DGS II 2013 - International Conference and Advanced

School Planet Earth, Dynamics, Games and Science II

Portugal

28 August to 6 September 2013

Keynote SpeakersThematic SessionsAdvanced SchoolBook of Abstracts

Conference Schedule

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Welcome letter to the participants of the President of CIM

The International Center of Mathematics CIM is a partner institution of the International ProgramMathematics of Planet Earth 2013 (MPE 2013).

To this extent, CIM is organizing the following CIM-MPE events:

http://sqig.math.ist.utl.pt/cim/mpe2013/

- MECC 2013 - International Conference and Advanced School Planet Earth, Mathematics of Energyand Climate Change, 21-28 March 2013.

- DGS II 2013 - International Conference and Advanced School Planet Earth, Dynamics, Gamesand Science II, 28 August to 6 September 2013.

The first two volumes of the CIM Series in Mathematical Sciences published by Springer-Verlagwill consist of selected works presented in the conferences Mathematics of Planet Earth (CIM-MPE). The editors of these first two volumes are Jean Pierre Bourguignon, Rolf Jeltsch, AlbertoPinto and Marcelo Viana. If you would like to submit a review article, please send it by email toaapinto@fc.up.pt and to info.mpe2013@sqig.math.ist.utl.pt until 31 of December of 2013.

CIM thanks all CIM-MPE events sponsors.

CIM thanks and wishes all keynote speakers, thematic session organizers, invited speakers andparticipants a fruitful meeting.

Alberto Adrego PintoCIM President

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VenuesThe International Conference, 2-4 September 2013 will be hosted in Calouste Gulbenkian Founda-tion (FCL), Lisbon, Portugal.Rooms: Auditorio 2, Auditorio 3, Sala 1, Sala 2.

The Advanced School, 28-30 August and 5-6 September 2013 will be hosted at Instituto Superiorde Economia e Gestao, Universidade Tecnica de Lisboa (ISEG-UTL), Lisbon, Portugal.Room: Auditorio CGD.

Proceedings of the CIM seriesThe first two volumes of the CIM Series in Mathematical Sciences published by Springer-Verlag willconsist of selected works presented in the conferences Mathematics of Planet Earth (CIM-MPE).

Proceedings editors:- Jean Pierre Bourguignon, IHES, Paris, France- Rolf Jeltsch, ETH, Zurich, Switzerland- Alberto Pinto, INESC-TEC, University of Porto, Portugal- Marcelo Viana, IMPA, Rio de Janeiro, Brazil

Submission: If you would like to submit a review article, please send it by email to aapinto@fc.up.ptand to info.mpe2013@sqig.math.ist.utl.pt until 31 of December of 2013.

SponsorsThese activities are enthusiastically supported and co organized by the Portuguese Society of Math-ematics (SPM), the Portuguese Society of Statistics (SPE); the Portuguese Society of OperationalResearch (APDIO); UECE-Research Unit on Complexity and Economics; CEMAPRE-the Cen-tre for Applied Mathematics and Economics; INESC-TEC Instituto de Engenharia de Sistemase Computadores do Porto - Tecnologia e Ciencia; CEAUL-Centro de Estatıstica e Aplicacoes,UL; CMAL-UNL-Centro de Matematica e Aplicaoes, UNL; CMAF-UL-Centro de Matematica eAplicaoes Fundamentais, UL; ISR-Institute for Systems and Robotics, Lisbon; IDL-UL-InstitutoD. Luıs, UL; IN+ -Centro de Estudos em Inovacao Tecnologia e Polıticas de Desenvolvimento;ISEG-Instituto Superior de Economia e Gestao; Instituto de Telecomunicacoes; FCT - Fundacaopara a Ciencia e a Tecnologia; Ciencia Viva; FCUL-Faculdade de Ciencias da UL e FCG-FundacaoCalouste Gulbenkian.

Organization: CIM Direction

Local organization committee:Alberto Pinto, FCUP (President); Michel Benaim, Universite de Neuchatel; Henrique Silveira,

IST; Renato Soeiro, FCUP; Filipe Martins, FCUP; Joao Passos Coelho, FCUP; Joana Becker,FCUP; Joao Paulo Almeida, IPB; Carla Azevedo, FCUP; Ricardo Cruz, FCUP; Jose Martins,IPLeiria; Renato Fernandes, FCUP; Isabel Figueiredo, FCUP; Telmo Parreira, UM.

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Keynote Speakers

Contagion and Uninvadability in Social Networks with Bilingual OptionSatoru TakahashiDepartment of Economics, National University of SingaporeSeptember 2nd, 09:00-10:00, Auditorio 2

A vaccination game with infection and reinfectionJose MartinsPolytechnic Institute of Leiria and LIAAD-INESC TEC, PortugalSeptember 2nd, 10:30-11:30, Auditorio 2

Avoiding Catastrophic Climate Change: The Public Goods Game we cannot afford toloseJorge PachecoDepartamento de Matematica e Aplicacoes & CBMA, Universidade do Minho, CMAF, PortugalSeptember 2nd, 11:45-12:45, Auditorio 2

The Forward Generalized Kimura EquationFabio ChalubUniversidade Nova de Lisboa, PortugalSeptember 2nd, 14:15-15:15, Auditorio 2

Stability of quasi-periodic dynamicsJoao Lopes DiasUniversidade Tecnica de Lisboa, PortugalSeptember 2nd, 15:30-16:30, Auditorio 2

Symmetric Invariant Probability Measures and RigidityYunping JiangCity University of New York, USASeptember 2nd, 17:00-18:00, Auditorio 2

Optimal strategies in prices and locations in the Hotelling networkAlberto A. PintoUniversidade do Porto, PortugalSeptember 3rd, 09:00-10:00, Auditorio 2

On value allocations in economies with commodity differentiationMarta FaiasUniversidade Nova de Lisboa, PortugalSeptember 3rd, 10:30-11:30, Auditorio 2

Inverse Problems and Structured Population ModelsJorge ZubelliIMPA, BrasilSeptember 3rd, 11:45-12:45, Auditorio 2

Fast Convergence in Finite PopulationsLorens ImhofUniversity of Bonn, GermanySeptember 3rd, 14:15-15:15, Auditorio 2

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Dynamical embeddings in Lotka-Volterra SystemsPedro DuarteUniversidade de Lisboa, PortugalSeptember 3rd, 15:30-16:30, Auditorio 2

Dynamics and Mathematical Institutional Economics(video lecture)Martin ShubikYale University, USASeptember 3rd, 17:00-18:00, Auditorio 2

Population persistence under climate change: applications of the Fundamental Bifur-cation Theorem for matrix population modelsJim CushingUniversity of Arizona, USASeptember 4th, 09:00-10:00, Auditorio 2

Cournot duopolies with R&D investmentBruno OliveiraUniversidade do Porto, PortugalSeptember 4th, 10:30-11:30, Auditorio 2

Decentralized Markets of Two-Sided MatchingJoana PaisISEG/Technical University of Lisbon, PortugalSeptember 4th, 11:45-12:45, Auditorio 2

Complementarity and Imitative Behavior in the Populations of Firms and WorkersElvio AccinelliUASLP, MexicoSeptember 4th, 14:15-15:15, Auditorio 2

Influence of individual decisions on competitive market policiesRenato SoeiroUniversidade do Porto, PortugalSeptember 4th, 15:30-16:30, Auditorio 2

Stochastic Models of Learning in GamesMichel BenaimUniversite de Neuchatel, SwitzerlandSeptember 4th, 17:00-18:00, Auditorio 2

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Thematic Sessions

Bayesian Statistics: Applications in Biology and EcologyOrganizer / Chairman: Luıs SilvaCIBIO, Centro de Investigacao em Biodiversidade e Recursos Geneticos, Universidade dos Acores

Speakers:- Joao Casaca, Laboratorio Nacional de Engenharia Civil, “Bayesian inference: general framework”.- Luıs Silva, Departamento de Biologia, Universidade dos Acores, “Multinomial and Dirichlet dis-tributions in Bayesian inference: applications to Biology and Ecology”.- Giovani L. Silva, Departamento de Matematica, Instituto Superior Tecnico, Universidade Tecnicade Lisboa, “A Bayesian spatio-temporal analysis of forest fires in Portugal”.- Francesco Minunno, PhD programme in Forestry Modelling, Instituto Superior de Agronomia,Universidade Tecnica de Lisboa, “Selecting parameters for Bayesian calibration of a process-basedmodel: A methodology based on canonical correlation analysis”.September 2nd, 10:30-11:30, Auditorio 3

