resampling Particle Filter Parameter Estima-tion For Electricity Prices With Jump Diffusion

In this paper we propose a particle ?lter for parameter es-timation of jump diffusion models employed for modellingelectricity prices 1,2,3,4,5. We consider a jump-diffusionmodel 4. The jumps has the possibility to give a better ex-planation of the behaviour of electricity prices, however es-timation of parameters becomes more complicated 4.Com-plications in parameter estimation will be introduced bythe inclusion of the jump component. The inclusion ofjumps will add several new parameters 4. These parame-ters will describe the jump frequency and distribution. Thejump models are non-Gaussian and this increases the com-plexity of the models 1,2,3,4. A known ?ltering techniquefor these models is particle ?lter 1,2,3. Particle ?lter (PF)is a fully non-linear ?lter with Bayesian conditional prob-ability estimation, compared here with the well-known en-semble Kalman lter (EnKF). A Gaussian resampling (GR)method is proposed to generate the posterior analysis en-semble in an effective and efficient way 3. The performanceof gaussian particle ?lter to model the jump frequency anddistribution parameters will be investigated and bench-marked to other maximum likelihood state estimators.

Bahri UzunogluGotland Universitybahri.uzunoglu@hgo.se

Dervis BayazitFederal Home Loan Bank of Atlantadbayazit@fhlbatl.com

CP3Basket and Spread Options in a Variance GammaModel

Financial asset returns exhibit higher skewness and kurto-sis than those implied by the Normal distribution. Pricepaths can also exhibit jumps, which is particularly true foremerging and commodity markets. In this case, the Vari-ance Gamma (VG) process is more realistic than the geo-metric Brownian motion (GBM) to model the asset pricedynamics. However, valuation of basket and spread options(common derivatives in commodity, FX and other markets)under this model is a very challenging and time-consumingtask. We propose a novel and elegant method for valuationof basket and spread options under VG model, by condi-tioning the VG processes on a realization of the stochasticGamma time change and combining it with the GeneralizedLogNormal (GLN) approximation. We consider a simpler(and easily tractable) case of the identical stochastic timechange for all underlying assets, as well as the more gen-eral case of dierent (but dependent) Gamma time changes.Numerical study shows that the proposed method performsremarkably well in term of option pricing, even for a sim-pler model. Our method is intuitive, computationally veryfast, ecient and exible enough to allow for basket options onarbitrary number of assets and negative portfolio weights.

Svetlana BorovkovaVrije Universiteit Amsterdams.a.borovkova@vu.nl

CP3High-order Short-time Expansions for ATM Op-tion Prices Under the CGMY Model

In this presentation, we derive a novel second-order ap-proximation for ATM option prices under the CGMY Lvymodel, and then extend to a model with an addition Brow-nian motion. The third-order asymptotic behavior of theoption prices as well as the asymptotic behavior of the cor-responding Black-Scholes implied volatilities are also ad-dressed. Our numerical results show that in most casesthe second-order term significantly outperform the first or-der approximation.

Ruoting GongSchool of MathematicsGeorgia Institute of Technologyrgong@math.gatech.edu

CP3Efficiently Simulating the Double-Barrier First-Passage Time in Jump-Diffusion Models

We present a fast and accurate Monte-Carlo simulationto obtain double-barrier first-passage time probabilities ina jump-diffusion model with arbitrary jump size distri-bution; extending single-barrier results by Metwally andAtiya [2002]. The presented algorithm is unbiased and sig-nificantly faster than a brute-force Monte-Carlo simulationon a grid. As an application, we discuss corridor bonus cer-tificates, floor certificates, and digital first-touch options.

Peter HieberUniversity of Torontopeter.hieber@utoronto.ca

130 FM12 Abstracts

Lexuri FernandezUniversidad Autonoma de Madridlexuri.fernandez@ehu.es

Matthias SchererTechnische Universitat MunchenChair of Mathematical Financescherer@tum.de

CP3Numerical Solution of Jump-Diffusion SDEs

Jump-diffusions are ubiquitous in finance and economics.This paper develops, analyzes and tests a discretizationscheme for multi-dimensional jump-diffusion SDEs withgeneral state-dependent drift, volatility, and jump inten-sity function. Unlike conventional schemes, our schemeallows for an unbounded jump intensity–a feature of manystandard jump-diffusion models in credit, equity, FX andcommodity markets. The convergence of the discretizationerror is proved to be of weak order one. Numerical experi-ments illustrate our results.

Gerald TengStanford Universitygteng1@stanford.edu

Kay GieseckeStanford UniversityDept. of Management Science and Engineeringgiesecke@stanford.edu

CP4Model Risk Based on the Distribution of the HedgeError

When pricing and hedging a derivative, we face model risk,that is, the risk of choosing the wrong dynamics for the fi-nancial market. We propose a measure of model risk basedon the hedge error that can be interpreted as a capitalcharge. This has several positive implications beyond esti-mating the riskiness of a claim in terms of model risk. Wecalculate these model risk measures for several examplesand derive its general properties.

Nils DeteringFrankfurt School of Finance and Managementn.detering@fs.de

CP4Why Is It So Hard to Estimate Expected Returns?

A key part of experiment design is determining how muchdata to collect. When the data comes in the form of atimeseries, the sample size is expressed both by the countN of the observations and the duration T of the historicalperiod over which observations were made. For an assetwhose price has continuous sample paths, we demonstratethat the standard error of any unbiased estimator of theprice of risk is bounded below by 1/

√T .

John A. DodsonUniversity of MinnesotaCenter for Financial and Actuarial Mathematicsjdodson@math.umn.edu

CP4A New Perspective on Dependence Within Finan-cial Markets

Many financial instruments are inherently multivariatein their origination. A rigorous empirical valuation re-quires simultaneous analysis of many components. Nonlin-ear and inter-temporal dependencies, extreme events, andlarge datasets introduce additional challenges. Indepen-dent component analysis is an indispensable tool for find-ing suitable representations of the complex multivariate in-formation within financial markets. We introduce a novelstatistical framework for independent component analysisof financial data and illustrate its use on several importantfinancial applications.

David S. MattesonCornell UniversityDepartment of Statistical Sciencematteson@cornell.edu

CP4The Herd Behavior Index: a New Measure for theImplied Degree of Co-Movement in Stock Markets

We introduce a new measure for the implied degree ofherd behavior, one of the driving factors of systemic risk.This forward looking Herd Behavior Index (HIX) is model-independent and based on observed option data. As anillustration, we determine historical values of the 30-daysHIX for the Dow Jones Industrial Average.

David VynckeGhent UniversityDepartment of Applied Mathematics and ComputerSciencedavid.vyncke@ugent.be

Jan Dhaene, Daniel Linders, Wim SchoutensUniversity of Leuvenjan.dhaene@econ.kuleuven.be,daniel.linders@econ.kuleuven.be,wim.schoutens@wis.kuleuven.be

CP5Incorporating Parameter Risk into DerivativesPrices - An Approach to Bid-Ask Spreads

We present a new method based on convex risk measures toincorporate parameter risk (e.g. estimation and calibrationrisk) into derivative prices. As an application we calculateparameter risk-implied bid-ask spreads of exotics, enablingus to compare the parameter risk of different models anddifferent exotics. Furthermore, we introduce a nonpara-metric calibration procedure to real bid-ask prices usingdistortion risk measures, compare our results to given para-metric distortion calibrations and present a new parametricfamily.

Karl F. Bannor, Matthias SchererTechnische Universitat MunchenChair of Mathematical Financebannoer@tum.de, scherer@tum.de

CP5Analytical Calculation of Risk Measures for Vari-

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able Annuity Guaranteed Benefits

With the increasing complexity of investment options in lifeinsurance, more and more insurers have adopted stochasticmodeling methods for the assessment and management ofinsurance and financial risks, with the most prevalent beingMonte Carlo simulation. In this paper we propose an al-ternative analytical method for the calculation of risk mea-sures for variable annuity guaranteed benefits. The tech-niques for analytical calculations are based on the study ofan integral of geometric Brownian motion as well as asymp-totic analysis of special functions. As we demonstrate bynumerous examples on quantile risk measure and condi-tional tail expectation, the numerical algorithms developedin this paper appear to be accurate and computationallyefficient.

Runhuan Feng, Hans W VolkmerUniversity of Wisconsin-MilwaukeeDepartment of Mathematical Sciencesfengr@uwm.edu, volkmer@uwm.edu

CP5Fair Valuation of Drawdown Insurance

Drawdowns are path-dependent measures of risk and havebeen used extensively in the description of market crashes.We evaluate the market price of a market crash as mea-sured through drawdowns by considering an investor whowishes to insure herself against the risk of a market crashand does so by purchasing insurance claims against draw-downs. We further examine the fair valuation of drawdowninsurance in the possibility of early cancellation and iden-tify optimal cancellation strategies.

Olympia HadjiliadisGraduate Center of CUNY, New YorkBrooklyn College, CUNYohadjiliadis@brooklyn.cuny.edu

Tim LeungDepartment of Operations Research and IndustrialEngineeringColumbia Universitytl2497@columbia.edu

Hongzhong ZhangDepartment of StatisticsColumbia Universityhz2244@columbia.edu

CP5Diversification and Crash-Protection Using Vari-ance Swap Calendar Spreads

Volatility can be also considered an asset class. Varianceswaps, one of the main investment vehicles, provide expo-sure to realized volatility. Implied volatility is often higherthan the realized volatility will turn out to be. We ex-plain how a variance swap calendar spread benefits fromboth negative risk premium and negative correlation withthe underlying stock index. Via backtesting we show howthe strategy added to a stock/bond portfolio significantlydiversifies crash risk.

Qixiang ZhouMathFinance AGqixiang.zhou@mathfinance.com

Nils DeteringFrankfurt School of Finance and Managementn.detering@fs.de

Uwe WystupMathFinance AGu.wystup@mathfinance.com

CP6Optimal Cash Holdings in a Firm

The precautionary principle of cash-holdings is empiricallywell analysed. However, the quantitative modelling of suchcash holdings is exceptionally sparse. This is due to thepath dependent nature of the problem and the fact thatcash holdings may both increase and decrease in time. Assuch, novel numerical solutions to the problem are required.We show how to model endogenous cash holdings within aFirms valuation and extract numerical solutions. In doingso we provide a solid basis by which Real Options analy-sis, dividend payments, debt issuance, cash holdings, andcorporate finance decisions (investments) can finally all beviewed in a consistent, non-contradictory and more realis-tic fashion. This analysis and need for consistency has beencalled for within many papers, and we hope our (economi-cally robust) approach shows how mathematics can providea more unifying approach to the theory of the Firm.

Paul V. Johnson, Geoff Evatt, Mingliang ChengUniversity of ManchesterSchool of Mathematicspaul.johnson-2@manchester.ac.uk,geoffrey.evatt@manchester.ac.uk,mingliang.cheng@postgrad.manchester.ac.uk

CP6Risk Aversion and Managerial Cash-Flow Esti-mates in Real Options

While there are a number of academic papers discussingthe importance of accounting for risk aversion in real optionvaluation, none of them are applicable to discrete cash-flowestimates supplied by managers. Here, we develop an ap-proach which explicitly incorporates managerial cash-flowestimates and accounts for risk-aversion through indiffer-ence valuation. Interestingly, we find that the real optionvalue not only deteriorates as risk-aversion increases, itdrops to zero above a critical risk-aversion level.

Yuri LawryshynUniversity of Torontoyuri.lawryshyn@utoronto.ca

CP6Irreversible Investment with Regime Switching :Revisit with Linear Algebra

We consider irrevesible investment problems with regimeswitching feature under a monopoly setting. Several pa-rameters describing the economic environment varies ac-cording to a regime switching with general number ofstates. We present the derivation of the value functionvia solving a system of simultaneous ordinary differentialequations with knowledge of linear algebra. It is found thatthe functional form of the value function depends on thedecomposition of a coefficient matrix.

Keiichi Tanaka

132 FM12 Abstracts

Tokyo Metropolitan Universitytanaka-keiichi@tmu.ac.jp

CP6Embedded Currency Exchange Options in Roll-over Loans

In ship and aircraft financing long term roll-over loans areoften equipped with the right to change the currency everyquarter at spot. The loan taker then pays LIBOR of therespective currency plus a pre-determined constant salesmargin. If the capital outstanding exceeds 105% calcu-lated in the original currency, the amortization is requiredto the level of 105% of the original currency. By clever cur-rency management the loan taker can amortize the loanfaster and terminate the loan early. Essentially the loantaker owns a series of options on the cross currency ba-sis spread with unknown notional amounts. We determinethe key drivers of risk, an approach to valuation and hedg-ing, taking into consideration the regulatory constraintsof a required long term funding. We present a closed-formapproximation to the pricing problem and illustrate its sta-bility.

Uwe WystupFrankfurt School of Finance & ManagementMathFinance AGuwe.wystup@mathfinance.com

CP7Dynamic Quadratic Hedging in the Presence ofPartially Hedgeable Assets and Liabilities

We consider an incomplete market where an investor whoowns a partially hedgeable asset faces a liability at time T.The investor’s aim is to minimize the terminal replicationerror based on a quadratic loss criterion in this setting.We investigate the solution to the quadratic hedging prob-lem using the stochastic linear-quadratic optimal controlapproach through the corresponding (stochastic Riccati)BSDEs and provide some examples.

Coskun CetinCalifornia State University, Sacramentocetin@csus.edu

CP7BSDEs with BMO Market Price of Risk

We study quadratic semimartingale BSDEs arising inpower utility maximization when the market price of risk isof BMO type. In a Brownian setting we provide a necessaryand sufficient condition for the existence of a solution butshow that uniqueness fails to hold in the sense that thereexists a continuum of distinct square-integrable solutions.This feature occurs since, contrary to the classical Ito rep-resentation theorem, a representation of random variablesin terms of stochastic exponentials is not unique. We studywhen the BSDE has a bounded solution and derive a newdynamic exponential moments condition which is shown tobe the minimal sufficient condition in a general filtration.The main results are complemented by several interestingexamples which illustrate their sharpness as well as impor-tant properties of the utility maximization BSDE.

Christoph FreiUniversity of Albertacfrei@ualberta.ca

Markus MochaHumboldt-Universitat zu Berlinmocha@math.hu-berlin.de

Nicholas WestrayImperial College Londonn.westray@imperial.ac.uk

CP7A Continuous Time Bank Run Model for Insol-vency, Recovery and Rollover Risks

We propose a continuous time bank run model for incor-porating insolvency, recovery and rollover risks. The firmfinances by issuing both long and short term debt, and theshort term debt holders need to decide whether to roll overor to withdraw their debt (i.e. to run the bank) when theircontracts expire. We show there exists a threshold strat-egy (i.e. the bank run barrier) for the short-term creditorsto decide when to run. We decompose the total credit riskinto an insolvency component and an illiquidity componentbased on such an endogenous bank run barrier togetherwith an exogenous insolvency barrier. The short term debtin our model can have either a discrete tenor structure, ora more realistic staggered tenor structure. The problemis reduced to an optimal stopping time problem with con-straint, which is solved by the BSDE method.

Gechun LiangUniversity of Oxfordliangg@maths.ox.ac.uk

CP7Quadratic Reflected Bsdes with Bounded Condi-tions. Application to American Options.

In this talk, I present an elementary and totally pertur-bative method for dealing with the well-posedness of somereflected BSDEs : existence, uniqueness and stability. Itworks for a smooth coefficient f which has a growth atmost quadratic in z, when the terminal condition as wellas the lower obstacle are bounded. I then connect theseequations with the problem of pricing american options inan incomplete market.

Arnaud LionnetOxford-Man Institute for Quantitative Finance,University of Oxfordarnaud.lionnet@maths.ox.ac.uk

CP7A Simple Proof of BichtelerDellacherieMokobodzkiTheorem

We give a simple and quite elementary proof of the cel-ebrated BichtelerDellacherieMokobodzki Theorem, whichstates that a process is a good integrator if and only if it isa semi-martingale. Moreover we reformulate its statementin a way that -we believe- is more natural.

Pietro SiorpaesUniversity of Vienna (Universitat Wien)math departmentpietro.siorpaes@univie.ac.at

Mathias BeiglbockUniversity of Vienna (Universitat Wien) math departmentmathias.beiglboeck@univie.ac.at

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CP8Inference for the Fractional Heston Model Usingthe Auxiliary Particle Filter

The fractional Heston Model is a generalization of the Hes-ton Model obtained by replacing Brownian motion by frac-tional Brownian motion in the two equations that definethe Heston model. After defining the fractional Hestonmodel and showing its representation as a Dynamic statespace model, we will use that auxiliary particle filter bothto sample the volatility process and to update the posteriordistribution of the parameters sequentially as data arriveover time. We apply our approach to simulated and realdata with success. Keywords:- Fractional Heston Model,maximum likelihood estimation, particle filter, auxiliaryparticle filter, sequential Bayesian inference.

Muhannad Al-SaadonyUniversity of PlymouthUnited Kingdommuhannad.alsaadony@plymouth.ac.uk

CP8Non-Parametric Calibration of the Local VolatilitySurface for European Options

Assuming the volatility surface is smooth, a second or-der Tikhonov regularization is applied to the calibrationproblem. Additionally a new approach for choosing theTikhonov regularization parameter is proposed. Using theTAPENADE automatic differentiation tool in order to ob-tain adjoint code of the direct model is employed as anefficient way to obtain the gradient of cost function withrespect to the local volatility surface. Finally we performfour numerical tests aimed at assessing and verifying theaforementioned techniques.

Jian GengDepartment of Mathematics Florida State Universityjgeng@math.fsu.edu

Michael NavonFlorida State Universityinavon@fsu.edu

Xiao ChenLawrence Livermore National LaboratoryCenter for Applied Scientific Computingchen73@llnl.gov

CP8Small-time Asymptotics For Some StochasticVolatility Models

In the paper SMALL-TIME ASYMPTOTICS FORFAST MEAN-REVERTING STOCHASTIC VOLATIL-ITY MODELS they investigate two rates for the mean-reversion time δ in terms of the maturity ε, namely δ = εγ

for γ = 2, 4. Looking at this model and a few others wecharacterize the behaviors for γ > 2 and for 1 < γ < 2 andshow how this relates to Moderate Deviations and Super-large Deviations, respectively. This argument also showswhy γ = 2 is special.

Jerome Grand’maisonUniversity of Southern Californiajerome.grandmaison@usc.edu

CP8Stochastic Calibration to Implied Volatility Sur-faces

This paper provides a two-step method to fully calibratethe implied volatility surface in the environment of ran-dom volatility. The first step consists of the Fourier trans-form method (Malliavin and Mancino (2009)) for estimat-ing model parameters of stochastic volatility models, andthe second step solves an optimization problem by meansof Monte Carlo simulation with variance reduction tech-niques. We compare fitting accuracies with the fast Fouriertransform method (Carr and Madan (1999)) and perturba-tion method (Fouque et al. (2003, 2011)). In addition, itis natural to generalize our calibration procedure to theimplied volatility surface of American options.

Chuan-Hsiang HanNational Tsing-Hua Universitychhan@mx.nthu.edu.tw

CP8Understanding Jumps in the High-Frequency VIX

This article provides a comprehensive nonparametric high-frequency analysis of jumps in the VIX (S&P500 volatilityindex). A comparison of the VIX and the S&P500 futurestime series (1992-2010) shows that 97% of jumps in the VIXare spurious. This finding not only leads to a new interpre-tation of the broadly used VIX dataset but also extends theliterature on volatility jumps and on the return-volatilityrelationship.

Inna KhagleevaUniversity of Illinois at Chicagoikhagl2@uic.edu

CP8Implied Volatiltiy from Black-Scholes and OtherFormulas

We show that if the parameters of an arbitrary stock pricemodel are used in the Black-Scholes formula for calculatingoption prices for finitely many strikes, the implied volatility(a function of time t) will be bounded by a value whichdepends only on strikes. Our model-free results, which canbe used in calibration, provide sets of constraints limitingthe acceptable values of the implied volatility parameters.We use the Heston model for illustration.

Olivia MahMonash Universityolivia.mah@monash.edu

Kais Hamza, Fima KlebanerSchool of Mathematical SciencesMonash University, Clayton Campus Victoria 3800Australiakais.hamza@monash.edu, fima.klebaner@monash.edu

CP9Extensions of the Lt Method for Option Pricing

Monte Carlo (MC) and quasi-Monte Carlo (QMC) meth-ods are often used in pricing complex derivatives. Themerit of QMC is that, theoretically at least, higher conver-gence rates can be obtained than regular MC. The payofffunction is usually high-dimensional and non-smooth, elim-

134 FM12 Abstracts

inating the advantage of using QMC. Imai & Tan (2006)introduced the LT method which minimizes the effectivedimension of the problem by transforming the normal vari-ates using an orthogonal transformation, thereby improv-ing the QMC method. We extended their method for valu-ing options that have a barrier feature on an underlyingasset, incorporating and extending an idea from Staum &Glasserman (2001). These options have a payoff that de-pends on whether the asset does or does not cross a certainlevel during the life of the option. If the probability of (not)hitting is large enough, then much more paths have to besampled for reliable results. Our method greatly reducesthe required number of paths and our aim is to extend thismethod to Levy market models.

Nico AchtsisK.U.Leuvennico.achtsis@cs.kuleuven.be

Ronald Cools, Dirk NuyensDept. of Computer ScienceK.U.Leuvenronald.cools@cs.kuleuven.be, dirk.nuyens@cs.kuleuven.be

CP9Variance Reduction for Monte Carlo Simulationof European Call Options Under the CoupledAdditive-Multiplicative Noise Model

We propose a variance reduction method for Monte Carlocomputation of option prices in the context of the Cou-pled Additive-Multiplicative Noise model. Four differentschemes are applied for the simulation. The methods selectcontrol variates which are martingales in order to reducethe variance of unbiased option price estimators. Numer-ical results for European call options are presented to il-lustrate the effectiveness and robustness of this martingalecontrol variate method.

Wanwan HuangFlorida State Universitybsbhuang8527@hotmail.com

Brian EwaldDepartment of MathematicsFlorida State Universityewald@math.fsu.edu

CP9Central Limit Theorem for the Multi-Level MonteCarlo Algorithm and Applications to Option Pric-ing

This paper deals with the problem of the multi-level MonteCarlo method, introduced by Giles (Multilevel Monte Carlopath simulation Operations Research, 2008; 56:607-617) asan extended method of the statistical Romberg one intro-duced by Kebaier (Romberg Extrapolation: A New Vari-ance Reduction Method and Applications to Option Pric-ing. Ann. Appl. Probab. 15 (2005), no. 4, 2681-2705).When approximating the expected value of a function ofa stochastic differential equation solution, these methodsimprove efficiently the computational complexity of stan-dard Monte Carlo. In this work, we analyze the asymp-totic error of this algorithm and establish a central limittheorem based on a new stable functionalcentral limit the-orem on the error in the Euler scheme for a given level.This allows us to obtain the optimal choice of the param-eters method.Then, weinvestigate the application of this

method to the pricing of Asian options. In this setting, theapproximation relies on the discretization of the integralof the price process over a time interval. We also analyzethe error process and prove a stable functional central limittheorem. Finally, We use our result in order to optimizethe choice of the parameters, which are different from theones in the Euler scheme. Numerical simulations were pro-cessed.

Ahmed Kebaier, Ben Alaya MohamedUniversity Paris XIIIkebaier@math.univ-paris13.fr, mba@math.univ-paris13.fr

CP9A Hybrid Pricing Method for Options with MultiAssets

A numerical method is studied for options with multi-underlying assets. Instead of imposing artificial boundarycondition for the multi-dimensional Black-Scholes equa-tion, we calculate certain one-dimensional model equationat each time-step using pre-simulated Monte-Carlo timeseries. With standard finite difference method using ninepoint stencil, our method reduce the computational do-main of the governing equation (the two dimensional Black-Scholes equation) exceedingly. As benchmark tests, weconsider the call on the maximum option which has ananalytic solution, and a complicated structured note fromthe derivative market.

Yongsik KimDepartment of MathematicsYonsei Universityyskim67@ajou.ac.kr

Hyeong-Ohk BaeDepartment of Financial EngineeringAjou Universityhobae@ajou.ac.kr

Tae-Chang JoInha Universitytaechang@inha.ac.kr

CP9Control Variate Methods and Applications in Asianand Basket Options Pricing and Hedging underJump-Diffusion Models

We discuss control variate methods with applications toAsian and basket option pricing under exponential jumpdiffusion models for the underlying asset prices. We firstrevisit the single control variate method and then discussthe multivariate control variate method in detail. Con-ditions which ensure the variance of an m−variate con-trol variates is smaller than that of a k−variate controlvariates (1 ≤ k < m) are given and proved. Based onthese conditions, more efficient control variates can be con-structed. For arithmetic Asian and basket options, controlvariates conditional on geometric means of asset prices areconstructed. Numerical results show that the constructedcontrol variate is much more efficient than the classicalcontrol variate when pricing Asian options even in highdimensional cases.

Yongzeng LaiDepartment of MathematicsWilfrid Laurier Universityylai@wlu.ca

FM12 Abstracts 135

Zhongfei LiLingnan (University) collegeSun Yat-Sen Universitylnslzf@mail.sysu.edu.cn

Yan ZengLingnan (University) CollegeSun Yat-Seng Universityzengyan6@mail2.sysu.edu.cn

CP9Taylor-Like Anova Expansion for High DimensionalPdes Arising in Finance

The solution of high dimensional problems in short timeas well as with high precision is of great importance in fi-nance. For this purpose we propose an approximation toan ANOVA decomposition of the problem, which is only oflinear order in the dimension of the full problem and supe-rior in precision. We will call this approximation Taylor-like ANOVA. We develop this approximation up to higherorders and show its efficiency by numerical experiments.

Philipp SchroederGoethe Center for Scientific ComputingGoethe University Frankfurtphilipp.schroeder@gcsc.uni-frankfurt.de

Thomas GerstnerGoethe University Frankfurtgerstner@math.uni-frankfurt.de

Gabriel WittumGoethe Center for Scientific ComputingGoethe University Frankfurtwittum@gcsc.uni-frankfurt.de

CP10Optimal Order Routing in Limit Order Markets

When executing a trade, traders in electronic equity mar-kets can choose to submit a limit order or a market order,as well as the venue to submit this order, if the stock istraded in several exchanges. This decision is influenced bythe order flow characteristics and queue sizes in each limitorder book, as well as the structure of transaction fees andrebates across exchanges. We show that this optimal orderrouting problem may be formulated as a convex optimiza-tion problem and propose a stochastic algorithm for solvingit. We study this problem under various statistical assump-tions on the order flow and show the interplay between thefee structure, the order flow and the risk preferences of thetrader in determining the optimal routing decision.

Arseniy KukanovColumbia Universityak2870@columbia.edu

Rama ContCNRS (France) & Columbia UniversityRama.Cont@gmail.com

CP10Optimal Trade Execution with Dynamic Risk Mea-sures

We propose a model for optimal trade execution in an illiq-uid market that minimizes a coherent dynamic risk of the

sequential transaction costs. The prices of the assets aremodeled as a discrete random walk perturbed by both tem-poral and permanent impacts induced by the trading vol-ume. We show that the optimal strategy is time-consistentand deterministic if the dynamic risk measure satisfies aMarkovian property. We also show that our optimal ex-ecution problem can be formulated as a convex program,and propose an accelerated first-order method that com-putes its optimal solution. The efficiency and scalability ofour approaches are illustrated via numerical experiments.

Qihang LinCarnegie Mellon UniversityTepper School of Businessqihangl@andrew.cmu.edu

Javier PenaCarnegie Mellon Universityjfp@andrew.cmu.edu

CP10An Optimal Trading Rule under Switchable MeanReversion Market

This work provides an optimal trading rule that allowsbuying or selling of an asset whose price is governed bymean-reversion model. In the model, the equilibrium levelis controlled by an 2-state Markov chain. With the slippagecost imposed, the goal is to maximize the overall return.The value functions are characterized by considering theassociated HJB equations. This paper also shows that thesolution of the original optimal problem can be obtained bysolving four quasi-algebraic equations. Finally, numericalexamples are given for demonstration.

Duy NguyenUniversity of Georgiadnguyen@math.uga.edu

CP10Price Impact and Market Indifference Prices withPower Utilities

We investigate the price impact of large transactions in anequilibrium pricing model with HARA utility functions.A market maker trades with a large investor at a pricethat allows him to preserve his expected utility, the so-called market indifference price. In this setting we look atmarginal prices and illiquidity premia in comparison to theBlack-Scholes model as well as hedging and replication ofnon-traded (OTC) claims.

Nadim SahTU Berlinsah@math.tu-berlin.de

CP10A Self-exciting Point Process Model for Limit Or-der Books

The statistical properties of events affecting a limit or-der book -market orders, limit orders and cancellations-reveal strong evidence of clustering in time, significantcross-correlation across event types and significant depen-dence of the order flow on the bid-ask spread. We showthat these dependencies may be adequately represented bya multi-dimensional self-exciting point process, for whicha tractable parameterization is proposed. Using high-

136 FM12 Abstracts

frequency data from the Trades and Quotes database, weperform a Maximum Likelihood Estimation of the modeland assess its predictive performance for a variety of stocks.

Ekaterina VinkovskayaColumbia UniversityDept of Statisticseov2101@columbia.edu

Allan AndersenCopenhagen Business Schoolaa.fi@cbs.dk

Rama ContCNRS, France, and Columbia Universityrama.cont@gmail.com

CP10Evolutionary Game Dynamics Using a Non-Equilibrium Price Formation Rule for Trading withMarket Orders

Markets have dynamics that may result in excess volatilityand other phenomena that are a challenge to explain us-ing rational expectation models. Following Farmer (2002)and identifying trading strategies with species and capitalinvested in a strategy with a population, we use the repli-cator equation to identify the evolutionary game dynamicsbetween the relevant agents. We then extend the dynamicsspatially in order to examine the progression toward mar-ket efficiency caused by the evolution of capital. We ob-serve interesting dynamics including the phenomenon thatthe market becomes efficient as new strategies find themand cause them to disappear.

Gareth Q. WittenUniversity of Cape TownPontificia Universidad Catolica del Per, CENTRUMCatolicagareth.witten@uct.ac.za

CP11On the Existence of Shadow Prices.

For utility maximization problems under proportionaltransaction costs, it is known that the original market withtransaction costs can sometimes be replaced by a friction-less shadow market that yields the same optimal strategyand utility. In this paper we present a counterexamplewhich shows that shadow prices may fail to exist. We thenprove that short selling constraints are a sufficient condi-tion for their existence, even in very general multicurrencymarket models with discontinuous bid-ask-spreads.

Giuseppe BenedettiCRESTgiuseppe.benedetti@ensae.fr

Luciano CampiParis 13 Universitycampi@math.univ-paris13.fr

Johannes Muhle-KarbeDepartement MathematikETH Zurichjohannes.muhle-karbe@math.ethz.ch

Jan Kallsen

Kiel Universitykallsen@math.uni-kiel.de

CP11Indifference Pricing with Uncertainty Averse Pref-erences

We consider the indifference valuation of an uncertain mon-etary payoff from the perspective of an uncertainty aversedecision-maker. We study how the indifference valuationdepends on the decision-maker’s attitudes toward uncer-tainty. We obtain a characterization of comparative uncer-tainty aversion and various characterizations of increasing,decreasing, and constant uncertainty aversion.

Flavia Giammarino, Pauline BarrieuLondon School of Economicsf.giammarino@lse.ac.uk, p.m.barrieu@lse.ac.uk

CP11Portfolio Optimization Based on Independent Setsof Market Cliques

We consider the problem of selecting an optimal mar-ket portfolio that maximizes expected return and includeshighly correlated disjoint market cliques (i.e., memberswithin a clique are pairwise highly correlated) which arepairwise anticorrelated based on a correlation function de-fined on the set of cliques. We present integer program-ming models that can be effectively used to construct suchan optimal portfolio that satisfies given clique correlationthresholds.