Discrete Dynamics and Numerical SemigroupsOrganizer / Chairman: Sara FernandesUniversidade de Evora

Speakers:

- Clara Gracio, Universidade de Evora, “Ihara zeta function, symbolic dynamics and seismic eventsnetworks”.- Susana Santos, PhD student Universidade de Evora, “Discrete Dynamical Systems and NumericalSemigroups”.- Teresa Silva, PhD student Universidade de Evora e ISEL, “About equilibrium distributions ofdiscrete non autonomous systems”.- Denise Torrao, PhD student Universidade de Evora, “On the enumeration of the set of saturatednumerical semigroups with fixed Frobenius number”.September 2nd, 10:30-11:30, Sala 1

Mean-Field Models, Optimal Control and Calculus of VariationsOrganizer / Chairman: Edgard PimentelUniversidade Tecnica de Lisboa

Speakers:- Gabriele Terrone, CAMGSD-IST-UTL, “Homogenization of certain optimal control problems”.- Edgard Pimentel, CAMGSD-IST-UTL, “Regularity for mean-field games in the subquadratic case”.- Rita Goncalves Ferreira, Instituo Superior Tecnico (IST) & Centro de Matematica e Aplicacoesof the FCT-UNL (CMA of the FCT-UNL), “Finite state (potential) mean-field games: long timebehavior via Γ-convergence”.September 2nd, 10:30-11:30, Sala 2

Marine Life in the Wild Wider OceanOrganizer / Chairman: Ricardo Serrao SantosCentro do IMAR da Universidade dos Acores (IMAR-DOP/UAc) & LARSyS - Horta/Acores

Speakers:- Telmo Morato, University of the Azores, “Seamounts are hotspots of pelagic biodiversity in theopen ocean”.- Fernando Tempera, IMAR - Instituto do Mar, University of the Azores e LARSyS, “Predictingdeep-sea biological distributions using scarce information”.- Pedro Afonso, Centro do IMAR da Universidade dos Acores (IMAR-DOP/UAc) & LARSyS

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Laboratorio Associado, “Fish in space: Modeling movements and essential habitat”.September 2nd, 11:45-12:45, Auditorio 3

Synchronization and Discrete DynamicsOrganizer / Chairman: Clara GracioUniversidade de Evora

Speakers:

- Sara Fernandes, Universidade de Evora, “Conductance and clique formation and its applications”.- Luıs Lopes, PhD student Universidade de Evora e ISEL, “’Linear couplings’, ’commanded cou-plings’ and their synchronization”.- Andre Albino, PhD student Universidade de Evora, “Analyze of dynamic behavior of BurridgeKnopoff model in synchronized and nonsynchronized regime: potential implications”.September 2nd, 11:45-12:45, Sala 1

Statistics in Environmental and Life SciencesOrganizer / Chairman: Marta FaiasFCT-UNL and CMA

Speakers:- Dora Prata Gomes, Universidade Nova de Lisboa, FCT and CMA, “Spatial analysis of extremeprecipitation”.- Ines J. Sequeira, FCT/UNL and CMA, “Analysis of HIV integration sites in human chromosomesby genetic and statistical methods”.- Vanda Lourenco, FCT/UNL, Dep. Mathematics and CMA, “Robust outlier testing with applicationto a maize data set”.- Isabel Natario, CEAUL and Dep. de Matematica, FCT/UNL, “A State Space Model Approachfor Modelling the Population Dynamics of Black Scabbardfish”.September 2nd, 11:45-12:45, Sala 2

Biological Invasions in the AzoresOrganizer / Chairman: Ricardo TeixeiraDepartamento de Matematica da Universidade dos Acores

Speakers:- Joao Canning-Clode, Centre of IMAR of the University of the Azores, Department of Oceanogra-phy and Fisheries/UAz & LARSyS Associated Laboratory, “Marine invasions in offshore islands:a case study from the Macaronesia region”.- Luıs Silva, CIBIO, Centro de Investigacao em Biodiversidade e Recursos Geneticos, InBIO Labo-ratorio Associado, Polo dos Acores, Departamento de Biologia, Universidade dos Acores, “Invasionsversus endemisms: quantitative approaches to the study of invasive and rare plants in the Azores”.- Orlando Guerreiro, Azorean Biodiversity Group (GBA, CITA-A) and Portuguese Platform for En-hancing Ecological Research & Sustainability (PEERS), Universidade dos Acores, Portugal, “Pre-diction of the spread of the drywood termite Cryptotermes brevis using Maximum Entropy algorithmsand Agent Based Modeling approaches”.September 2nd, 14:15-15:15, Auditorio 3

Dynamics, Modelling and OptimisationOrganizer / Chairman: Joao Paulo AlmeidaInstituto Politecnico de Braganca

Speakers:- Ana I. Pereira, ALGORITMI and I.P. Braganca, “Solving Flexible Job Shop Scheduling usingGenetic Algorithm”.- Carlos Balsa, I.P. Braganca, “Clustering Techniques Applied on Cross-Sectional UnemploymentData”.

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- Joao P. Almeida, LIAAD - INESC TEC and I.P. Braganca, “Anosov diffeomorphisms and tilings”.- Renato Fernandes, University of Porto, “Rivers and the Stock Market”.September 2nd, 14:15-15:15 and 15:30-16:30, Sala 1

PDE’s and Calculus of VariationsOrganizer / Chairman: Ana Margarida Ribeiro and Rita FerreiraFCT-UNL and IST-UTL & FCT-UNL

Speakers:

- Graca Carita, Universidade de Evora, “3D-2D dimension reduction for nonlinear optimal designwith perimeter penalization”.- Jose Maria Gomes, Faculdade de Ciencias e Tecnologia da Universidade Nova de Lisboa, “Ageometrical view of the Nehari manifold”.- Giovanni Pisante, Seconda Universita di Napoli, “Second order analysis for non local isoperimetricproblems in microphase separation”.September 2nd, 14:15-15:15, Sala 2

Chaotic Dynamics in Growth modelsOrganizer: Jose Leonel RochaChairman: Acilina CanecoInstituto Superior de Engenharia de Lisboa -ISEL, IPL

Speakers:- Sandra M. Aleixo, Instituto Superior de Engenharia de Lisboa -ISEL, IPL, “An Extension ofGompertzian Growth Dynamics: Weibull and Frechet Models”.- Acilina Caneco, Instituto Superior de Engenharia de Lisboa -ISEL, IPL, “Synchronization inRichards’ Chaotic Systems”.September 2nd, 15:30-16:30, Auditorio 3

Discrete-valued time seriesOrganizer / Chairman: Isabel PereiraUniversidade de Aveiro

Speakers:- Maria Eduarda Silva, Faculdade de Economia - Universidade do Porto, “Multivariate models forinteger-valued time series”.- Isabel Pereira, Departamento de Matematica - Universidade de Aveiro, “Threshold Models in TimeSeries of Counts”.- Magda Monteiro, Escola Superior de Tecnologia e Gestao de Agueda - Universidade de Aveiro,“A periodic bivariate Integer-valued Autoregressive model - An application to fire activity”.- Maria da Conceicao Costa, Departamento de Matematica - Universidade de Aveiro, “Optimalalarm systems and application to the INAPARCH model”.September 2nd, 15:30-16:30, Sala 2

Some economic applicationsOrganizer / Chairman: Alberto A. Alvarez LopezUNED, Spain

Speakers:- Orlando Montoro Peinado, UNED, “Emancipation and Household Formation”.- Meliyara Consuegra, UNED, “Quantification of functional efficiency in energy futures markets”.- Eduardo Oliva, UNED, “Entropy and negentropy: applications in Game Theory”.- Alberto A. Alvarez-Lopez, UNED, “Properties and comparative-static effects in models of decisionunder uncertainty: applications to the theory of the firm”.September 3rd, 10:30-11:30, Auditorio 3

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Graphs and CombinatoricsOrganizer / Chairman: Domingos CardosoCIDMA, DMat, Universidade de Aveiro