Athula D. GunawardenaUniversity of Wisconsin-Whitewatergunawara@uww.edu

Robert MeyerComputer Science DepartmentUniversity of Wisconsin-Madisonrrm@cs.wisc.edu

Thisath KularatnaOptSolv LLC.thisath@gmail.com

Michael MonaghanBlackthorne Capital Management, LLCmichael.monaghan@blackthornetrader.com

Joseph HaskeUniversity of Wisconsin-Whitewaterhaskejl25@uww.edu

CP11Portfolio Optimization under Convex IncentiveSchemes

We consider the utility maximization problem of terminalwealth from the point of view of a portfolio manager paidby an incentive scheme given as a convex function g of theterminal wealth. The manager’s own utility function Uis assumed to be smooth and strictly concave, however theresulting utility function U g fails to be concave. As a con-sequence, this problem does not fit into the classical port-folio optimization theory. Using duality theory, we provewealth-independent existence and uniqueness of the opti-mal wealth in general (incomplete) semimartingale markets

FM12 Abstracts 137

as long as the unique optimizer of the dual problem has acontinuous law. In many cases, this fact is independent ofthe incentive scheme and depends only on the structure ofthe set of equivalent local martingale measures. We pro-vide explicit examples for complete and incomplete marketmodels.

Stephan SturmORFE DepartmentPrinceton Universityssturm@princeton.edu

Maxim BichuchDepartment of Operations Research and FinancialEngineeringPrinceton Universitymbichuch@princeton.edu

CP11Optimal Portfolios for Hedge Funds and TheirManagers

Hedge fund managers receive fees proportional to profits,and may reinvest them. We find the fund and personalportfolio that maximize managers’ expected utility frompersonal wealth, when relative risk aversion is constant,and investment opportunities constant and separate, butcorrelated. Managers do not reinvest fees, allocating ex-cess personal wealth in Merton portfolio. But they man-age funds like Merton investors with risk aversion shrunktowards one. Managers do not hedge fund exposure withpersonal positions.

Gu WangBoston University, Department of Mathematics andStatisticsguwang@bu.edu

Paolo GuasoniBoston UniversityDublin City Universityguasoni@bu.edu

CP11An Equilibrium Approach to Utility-Based and In-difference Pricing

The utility-based and utility indifference pricing are frame-works for pricing contingent claims. Since these principlesare based on utility maximization principle, prices are op-timal for each investor with utility function. Our purposeis to expand these frameworks for deducing the equilib-rium price. Another purpose is to clarify the relationshipbetween utility-based and utility indifference framework.This discussion will be also done in the setting of the mar-ket with transaction costs.

Daisuke YoshikawaMizuho-DL Financial Technology co., ltd.daisuke-yoshikawa@fintec.co.jp

Mark DavisImpreial College londonmark.davis@imperial.ac.uk

CP12Optimal Decumulation: An

Investment-Consumption Models for Retirees

We consider the optimal investment-consumption problemfor retirees with uncertain lifespan. We assume that theirinitial wealth can spread between both risky and riskless(liquid) investments and an income-producing (irrevoca-ble) life annuity with default risk. We examine whetherdefault risk (or the perception of default risk) rationallyaffects a retirees decision to purchase an annuity upon re-tirement. We formulate our problem as a Hamilton-Jacobi-Bellman equation and do a thorough numerical study forCRRA investors.

Jeffrey HumpherysBrigham Young Universityjeffh@math.byu.edu

David BabbelUniversity of PennsylvaniaWharton School of Businessbabbel@wharton.upenn.edu

Craig MerrillBrigham Young UniversityMarriott School of Businesscraig merrill@byu.edu

CP12Voluntary Retirement and Annuity Contract

We consider an optimal financial planning problem of aneconomic agent who has an option to retire from laborvoluntarily. The economic agent with labor income deter-mines his/her investment strategy, consumption, and re-tirement strategy along with annuity. We investigate therelation between the annuity contract and the condition forthe voluntary retirement. We also analyze how the pres-ence of voluntary retirement option affects the purchase ofan annuity and the annuity market.

Minsuk KwakKorea Advanced Institute of Science and Technologyminsuk.kwak@gmail.com

Yong Hyun ShinSookmyung Women’s Universityyhshin@sookmyung.ac.kr

CP12Bang-Bang Controls on Some Optimal InsuranceProblems

In this talk, we are interested in finding an optimal solutionfor a large class of optimal insurance problems. This classof problems includes those whose risks are measured byValue at Risk, Average Value at Risk, Conditional TailExpectation and law-invariant convex risk measures. Wehave found that Bang-Bang controls are optimal to all ofthem. This result also holds for multi-dimensional optimalinsurance problems such as those in adverse selections.

Siu Pang YungMath. Dept., University of Hong Kongspyung@hku.hk

CP12Optimal Consumption and Portfolio Choice withLife Insurance under Uncertainty and Borrowing

138 FM12 Abstracts

Constraints

We develop a duality approach to study a family’s optimalconsumption, portfolio choice and life insurance purchasewhen the family receives deterministic labor income whichmay be terminated due to premature death or retirementof the family’s wage earner. The family faces a borrowingconstraint and the wage earner has an uncertain lifetime.We establish the existence of an optimal solution to theoptimization problem and solve the problem explicitly forseveral cases.

Xudong ZengShanghai University of Finance and Economicsxudongzeng@gmail.com

CP12Optimal Dividend Payments for the Piecewise-Deterministic Compound Poisson Risk Model

This work deals with optimal dividend payment problemfor a piecewise-deterministic compound Poisson insurancerisk model. The objective is to maximize the expecteddiscounted dividend payout up to ruin time. When thedividend payment rate is restricted, the value function isshown to be a solution of the corresponding HJB equa-tion. For the case of unrestricted payment rate, the valuefunction and an optimal barrier strategy are determinedexplicitly with exponential claim size distributions.

Runhuan FengUniversity of Wisconsin-MilwaukeeDepartment of Mathematical Sciencesfengr@uwm.edu

Shuaiqi ZhangCentral South UniversitySchool of Mathematical Science and ComputingTechnologyshuaiqiz@yahoo.com.cn

Chao ZhuUniversity of Wisconsin-Milwaukeezhu@uwm.edu

CP13On the Credit Risk of Secured Loans

We use stochastic control techniques to analyze the creditrisk of secured revolving loans, whose collateral cannot beliquidated immediately. The objective function is a trade-off between the expected loss due to a liquidation event andthe shortfall due to the borrower drawing on the credit lineless than the full amount available. We exhibit the lender’soptimal strategies and compare them with the standardLTV-based lending policy favored by practitioners.

Agnes TourinPolytechnic Institute of NYUatourin@poly.edu

Fabian AsticMoody’s Investors serviceCredit policy/researchfabian.astic@moodys.com

CP13Conditional Expected Default Rate Calculations

for Credit Risk Applications

Calculation of portfolio loss distributions for large numbersof correlated losses (e.g. credit risk applications) typicallyuse brute force Monte Carlo simulation. We use an asymp-totic probabilistic model based on the Central Limit The-orem for solving the portfolio risk aggregation problem forcredit risky portfolios. We then prove a theorem that en-ables efficient computation of the conditional expectationof the default rate for any subportfolio, conditioned on thetotal portfolio loss. This theorem enables us to solve thecapital allocation problem (using expected shortfall as therisk measure) without resorting to Monte Carlo simulation.The approach is very efficient, even for portfolios with sev-eral million positions.

Andrew BarnesGeneral ElectricGlobal Research Centerbarnesa@research.ge.com

CP13Measure Changes for Reduced-Form Affine CreditRisk Models

We consider a reduced-form credit risk model, with defaultintensity driven by an affine process. We fully character-ize the family of all locally equivalent probability measureswhich preserve the structure of the model, providing nec-essary and sufficient conditions on their density process.In particular, this allows for a rigorous treatment of dif-fusive and jump-type risk premia. As an application, wecharacterize the family of all risk-neutral measures for ajump-to-default Heston model.

Claudio FontanaUniversity of Padovaclaudio.fontana@polimi.it

CP13Killed Brownian Motion with a Prescribed LifetimeDistribution and Models of Default

The inverse first passage time problem asks for some dis-tribution whether there is a barrier such that the first timea Brownian motion crosses the barrier has the given dis-tribution. We consider a ‘smoothed’ version of this prob-lem in which the first passage time is replaced by the firstinstant that the time spent below the barrier exceeds anindependent exponential random variable. We show thatany distribution results from some unique barrier.

Alexandru Hening, Steven Evans, Boris EttingerUC Berkeleyahening@math.berkeley.edu, evans@stat.berkeley.edu, et-tinger@math.berkeley.edu

CP13Analysis of Recovery Rate of Non-Performing Con-sumer Credit

There have been more studies on recovery rate modeling ofbonds than on recovery rate modeling of personal loans andretail credit. Little to no research have been conducted onrecovery rates in non-performing retail credit with empha-sis on third-party buyers. From an empirical point of view,in order to analyze the recovery rate distributions acrossthe different industries, over nine million defaulted or non-performing consumer credit data provided by a German

FM12 Abstracts 139

debt collection company are used. A variety of statisticaland data mining methods will be examined with respect toprediction and classification. A two-stage model which firstclassifies debts as extreme or non-extreme with respect torecovery rate is applied; then, the extreme debts are clas-sified into full payment and non-payment. Moreover, thenon-extreme recovery rates are predicted in the entire unitinterval [0,1].

Markus HoechstoetterChair of Statistics, Econometrics and MathematicalFinanceKarlsruhe Institute of Technology (KIT), Germanymarkus.hoechstoetter@kit.edu

Abdolreza NazemiKarlsruhe Institute of Technology (KIT), Germanynazemi@statistik.uni-karlsruhe.de

Svetlozar T. RachevDepartment of Applied Mathematics at Stony BrookUniversityNew York, USArachev@ams.sunysb.edu

CASLAV BozicInformatics Institute, Faculty of Business Engineering,Karlsruhe Institute of Technology, Germanycaslav.bozic@kit.edu

CP13Maximum Likelihood Estimation for Large Inter-acting Stochastic Systems

Parameter estimation for a large system is facilitated byuse of the asymptotic SPDE to which the system weaklyconverges. Standard particle filtering methods are oftennot applicable for parameter estimation of the SPDE. Amethod of moments reduces the SPDE into an SDE sys-tem. We then develop a particle filtering method for theSDE system. Theoretical convergence of the finite sys-tem’s likelihood to the asymptotic likelihood is discussed.Important credit risk and mortgage applications motivatethe method.

Justin SirignanoStanford Universityjasirign@stanford.edu

Gustavo SchwenklerStanford UniversityDep. of Management Science and Engineeringgschwenk@stanford.edu

Kay GieseckeStanford UniversityDept. of Management Science and Engineeringgiesecke@stanford.edu

MS1Price Dynamics in Limit Order Markets: LimitTheorems and Diffusion Approximations

We propose a queueing model for the dynamics of a limitorder book in a liquid market where buy and sell ordersare submitted at high frequency. We derive a functionalcentral limit theorem for the joint dynamics of the bid andask queues and show that, when the frequency of order

arrivals is large, the intraday dynamics of the limit orderbook may be approximated by a Markovian jump-diffusionprocess in the positive outhunt, whose characteristics areexplicitly described in terms of the statistical properties ofthe underlying order flow [Cont Larrard 2011]. This resultallows to obtain analytical expressions for the probability ofa price increase or the distribution of the duration until thenext price move, conditional on the state of the order bookand characterize various other quantities as solutions of el-liptic PDEs in the positive orthant [Cont Larrard 2012].Our results allow for a wide range of distributional and de-pendence assumptions in the orders and apply to a wideclass of stochastic models proposed for order book dynam-ics, including Poisson point processes, self-exciting pointprocesses [Cont, Andersen Vinkovskaya 2011] and modelsof the ACD-GARCH family.

Rama ContCNRS (France) & Columbia UniversityRama.Cont@gmail.com

Adrien DE LARRARDLaboratoire de Probabilites & Modeles AleatoiresUniversite Pierre & Marie Curie (Paris VI)adriendelarrard@gmail.com

MS1Information and the Value of Guaranteed TradeExecution

In many markets, uncertainty about whether a trade is ex-ecuted can be removed by paying a price premium. Weuse financial markets as a particular setting in which tostudy this trade-off. In particular, we assess the role ofinformation in the choice between certain trade at a pricepremium in an intermediated market such as a dealer mar-ket or a limit order book and contingent trade in a darkpool. Our setting consists of intrinsic traders and specula-tors, each endowed with heterogeneous fine-grained privateinformation as to an assets value, that endogenously decidebetween these two venues. We solve for an equilibrium inthis setting, and address three main questions: First, weillustrate how the choice between certain and contingenttrade depends on information available to an individualagent, as well as the overall distribution of informationacross all agents. Second, we analyze how the premium forcertain trade over contingent trade affects the strategic be-havior of traders. Finally, we demonstrate how the optionfor contingent trade affects the ability of intermediatingmarket makers to set transaction costs to maximize profit.

Krishnamurthy Iyer, Ramesh JohariStanford Universitykriyer@stanford.edu, ramesh.johari@stanford.edu

Ciamac C. MoallemiColumbia Uciamac@gsb.columbia.edu

MS1Mean-variance Optimal Adaptive Order Executionand Dawson-Watanabe Superprocesses

It is well-known that the mean-variance optimization ofadaptive order execution strategies is not dynamically con-sistent. By localizing the mean-variance criterion, one isled to the optimization of the mean versus quadratic vari-ation, which is a dynamically consistent stochastic controlproblem with fuel constraint. We show how this latter

140 FM12 Abstracts

problem can be solved by means of Dawson-Watanabe su-perprocesses.

Alexander SchiedUniversity of Mannheimalex.schied@gmail.com

MS1Optimal Liquidation in a Limit Order Book

We consider an asset liquidation problem at the market mi-crostructure level, conditional on observing the limit orderbook. The optimization problem is formulated in terms ofa sequence of stopping times, at which we submit marketsell orders. We describe the shape of the trade and notrade regions for various assumptions on the price processand the latency of the trader. In the empirical section,we show that our optimal policy significantly outperformsa benchmark TWAP algorithm on US treasury bonds. Inaddition we can efficiently calculate the cost of latency inthe trade execution.

Sasha F. Stoikov, Rolf WaeberCornell Universitysashastoikov@gmail.com, rw339@cornell.edu

MS2Pricing a Contingent Claim Liability with Transac-tion Costs Using Asymptotic Analysis for OptimalInvestment

We price a contingent claim liability using the utility in-difference argument. We consider an agent, who investsin a stock and a money market account with the goal ofmaximizing the utility of his investment at the final timeT in the presence of a proportional transaction cost in twocases with and without the liability. In both cases, we pro-vide a rigorous derivation of the asymptotic expansion ofthe value function and obtain a “nearly optimal” strategy.Additionally, we derive the asymptotic price of the contin-gent claim liability.

Maxim BichuchDepartment of Operations Research and FinancialEngineeringPrinceton Universitymbichuch@princeton.edu

MS2Shadow Prices and Well Posedness in the OptimalInvestment and Consumption Problem with Trans-action Costs

We revisit the optimal investment and consumption modelof Davis and Norman (1990) and Shreve and Soner (1994),following a shadow-price approach similar to that ofKallsen and Muhle-Karbe (2010). Making use of the com-pleteness of the model without transaction costs, we re-formulate and reduce the HJB equation for this singularstochastic control problem to a free-boundary problem for afirst-order ODE with an integral constraint. Having shownthat the free boundary problem has a twicely differenciablesolution, we use it to construct the solution of the origi-nal optimal investment/consumption problem without anyrecourse to the dynamic programming principle. Further-more, we provide an explicit characterization of model pa-rameters for which the value function is finite.

Jin Hyuk Choi

Department of MathematicsUniversity of Texas at Austinjchoi@math.utexas.edu

Gordan ZitkovicThe University of Texas at AustinDepartment of Mathematicsgordanz@math.utexas.edu

Mihai SirbuUniversity of Texas at Austinsirbu@math.utexas.edu

MS2Optimal Investment with Small Transaction Costsand General Stochastic Opportunity Sets

For an investor with constant absolute risk aversion, we in-formally derive the first-order asymptotics of the optimalinvestment strategy as the bid-ask spread becomes small.For general Ito processes, the first order correction term isexpressed in terms of the quadratic variation of the friction-less optimizer. This result allows to quantify the impactof, e.g., predictability and stochastic volatility on portfo-lio choice in the presence of transaction costs. Appliedto an investor holding a random endowment, it also leadsto a generalization of the asymptotic utility-based hedgingstrategies determined by Whalley and Wilmott (1997) fora constant opportunity set. This is joint work with JanKallsen.

Johannes Muhle-KarbeDepartement MathematikETH Zurichjohannes.muhle-karbe@math.ethz.ch

Jan KallsenKiel Universitykallsen@math.uni-kiel.de

MS2The Optimal Use of Options to Reduce the Effectof Transaction Costs in a Portfolio

Options are redundant in a portfolio of cash and stock ifwe assume the market of Black and Scholes, which includesno transaction costs. When we include transaction costs,however, options, when used correctly, can become quiteuseful in reducing the ill-effects these costs create. Specif-ically, let ε represent the scale of a small proportional lossfrom any trade. Given an investor’s utility preference, theloss in expected utility due to transaction costs in a cash

and stock portfolio is, at best, O(ε

23

). However, by in-

cluding options in the portfolio, we can improve this to

O(ε

67

), which is much closer to the O (ε) loss guaranteed

by even one trade. We detail the specific optimal strategythat accomplishes this.

Dan OstrovSanta Clara Universitydostrov@scu.edu

Jonathan GoodmanCourant InstituteUSAgoodman@cims.nyu.edu

FM12 Abstracts 141

MS3Modeling and Simulation of Systemic Risk inInsurance-Reinsurance Networks

We propose a dynamic insurance network model that al-lows to deal with reinsurance counter-party default riskswith a particular aim of capturing cascading effects at thetime of defaults.An equilibrium allocation of settlements isfound as the unique optimal solution of a linear program-ming problem. This equilibrium allocation recognizes 1)the correlation among the risk factors, which are assumedto be heavy-tailed, 2) the contractual obligations, whichare assumed to follow popular contracts in the insuranceindustry (such as stop-loss and retro-cesion), and 3) theinterconnections of the insurance-reinsurance network. Weare able to obtain an asymptotic description of the mostlikely ways in which the default of a specific group of in-surers can occur, by means of solving a multidimensionalKnapsack integer programming problem. Finally, we pro-pose a class of provably strongly efficient estimators forcomputing the expected loss of the network conditioningthe failure of a specific set of companies.

Jose BlanchetColumbia Universityjose.blanchet@columbia.edu

Yixi SHIIEOR Dept, Columbia Universityys2347@columbia.edu

MS3Pricing of Path-Dependent Vulnerable Claims inRegime Switching Markets

We study pricing of path-dependent vulnerable claims inregime-switching markets. The key theoretical tool under-lying our results is a Poisson series representation of vulner-able claims, which we develop using a change of probabil-ity measure technique. We employ such a representation,along with a short-time asymptotic expansion of the claim’sprice in terms of the Laplace transforms of the symmetricDirichlet distribution, to develop an efficient method forpricing claims which may depend on the full path of the un-derlying Markov chain. The proposed approach is appliedto price not only simple European claims such as default-able bonds, but also a new type of path-dependent claimsthat we term self-decomposable, as well as the importantclass of vulnerable call and put options on a stock. Weprovide a detailed error analysis and illustrate the accuracyand computational complexity of our algorithms on mar-ket traded instruments, such as defaultable bond prices,barrier options, and vulnerable European options.

Agostino CapponiSchool of Industrial EngineeringPurdue Universitycapponi@purdue.edu

Jose E. Figueroa-LopezPurdue Universityfigueroa@purdue.edu

Jeff NisenPurdue UniversityStatistics Departmentjnisen@purdue.edu

MS3Default and Systemic Risk in Equilibrium

In a finite horizon continuous time market model, we con-sider risk averse utility maximizers who invest dynamicallyin a risk-free money market account, a stock written ona default-free dividend process, and a defaultable bond.Prices are determined via equilibrium. We analyze conta-gion arising endogenously between the stock and the de-faultable bond via the interplay between equilibrium be-havior of investors, risk preferences, and cyclicality prop-erties of the default intensity. The equilibrium price ofthe stock experiences a jump at default, despite that thedefault event has no causal impact on the dividend pro-cess. We characterize the direction of the jump in termsof a relation between investor preferences and the cyclical-ity properties of the default intensity. A similar analysis isperformed for the market price of risk and investor wealthprocesses. The impact of heterogeneity of preferences onthe default exposure carried by different investors is alsoinvestigated.

Martin LarssonCornell Universitymol23@cornell.edu

Agostino CapponiSchool of Industrial EngineeringPurdue Universitycapponi@purdue.edu

MS3Filtered Likelihood for Point Processes

We develop likelihood estimators of the parameters of amarked point process and of incompletely observed ex-planatory factors that influence the arrival intensity alongwith the point process itself. The factors follow jump-diffusions whose drift, diffusion, and jump coefficients areallowed to depend on the point process. We provide condi-tions guaranteeing consistency and asymptotic normalityas the sample period grows. We also establish an approxi-mation to the likelihood and analyze the convergence andasymptotic properties of the associated estimators. Nu-merical results illustrate our approach.

Gustavo SchwenklerStanford UniversityDep. of Management Science and Engineeringgschwenk@stanford.edu

Kay GieseckeStanford UniversityDept. of Management Science and Engineeringgiesecke@stanford.edu

MS4Excursions in Atlas Models of Equity Market

Let us consider an equity market of finite number of stockswhere behavior of their capitalization is a multidimensionaldiffusion characterized with their rankings. Such model cancapture flows of market capitalizations as it was observedby Fernholz et al. In this talk we consider some questionson excursion measure and time-reversibility for these flowsof market capitalization with application to portfolio man-agement under such abstract equity market.

Tomoyuki Ichiba

142 FM12 Abstracts

University of California, Santa BarbaraDepartment of Statisticsichiba@pstat.ucsb.edu

MS4Optimal Investment for All Time Horizons andMartin Boundary of Space-time Diffusion

I review the definition and basic properties of the forwardperformance processes, including their relation to the morestandard investment criteria, and the associated SPDEcharacterization. I, then, concentrate on the problem ofconstructing the forward investment performance processesin a Markovian setting. In this case, the problem reducesto the so-called ”forward Hamilton-Jacobi-Bellman equa-tion”, which, in some cases, can be transformed into a time-reversed linear parabolic equation. I characterize the so-lutions of this (ill-posed) problem explicitly, extending theclassical Widders theorem on positive solutions to the time-reversed heat equation. Finally, I consider closed-form ex-amples of the Markovian forward performance processesin some specific stochastic volatility models, including themean-reverting log-price (Schwartz) model.

Sergey NadtochiyOxford UniversityOxford-Man Institutesergey.nadtochiy@oxford-man.ox.ac.uk

MS4Volatility-Stabilized Markets

We consider models which generalize the Volatility-stabilized markets introduced in Fernholz and Karatzas(2005). We show how to construct a weak solution of theunderlying system of stochastic differential equations, ex-press the solution in terms of time changed squared-Besselprocesses, and argue that this solution is unique in distri-bution. Moreover, we discuss sufficient conditions for theexistence of a strong solution and show that strong relativearbitrage opportunities exist in these markets.

Radka PickovaColumbia Universityradka@stat.columbia.edu

MS4Generalizations of Functionally Generated Portfo-lios

I will present generalizations on functionally generatedportfolios (FGPs) of stochastic portfolio theory. The as-sets and the benchmark may be any strictly positive wealthprocesses, as opposed to merely the stocks and the marketportfolio, respectively. Another generalization is that thegenerating function may be stochastic, so that the gen-erated portfolio can be adjusted to changing market con-ditions. These FGPs can be applied to arbitrary cointe-grated market modes exploiting their mean-reversion in arisk-controlled manner.

Winslow C. StrongUniversity of California Santa Barbarawinslow.strong@gmail.com

MS5Optimal Investment in the Presence of High-water

Mark Fees

In this talk, we consider the Merton problem for an agentwho may invest in a money market fund, a stock, and ahedge fund that is subject to a performance fee. This feeis assessed each time the cumulative profit-to-date derivedfrom the investment in the hedge fund reaches a new run-ning maximum. We will study the associated HJB equa-tion and examine some qualitative properties of the opti-mal strategy.

Gerard BrunickUniversity of CaliforniaSanta Barbarabrunick@pstat.ucsb.edu

Karel JanecekRSJ algorithmic tradingkarel.janecek@rsj.cz

Mihai SirbuUniversity of Texas at Austinsirbu@math.utexas.edu

MS5A Uniqueness Theorem for a Degenerate QVI Ap-pearing in An Option Pricing Problem

We prove the missing uniqueness theorem for the viscositysolution of a degenerate quasi-variational inequality, whichmakes the probability-free theory of option pricing in theinterval market model, essentially complete.

Naıma El FarouqUniversity Blaise Pascal, Clermont-Ferrand, Francenaima.elfarouq@.univ-bpclermont.fr

Pierre bernhardINRIA-Sophia Antipolis-MediterraneeFrancepierre.bernhard@inria.fr

MS5Existence, Uniqueness, and Global Regularity forDegenerate Obstacle Problems in Mathematical Fi-nance

The Heston stochastic volatility process, which is widelyused as an asset price model in mathematical finance, is aparadigm for a degenerate diffusion process where the de-generacy in the diffusion coefficient is proportional to thesquare root of the distance to the boundary of the half-plane. The generator of this process with killing, calledthe elliptic Heston operator, is a second-order degenerateelliptic partial differential operator whose coefficients havelinear growth in the spatial variables and where the degen-eracy in the operator symbol is proportional to the distanceto the boundary of the half-plane. With the aid of weightedSobolev spaces, we prove existence, uniqueness, and globalregularity of solutions to stationary variational inequalitiesand obstacle problems for the elliptic Heston operator onunbounded subdomains of the half-plane. In mathematicalfinance, solutions to obstacle problems for the elliptic He-ston operator correspond to value functions for perpetualAmerican-style options on the underlying asset.

Paul FeehanRutgers Universityfeehan@rci.rutgers.edu

FM12 Abstracts 143

Panagiota DaskalopoulosColumbia Universitypdaskalo@math.columbia.edu

MS5Approximate Solutions to Second Order ParabolicEquations with Time-dependent Coefficients

We consider second order parabolic equations with co-efficients that vary both in space and in time (non-autonomous). We derive closed-form approximations tothe associated fundamental solution by extending theDyson-Taylor commutator method that we recently es-tablished for autonomous equations. We establish errorbounds in Sobolev spaces and show that by includingenough terms, our approximation can be proven to be ac-curate to arbitrary high order in the short-time limit. Weshow how our method extends to give an approximation ofthe solution for any fixed time and within any given toler-ance. Some applications to option pricing are presented. Inparticular, we perform several numerical tests, and specif-ically include results on Stochastic Volatility models.

Victor NistorPennsylvania State Universitynistor@math.psu.edu

Anna MazzucatoDepartment of Mathematics, Penn State Universitymazzucat@math.psu.edu

Wen ChengPenn State universitycheng@math.psu.edu

MS6Mixed Deterministic Monte-Carlo Simulations forFinance

Mixing Monte-Carlo and PDE methods can substantiallyspeed-up computations because it allows use of closedform solutions for some of the components. It can alsosolve problems like unknown boundary conditions for com-plex stochastic volatility models. Applying the methodcombined with Longstaff-Schwartz projection can lead toefficient computations of early exercise contracts. Theconvergence of the methods will be established with er-ror estimates and we shall report performance on multi-dimensional problems.

Olivier PironneauUniversity of Paris VI (Pierre et Marie Curie)pironneau@ann.jussieu.fr

Gregoire LoeperNatixisgregoire.loeper@natixis.com

MS6Two-dimensional Fourier Cosine Series ExpansionMethod for Pricing Financial Options

The COS method for pricing European and Bermudan op-tions with one underlying asset was developed by Fang andOosterlee (2008, 2009). We extend the method to higherdimensions, with a multi-dimensional asset price process.The algorithm can be applied to, for example, pricing two-color rainbow options, but also to pricing under the Heston

stochastic volatility model. For smooth density functions,the method converges exponentially in the number of termsin the Fourier cosine series summations.

Marjon Ruijter, Kees OosterleeCWI - Center for Mathematics and Computer Sciencemarjon.ruijter@cwi.nl, c.w.oosterlee@cwi.nl

MS6Risk-Neutral Valuation of Real Estate Options

We propose a novel and intuitive risk-neutral valuationmodel for real estate derivatives. The resulting index be-havior can easily be analyzed and closed-form pricing so-lutions are derived for forwards, swaps and European putand call options. We demonstrate the application of themodel by valuing a put option on a house price index. Au-tocorrelation in the index returns appears to have a largeimpact on the option value. We also study the effect ofan over- or undervalued real estate market. The observedeffects are significant and as expected.

Stefan SingorOrtec-FinanceStefan.Singor@ortec-finance.com

David van BragtAegondbragt@aegon.nl

Marc FranckeOrtec Financemarc.francke@ortec-finance.com

Antoon PelsserUniversity of Maastrichta.pelsser@maastrichtuniversity.nl

MS6Efficient Option Pricing of Asian Options based onFourier Cosine Expansions

In this talk we present an efficient pricing method for Asianoptions under Levy processes, based on Fourier–cosine ex-pansions and Clenshaw–Curtis quadrature. The pricingmethod has been developed for both European–style andAmerican–style Asian options, written on different typesof average (arithmetic, geometric and harmonic), and fordiscretely and continuously monitored versions. Fast con-vergence of Fourier cosine expansions and Clenshaw–Curtisquadrature ensures exponential convergence in the Asianoption prices in most cases, which reduces the computingtime of the method to milliseconds for geometric Asian op-tions and a few seconds for arithmetic Asian options. Themethod’s convergence behavior is explained by an erroranalysis. Its performance is further demonstrated by vari-ous numerical examples, where we also show the power ofan implementation on the Graphics Processing Unit (GPU)where hundreds of speedup is achieved for pricing early–exercise Asian options, in particular.

Bowen ZhangDelft University of Technologybowen.zhang@tudelft.nl

Cornelis W. OosterleeDelft University of TechnologyCentrum Wiskunde en Informatica (CWI)c.w.oosterlee@cwi.nl

144 FM12 Abstracts

MS7Sampling Error of the Supremum of a Levy Process

Lvy processes are often used in finance to model the dy-namics of asset prices. The supremum of a Lvy processis of interest when one is pricing financial contracts whosepayoffs depend on the supremum of the underlying assetprice process. While the maximum of a discretely sampledLvy process can often be handled very efficiently using nu-merical methods, not much is known about the continuoussupremum of a general Lvy process. We present results onthe discrepancy between the discrete maximum and contin-uous supremum of a Lvy process. Using Spitzers identityand results from analytic number theory, we derive explicitexpressions for the sampling errors for various commonlyused Lvy processes. The results help us better understandthe error of approximating the continuous supremum of aLvy process by a discrete maximum.

Liming FengDepartment of Industrial and Enterprise SystemsEngineeringUniversity of Illinois at Urbana-Champaignfenglm@uiuc.edu

MS7Positive Subordinate CIR Processes with Two-Sided Mean-Reverting Jumps

We present the SubCIR jump-diffusion process. TheSubCIRsdiffusion dynamics are those of a CIR pro-cess. The SubCIRs jump componentincludes two-sidedmean-reverting (state-dependent) jumps. The process re-mainsstrictly positive if the CIR process satisfies Fellerscondition. Theanalytical tractability of the SubCIR pro-cess makes it a richer extension tothe CIR process (com-pared to previous models) and it is also a naturalalternativefor interest rates and credit models.