Speakers:- Sofia Pinheiro, Univ. de Aveiro, “The maximum k-regular induced subgraph problem”.- Fatima Pacheco, Inst. Politecnico de Braganca, “(0,2)-regular sets and applications”.- Ines Barbedo, Inst. Politecnico de Braganca, “The construction of the poset of regular exceptionalgraphs using equitable partitions”.- Maria Manuel Torres, Univ. de Lisboa, “Matchings and orthogonality of symmetrized tensors”.- Teresa Sousa, Univ. Nova de Lisboa, “Graph Decomposition: A blend of Turan numbers andRamsey numbers”.- Paula Carvalho, Univ. de Aveiro, “Topological Indices of graphs”.- Marta Pascoal, Univ. de Coimbra, “Min-max regret robust shortest path problem in a finite mult-scenario model”.- Vasco Mano, Univ. de Porto, “A Generalization of the Krein parameters and some admissibilityconditions for strongly regular graphs”.- Paula Rama, Univ. de Aveiro, “Some results on the modified Schultz index”.- Ricardo Mamede, Univ. de Coimbra, “Singleton free set partitions avoiding a 3-element set”.- Rui Duarte, Univ. de Aveiro, “Maps and hypermaps with large symmetry group”.- Ilda Perez, Univ. de Lisboa, “Shannon switching games and directed variants”.- Olga Azenhas, Univ. de Coimbra, “Growth diagrams, crystal operators and Cauchy kernel expan-sions”.September 3rd, 10:30-11:30, 11:45-12:45 and 14:15-15:15 / September 4th, 10:30-11:30 and 11:45-12:45, Sala 1

Dynamical models and data analysis in epidemiologyOrganizer / Chairman: Nico StollenwerkCMAF, Universidade de Lisboa

Speakers:- Maira Aguiar, CMAF, Universidade de Lisboa, “Modelling dengue fever epidemiology: complexdynamics and its implication for data analysis”.- Filipe Rocha, CMAF, Universidade de Lisboa, “Understanding dengue fever dynamics: study ofseasonality in the models”.- Urszula Skwara, CMAF, Universidade de Lisboa, “Spatial epidemiological models, superdiffusion”.- Luis Mateus, CMAF, Universidade de Lisboa, “Bayesian Model Comparison and SemiclassicalApproximations in Population Biology”.- Peyman Ghaffari, CMAF, Universidade de Lisboa, “Evolution towards critical fluctuations andSelf-Organized Criticality (SOC) in a system of accidental pathogens”.- Nico Stollenwerk, CMAF, Universidade de Lisboa, “Parameter estimation in complex systems”.- Max Souza, Universidade Federal Fluminense, Niteroi, Brasil, “Multiscale tales in epidemiology”.September 3rd, 10:30-11:30 and 11:45-12:45, Sala 2

Dynamical Systems and BifurcationsOrganizer / Chairman: Alexandre RodriguesFCUP, CMUP

Speakers:- Sofia Castro, FEP, CMUP, “Global Dynamics for Symmetric Planar Maps”.- Jose Pedro Gaivao, CEMAPRE, ISEG, “Splitting of separatrices near a Hamiltonian-Hopf bifur-cation”.- Begona Alarcon, Oviedo University, Spain, “Rotation numbers for planar attractors of equivarianthomeomorphisms”.- Maria Joana Torres, CMAT, University of Minho, “On C2-stability of hamiltonians”.

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September 3rd, 11:45-12:45, Auditorio 3

Evolutionary games and economyOrganizer / Chairman: Elvio AccinelliFacultad de Economia de la UASLP

Speakers:- Edgar Carrera Facultad de economıa de la UASLP, “Migrant behavior by imitation”.- Elvio Accinelli, Facultad de Economia de la UASLP, “On the dynamics of corruption and pollutingfirms”.September 3rd, 14:15-15:15, Auditorio 3

Extremes and other statistical properties of dynamical systemsOrganizer: Jorge FreitasUniversidade do porto

Chairman: Helder VilarinhoSpeakers:- Laura Cavalcante, CMUP e FCUP, “Limiting behaviour of high order quantiles estimators”.- Hale Aytac, CMUP e FCUP, “Rare events for random dynamics”.September 3rd, 14:15-15:15, Sala 2

Piecewise smooth dynamicsOrganizer / Chairman: Jose Pedro GaivaoISEG, UTL

Speakers:- Alexandre Plakhov, Universidade de Aveiro, “Invisibility and retro-reflection in billiards”.- Paulo Brito, ISEG-UTL, “A joint discontinuity and singularity induced bifurcation arising in aCournot-Ramsey model”.- Alessandro Margheri, FCUL, “Complex dynamics in pendulum-type equations with variable length”.September 3rd, 15:30-16:30, Auditorio 3

BiomathematicsOrganizer / Chairman: Jose MartinsSchool of Technology and Management, Polytechnic Institute of Leiria; LIAAD-INESC TEC

Speakers:- Jose Martins, School of Technology and Management, Polytechnic Institute of Leiria; LIAAD-INESC TEC, “A recursive approximation to the quasi-stationary distribution in epidemiologicalmodels”.- Jorge Pereira, Instituto de Telecomunicacoes, Leiria, “An adaptive approach for skin lesion seg-mentation in dermoscopy images using a multiscale Local Normalization”.- Rui Santos, School of Technology and Management, Polytechnic Institute of Leiria; CEAUL -Center of Statistics and Applications of University of Lisbon, “ An Overview of Quantitative Com-pound Tests ”.September 3rd, 15:30-16:30, Sala 1

Economic dynamics and computationOrganizer / Chairman: Paulo B. VasconcelosFaculdade Economia Porto and Centro Matematica da UP

Speakers:- Tiago Pinheiro, Faculdade Economia Porto, “The dynamics of a cycle smoothing policy in adiscrete stochastic growth model with taxes”.- Paulo Mota, Faculdade Economia Porto and NIFIP, “The Macrodynamics of Employment underUncertainty”.

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- Oscar Afonso, Faculdade Economia Porto and CEF.UP, “Dynamic Political Effects in a NeoclassicGrowth Model with Healthcare and Creative Activities”.- Pedro Mazeda Gil, Faculdade Economia Porto and CEF.UP, “Industry Dynamics and AggregateStability”.September 3rd, 15:30-16:30, Sala 2

Bio-DynamicsOrganizer / Chairman: Bruno OliveiraFCNA, University of Porto

Speakers:- Isabel Figueiredo, FC - University of Porto and ISEP - Polythecnic Institue of Porto, “Equilibriawhen considering asymmetric death rates for active and inactive T cells and Tregs”.- Bruno Oliveira, FCNA and INESC TEC - University of Porto, “Immune response dynamics by Tcells with asymmetry in the death rates”.- Joao Coelho, FC - University of Porto, “A mathematical model of carbon life in vineyards”.- Joana Becker, FC - University of Porto, “Investing to reduce the production costs in a Cournotduopoly”.September 3rd, 17:00-18:00, Sala 1

Coupled Cell NetworksOrganizer / Chairman: Celia MoreiraUniversity of Porto (CMUP)

Speakers:- Celia Moreira, University of Porto (CMUP), “Exploring coupled cell networks”.- Ana Dias, University of Porto (FCUP & CMUP), “Coupled cell networks and the synchronylattice”.- Manuela Aguiar, University of Porto (FEP & CMUP), “Synchrony and graph operations on coupledcell networks”.- Rui Paiva, Instituto Politecnico de Leiria (ESTG) & CMUP, “Hopf bifurcation in coupled cellnetworks with abelian symmetry”.September 4th, 10:30-11:30, Auditorio 3

Marine Systems for Ocean Exploration and Exploitation: Theory and PracticeOrganizer / Chairman: Fatima Leite and Antonio PascoalUniversidade de Coimbra and Universidade Tecnica de Lisboa

Speakers:- A. Pascoal, LARSyS/ISR-Lisbon, IST, Lisbon, PT, “Cooperative Motion Control of Multiple Au-tonomous Marine Vehicles: Science and Technology”.- F. Lobo Pereira, ISR-Porto and FEUP, Porto, PT, “Dynamic Optimization Control for Au-tonomous Vehicle Systems”.- F. Curado, Centre for Environmental and Marine Studies (CESAM) & Geosciences Dept. Univer-sity of Aveiro, PT, “Potential Field Inverse Problems: from Geophysical Prospecting to AutonomousUnderwater Navigation”.- A. Silva, SiPLAB, FCT - Univ. of Algarve, Campus de Gambelas, Faro, PT, “Ocean acousticpropagation modeling and communication in the vicinity of submerged structures”.- J. Gomes, LARSyS/ISR-Lisbon, IST, Lisbon, PT, “Range-based localization of nodes in underwa-ter acoustic networks through convex relaxation”.- A. Aguiar, LARSyS/ISR-Lisbon and FEUP, Porto, PT, “Cooperative Marine Vehicle Navigation”.September 4th, 10:30-11:30 and 11:45-12:45, Sala 2