Rafael Mendoza-ArriagaUniversity of Texas at AustinRafael.Mendoza-Arriaga@mccombs.utexas.edu

MS7Default Swap Games

We consider the valuation of game-type credit defaultswaps that allow the protection buyer and seller to raise orreduce the respective position once prior to default. Undera structural credit risk model based on spectrally negativeLevy processes, we analyze the existence of the Nash equi-librium and derive the associated saddle point. Using theprinciples of smooth and continuous fit, we determine thebuyer’s and seller’s equilibrium exercise strategies, whichare of threshold type.

Kazutoshi YamazakiOsaka Universityk-yamazaki@sigmath.es.osaka-u.ac.jp

Tim LeungJohns Hopkins Universityleung@ieor.Columbia.edu

MS7Multifactor Term Structure of Interest Rates under

Regime Shifts and Levy Jumps

We develop a tractable dynamic term structure models un-der jump-diffusion with Levy Jumps and regime shifts withtime varying transition probabilities. The model allows forregime-dependent jumps while both jump risk and regime-switching risk are priced. Two types solutions, including(log-linear) approximate solutions and exact solutions forthe term structure are obtained for affine-type models un-der different conditions. For the approximate solutions, wederive the error bound, which is in the first order only. Forthe exact solutions, we further obtain closed-form expres-sions for special cases. Joint work with Xiangdong Liu,Lawrence C. Evans, and Shu Wu.

Yong ZengUniversity of Missouri at Kansas CityDepartment of Mathematics and Statisticszengy@umkc.edu

Xiangdong LiuJinan Universitytliuxd@jnu.edu.cn

Lawrence EvansUniversity of Missourievanslc@missouri.edu

Shu WuUniversity of Kansasshuwu@ku.edu

MS8Risk Measures and Fine Tuning of High FrequencyTrading Strategies

Alvaro CarteaUniversidad Carlos IIIalvaro.cartea@uc3m.es

Sebastian JaimungalUniversity of Toronto, Canadasebastian.jaimungal@utoronto.ca

MS8New Models for Optimal Execution and High-frequency Market Making

Two related papers will be presented that rely on the samemathematical finding. The first one ”Dealing with the in-ventory risk” solves the Avellaneda-Stoikov problem. Itcorresponds to the case of a market maker who has tocontinuously set a bid and a ask quote and we derive theoptimal quotes with closed-form approximations based onspectral ideas. The second one deals with the classicalsubject of optimal liquidation and is one of the first at-tempts to solve the problem with limit orders instead ofliquidity-consuming market orders. This second paper willbe presented for very general intensity functions.

Olivier GueantUniversite Paris-DiderotUFR de Mathematiquesolivier.gueant@gmail.com

FM12 Abstracts 145

MS8Optimal HF Trading in a Prorata Microstructure

We propose a framework to study optimal trading poli-cies in a one-tick pro-rata limit order book, as typicallyarises in short-term interest rate futures contracts. Thehigh-frequency trader has the choice to trade via marketorders or limit orders, which are represented respectively byimpulse controls and continuous controls. We model anddiscuss the consequences of the two main features of thisparticular microstructure: first, the limit orders sent bythe high frequency trader are only partially executed, andtherefore she has no control on the executed quantity. Forthis purpose, cumulative executed volumes are modelled bycompound Poisson processes. Second, the high frequencytrader faces the overtrading risk, which is the risk of bru-tal variations in her inventory. The consequences of thisrisk are investigated in the context of optimal liquidation.The optimal trading problem is studied by stochastic con-trol and dynamic programming methods, which lead to acharacterization of the value function in terms of an inte-gro quasi-variational inequality. We then provide the as-sociated numerical resolution procedure, and convergenceof this computational scheme is proved. Next, we exam-ine several situations where we can one one hand simplifythe numerical procedure by reducing the number of statevariables, and on the other hand focus on specific casesof practical interest. We examine both a market makingproblem and a best execution problem in the case wherethe mid-price process is a martingale. We also detail a highfrequency trading strategy in the case where a (predictive)directional information on the mid-price is available. Eachof the resulting strategies are illustrated by numerical tests.

Huyen PhamUniversity Paris Diderothuyn pham ¡pham@math.univ-paris-diderot.fr¿

Fabien GuilbaudUniversity Paris Diderotfabien.guilbaud@gmail.com

MS9Stochastic Perron’s Method and Verification with-out Smoothness using Viscosity Comparison: Ob-stacle Problems and Dynkin Games

We adapt the Stochastic Perron’s method in Bayraktar andSirbu (to appear in the Proceedings of the American Math-ematical Society) to the case of double obstacle problemsassociated to Dynkin games. We construct, symmetrically,a viscosity sub-solution which dominates the upper valueof the game and a viscosity super-solution lying below thelower value of the game. If the double obstacle problemsatisfies the viscosity comparison property, then the gamehas a value which is equal to the unique and continuous vis-cosity solution. In addition, the optimal strategies of thetwo players are equal to the first hitting times of the twostopping regions, as expected. The (single) obstacle prob-lem associated to optimal stopping can be viewed as a veryparticular case. This is the first instance of a non-linearproblem where the Stochastic Perron’s method can be ap-plied successfully. (Joint work with Mihai Sirbu. Availableon ArXiv.)

Erhan BayraktarUniversity of MichiganDepartment of Mathematicserhan@umich.edu

MS9Optimal Consumption and Investment in Incom-plete Markets with General Constraints

We study an optimal consumption and investment problemin a possibly incomplete market with general, not neces-sarily convex, stochastic constraints. We give explicit solu-tions for investors with exponential, logarithmic and powerutility. Our approach is based on martingale methodswhich rely on recent results on the existence and uniquenessof solutions to BSDEs with drivers of quadratic growth.

Patrick CheriditoPrinceton Universitydito@princeton.edu

MS9Dynamic Portfolio Choice with Multiple Decentral-ized Agents

Abstract not available at time of publication.

Andrew LimIndustrian Engineering and Operations ResearchUniversity of California, Berkeleylim@ieor.berkeley.edu

MS9Constructing Sublinear Expectations on PathSpace

We provide a general construction of time-consistent sub-linear expectations on the space of continuous paths. Ityields the existence of the conditional G-expectation of aBorel-measurable (rather than quasi-continuous) randomvariable, a generalization of the random G-expectation,and an optional sampling theorem that holds without ex-ceptional set.

Marcel NutzDepartment of MathematicsColumbia Universitymnutz@math.columbia.edu

Ramon Van HandelPrinceton Universityrvan@princeton.edu

MS10Resilience to Contagion in Financial Networks

Propagation of balance-sheet or cash-flow insolvency acrossfinancial institutions may be modeled as a cascade processon a network representing their mutual exposures. We de-rive rigorous asymptotic results for the magnitude of conta-gion in a large financial network and give an analytical ex-pression for the asymptotic fraction of defaults, in terms ofnetwork characteristics. Our results extend previous stud-ies on contagion in random graphs to inhomogeneous di-rected graphs with a given degree sequence and arbitrarydistribution of weights. We introduce a criterion for theresilience of a large financial network to the insolvency of asmall group of financial institutions and quantify how con-tagion amplifies small shocks to the network. Our resultsemphasize the role played by ”contagious links’ and showthat institutions which contribute most to network insta-bility in case of default have both large connectivity and alarge fraction of contagious links. The asymptotic results

146 FM12 Abstracts

show good agreement with simulations for networks withrealistic sizes.

Hamed AminiSwiss Finance Institute, Ecole polytechnique federale deLahamed.amini@epfl.ch

Rama ContCNRS (France) & Columbia UniversityRama.Cont@gmail.com

Andreea MincaCornell Universityacm299@cornell.edu

MS10Coupled Diffusions, Swarming and Systemic Risk

Abstract not available at time of publication.

Jean Pierre FouqueUniversity of California Santa Barbarafouque@pstat.ucsb.edu

MS10Failure and Rescue in an Interbank Network

This paper is concerned with systemic risk in the inter-bank market. We model this market as a directed graphin which the banks represent the nodes and the liabilitiesbetween the banks represent the edges. Our work buildson the modelling paradigm of Eisenberg and Noe (2001),extending it by introducing default costs in the system.We provide a rigorous analysis of those situations in whichbanks have incentives to bailout distressed banks. Suchincentives exist under very mild conditions. We illustrateour results with some simple examples, and go on to dis-cuss possible measures of soundness of a financial system,together with possible policy implications for resolution ofdistress.

Luitgard VeraartDepartment of MathematicsLondon School of Economicsl.veraart@lse.ac.uk

Chris RogersChair of Statistical ScienceCambridge Universityl.c.g.rogers@statslab.cam.ac.uk

MS10Feedback Effects and Endogenous Risk in FinancialMarkets

We present a mathematical model which allows to quan-tify the impact of fire sales of assets of a fund undergoinglosses on the volatilities and correlations of assets held bythe fund. Our model shows that the liquidation of largepositions by funds may result in spikes in volatilities andcorrelations, even in absence of liquidity dry-up, and givesplausible explanations for the large hedge fund losses ofAugust 2007. We show that our model can be used forforensic analysis of financial data, to recover characteris-tics of the portfolio undergoing fire sales from public data,by solving an inverse problem. We show the consistencyof the estimator obtained and apply it to simulated and

empirical data.

Lakshithe WagalathUniversite Pierre & Marie Curiewagalath@gmail.com

Rama ContCNRS (France) & Columbia UniversityRama.Cont@gmail.com

MS11Dynamic Modeling of Systemic Risk

We generalize the Eisenberg-Noe model to allow for multi-ple clearing dates, as well as uncertainty in future liabilitiesand cash inflows. The clearing payment vectors are sequen-tially recovered as the solutions of robust linear program-ming problems solved over the planned horizon. We showexistence and uniqueness of the clearing payment vectorsover time. We perform a sensitivity analysis of the lossand payment vector with respect to borrowing and equityconstraints. We employ the Shapley value methodologyto dynamically attribute the systemic risk to the individ-ual nodes in the network. We conclude with a numericalassessment of the proposed methodology on a systemic net-work consisting of a large number of highly interconnectedfinancial institutions.

PengChu ChenPurdue Universitychen621@purdue.edu

Agostino CapponiSchool of Industrial EngineeringPurdue Universitycapponi@purdue.edu

MS11Estimating Hedge Fund Risk Factors

The estimation of hedge fund returns and the risk factorsthat impact them is a critical step in the construction ofportfolios. In particular, so called fund-of-funds have thearduous task of building portfolios of hedge fund strategiesbased on limited and low frequency observations. This isquite daunting in the hedge fund space due to the gen-erally small sample sizes and opaque nature of that in-dustry’s data. To overcome these difficulties, it is desiredto estimate risk factors based on market observables andreverse engineer a hedge fund exposure to those factors.The model that we propose will be used to analyze anddecompose the risk of various hedge fund indices on com-mon factors at a high frequency (e.g., daily, or intra-day)based on their habitual low frequency observations (typi-cally monthly). Specifically, we will jointly model the risk-factors (e.g., stock returns) and the asset returns (e.g.,a hedge fund strategy) in a fat-tailed, stochastic volatil-ity environment implemented with a Bayesian approachvia a Rao-Blackwellised (R-B) particle filter. We utilize avector Stochastic-Volatility model with smoothed observ-able returns to extract the potentially time-varying ex-posure of low frequency hedge fund performance on highfrequency data. By making use of a particle filter withRao-Blackwellization, we reduce the parameter space sig-nificantly resulting in a more accurate estimate of the dis-tibution of the parameter state. This approach can beused for analyzing hedge fund performance and their ad-vertized strategies as well as in forensic risk-management.The latter of which is a critical need given the generally

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low transparency of the hedge fund industry.

Douglas JohnstonQuantalysis, LLCdjohnst@verizon.net

Petar DjuricStony Brook Universitydjuric@ece.sunysb.edu

MS11Smooth and Monotone Covariance Estimation forElliptical and Generalized Hyperbolic Distribu-tions

We consider the problem of high-dimensional covarianceestimation from severely limited observations. Strong as-sumptions on the structure of the underlying random vec-tor have to be made for the problem to be well-defined.Some examples developed in the literature include: covari-ance selection models with sparse inverse covariances, low-rank structures (PCA models and factor analysis), sparseplus low-rank structures, multi-scale structures. We con-sider another assumption which is important for a varietyof applications including term-rate risk-modeling in com-putational finance: smoothness and monotonicity. We re-view our previous formulation for multivariate Gaussianrandom vectors based on semi-definite programming, andextend the method for elliptical and generalized hyperbolicdistributions. We use efficient convex optimization algo-rithms and compare the methods using various penalizedBregman divergences as objective functions with examplesfrom interest rate modeling.

Dmitry MalioutovDRW Holdingsdmaliout@gmail.com

Xiaoping ZhouStony Brook Universityxizhou@ams.sunysb.edu

MS11Nonparametric Prediction in a Limit Order Book

We propose a novel non-parametric approach to short-termforecasting of the mid-price in a limit order book. We in-troduce a state vector describing the state of the orderbook at each time. The predictor is based on two features,computed for each value of the state vector. Implicit as-sumptions of our method are very mild and are supportedby our preliminary real-data experiments on NYSEs Open-Book which yield promising empirical results.

Ilya Pollak, Deepan PalgunaPurdue Universityipollak@ecn.purdue.edu, dpalguna@gmail.com

MS12Dynamic Assessment Indices

Measuring performance and risk of cash flows is a crucialissue in finance. A Dynamic Assessment Index (DAI) is aquasiconcave, monotone function, mapping cash flows intoprocesses which represent their risk or performance evalu-ations in time. Using L0-separation theorems, we providean upper semicontinuous robust representation and studythe impact of different time consistency conditions; in par-

ticular, how past performances may impact the present as-sessment of risk. Illustrative examples will be discussed.

Martin KarliczekDepartment of Mathematics, Humboldt University BerlinGermanykarliczm@math.hu-berlin.de

MS12Minimal Supersolutions of BSDEs and RobustHedging

We study minimal supersolutions of BSDEs - related toPeng’s g-expectation - which can be seen as superhedg-ing functionals. We prove existence, uniqueness, mono-tone convergence, Fatou’s Lemma and lower semicontinuityof our functional. Unlike usual BSDE methods, based onfixed point theorems, the existence relies on compactnessmethods. We then study some robust extensions whichcorrespond to the problem of superhedging under volatilityuncertainty. The talk is based on joint works with SamuelDrapeau and Gregor Heyne.

Michael KupperHumboldt University Berlinkupper@math.hu-berlin.de

MS12Set-valued Dynamic Risk Measures in Marketswith Transaction Costs

Set-valued risk measures appear naturally when marketswith transaction costs are considered and capital require-ments can be made in a basket of currencies or assets.In this talk we study dual representation and time con-sistency properties of dynamic set-valued risk measures.It turns out that only a stronger time consistency calledmulti-portfolio time consistency is equivalent to a recur-sive form of the risk measure as well as to an additiveproperty for the acceptance sets, which is a central resultin the scalar case.

Birgit RudloffPrinceton Universitybrudloff@princeton.edu

MS12Portfolio Choice with Time-consistent DynamicRisk Measures

We study portfolio selection based on time-consistent dy-namic risk measures in a general continuous-time setting.The setting features discontinuities in the asset price pro-cesses, with a general and possibly infinite activity jumppart besides a continuous diffusion part, and general andpossibly non-convex trading constraints. We character-ize the minimal risk processes as solutions to BackwardStochastic Differential Equations (BSDEs). We prove ex-istence and uniqueness of the solution in the general classof jump BSDEs having a driver function that grows at mostquadratically. We further compute these solutions in a fewexamples by numerically solving the corresponding BSDEsusing regression techniques.

Mijda StadjeDepartment of Econometrics and Operations ResearchTilburg School of Economics and Management,Netherlandsm.a.stadje@uvt.nl

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Roger LaevenDepartment of Quantitative EconomicsUniversity of Amsterdamr.j.a.laeven@uva.nl

MS13The Valuation of Double Barrier Options underMultifactor Pricing Models

The (vast) literature on the pricing of barrier options ismainly focused on the valuation of European-style con-tracts under single-factor option pricing models (such asthe geometric Brownian motion and the CEV processes).This paper extends the literature in two directions. First,European-style (double) barrier options are priced undera multifactor and Markovian financial model that is ableto accommodate stochastic volatility, stochastic interestrates, endogenous bankruptcy, and time-dependent barri-ers. Second and more importantly, quasi-analytical pric-ing solutions are also proposed for American-style (double)barrier option contracts under the same general financialmodel. The proposed pricing solutions are shown to beaccurate, easy to implement, and efficient.

Jose C. DiasISCTE-IUL Business Schooljose.carlos.dias@iscte.pt

Joo NunesBRU-UNIDE and ISCTE Business Schooljoao.nunes@iscte.pt

MS13Exponential Time Differencing Methods for Pric-ing and Hedging American Options

Exponential time differencing (ETD) methods based on theCox and Matthews approach are developed to solve a non-linear BlackScholes model for pricing and hedging Ameri-can options with transaction cost. Each of these methodsavoids solving nonlinear systems, whilst, well known stan-dard methods would require solving nonlinear systems ateach time step. Numerical experiments are performed onexotic path-dependent American options with transactioncost to demonstrate the computational efficiency, accuracyand reliability of the methods.

Abdul M. KhaliqMiddle Tennessee State UniversityDepartment of Mathematical Sciencesakhaliq@mtsu.edu

Mohammad YousufKing Fahd University of Petroleum and MineralsSaudi Arabiamyousuf@kfupm.edu.sa

Britta KleefeldBrandenburgische Technische Universitat CottbusGermanybritta.kleefeld@tu-cottbus.de

MS13Efficient and Robust Time Stepping Under Jump-diffusion Models

Partial-integro differential (PIDE) formulations are oftenused to solve option pricing problems where the underlying

asset follows a jump-diffusion process. The main challengelies in the efficient treatment of the jump term resulting afull matrix. We discuss some efficient, robust, and accuratetime discretization methods including schemes treating thejump term explicitly.

Santtu SalmiUniversity of Jyvaskylasanttu.salmi@jyu.fi

Jari ToivanenStanford Universitytoivanen@stanford.edu

MS13Pricing American Options Under Jump-diffusionModels

Under jump-diffusion models, a linear complementarityproblem (LCP) with a partial-integro differential opera-tor can formulated for the price of an American option. Asthe discretization of the jump term leads to a full matrix,it preferable to use special techniques to solve the result-ing LCPs. We discuss various efficient methods for theseLCPs.

Jari ToivanenStanford Universitytoivanen@stanford.edu

Santtu SalmiUniversity of Jyvaskylasanttu.salmi@jyu.fi

MS14Efficient Laplace Inversion, Wiener-Hopf Factor-ization and Pricing Lookbacks

We construct very fast and accurate methods of approx-imate Laplace inversion, calculation of the Wiener-Hopffactors for wide classes of Levy processes with exponen-tially decaying Levy densities, and pricing lookback op-tions. In all cases, we use appropriate conformal changesof variables, which allow us to apply the simplified trape-zoid rule with small number of terms. The same techniqueis applicable for calculation of pdf’s of the supremum andinfimum processes, and prices and sensitivities of optionswith lookback and barrier features.

Svetlana Boyarchenko, Department of Economics, University of Texas atAustin,1 University Station C3100, Austin,TX 78712–0301, USAsboyarch48@gmail.com

MS14Quadratic Hedging of Barrier Options under Lep-tokurtic Returns Driven by an Exponential LvyModel

We examine quadratic hedging of barrier options in a modelrealistically calibrated to reflect the leptokurtic nature ofequity returns. We compute the hedging error of the opti-mal hedging strategy andevaluate prices that yield reason-able risk-adjusted performance for the hedger. Our mainfinding is that the impact of hedging errors on prices is sev-eral times higher than the impact of other pricing biasesstudied in the literature, in particular the effect of barrier

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misalignment and of discrete monitoring.

Ale CernCass Business School, Londoncerny@martingales.info

MS14Exact Simulation of the Heston Jump-Diffusion

In this talk, we extend the Heston stochastic volatilitymodel to include state-dependent jumps in the price andthe volatility, and develop a method for the exact simu-lation of this model. The jumps arrive with a stochasticintensity that may depend on time, price, volatility andjump counts. They may have an impact on the price or thevolatility, or both. The random jump size may depend onthe price and volatility. Numerical experiments illustratethe features of the exact method. This is a joint work withProf. Erhan Bayraktar at the University of Michigan andProf. Kay Giesecke at Stanford University.

Xueying Hu, Erhan BayraktarUniversity of MichiganDepartment of Mathematicsxyhu@umich.edu, erhan@umich.edu

Kay GieseckeStanford UniversityDept. of Management Science and Engineeringgiesecke@stanford.edu

MS14Efficient Pricing and Reliable Calibration in theHeston Model and its Generalizations

We suggest a general scheme for improvement of FT-pricing formulas for European option and give efficient rec-ommendations for the choice of the parameters of the nu-merical scheme, which allow for very accurate and fast cal-culations. We demonstrate that an indiscriminate choiceof parameters of a numerical scheme leads to an inaccu-rate pricing and calibration. As applications, we considerthe Heston model and its generalization, and several otheraffine models. For many parameter sets documented in em-pirical studies of financial markets, relative accuracy bet-ter than 0.01 % can be achieved by summation of less than10-20 terms even in the situations in which the standardapproach requires more than 200. In some cases, the one-term formula produces an error of several percent, and thesummation of two terms — less than 0.5 %. Typically, 10terms and fewer suffice to achieve the error tolerance ofseveral percent and smaller.high-level commands.

Sergei LevendorskiiUniversity of Leicesterlevendorskii@gmail.com

MS15Central Clearing Mechanisms for Credit DefaultSwaps

Central clearing of Credit default swaps through CentralCounterparties (CCPs) has been proposed as a tool formitigating systemic risk and counterpart risk in CDS mar-kets. The design of CCPs for CDS involves the implemen-tation of margin requirements and a clearing fund (or de-fault fund), for which various designs have been proposed.We study the impact of the design of these requirements

on the risk of the CCP and the incentives for CDS clearing.

JinBeom KIMIEOR Dept, Columbia Universityjk3071@columbia.edu

Rama ContCNRS (France) & Columbia UniversityRama.Cont@gmail.com

MS15Central Clearing of OTC Derivatives : Bilateral vsMultilateral Netting

We study the impact of a central counterparty (CCP) forOTC derivatives on expected interdealer exposures. Theresults are sensitive to assumptions on heterogeneity ofrisk across asset classes as well as correlation of exposuresacross asset classes; empirically plausible specifications ofthese parameters lead to the conclusion that the gain frommultilateral netting in a CCP largely overweighs the loss ofnetting across asset classes in bilateral netting agreements.

Thomas KOKHOLMAarhus Universitythko@asb.dk

Rama ContCNRS (France) & Columbia UniversityRama.Cont@gmail.com

MS15Measuring Contagion in Financial Networks

Liabilities between financial entities form a network. Theclearing of liabilities and thereby contagion of risk anddefault depend on this network structure. We provide amathematical model to understand clearing and propaga-tion of default in such financial networks. This yields aprecise measure for the systemic risk induced by individ-ual financial entities. The model allows to compute opti-mal bailout strategies that either minimize the cost of theintervention or maximize the stabilizing effect for a givenbailout budget. Finally, the computational efficiency of themodel allows to analyze large scale networks quickly.

Sebastian StillerTechnische Universitat Berlinsebastian.stiller@tu-berlin.de

MS15Are CDS Auctions Biased?

We study settlement auctions for credit default swaps(CDS). We find that the one-sided design of CDS auctionsused in practice gives CDS buyers and sellers strong incen-tives to distort the final auction price, in order to maximizepayoffs from existing CDS positions. Consequently, theseauctions tend to overprice defaulted bonds conditional onan excess supply and underprice defaulted bonds condi-tional on an excess demand. We propose a double auctionto mitigate this price bias. We find the predictions of ourmodel on bidding behavior to be consistent with data onCDS auctions.

Haoxiang ZHUStanford University

150 FM12 Abstracts

haoxiang.zhu@stanford.edu

SongZi DUGraduate School of BusinessStanford Universitysongzidu@stanford.edu

MS16Endogenous Equilibria in Liquid Markets with Fric-tions and Boundedly Rational Agents

We propose a simple binary mean field game, where Nboundedly rational agents may decide to trade or not ashare of a risky asset in a liquid market. Agents’ utilitydepends on returns, which are endogenously determinedtaking into account observed and forecasted demand andan exogenous transaction cost. The explicit dependence onpast demand generates endogenous dynamics of the sys-tem. It is shown that pure strategy Nash equilibria exist.We study under a rather general setting (risk attitudes,pricing rules and noises) the aggregate demand for the as-set, the emerging returns and the structure of the equilibriaof the asymptotic game. We prove that boom and crash cy-cles may arise and that transaction costs have a stabilizingeffect on the market.

Paolo Dai Prauniversity of Paduadaipra@math.unipd.it

Fulvio FontiniDepartment of Economics and ManagementUniversity of Padovafulvio.fontini@unipd.it

Elena Sartori, Marco TolottiDepartment of ManagementCa’ Foscari University of Veniceesartori@unive.it, tolotti@unive.it

MS16Large Portfolio Asymptotics for Loss From Default

We prove a law of large numbers for the loss from defaultand use it for approximating the distribution of the lossfrom default in large, potentially heterogenous portfolios.The density of the limiting measure is shown to solve anon-linear SPDE, and the moments of the limiting mea-sure are shown to satisfy an infinite system of SDEs. Thesolution to this system leads to the distribution of the limit-ing portfolio loss, which we propose as an approximation tothe loss distribution for a large portfolio. Numerical testsillustrate the accuracy of the approximation, and highlightits computational advantages over a direct Monte Carlosimulation of the original stochastic system.

Kay GieseckeStanford UniversityDept. of Management Science and Engineeringgiesecke@stanford.edu

Konstantinos SpiliopoulosBrown Universitykspiliop@dam.brown.edu

Richard SowersUniversity of Illinois at Urbana-Champaignrichard.sowers@gmail.com

Justin SirignanoStanford Universityjasirign@stanford.edu

MS16Branching and Interacting Particle Models of Sys-temic Risk

We propose an interacting particle system description ofthe banking system. While net bank assets evolve in-dependently under normal conditions, defaults trigger amean-field type interaction that creates systemic risk. Wework with a stochastic size of the economy, with new banksadded spontaneously according to a mean-field birth pro-cess. We present some preliminary results about systemstability and the properties of the corresponding mean-fieldlimit.

Michael LudkovskiUC Santa Barbaraludkovski@pstat.ucsb.edu

Tomoyuki IchibaUniversity of California, Santa BarbaraDepartment of Statisticsichiba@pstat.ucsb.edu

MS16Most Likely Path to Systemic Failure

In this talk, I will present recent results on modeling thedynamics of correlated default events in the financial mar-ket. An empirically motivated system of interacting pointprocesses is introduced and we study how different types ofrisk, like contagion and exposure to systematic risk, com-pete and interact in large-scale systems. Large deviationarguments are used to approximate the tail of the defaultloss in large portfolios and to identify the way that atyp-ically large (i.e. “rare’) default clusters are most likely tooccur. The results give insights into how different sourcesof default correlation interact to generate atypically largeportfolio losses.

Konstantinos SpiliopoulosBrown Universitykspiliop@dam.brown.edu

Kay GieseckeStanford UniversityDept. of Management Science and Engineeringgiesecke@stanford.edu

Richard SowersDepartment of MathematicsUniversity of Illinoisr-sowers@illinois.edu

MS17Quasi-convex Dynamic Programming for StorageEvaluation

The value of a storage facility can often be representedas a quasi-convex function of the market price and cur-rent capacity utilization. This talk will describe a dynamicprogramming procedure to take advantage of this struc-ture. The method relies on progressive refinement of outerapproximations of the sub-level sets of the value function

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in each stage.

John BirgeUniversity of ChicagoBooth School of Businessjohn.birge@chicagobooth.edu

MS17A Kernel Based Approach to Gas Storage andSwing Contracts Valuations in High Dimensions

We are expanding upon our previous work [Boogert andMazieres, “A Radial Basis Function Approach to Gas Stor-age Valuation”, 2011], by introducing multi-factor priceand volume dimensions encountered in both gas storageand swing contracts. This is achieved by introducing newmultivariate methods (Kernel based: Radial Basis Func-tions and the Tensor of Radial Basis Functions) to themulti-dimensional Least-Squares Monte Carlo method usedto value these contracts with the spot approach.

Denis MazieresLondon UniversityBirkbeckd.mazieres@ems.bbk.ac.uk

Alexander BoogertEnergyQuants BVboogert@energyquants.com

MS17Approximate Linear Programming Relaxations forCommodity Storage Real Option Management

The real option management of commodity conversion as-sets based on high dimensional forward curve evolutionmodels commonly used in practice gives rise to intractableMarkov decision processes. Focusing on commodity stor-age, we derive approximate dynamic programs from re-laxations of approximate linear programs formulated usinglow dimensional value function approximations. We evalu-ate the performance of our approximate dynamic programson natural gas and oil instances.

Selvaprabu Nadarajah, Francois MargotCarnegie Mellon UniversityTepper School of Businesssnadarajah@cmu.edu, fmargot@andrew.cmu.edu

Nicola SecomandiCarnegie MellonTepper School of Businessns7@andrew.cmu.edu

MS17Natural Gas Storage Valuation, Optimization,Market and Credit Risk Management

We present a model for the valuation, optimization, andpricing of the credit risk of gas storage contracts. A re-duced form term structure model of the curve dynam-ics is derived that facilitates dimension reduction with-out sacrificing realism. A system of PDEs is derived andsolved using RBF collocation. When the number of injec-tion/withdrawal opportunities is large, RBF-PDE methodcan solve problems where heuristic approaches would beimpractical. The RBF expansions facilitate pricing of

credit risk.

Matt ThompsonQueen’s UniversityQueen’s School of Businessmthompson@business.queensu.ca

MS18Small-time Expansions for Stochastic VolatilityModels with Levy Jumps

We analyze the short-time (equivalently, near expiration)behavior of the tail distributions and option prices of aclass of stochastic volatility (SV) models obtained by su-perposing a classical continuous SV process (say, the Hes-ton process) with an independent pure-jump Levy process.Polynomial expansions in time of arbitrary order are ob-tained for the tail distributions and out-of-the money op-tion prices, assuming certain smoothness conditions on theLevy density of the jump component and a small-time largedeviation principle for the continuous component. As a re-sult, we are able to disentangle the effects of the variousmodel parameters in the short-time behavior of the optionprices and rank their contribution according to the firstpower at which they appear in the polynomial expansion.This talk is based on a joint work with C. Houdre and R.Gong.

Jose E. Figueroa-LopezPurdue Universityfigueroa@purdue.edu

MS18Large Deviations and Stochastic Volatility withJumps: Asymptotic Implied Volatility for AffineModels

We consider the implied volatility of European options inan affine stochastic volatility model with jumps, as timetends to infinity. We show that under a simultaneousrescaling of the option strike a non-degenerate limitingvolatility smile exists and describe it by a formula whichcan be expressed in terms of the parameters of the under-lying model. The result is based on a large-deviation prin-ciple for affine stochastic volatility models, that is derivedvia the Gartner-Ellis theorem. We exhibit some specific ex-amples including a Heston model with and without jumps,Bates’ model with state-dependent jump intensity and theBarndorff-Nielsen-Shephard model.

Martin Keller-ResselTU Berlinmkeller@math.tu-berlin.de

Antoine Jacquier, Aleksandar MijatovicImperial College Londonajacquie@imperial.ac.uk, a.mijatovic@imperial.ac.uk

MS18A New Look at Short-term Implied Volatility inModels with Jumps

This talk analyses the behaviour of the implied volatil-ity smile for short-dated options in semimartingale modelswith jumps. We introduce a new renormalization of thestrike variable such that the implied volatility for short-maturity options converges to a nonconstant finite limit,characterised by the diffusion and jump components of the

152 FM12 Abstracts

model. This limit yields calibration algorithms for short-dated options and sheds new light on the difference betweenfinite and infinite variation jumps in pricing models.