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Interest Rate, Credit Risk and Investment ModelsOrganizer / Chairman: Claudia NunesIST/CEMAT

Speakers:- Claudia Nunes, IST/CEMAT, “Investment, suspension or exit from the market, in a decliningmarket”.- Raquel Gaspar, ISEG/CEMAPRE, “ ”.- Joao Bastos, ISEG/CEMAPRE, “Ensemble predictions of recovery rates”.- Daniel Schwarz, CMU and IST/CEMAT, “Price Modelling in Carbon Emission and ElectricityMarkets”.September 4th, 11:45-12:45, Auditorio 3

Wave Interaction with Floating BodiesOrganizer / Chairman: Juha Videman and Goncalo DiasInstituto Superior Tecnico/CAMGSD and CAMGSD/IST

Speakers:- Goncalo Dias, CAMGSD/IST, “Interaction of water waves with freely floating structures”.- Filipe Cal, ISEL/CAMGSD, “Trapped modes around freely floating bodies”.- Bruno Pereira, ISEL/CAMGSD, “Edge waves along a sloping beach”.September 4th, 14:15-15:15, Auditorio 3

Stochastic ModelsOrganizer / Chairman: Alberto PintoUniversity of Porto

Speakers:- Filipe Martins, University of Porto, “ Optimal consumption, life insurance and investment strate-gies in a general financial market ”.- Ricardo Cruz, University of Porto, “Semi-stationarity under the prisoner’s dilemma”.- Mikhail Smilovic, Department of Civil Engineering at McGill University, “Games, Groundwaterand Governance”.- Michal Krzeminski, Department of Probability and Biomathematics, Gdansk University of Tech-nology, Poland, “Survival analysis under a Markov model of disease”.- Malgorzata Pulka, Department of Probability and Biomathematics, Gdansk University of Tech-nology, Poland, “Asymptotic stability of quadratic stochastic operators and their applications inpopulation genetics ”.September 4th, 14:15-15:15 and 15:30-16:30, Sala 1

Dynamic Optimization: Applications to Economics and ManagementOrganizer / Chairman: Orlando Costa GomesISCAL / IPL

Speakers:- Armando Mendes, Universidade dos Acores, “Dairy Farming Systems’ Adaptation to ClimateChange”.- Jorge Santos, Universidade de Evora, “Efficiency measurement in Economics and Management”.- Luıs Cavique Santos, Universidade Aberta, “Strong and Weak Ties in Social Networks”.- Orlando Gomes, ISCAL / IPL, “A Budget Setting Problem”.September 4th, 14:15-15:15, Sala 2

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Lyapunov Exponents and ApplicationsOrganizer / Chairman: Mario BessaUniversidade da Beira interior

Speakers:- Silvius Klein, CMAF, “Positive Lyapunov exponents for higher dimensional quasiperiodic cocy-cles”.- Helder Vilarinho, UBI, “On the spectrum of Lp cocycles”.- Cesar M. Silva, UBI, “General dichotomic behavior for trajectories of nonautonomous differenceequations”.- Alexandre Rodrigues, FCUP, “The Lyapunov exponents of toral maps with a reversing symmetry”.September 4th, 15:30-16:30, Auditorio 3

Symbolic dynamics and Lorenz-like knotsOrganizer / Chairman: Luıs SilvaISEL and CIMA-UE

Speakers:- Luıs Silva, CIMA-UE, ISEL Lisbon, “Invariants of templates, knots and links generated by renor-malizable Lorenz maps”.- Nuno Franco, CIMA-UE, University of Evora, “Thurston’s classification of a family of Lorenzknots”.- Paulo Gomes, ISEL-Lisbon, “Lorenz braids, symbolic dynamics and hyperbolic knots”.- Pedro Simoes, University of Evora, “Genus for knots and links in renormalizable templates withseveral branch nodes”.September 4th, 15:30-16:30, Sala 2

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Advanced School

Reducibility of quasi-periodically forced linear flowsJoao Lopes DiasUniversidade Tecnica de Lisboa, PortugalAugust 28th, 11:30-13:00 / August 29th, 11:30-13:00, Auditorio CGD, ISEG-UTL

Replicator and Lotka-Volterra SystemsPedro DuarteUniversidade de Lisboa, PortugalAugust 28th, 14:30-16:30 / August 29th, 14:30-16:30, Auditorio CGD, ISEG-UTL

Geometric Invariant Measures and Teichmuller StructuresYunping JiangCity University of New York, USAAugust 28th, 17:00-18:30 / August 29th, 17:00-18:30 / August 30th, 17:00-18:30, Auditorio CGD,ISEG-UTL

On interaction gamesSatoru TakahashiPrinceton University, USAAugust 30th, 11:30-13:00 / 14:30-16:30, Auditorio CGD, ISEG-UTL

Learning in games and stochastic approximationMichel BenaimUniversite de Neuchatel, SwitzerlandSeptember 5th, 11:30-13:00, Auditorio CGD, ISEG-UTL

Evolution, Crisis and General EquilibriumElvio AccinelliUASLP, MexicoSeptember 5th, 14:30-16:30, Auditorio CGD, ISEG-UTL

Discrete time models for the population and evolutionary dynamics of structured pop-ulationsJim CushingUniversity of Arizona, USASeptember 5th, 17:00-18:30 / September 6th, 17:00-18:30, Auditorio CGD, ISEG-UTL

Discrete and continuous models in evolutionary dynamicsFabio Chalub / Max SouzaUniversidade Nova de Lisboa, Portugal / Universidade Federal Fluminense, Niteroi, BrasilSeptember 6th, 14:30-16:30, Auditorio CGD, ISEG-UTL

Optimal Stochastic Control of Life insurance and investment in a financial marketAlberto A. Pinto / Filipe MartinsUniversidade do Porto, PortugalSeptember 6th, 14:30-16:30, Auditorio CGD, ISEG-UTL

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Book of Abstracts

Keynote Speakers

Contagion and Uninvadability in Social Networks with Bilingual OptionSatoru Takahashi 1,∗

1 Department of Economics, National University of SingaporeSeptember 2nd, 09:00-10:00, Auditorio 2

In a setting where an infinite population of players interact locally and repeatedly, we study theimpacts of payoff structures and network structures on contagion of a convention. For the “bilingualgame”, where each player chooses one of two conventions or adopts both (i.e., chooses the “bilingualoption”) at an additional cost, we completely characterize when a convention spreads contagiouslyfrom a finite subset of players to the entire population in some network, and conversely, when a con-vention is never invaded by the other convention in any network. In particular, depending on the costof bilingual option, the risk-dominated but Pareto-dominant convention can be contagious, and fur-thermore, for a fixed profile of payoff parameter values, the risk- dominant and the Pareto-dominantconventions can each be contagious in respective networks. Non-linear networks can be critical indeter- mining the contagious conventions in some range of parameter values. We also introduce theconcept of weight-preserving node identification and show that if there is a weight-preserving nodeidentification from one network to another, then the latter is more contagion-inducing than theformer in all supermodular games. We demonstrate that with our three-action game, our analysisreveals strictly finer structures of networks than that with two-action coordination games.∗ Work carried out in collaboration with Daisuke Oyama, Faculty of Economics, University of Tokyo.

A vaccination game with infection and reinfectionJose Martins 1,∗1 Polytechnic Institute of Leiria and LIAAD-INESC TECSeptember 2nd, 10:30-11:30, Auditorio 2

abstract In the case of voluntary vaccination, people have to face the benefit of vaccinate against theadverse effects that may result from the act of vaccination. This dilemma is even more importantwhen parents have to decide whether or not to vaccinate their children. The decision depends onthe perceived risks from vaccination and infection, but also depends on the decision of all otherpeople: if the most part of population decides to vaccinate, the probability of infection will decreaseand the personal interest of an individual may lead to non-vaccination. This game of vaccinate ornot vaccinate is analyzed in this work, considering an epidemic model for infection and reinfection.People’s decisions are clear in the case of only one infection, but the possibility of reinfection providesa further diversity and complexity in the decisions that people can take.∗ Work carried out in collaboration with Alberto A. Pinto.