Aleksandar MijatovicImperial College Londona.mijatovic@imperial.ac.uk

Peter TankovParis 7peter.tankov@gmail.com

MS18Parametric Inference and Dynamic State Recoveryfrom Option Panels

We develop parametric estimation procedure for optionpanels observed with error. We provide semiparametrictests for the option price dynamics based on the distancebetween the spot volatility extracted from the options andthe one obtained nonparametrically from high-frequencydata on the underlying asset. We further construct newformal tests of the model fit for specific regions of thevolatility surface and for the stability of the risk-neutraldynamics over a given period of time.

Viktor TodorovKellogg School of ManagementNorthwestern Universityv-todorov@kellogg.northwestern.edu

Torben G. Andersen, Nicola FusariNorthwestern Universityt-andersen@northwestern.edu, n-fusari@northwestern.edu

MS19A Decomposition Formula for Option Prices in theHeston Model and Applications to Option PricingApproximation

By means of classical Its calculus we decompose optionprices in the Heston volatility framework as the sum ofthe classical Black-Scholes formula with volatility param-eter equal to the root-mean-square future average volatil-ity plus a term due to correlation and a term due to thevolatility of the volatility. This decomposition formula al-lows us to construct first and second order option pricingapproximation formulas that are extremely easy to com-pute, as well as to study their accuracy for short maturi-ties. Moreover we see the corresponding approximationsfor the implied volatility are linear (first-order approxima-tion) and quadratic (second-order approximation) in thelog-stock price variable.

Elisa AlosUniversitat Pompeu Fabraelisa.alos@upf.edu

MS19Small-noise Expansion for Projected Diffusions andImplied Volatility Asymptotics

Given a diffusion in Rn, we prove a small-noise expan-sion for the density of its projection on a subspace of di-mension p ≤ n. Our proof relies on the Laplace methodon Wiener space and stochastic Taylor expansions in thespirit of Azencott-Benarous-Bismut. Our result (assumingHormander’s condition on the vector fields) applies to (i)

small-time asymptotics, (ii) tails of the distribution and(iii) small-noise expansions. In the context of stochasticvolatility models, we recover the Busca-Berestycki-Florentformula (applying (i)) and Gulisashvili-Stein expansion(from (ii)). This is a joint work with J.D. Deuschel (TUBerlin), P. Friz (TU Berlin) and S. Violante (Imperial Col-lege London).

Antoine JacquierImperial College Londonantoine.jacquier08@imperial.ac.uk

Peter FrizTU BerlinWeierstrass Institute

Jean-Dominique DeuschelTU Berlin

Sean ViolanteImperial College London

MS19Asymptotics of Implied Volatility to Arbitrary Or-der

In a unified model-free framework that includes long-expiry, short-expiry, extreme-strike, and jointly-varyingstrike-expiry regimes, we find asymptotic implied volatilityand implied variance formulas in terms of L, with rigorouserror estimates of order 1/L to any given power, where Ldenotes the absolute log of an option price that approacheszero. Our results therefore sharpen, to arbitrarily highorder of accuracy, the model-free asymptotics of impliedvolatility in extreme regimes. We then apply these generalformulas to particular examples: Levy and Heston. Jointwork with Kun Gao.

Roger Lee, Kun GaoUniversity of Chicagorogerlee@math.uchicago.edu, kungao@math.uchicago.edu

MS19Multi-Factor Stochastic Volatility Models for Op-tions and Options on Variance

Through perturbation methods we reconcile skews of im-plied volatilities for options and options on variance in thecontext of multi-scale stochastic volatility models.

Jean Pierre FouqueUniversity of California Santa Barbarafouque@pstat.ucsb.edu

Yuri SaporitoUC Santa Barbarayuri.saporito@gmail.com

Jorge P. ZubelliIMPAzubelli@impa.br

MS20On the Multi-Dimensional Controller and StopperGames

We consider a zero-sum stochastic differential controller-and-stopper game in which the state process is a controlled

FM12 Abstracts 153

diffusion evolving in a multi-dimensional Euclidean space.In this game, the controller affects both the drift and thevolatility terms of the state process. Under appropriateconditions, we show that the game has a value and thevalue function is the unique viscosity solution to an obsta-cle problem for a Hamilton-Jacobi-Bellman equation.

Yu-Jui HuangUniversity of Michigan, Department of Mathematicsjayhuang@umich.edu

Erhan BayraktarUniversity of MichiganDepartment of Mathematicserhan@umich.edu

MS20Numerical Solutions of Optimal Risk Control andDividend Optimization Policies

This work develops numerical methods for finding optimaldividend pay-out and reinsurance policies. The surplusis modeled by a regime-switching process subject to bothregular and singular controls. Markov chain approximationtechniques are used to approximate the value function andoptimal controls. The proofs of the convergence of the ap-proximation sequence to the surplus process and the valuefunction are given. Examples are presented to illustratethe applicability of the numerical methods.

Zhuo JinUniversity of Melbourne, Australiazjin@unimelb.edu.au

George YinWayne State UniversityDepartment of Mathematicsgyin@math.wayne.edu

Chao ZhuUniversity of Wisconsin-Milwaukeezhu@uwm.edu

MS20Outperformance Portfolio Optimization via theEquivalence of Pure and and Randomized Hypoth-esis Testing

We study the portfolio problem of maximizing the outper-formance probability over a random benchmark throughdynamic trading with a fixed initial capital. Under a gen-eral incomplete market framework, this stochastic controlproblem can be formulated as a composite pure hypothesistesting problem. We analyze the connection between thispure testing problem and its randomized counterpart, andfrom latter we derive a dual representation for the maxi-mal outperformance probability. Moreover, in a completemarket setting, we provide a closed-form solution to theproblem of beating a leveraged exchange traded fund. Fora general benchmark under an incomplete stochastic fac-tor model, we provide the Hamilton-Jacobi-Bellman PDEcharacterization for the maximal outperformance probabil-ity.

Jie YangUniversity of Illinois at Chicagojyang06@math.uic.edu

Tim Leung

Johns Hopkins Universityleung@ieor.Columbia.edu

Qingshuo SongCity University of Hong Kongsong.qingshuo@cityu.edu.hk

MS20Optimal Trend-following Trading Rules under aThree-state Regime-switching Mode

Assume the market follows a regime switching model withthree states, a set of sufficient conditions are developed toguarantee the optimality of trend-following trading strate-gies. A dynamic programming approach is used to verifythese optimality conditions. The value functions are char-acterized by the associated HJB equations. The results inthis paper will help an investor to identify market condi-tions and to avoid trades which might be unprofitable evenunder the best market information.

Jie YuRoosevelt Universityjyu@roosevelt.edu

Qing ZhangUniversity of GeorgiaDepartment of Mathematicsqingz@math.uga.edu

MS21Evaluating Callable and Putable Bonds: An Eigen-function Expansion Approach

Abstract not available at time of publication.

Dongjae LimNorthwesterndongjae@u.northwestern.edu

MS21Building Financial Models with Time Changes

Abstract not available at time of publication.

Vadim LinetskyNorthwestern Universitylinetsky@iems.northwestern.edu

MS21Pricing Derivatives on Multiscale Diffusions: AnEigenfunction Expansion Approach

Using tools from spectral analysis, singular and regu-lar perturbation theory, we develop a systematic methodfor analytically computing the approximate price of aderivative-asset. The payoff of the derivative-asset maybe path-dependent. Additionally, the process underlyingthe derivative may exhibit killing (i.e. jump to default) aswell as combined local/nonlocal stochastic volatility. Thenonlocal component of volatility is multiscale, in the sensethat it is driven by one fast-varying and one slow-varyingfactor. The flexibility of our modeling framework is con-trasted by the simplicity of our method. We reduce thederivative pricing problem to that of solving a single eigen-value equation. Once the eigenvalue equation is solved,the approximate price of a derivative can be calculated

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formulaically. To illustrate our method, we calculate theapproximate price of three derivative-assets: a vanilla op-tion on a defaultable stock, a path-dependent option on anon-defaultable stock, and a bond in a short-rate model.

Matthew LorigPrinceton UniversityORFE Departmentmlorig@princeton.edu

MS21Closed-form Expansions of Option Prices underTime-changed Dynamics

We consider a broad class of option pricing models andderive a simple closed-form expansion of option prices inthese models in terms of Black-Scholes prices and higher-order Greeks. The expansion provides a transparent andinformative decomposition of option prices. Moreover, itcan be used for a large class of flexible models which allowfor both stochastic volatility and jumps. Finally, it allowsfor fast model calibration.

David PedersenAarhus Universitydasp@asb.dk

Elisa NicolatoUniversity of Aarhuseln@asb.dk

MS22Optimal Portfolios under Worst Case Scenarios

Standard portfolio theories such as Expected Utility The-ory, Yaari’s Dual Theory, Cumulative Prospect Theory andMean-Variance optimization all assume that investors onlylook at the distributional properties of strategies and donot care about the states of the world in which the cash-flows are received. In a very interesting paper, Dybvig(1988a, 1988b) essentially showed that in these instancesoptimal portfolios are decreasing in the state-price density,also pointing indirectly to the important role of diversifiedportfolios. In this paper we first observe that the worst out-comes for optimal strategies exactly occur when the marketdeclines (i.e. during a financial crisis), but this is at oddswith the aspirations and requirements of many investors.Hence we depart from the traditional behavioral settingand study optimal strategies for investors who do not onlycare about the distribution of wealth but, additionally, alsoimpose constraints on its interaction with the (stressed) fi-nancial market. Preferences become state-dependent andwe are able to assess the impact of these on trading deci-sions. We construct optimal strategies explicitly and showhow they outperform traditional diversification strategiesunder worst-case scenarios.

Carole Bernard, Jit-Seng ChenUniversity of Waterlooc3bernar@uwaterloo.ca, jitseng.chen@gmail.com

Steven VanduffelVrije Universiteit Brussel, Belgium.steven.vanduffel@vub.ac.be

MS22Myopic Loss Aversion, Reference Point, and

Money Illusion

We use the portfolio selection model presented in He andZhou (2011, Management Science, Volume 57, Issue 2,pages 315–331) and the NYSE equity and U.S. treasurybond returns for the period 1926-1990 to provide a rigor-ous treatment of Benartzi and Thaler’s myopic loss aver-sion theory. We find that in addition to the agent’s lossaversion and evaluation period, his reference point also hasa significant effect on optimal asset allocation. We demon-strate that the agent’s optimal allocation to equities is con-sistent with the market observation when he has reasonablevalues of degree of loss aversion, evaluation period, and ref-erence point. We also find that the optimal allocation toequities is sensitive to these parameters. We then examinethe implications of money illusion for asset allocation andpricing. Finally, we extend the model to a dynamic setting.

Xuedong HeColumbia UniversityDepartment of Industrial Engineering and OperationsResearchxh2140@columbia.edu

Xunyu ZhouUniversity of Oxford andThe Chinese University of Hong Kongzhouxy@maths.ox.ac.uk

MS22Consumption-based Behavioral Portfolio Selectionin Continuous Time

We study the optimal consumption-investment problem ina continuous-time financial market with behavioural cri-teria featured by S-shaped utility function and probabilitydistortions. Different formulations of the problem are stud-ied. When optimal solutions exist, we get explicit formsbased on some algebraic equations.

Hanqing JinOxford Universityjinh@maths.ox.ac.uk

MS22Utility Maximization with Addictive ConsumptionHabit Formation in Incomplete Markets

We study the utility maximization problem of consumptionwith addictive habit formation in the general incompletesemimartingale market. By introducing the auxiliary stateand dual processes and defining the value function both oninitial wealth and initial habit, we embed our original pathdependent problem into an abstract time separable opti-mization problem with the shadow random endowment.We establish existence and uniqueness of the optimal solu-tion using convex duality approach on L0+ spaces.

Xiang YuDepartment of Mathematics,The University of Texas at Austinxiangyu@math.utexas.edu

MS23The Log Optimal Portfolio under TransactionCosts and the Shadow Price: The GeometricOrnstein-Uhlenbeck Process and a Counterexam-

FM12 Abstracts 155

ple

As in (Gerhold/Muhle-Karbe/Schachermayer 2011) wefind the growth optimal portfolio for the geometricOrnstein-Uhlenbeck process under proportional transac-tion costs by constructing a shadow price. This is a priceprocess, such that the optimization problem without fric-tions for that price has the same solution as the one undertransaction costs. This technique allows us to explicitlycompute fractional Taylor expansions of arbitrary order forall quantities of interest. Similar results have (to the best ofour knowledge) so far only been obtained for the Black Sc-holes model. Moreover, we present a counterexample thatshadow prices may not exist in general even in discrete timeand for “well-behaved’ markets.

Christoph Czichowsky, Philipp DeutschU of Viennachristoph.czichowsky@univie.ac.at,philipp.deutsch@univie.ac.at

Johannes Muhle-KarbeDepartement MathematikETH Zurichjohannes.muhle-karbe@math.ethz.ch

Walter SchachermayerU of Viennawalter.schachermayer@univie.ac.at

MS23Market Depth and Trading Volume Dynamics

We derive the process followed by trading volume, in amarket with finite depth and constant investment oppor-tunities. A representative investor, with a long horizon andconstant relative risk aversion, trades a safe and a risky as-set with a liquidity cost proportional to trading speed. Anordinary differential equation identifies the trading policyand welfare. In the high-liquidity limit, trading volumefollows approximately an Ornstein-Uhlenbeck process, andincreases with liquidity, volatility, and risk aversion.

Paolo GuasoniBoston UniversityDublin City Universityguasoni@bu.edu

Marko WeberDublin City UniversityScuola Normale Superioremarko.weber5@mail.dcu.ie

MS23Long-run Investment under Drawdown Con-straints: optimal portfolios and numeraire prop-erty

We consider long-run investment problems under draw-down constraints: the current wealth can not fall belowa given function of its past maximum. We work in a gen-eral semimartingale setting. First, we show that this prob-lem is equivalent to an unconstrained problem but with amodified utility function: both the value and the optimalportfolio are given explicitly in terms of their unconstrainedcounterparts (joint work with Vladimir Cherny). Second,we analyse in more detail the growth optimal portoflio un-der linear drawdowns. We show it enjoys the numeraireproperty along specific sequences of stopping times and

asymptotically but not for all times. A turnpike theoremshows it is a limit of numeraire strategies on finite hori-zons (joint work with Constantinos Kardaras and EckhardPlaten).

Jan OblojMathematical Institute, University of Oxfordand the Oxford-Man Institute of Quantitative Financejan.obloj@maths.ox.ac.uk

MS23Wealth vs Risk in a Continuous Time Model

We discuss a continuous time optimization problem whichcombines two conflicting objectives of maximizing the port-folio wealth up to a level and minimizing the conditionalvalue-at-risk of the portfolio wealth loss. The associatedutility function is not differentiable nor strictly concaveand does not satisfy Inada’s condition. We use the dualcontrol method to show that there is a classical solution tothe HJB equation and that the optimal value function issmooth if the optimal control satisfies an exponential mo-ment condition. We find the closed-form optimal feedbackcontrol and optimal value function for a wealth maximiza-tion problem.

Harry ZhengImperial College Londonh.zheng@imperial.ac.uk

MS24Stress Tests: From Arts to Science (Overview)

Expectations on stress tests are high in the financial in-dustry: they should measure the resilience of individualfinancial institutions and of the whole banking system aspart of an economy. Additionally, they should act as acalmative for nervous markets. It is time to assess theexpectations about what information can realistically beobtained from stress tests. How should we choose scenar-ios which are at the same time plausible and informativeof potential weaknesses? How can we assess the validityof our models and the potential consequences where ourmodels break down? How can we adequately discriminateadverse external shocks and dangerous endogenous effects?