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Avoiding Catastrophic Climate Change: The Public Goods Game we cannot afford toloseJorge Pacheco 1,2,∗1 Departamento de Matematica e Aplicacoes & CBMA, Universidade do Minho, 4710 - 057 Braga,Portugal2 CMAF, Instituto para a Investigacao Interdisciplinar, 1649-003 Lisboa-Codex, PortugalSeptember 2nd, 11:45-12:45, Auditorio 2

When attempting to avoid global warming, individuals often face a social dilemma in which, besidessecuring future benefits, it is also necessary to reduce the chances of future losses. This turns the“risk of failure” into a central issue in individual decision. We model this social dilemma in termsof a public goods game of cooperation, and show that global coordination towards a common goodshould be attempted by segmenting tasks in many small to medium sized groups in which perceptionof risk is high and achievement of goals involves stringent requirements. Furthermore, I will alsoshow how networking the groups and setting up sanctioning institutions further enhance the chancesof coordinating to tame the planet’s climate.∗ Work carried out in collaboration with Francisco Santos & Vıtor Vasconcelos.

The Forward Generalized Kimura EquationFabio Chalub 1

1 Universidade Nova de Lisboa September 2nd, 14:15-15:15, Auditorio 2

We consider the Forward Generalized Kimura Equation:

∂tp =k

2∂2x(x (1− x) p)− ∂x (x (1− x)ψ(x) p),

where p(x, t) is the probability to find x mutants at time t in a population consisting of two differentgenotypes: the wild-type and the mutant. The fitness difference between the mutant and the wildtype is given by ψ : [0, 1] → R and k is the “intensity of selection”. We will show that thisequation, when supplemented by two appropriate conservation laws, approximates the evolutiongiven by certain Markov processes (e.g, the Moran process or the Wright-Fisher process). Theseconservation laws can be obtained from the discrete processes. We will obtain expressions for thefixation probability of the mutant and also for the expected time for fixation of any type. Theseequations are of no practical use and will be simplified using asymptotic expansions, given differentexpressions depending on the sign of the function ψ on the interval [0, 1]. We also show existenceand uniqueness of solution in measure sense of the Forward Generalized Kimura equation. Finally,we will study the same equation for time dependent fitness. This is a joint work with Max Souza(Brazil) and Olga Danilkina (Russia).

Stability of quasi-periodic dynamicsJoao Lopes Dias 1

1 Universidade Tecnica de Lisboa, PortugalSeptember 2nd, 15:30-16:30, Auditorio 2

We review some results and open problems on the stability of quasi-periodic dynamics for conser-vative systems that are related to several models in nature.

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Symmetric Invariant Probability Measures and RigidityYunping Jiang 1

1 City University of New York, USASeptember 2nd, 17:00-18:00, Auditorio 2

In the study of modern dynamical systems, an invariant measure is an important topic and in thestudy of modern complex analysis, the quasisymmetric condition on a map is an important topic.In this talk, I will combine these two topics together introducing a new interesting topic, symmetricinvariant probability measure.

I will discuss the existence and the uniqueness of a symmetric invariant probability measure fora uniformly symmetric circle endomorphism. I will also discuss uniqueness, ergodicity, and rigidityfor such a symmetric invariant probability measure.

Optimal strategies in prices and locations in the Hotelling networkAlberto A. Pinto 1

1 Universidade do PortoSeptember 3rd, 09:00-10:00, Auditorio 2

This paper develops a theoretical framework to study price competition in a Hotelling-type networkgame, extending the Hotelling model of price competition with linear transportation costs from aline to a network. Under explicit conditions on the production costs and road lengths we show theexistence of a pure Nash equilibrium price strategy. Furthermore, we prove that the local optimallocalization of the firms are at the vertices of the network.

On value allocations in economies with commodity differentiationMarta Faias 1,∗1 Universidade Nova de Lisboa, PortugalSeptember 3rd, 10:30-11:30, Auditorio 2

In this paper, we provide a well-defined coalitional game for atomless economies with commoditydifferentiation, where a monopolistic competition situation may arise. We consider a notion of limitvalue for the associated game and discuss the relation between value allocations and competitiveallocations in these non-atomic markets.∗ Work carried out in collaboration with Emma Moreno-Garcıa, Universidad de Salamanca andMario Pascoa, University of Surrey.

Inverse Problems and Structured Population ModelsJorge Zubelli 1

1 IMPA, BrasilSeptember 3rd, 11:45-12:45, Auditorio 2

Inverse problems are fundamental in mathematical modelling. Indeed, they play a crucial role whentrying to fit theoretical models to practical observations. They are deeply connected to Statisticsand its applications to the natural sciences. In this talk we shall exemplify the use of na inverseproblem to study the dynamics of certain populations.

Structured population models in biology lead to integro-differential equations that describe theevolution in time of the population density taking into account a given feature such as the age,the size, or the volume. These models possess interesting analytic properties and have been usedextensively in a number of areas.

After giving an introduction to population dynamics modelling, we shall discuss the inverseproblem. Here, we consider a size-structured model for cell division and address the question of

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determining the division (birth) rate from the measured stable size distribution of the population.We formulate such question as an inverse problem for an integro-differential equation posed on thehalf line. We develop firstly a regular dependency theory for the solution in terms of the coefficientsand, secondly, a regularization technique for tackling this inverse problem which takes into accountthe specific nature of the equation. Our results rely also on generalized relative entropy estimatesand related Poincare inequalities.

Finally, if time allows, we will discuss novel applications to stem cell modelling. In this partwe study different mathematical aspects of a continuous model of stem cell developments. This isjoint work with Anna Marciniak (Heidelberg), Benoit Perthame (UPMC, Paris), and Marie Doumic(INRIA, Paris).

Fast Convergence in Finite PopulationsLorens Imhof 1

1 University of Bonn, GermanySeptember 3rd, 14:15-15:15, Auditorio 2

We consider stochastic evolutionary game dynamics in a finite population. We are interested in thetime needed by the dynamics to reach and stay close to a given subset of the state space. SomeLyapunov criteria are discussed that can help to determine whether a set is reached fast. As anapplication we compare dynamics where agents have full information on the composition of thepopulation and dynamics where agents can only sample some agents. The talk is based on jointwork with G. Ellison and D. Fudenberg.

Dynamical embeddings in Lotka-Volterra SystemsPedro Duarte 1

1 Universidade de Lisboa, PortugalSeptember 3rd, 15:30-16:30, Auditorio 2

Which dynamical systems can be embedded in a Lotka-Volterra System? Older and newer answerswill be surveyed.

Dynamics and Mathematical Institutional Economics(video lecture)Martin Shubik 1

1 Yale University, USASeptember 3rd, 17:00-18:00, Auditorio 2

Money and Financial institutions are the natural carriers of economic process. The concept ofGeneral Equilibrium is critical to understanding the logic of the price system, but it tells younothing about the dynamics that is crucial to describing motion out of equilibrium. In order tounderstand economic dynamics we must construct models that are playable games; they must actas carriers of process. The concept of a strategic market game as a carrier of process is developed,and with the concept of a minimal economic institution is noted.

Population persistence under climate change: applications of the Fundamental Bifur-cation Theorem for matrix population modelsJim Cushing 1

1 University of Arizona, USASeptember 4th, 09:00-10:00, Auditorio 2

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Several field studies of marine birds (glaucous-winged gull breeding colonies) on Protection IslandNational Wildlife Refuge in the Strait of Juan de Fuca (State of Washington, USA) motivate math-ematical “proof-of-concept” models designed to investigate plausible causal mechanisms of observedchanges in population dynamics and life history strategies. This lecture will focus on two of thesephenomena: increased cannibalism in response to decreased environmental resource availability(caused by a rise in mean sea surface temperature) and reproductive synchrony in response toincreased cannibalism. Mathematical analysis is based on the Fundamental Bifurcation Theoremfor matrix population dynamic models. The analysis shows that cannibalism and reproductivesynchrony can be adaptive responses that result from, and promote population persistence in thepresence of, decreased environmental resource.

Cournot duopolies with R&D investmentBruno Oliveira 1

1 Universidade do Porto, PortugalSeptember 4th, 10:30-11:30, Auditorio 2

We present the Ferreira, Oliveira e Pinto R&D investment function in a Cournot competition model.We do a full characterization of the associated game and study the short- and long-term economicaleffects derived from using this new R&D investment function. In particular, we find the existence ofregions with multiple Nash investment equilibria. For low production costs, that can correspond tothe production of old technologies, the long-term economical effects are not very sensitive to smallchanges in the efficiency of the R&D programmes neither to small changes in the market structure.However, for high production costs, that can correspond to the production of new technologies,the long-term economical effects are very sensitive to small changes in the efficiency of the R&Dprogrammes and also to small changes in the market structure.

Decentralized Markets of Two-Sided MatchingJoana Pais 1

1 ISEG/Technical University of Lisbon, PortugalSeptember 4th, 11:45-12:45, Auditorio 2

Much of the literature on two-sided matching markets, both cooperative game-theoretical and empir-ical, has investigated centralized markets. However, decentralized interaction in matching marketsis the norm, not the exception. We present an overview of two-sided matching theory applied to de-centralized markets, as well as laboratory studies of decentralized matching and identify conditionsunder which a stable matching is likely to emerge in equilibrium.

Complementarity and Imitative Behavior in the Populations of Firms and WorkersElvio Accinelli 1

1 UASLP, MexicoSeptember 4th, 14:15-15:15, Auditorio 2

In this paper, we study the dynamics of the complementarities between innovative firms and skilledworkers and its effect on economic growth. We set up a model on imitation game between firms andworkers with asymmetric information. There is strategic complementarity between the percentageof high-skill workers and innovative firms, human capital and R&D, respectively. This is a certainkind of coordination game. We show that this model has two pure rational Nash equilibria, oneof them with high investment in R&D and skilled workers while the other one, which we interpretas poverty trap, exhibits lack of skills and underinvestment. Furthermore, we show that we canavoid the poverty trap if the number of innovative firms is larger than a threshold value leading

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to an increase of the number of skilled workers. We conclude that the policy makers may have animportant role in obtaining the high-level equilibria.

Influence of individual decisions on competitive market policiesRenato Soeiro 1

1 Universidade do Porto September 4th, 15:30-16:30, Auditorio 2

A decision model where individuals have to make a choice from a discrete set of alternatives willbe presented. Different types of individuals are grouped according to their preferences. Whenindividuals have gains in their utilities by making the same decision as other individuals of thesame group, the pure Nash equilibria are given by a cohesive group decision. However if there arefrictions among individuals of the same group, then there will be disparate Nash equilibria wherethe group is disrupted and its elements make different decisions.

In the case of two different groups facing a dichotomous decision, Nash equilibria form degen-erated hysteresis with respect to the replicator dynamics, with the property that the pure Nashequilibria are asymptotically stable and the strict mixed equilibria are unstable. Limit cycles forthe replicator dynamics exist, associated to situations where the individuals keep changing theirdecisions along time, but exhibiting a periodic repetition in their decisions.

By considering that individuals are choosing among different offers of public or private serviceswe will discuss how these interactions impact on market strategies and market outcomes.

Stochastic Models of Learning in GamesMichel Benaim 1

1 Universite de Neuchatel, SwitzerlandSeptember 4th, 17:00-18:00, Auditorio 2

I will first describe certain classical learning procedures arising in game theory (including stochasticfictitious play and large population dynamics) and explain how their long long term behaviour canbe precisely related to the nature of the game using tools of dynamical systems. Then I will describerecent results obtained in collaboration with Mathieu Faure (Marseille), proving the almost sureconvergence of stochastic fictitious play for supermodular games.

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Thematic Sessions

Bayesian Statistics: Applications in Biology and EcologyOrganizer Luıs SilvaCIBIO, Centro de Investigacao em Biodiversidade e Recursos Geneticos, Universidade dosAcoresSeptember 2nd, 10:30-11:30, Auditorio 3

Bayesian Inference: General FrameworkJoao M. M. Casaca 1,∗

1 National Laboratory for Civil Engineering∗jmmcasaca@gmail.com

The presentation deals with several topics considered to be the basic structure of Bayesian Infer-ence. Historical background: the classical, the frequencist, the logical and the subjective schools ofprobability and their relation to Bayesian Analysis. The formula of Bayes-Laplace: the likelihoodfunction of the sample, the prior and the posterior probability density functions (PDF) of the pa-rameters, the prior and the posterior predictive probability functions and the marginal posteriorsfor multidimensional parameters. Informative and non-informative priors: the priors of Laplace andJeffreys, the conjugate priors, the divergence of Kulback-Leibler (as a measure of the informationprovided by the prior PDF) and methods to elicitate conjugate prior hyper-parameters. Finally, ex-amples under four different scenarios: i) The beta-binomial model; ii) The normal random sample;iii) The multivariate normal random sample; iii) The multivariate regression analysis. Closed for-mulae for marginal posterior PDF of the parameters, under Laplace, Jeffreys and conjugate priors,are presented for the referred scenarios.

[1] Berger, J. O. 2010. Decision Theory and Bayesian Analysis. New York: Springer.

[2] Robert, C. P. 2007. The Bayesian Choice. Berlin: Springer.

Multinomial and Dirichlet distributions in Bayesian inference: applications in Biology andEcology

Luıs Silva 1,∗

1 CIBIO, Centro de Investigacao em Biodiversidade e Recursos Genteicos, InBIO Laboratorio Associado,

Polo dos Acores, Departamento de Biologia, Universidade dos Acores, 9501-801 Ponta Delgada, Portugal∗lsilva@uac.pt

The multinomial distribution has been used in many areas including population ecology [1] andepidemiology [2]. Dirichlet distribution has been used as a prior for the multinomial parameters,since it is the conjugate of the probabilities of the multinomial model [1], and in Bayesian modelsfor population genetics and phylogeny [3, 4]. We illustrate how plant community composition andstructure can be represented by a multinomial distribution when species are categorized accordingto their attributes (e.g. life-form, conservation status). It is possible to evaluate if environmentalfactors (e.g. anthropogenic disturbance, altitude) are linked to changes in community structure,originating different values for the multinomial parameters. Also, each multinomial distribution (i.e.each community or group of communities) can be graphically represented by a particular speciesspectra [5]. These two distributions still have the potential to model many other phenomena inbiology and ecology.

[1] King R, BJT Morgan, O Gimenez, SP Brooks. 2010. Bayesian analysis for Population Ecology. Chapman& Hall/CRC, Boca Raton, 442 pp.

[2] Kazembe L, J Namangale. 2007. A Bayesian multinomial model to analyse spatial patterns of childhoodco-morbidity in Malawi. European Journal of Epidemiology, 22: 545-556.

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[3] Pritchard JK, M Stephens, P Donnelly. 2000. Inference of population structure using multilocus genotypedata. Genetics, 155: 945-959.

[4] Ronquist F, JP Huelsenbeck, P van der Mark 2005. MrBayes 3.1 Manual. Draft 5/26/2005. 69 pp.

[5] Marcelino JAP, L Silva, PV Garcia, R Weber, O Soares 2012.Using species spectra to evaluate plantcommunity conservation value along a gradient of anthropogenic disturbance. Environmental Monitoringand Assessment. (DOI: 10.1007/s10661-012-3019-9).

A Bayesian spatio-temporal analysis of forest fires in Portugal Giovani L. Silva 1,2,∗, Paulo Soares1,2

1 Centro de Estatıstica e Aplicacoes da Universidade de Lisboa2 Departamento de Matematica - IST, Universidade de Lisboa∗gsilva@math.ist.utl.pt

In last decades, forest fires have become one of the worst natural disasters in Portugal due namelyto climate change, nature of Portuguese forest, and the decrescing of rural population. That causesgreat forest devastation, leads to both economic and environmental losses and put at risk populationsand the livelihoods of the forest itself.

In this paper we propose Bayesian hierarchical models to analyze spatio-temporal forest firedata on the proportion of burned area in Portugal, by municipalities and over three decades. Ourgoal is to identify ‘hotspot’ regions and trends over time through modelling and mapping of burnedforest area proportion by regions such as districts or municipalities.