Thomas BreuerResearch Centre PPE, Fachhochschule VorarlbergAustriatb@fhv.at

MS24Finding Stress Scenarios That Get the Job Done,with Credit Risk Applications

We introduce new methods to generate finite representa-tive collections of plausible yet severe scenarios. We applythese methods to generate credit risk scenarios and demon-strate, via numerical experiments, that with respect to cer-tain performance measures, our method is better able todiscover (ex ante) scenarios close to those that occurred(as determined ex post), than previously described meth-ods. Moreover, our methods discover these scenarios atsubstantially lower computational cost.

Craig A. FriedmanStandard & Poorscraigwengfriedman@yahoo.com

156 FM12 Abstracts

MS24Stress Testing Model Risk

Abstract not available at time of publication.

Paul KupiecFDICpkupiec@fdic.gov

MS24Must Stress Tests be Credible?

Abstract not available at time of publication.

Til SchuermannOliver Wymantil.schuermann@oliverwyman.com

MS25Utility Indifference Pricing in Energy Markets

Abstract not available at time of publication.

Luciano CampiParis 13 Universitycampi@math.univ-paris13.fr

MS25Probabilistic Approach to Mean Field Games andthe Control of McKean Vlasov Dynamics

Abstract not available at time of publication.

Rene CarmonaPrinceton UniversityDpt of Operations Research & Financial Engineeringrcarmona@princeton.edu

MS25Levy Semistationary Processes with Applicationsto Electricity Markets

So called Levy semistationary processes (LSS processes)constitute a rather general class of continuous time mov-ing average processes. Our motivation is employing theseprocesses to model electricity and commodity forwardsand spots. We discuss and analyze numerical simulationprocedures for LSS processes and energy forward randomfields, by means of stochastic partial differential equations,Fourier methods and finite dimensional approximations.

Heidar I. Eyjolfsson, Fred Espen BenthUniversity of Osloheidare@cma.uio.no, fredb@math.uio.no

MS25Forward-Backward SDE Games and StochasticControl under Model with Uncertainty

Abstract not available at time of publication.

Agnes SulemINRIAagnes.sulem@inria.fr

MS26Forward Equations and Mimicking Theorems for

Discontinuous Semimartingales

We derive a forward partial integro-differential equation forprices of call options in a model where the dynamics of theunderlying asset under the pricing measure is described bya -possibly discontinuous- semimartingale. A uniquenesstheorem is given for the solutions of this equation. Werelate this result to the construction of a Markovian pro-jection - a Markov process which mimics the marginalsdistributions of the semimartingale. This result gener-alizes Dupire’s forward equation to a large class of non-Markovian models with jumps.

Amel BentataUniversite Pierre & Marie Curie, Franceamel.bentata@gmail.com

Rama ContCNRS (France) & Columbia UniversityRama.Cont@gmail.com

MS26Functional Ito Calculus and the Pricing and Hedg-ing of Path-dependent Derivatives

We provide a brief overview of the Functional Ito Calcu-lus [Dupire 2009; Cont & Fournie 2010], which providesa convenient mathematical framework for analyzing path-dependent functionals of Ito processes, and show that itmay be used to derive a ’universal’ pricing equation whichholds for a wide class of path-dependent options on an un-derlying asset whose price follows an Ito process. This uni-versal pricing equation is a functional analog of the back-ward Kolmogorov equation: we present a uniqueness re-sult for solutions of this equation and show that it verifiesa comparison principle. Finally, we provide a unified ap-proach to the computation of hedging strategies for path-dependent options.

Rama ContCNRS (France) & Columbia UniversityRama.Cont@gmail.com

David FournieMorgan Stanleyd@vidfournie.com

MS26Local Vs Non-Local Forward Equations for OptionPricing

When the underlying asset is a continuous martingale,call option prices solve the Dupire equation, a forwardparabolic PDE in the maturity and strike variables. Bycontrast, when the underlying asset is described by adiscontinuous semimartingale, call price solve a partialintegro-differential equation (PIDE), containing a non-local integral term. We show that the two classes of equa-tions share no common solution: a given set of option pricesis either generated from a continuous martingale (”diffu-sion”) model or from a model with jumps, but not both.In particular, our result shows that Dupires inversion for-mula for reconstructing local volatility from option pricesdoes not apply to option prices generated from models withjumps.

Yu GuColumbia Universityyg2254@columbia.edu

FM12 Abstracts 157

Rama ContCNRS (France) & Columbia UniversityRama.Cont@gmail.com

MS26Degenerate Parabolic PDEs, Martingale Problemsand a Mimicking Theorem for Ito Processes

We prove existence, uniqueness and regularity of solutionsin weighted Holder spaces for a certain class of degener-ate parabolic partial differential equations with unboundedcoefficients on the half space. We show that the mar-tingale problem associate with the differential operator iswell-posed, which implies existence and uniqueness of weaksolutions to the corresponding stochastic differential equa-tions. The weak solutions match the one-dimensional prob-ability distributions of a certain class of Ito processes.

Camelia A. Pop, Paul FEEHANRutgers Universityapop@math.rutgers.edu, feehan@math.rutgers.edu

MS27Credit Risk Concentration under Stress

We present a general approach to implementing stress sce-narios in multi-factor credit portfolio models, which isbased on the truncation of risk factors. We derive ana-lytic formulae for credit correlations under stress and ana-lyze their asymptotic behavior in normal variance mixture(NVM) models. It turns out that correlations in heavy-tailed NVM models are less sensitive to stress than inmedium- or light-tailed models.

Michael KalkbrenerDeutsche BankFrankfurtmichael kalkbrener ¡michael.kalkbrener@db.com

MS27Risk Assessment Modelling of Systemic Institu-tions

The Bank of England has developed a top-down stress test-ing and systemic risk model (RAMSI). The model containsa network of banks, with each bank modelled in consider-able detail. RAMSI allows the banks to be shocked by(deterministic or stochastic ) macroeconomic scenarios todetermine the resilience of the system under stress. Thebanks can themselves propagate stress around the systemthrough second round effects. We present the model andan illustration of its use.

Jack McKeownBank of EnglandJack.Mckeown@bankofengland.gsi.gov.uk

MS27A Systematic Approach to Multi-period StressTesting of Portfolio Credit Risk

We propose a new method for analysing multiperiod stressscenarios for portfolio credit risk more systematically thanin current macro stress tests. The plausibility of a scenariois quantified by its distance from an average scenario. Fora given level of plausibility, we search systematically forthe most adverse scenario. We show how this method canbe applied to some models already in use by practitioners.

Martin SummerOeNB, Austrian Central Bankmartin.summer@oenb.at

Thomas Breuer, Martin JandackaResearch Centre PPE, Fachhochschule VorarlbergAustriatb@fhv.at, martin.jandacka@fhv.at

Javier MenciaFinancial Stability DepartmentBanco de Espanajavier.mencia@bde.es

MS27Lessons and Limits of Stress Tests as a Macropru-dential Supervisory Tool

Abstract not available at time of publication.

Konstantinos TsatsaronisBank for International Settlementskonstantinos.tsatsaronis@bis.org

MS28Derivatives on Non-Storable Renewable Resources:Fish Futures and Options, Not So Fishy after All.

We study forward prices and prices of European call op-tions, which are written on a non-storable renewable re-source. An example for such derivatives is provided by fu-tures and options on fresh salmon traded in large volumesat Fish Pool (Norway) since 2008. The introduction of sim-ilar exchanges in the United States and other countries iscurrently discussed. The pricing formulas are derived fromfirst principles, starting of by modeling the dynamics of theresource reserves, and assuming that resource extractionis managed as open access. We derive closed form solu-tions for the forward price of the renewable resource andstudy its dynamics. In contrast to Black (1976) we showthat forward prices do not evolve according to a geomet-ric Brownian motion, but follow a more complex process.For the case of an option we show that the Black (1976)formula needs to be adapted in such a way, that the nor-mal distribution is replaced by a reciprocal Γ-distribution,to get at least a very good approximation of the true op-tion price. We include numerical evidence to underline thisstatement. Finally, we derive pricing formulas for optionswritten on forward contracts, and show how forward con-tracts can be hedged under the assumption that there isa spanning asset. The full paper is available at SSRN:http://ssrn.com/abstract=1469135 The presentation willalso include material from a second working paper, whichincludes more empirical analysis.

Christian EwaldDepartment of Economics, University of Glasgowchristian.ewald@glasgow.ac.uk

MS28Adaptations of Least-squares Methods to ConvexControl Problems

Abstract not available at time of publication.

Juri Hinz

158 FM12 Abstracts

ETH Zurich, Department of Mathematics,Institute for Operations Researchhinz@ifor.math.ethz.ch

MS28Dark Pools and Hidden Markets

Abstract not available at time of publication.

Ulrich HorstHumboldt Universityhorst@mathematik.hu-berlin.de

MS28A Feedback Model for the Financialization of Com-modity Prices

Abstract not available at time of publication.

Ronnie SircarORFEPrinceton Universitysircar@princeton.edu

MS29A Flexible Matrix Libor Model with Smiles

We present a flexible approach for the valuation of inter-est rate derivatives based on Affine Processes. We extendthe methodology proposed in Keller-Ressel et al. (2009) bychanging the choice of the state space. We provide semi-closed-form solutions for the pricing of caps and floors. Wethen show that it is possible to price swaptions in a multi-factor setting with a good degree of analytical tractability.This is done via the Edgeworth expansion approach devel-oped in Collin-Dufresne and Goldstein (2002). A numeri-cal exercise illustrates the flexibility of the Wishart Libormodel in describing the movements of the implied volatilitysurface.

Alessandro GnoattoLMU Munichgnoatto@mathematik.uni-muenchen.de

Jose Da FonsecaAuckland University of Technologyjose.dafonseca@aut.ac.nz,

Martino GrasselliUniversity of Padovagrassell@math.unipd.it

MS29The Explicit Laplace Transform for the WishartProcess

We derive the explicit formula for the joint Laplace trans-form of the Wishart process and its time integral which ex-tends the original approach of [Bru, M. F. (1991): Wishartprocesses. Journal of Theoretical Probability, 4:725751].We compare our methodology with the alternative resultsgiven by the variation of constants method, the lineariza-tion of the Matrix Riccati ODEs and the Runge-Kutta al-gorithm. The new formula turns out to be fast, accurateand very useful for applications when dealing with stochas-tic volatility and stochastic correlation modelling.

Martino Grasselli

University of Padovagrassell@math.unipd.it

MS29Generalized Affine Transform Formulae and ExactSimulation of the WMSV Model

The aim of this talk is to introduce transform formulaefor linear functionals of affine processes and their bridgeswhose state space is a set of positive semidefinite matrices.Particularly, we investigate the relationship between suchtransforms and certain integral equations. We are, then,able to derive analytic expressions for Laplace transformsof some functionals of Wishart bridges. As an application,we suggest an exact simulation method of Wishart multi-dimensional stochastic volatility model.

Chulmin Kang, Wanmo KangDepartement of Mathematical Sciences, KAISTRepublic of Koreacm0222@kaist.ac.kr, wanmo.kang@kaist.edu

MS29Calibration of Multivariate Affine StochasticVolatility Models

We provide a new calibration algorithm for multivariateaffine stochastic covariance models using both option andtimeseries data. The option data is used to recover the pa-rameters determining the drift of the covariance process,while the timeseries allows us to identify the volatility ofthe covariance process and its correlation to the price pro-cesses. The procedure relies only on the knowledge of thefirst moments of log-prices and an estimation of volatilityusing Fourier series.

Christa CuchieroUniversity of Vienna, Faculty of Mathematicschrista.cuchiero@univie.ac.at

Elisa NicolatoUniversity of Aarhuseln@asb.dk

David SkovmandAarhus University, Department of Economics andBusinessdavids@asb.dk

Josef TeichmannDepartment of MathematicsETH Zjteichma@math.ethz.ch

MS30Calibrating Volatility Surfaces for CommodityDerivatives

Commodities and their derivatives have become key playersin the portfolios of many corporations, especially for thoseworking in the energy sector. In this talk we shall discussthe calibration of local volatility surfaces for commodityderivatives. In order to obtain stable and robust resultswe shall make use of regularization techniques to handlethe inverse problem. In particular we shall present someresults with Brent oil (WTI) and Natural Gas (HH) data.

FM12 Abstracts 159

Vinicius AlbaniIMPARio de Janeiro, Brazilviniciusalbani@gmail.com

MS30Volatility Surface Calibration andRelative-Entropy Minimization

In this talk we will survey the research developed jointlywith a number of collaborators during the past few yearsin connection with the calibration of Black-Scholes modelsunder stochastic volatility. We shall start with the rela-tion between uncertain volatility models, Hamilton-Jacobiequations, and the Kullback-Leibler distance. Then, weshall discuss calibration and entropy. Finally we will dis-cuss weighted Monte Carlo methods and applications.

Marco AvellanedaCourant InstituteNew York Universityavellaneda@courant.nyu.edu

MS30Calibrating Self-exciting Marked Point Processesfor Algorithmic Trading

Recently, marked point processes have been used to modelthe dynamics of assets at ultra-high frequencies. Cartea,Jaimungal and Ricci (2011) develop a multi-factor self-exciting model accounting for the arrival of market ordersthat influence activity, trigger one- and two-sided cluster-ing of trades, and induce temporary changes in the shape ofthe LOB. The classification of trades as influential versusnon-influential induces hidden state variables and makesonline calibration a necessity in high frequency trading achallenging endeavor. Here, we develop quasi-maximum-likelihood parameter estimators and a Sequential MonteCarlo estimator of the activity path for use in algorithmictrading strategies.

Sebastian JaimungalUniversity of Toronto, Canadasebastian.jaimungal@utoronto.ca

Jason RicciUniversity of Torontojason.ricci@utoronto.ca

MS30An Overview of Calibration Methods of LocalVolatility Surfaces

Local volatility models are extensively used and well rec-ognized for hedging and pricing in financial markets. Theyare frequently used, for instance, in the evaluation of exoticoptions so as to avoid arbitrage opportunities with respectto other instruments. Yet, the ill-posed character of localvolatility surface calibration from market prices requiresthe use of regularization techniques either implicitly or ex-plicitly. Such regularization techniques have been widelystudied for a while and are still a topic of intense research.In this talk we shall review different attempts that havebeen made in order to tackle the local volatility calibrationproblem. In particular, we shall discuss convex regulariza-tion tools and recent inverse problem advances to deal with

the calibration problem.

Jorge P. ZubelliIMPAzubelli@impa.br

PP1Adjoint Monte-Carlo Technique for Calibration ofFinancial Market Models

We present a Monte-Carlo based adjoint technique for solv-ing calibration problems of financial market models like theHeston model with time-dependent parameters. Any effi-cient optimization method for calibration requires at leastgradient information. The major advantage of the adjointtechnique lies in the fact that the calculation time requiredfor a gradient computation stays nearly constant, indepen-dent of the number of parameters. Our numerical resultsconfirm this improved speed-up.

Bastian GrossUniversity of Triergrossb@uni-trier.de

Ekkehard W. SachsUniversity of TrierVirginia Techsachs@uni-trier.de

PP1On Efficient Option Pricing Under Jump Diffusion

Merton’s jump-diffusion model leads to partial-integro dif-ferential equations (PIDE), which can be solved in orderto price options. Discretization of the integral in the PIDEleads to non-local terms and dense matrices. The presen-tation will discuss ways to solve the PIDE, avoiding densematrices. This is applied to European-style options.

Ruediger U. SeydelUniversity of CologneMathematical Instituteseydel@mi.uni-koeln.de

PP1The Impact of Constraints on the Views of theBlack-Litterman Model

The Black-Litterman model is a Bayesian portfolio opti-mization model that allows investors to impose prior viewson the expected returns of assets in the portfolio. Con-straints can be considered as prior views on the optimalportfolio weights. Constraints distort the views expressedby the investor, resulting in sub-optimal portfolio weights.Our research shows that a mild relaxation of the long-onlyconstraint results in Black-Litterman views that are moreefficiently represented in the portfolio weights.

Byron WilsonUniversity of Cape Townbyronwilson001@gmail.com

Gareth Q. WittenUniversity of Cape TownPontificia Universidad Catolica del Per, CENTRUMCatolicagareth.witten@uct.ac.za