The related models account for (i) spatial correlation (ii) nonlinear temporal effects, usingboth hierarchical spatial models and B-spline smoothing from a Bayesian perspective. Mixtureof distributions was employed to model jointly the proportion of area burned and the excess of noburned area for early years. For getting estimates of the model parameters, we used Monte CarloMarkov chain methods.

[1] Amaral-Turkman MA, Turkman KF, Le Page Y, Pereira JM. Hierarchical space-time models for fireignition and percentage of land burned by wildfires. In Environmental and Ecological Statistics 18, 601-617, 2011.

[2] Besag J, York JC, Mollie A. Bayesian image restoration, with two applications in spatial statistics (withdiscussion). In Annals of the Institute of Statistical Mathematics 43, 1-59, 1991.

[3] Ferrari SLP, Cribari-Neto F. Beta regression for modeling rates and proportions. In Journal of AppliedStatistics 31, 799-815, 2004.

[4] Silva GL, Dean CB, Niyonsenga T, Vanasse A. Hierarchical Bayesian spatiotemporal analysis of revascu-larization odds using smoothing splines. In Statistics in Medicine 27, 2381-2401, 2008.

Selecting parameters for Bayesian calibration of a process-based model: A methodology basedon canonical correlation analysis

F. Minunno 1, M. van Oijen, D.R. Cameron and J.S. Pereira1 Instituto Superior de Agronomia, Universidade Tecnica de Lisboa

Bayesian statistics is becoming increasingly common in the environmental sciences because of de-velopments in computers and sampling-based techniques for parameter estimation. However, theuse of the Bayesian approach is still limited in forest research, especially for models with many pa-rameters. Some studies have used parameter screening to make the calibration of a computationallyexpensive model possible. In this paper we introduce a new methodology for parameter screening,based on canonical correlation analysis. Furthermore we show how parameter screening impacts theperformance of a process-based model. The methodology presented here can be generally appliedand is particularly suitable for complex process-based models because it is not computationallydemanding and is easy to implement. It provides an overall ranking in relation to all outputs ofthe model, as opposed to common sensitivity methods that analyse one model output variable at a

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time. We found that parameter screening can be used to reduce the computational load of Bayesiancalibration, but only the least important parameters should be excluded from the calibration if wedo not want to affect model performance. In this exercise, 25% of the parameters of a process-basedforest model could be excluded from the calibration without affecting model performance. Whencalibration was limited to a more restricted number of parameters, model performance significantlydeteriorated.

Discrete Dynamics and Numerical SemigroupsOrganizer: Sara FernandesUniversidade de EvoraSeptember 2nd, 10:30-11:30, Sala 1

Ihara zeta function, symbolic dynamics and seismic events networksClara Gracio 1,∗

1 Department of Mathematics, University of Evora and CIMA-UE∗mgracio@uevora.pt

In recent years many complex systems in physics, biology, computer science, economics and thesocial sciences have been studied in terms of networks which represent the interaction patternsbetween interacting variables, see [1], see [2], see [3]. As an example, indeed attractive, is theconsideration, study and interpretation of the seismic events. Our aim here is to show that thegraph theory, the symbolic dynamics, and in particular, the Ihara zeta function, see [4] and see [5],are powerful and promising tools with which to calculate the important information on a graph,having particular importance in applications for real networks.

[1] R. Albert and A.L. Barabasi, Statistical mechanics of complex networks, Rev. Mod. Phys., 74, 47–97,2002.

[2] S.N. Dorogovtsev, A.V. Goltsev, and J.F.F. Mendes, Critical phenomena in complex networks, Rev. Mod.Phys., 80, 1275–1335, 2008.

[3] M.E.J. Newman, Networks: an Introduction, Oxford University Press, 2010.

[4] G. Scott and C. Storm, The Coefficients of the Ihara Zeta Function, Involve 1(2), 979–991, 2008.

[5] C. Gracio, A. C. C. Coolen; A. Annibale, Cycle statistics in complex networks and Ihara’s zeta function,Springer Proceedings in Mathematics & Statistics, Vol. 71, 2013.

Discrete Dynamical Systems and Numerical SemigroupsSusana Santos 1

1 Universidade de Evora

Interval maps constitute a very important class of discrete dynamical systems. The class of intervalmaps which we consider is a sub-class of expansive Markov maps. The Markov property allow us toassociate to the interval map a transition matrix and a subshift of finite type. This can be a graph,which is the graph whose adjacency matrix is the transition matrix associated with the map. Westudy a particular class of interval maps for which the set of periods is a numerical semigroup.

About equilibrium distributions of discrete non autonomous systemsTeresa M. Silva 1

1 CIMA-UE, Universidade de Evora, Department of Mathematics and Departmental area of mathematics,

ISEL-Instituto Superior de Engenharia de Lisboa

We have introduced the notions of equilibrium distribution and time of convergence in discretenon autonomous systems. Under some conditions we have given an estimate to the convergence

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time to the equilibrium distribution using the second largest eigenvalue of some matrices associatedto the system. In this talk we will present results concerning convergence of functions and theirimplications on the convergence to the equilibrium of the correspondent non autonomous systems.

[1] J. F. Alves, L. Silva, Periodic paths on nonautonomous graphs, Linear Algebra and Its Applications. 2012;3 (437).

[2] E. Behrends, Introduction to Markov chains with special emphasis on rapid mixing, Advanced lectures inmathematics, Vieweg, 2000.

[3] S. Kolyada and L. Snoha Topological entropy of non autonomous dynamical systems, Random and com-putational dynamics, 1996.

[4] G. Nannicini, L. Liberi, Shortest paths on dynamic graphs, 2008.

[5] D. D. Siljak, Dynamic graphs, The International Conference on Hybrid Sysems and Applications, 2006.

[6] P. Walters, An Introduction to ergodic theory, Graduate texts in Mathematics, Springer-Verlag, 1982.

On the enumeration of the set of saturated numerical semigroups with fixed FrobeniusnumberDenise Torrao 1

1 Universidade de Evora

In this talk we characterize the Frobenius number of a numerical semigroup with minimal SAT-system of generators. We give an algorithm for computing all (d1, , dp)-semigroups with a givenFrobenius number. Finally we describe an algorithm for computing all saturated numerical semi-groups with a given Frobenius number.

Mean-Field Models, Optimal Control and Calculus of VariationsOrganizer: Edgard PimentelUniversidade Tecnica de LisboaSeptember 2nd, 10:30-11:30, Sala 2

Homogenization of certain optimal control problemsGabriele Terrone 1

1 CAMGSD-IST-UTL

Consider a deterministic optimal control problem in which the velocity of the state variable x andthe running cost depend on the oscillating term x/ε (ε > 0). The homogenization problem consistsin studying the limit of the control problem as ε→ 0. This type of problems have been extensivelystudied in the framework of viscosity solution of Hamilton-Jacobi equation. However, little is knownabout the possibility of describing a limit optimal control problem: this is a crucial issue in view ofapplications. In this talk, I will describe different situations in which it is possible to show that thelimit as ε→ 0 of the oscillating problem is still an optimal control problem. Explicit expressions forthe limiting dynamics and cost are provided for problems enjoying special structure. The resultsdescribed have been obtained in collaboration with Martino Bardi (Universita degli Studi di Padova,Italy).

Regularity for mean-field games in the subquadratic caseEdgard Pimentel 1

1 CAMGSD-IST-UTL

We consider the following mean-field games problem

−ut +H (x,Du) = ∆u+ g(m) (1)

mt − div (DpH(x,Du)m) = ∆m,

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together with initial-terminal data

u (T, x) = uT (x) (2)

m (0, x) = m0(x)

and periodic boundary conditions in the space variable. For the case in which H satisfies a sub-quadratic growth condition, and g(m) = mα, by combining Gagliardo-Niremberg type estimates forthe first equation in (1) and additional estimates for the Fokker-Planck equation we obtain enoughregularity to ensure existence of smooth solutions of (1)-(2) for distinct values of α depending onthe dimension. This is a joint work with D. Gomes and H.S. Morgado.

Finite state (potential) mean-field games: long time behavior via Γ-convergenceRita Goncalves Ferreira 1

1 Instituto Superior Tecnico (IST) & Centro de Matematica e Aplicacoes of the FCT-UNL (CMA of the

FCT-UNL)

In this talk we address the study of long time convergence (trend to equilibrium problem) for finitestate mean-field games using Γ-convergence. Our techniques are based upon the observation thatan important class of mean-field games can be seen as the Euler-Lagrange equation of a suitablefunctional. Therefore, by a scaling argument, one can convert the long time convergence probleminto a Γ-convergence problem. Our results generalize previous results on long-time convergence forfinite state problems.

Marine Life in the Wild Wider OceanOrganizer: Ricardo Serrao SantosCentro do IMAR da Universidade dos Acores (IMAR-DOP/UAc) & LARSyS - Horta/AcoresSeptember 2nd, 11:45-12:45, Auditorio 3

Seamounts are hotspots of pelagic biodiversity in the open oceanTelmo Morato 1, Simon D. Hoyle, Valerie Allain, and Simon J. Nicol1 University of the Azores

The identification of biodiversity hotspots and their management for conservation have been hypoth-esized as effective ways to protect many species. There has been a significant effort to identify andmap these areas at a global scale, but the coarse resolution of most datasets masks the small-scalepatterns associated with coastal habitats or seamounts. Here we used tuna longline observer datato investigate the role of seamounts in aggregating large pelagic biodiversity and to identify whichpelagic species are associated with seamounts. GLM techniques were used to standardize rarefiedrichness and to evaluate whether the presence of habitat features and the distance to the featurewere significant explanatory variables. The explanatory variables included in the model were year asa proxy for temporal variability, moon phase as the relationship between lunar periodicity and catchrates as has been demonstrated for a wide variety of commercially exploited species, geographicalarea, fleet type, distance to the closest feature, and fishing effort. Akaike’s information criterion(AIC) was used to compare the model fits using different relationships with distance to feature, withlog-transformed having the better fit. Our analysis indicates that seamounts are hotspots of pelagicbiodiversity. Higher species richness was detected in association with seamounts than with coastalor oceanic areas. Seamounts were found to have higher species diversity within 30 − 40 km of thesummit, whereas for sets close to coastal habitat the diversity was lower and fairly constant withdistance. Higher probability of capture and higher number of fish caught were detected for someshark, billfish, tuna, and other by-catch species. The study supports hypotheses that seamountsmay be areas of special interest for management for marine pelagic predators.

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Predicting deep-sea biological distributions using scarce informationFernando Tempera1

1 IMAR Instituto do Mar, University of the Azores e LARSyS

Cataloguing, characterizing and mapping vulnerable marine ecosystems dominated by habitat-building megafauna has been the priority of recent research conducted in the Azores under a seriesof European projects. A total of 50 different megafauna-dominated benthic facies have been inven-toried from imagery collected by expeditions that visited the Azores region over the last 60 years.Such habitat diversity confirms the rugged seafloor of the Azores plateau as a NE Atlantic deep-seahotspot. Aiming to go beyond known point occurrences, spatially-explicit habitat suitability modelswere applied to predict the distribution of the most common habitat-building coral species. Sinceobtaining absence data in deep-sea environments is unreliable given sampling constraints like thelimited spatial coverage of surveying methods, habitat suitability was modeled using the presence-only MaxEnt package. This statistical modelling framework estimates the probability distributionof maximum entropy (i.e. closest to uniform) for presence-only data based on environmental con-straints. Instead of presences and true absences, it requires only species presence data and grids ofcontinuous or categorical environmental variables for the study area. MAXENT has been shownto surpass all other models when predicting distribution based on presence-only data and remaineffective despite small sample sizes. The covariates used are a selection of oceanographic, biological,geomorphological, physical and chemical parameters upscaled to a 300-m resolution from publiclyavailable databases and climatological atlases.

This work is a contribution towards the mapping of some of the most important deep-sea biotopesof conservation importance.

Fish in space: Modeling movements and essential habitatPedro Afonso1

1 Centro do IMAR da Universidade dos AA§ores (IMAR-DOP/UAA§) & LARSyS Laboratorio Associado

Knowing how marine animals distribute and move in the ocean space of has long been a goal formarine scientists. With todayA´s challenges posed by the ever growing pressure put by human de-velopment on the marine biodiversity and ecosystem, this has become one of the most urgent tasks.For example, the success of networks of coastal marine protected areas (MPAs) established in areaslargely depends on the good understanding of the residency, habitat preferences and migrationsof the various fish species’ that inhabit the reefs, so that MPAs can actually protect those fish;The movements of large, oceanic fishes such as pelagic sharks across boundaries and internationalwaters can provide the critical identification of multispecies hotspots in the open ocean that needto be protected from intensive fishing; the unveiling of the tri-dimensional, fine scale behaviour ofdeepwater fishes at seamounts can show how they interact and depend on local food resources. Thepivotal tool to achieve these goals is modelling and forecasting, whether it is the abundances of fishesfrom underwater counts or the individual positions of fishes tagged with electronic devices. Thesemodelling techniques, which typically use environmental variables as predictors of the populationbehaviour, have seen substantial developments in recent years. We draw examples on multidisci-plinary research conducted in the Azores, mid-north Atlantic, to illustrate these approaches andchallenges.

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Synchronization and Discrete DynamicsOrganizer: Clara GracioUniversidade de EvoraSeptember 2nd, 11:45-12:45, Sala 1

Conductance and clique formation and its applicationsSara Fernandes 1

1 CIMA-UE, Universidade de Evora, Departamento de Matematica

Several complex problems can be solved by reducing the number of elements by clustering. In thisway it is useful to identify common substructures between sets of vertices which will be consideredas clusters in a network. A good choice of clusters are the cliques, i.e., maximal complete subgraphs.We present a study that shows the direct influence of the conductance in the formation of cliquesin networks.

“Linear couplings”, “commanded couplings” and their synchronizationLuıs Mario Lopes1, Sara Fernandes 2,3, C. Gracio 2,3

1 ISEL2 University of Evora3 Research Centre in Mathematics and Applications

A coupling only synchronizes if some conditions are verified. We obtain those conditions for fourdifferent couplings, considering two types of synchronization. We also obtain their windows ofsynchronization. We use a analytical approach and numerical one. For the numerical approach weconsider four different maps.

Analyze of dynamic behavior of Burridge Knopoff model in synchronized and non-synchronized regime: potential implications.A. Albino 1, H. G. Silva 1,2, M. Bezzeghoud 1,2, B. Caldeira 1,2, J. Borges 1,2, M. Tlemcani 1,2

1 Geophysics Centre of Evora2 University of Evora

In this work we present and describe a mathematical model in order to simulate seismic dynamics.The model consists of plural nonlinear-coupled oscillators. This model is an improvement of theclassical Burridge-Knopoff model and it consists of an association of a multiple mass-spring oscil-lators under a nonlinear solid friction. The numerical data generated by the numerical simulationhave been analyzed and processed by a signal processing tools and chaos theory.

[1] R. Burridge and L. Knopoff, ”Model and theoretical seismicity,,” B. Seismol. Soc. Am., vol. 57 (3), pp.341–371, 1967.

[2] A. Love, Treatise on the Mathematical Theory of Elasticity, New York, 1944.

[3] J. Carlson, J. Langer and B. Shaw, ”Dynamics of earthquake faults,” Rev. Mod. Phys, vol. 66, pp.657–670, 1994.

[4] F.-J. Elmer, ”Nonlinear dynamics of dry friction,” J. Phys. A: Math. Gen., vol. 30, p. 6057–6063, 1997.

[5] A. Albino, H. G. Silva, M. Bezzeghoud, B. Caldeira, J. Borges and M. Tlemcani, ”Chaotic behaviour ofseismic mechanisms: observation and models,” in International Workshop on Nonlinear Maps and theirApplications, Evora, Portugal, 2011.

[6] B. Caldeira, H. G. Silva, J. F. Borges, M. Tlemcani and M. Bezzeghoud, ”Chaotic behavior of seismicmechanisms: experiment and observation,” ANNALS OF GEOPHYSICS, vol. 55, pp. 57–62, 2012.

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Statistics in Environmental and Life SciencesOrganizer: Marta FaiasFCT-UNL and CMASeptember 2nd, 11:45-12:45, Sala 2

Spatial analysis of extreme precipitationD. Prata Gomes 1,∗, M. Manuela Neves, 2, Elsa Moreira 1

1 Universidade Nova de Lisboa, FCT and CMA, Portugal2 Universidade Tecnica de Lisboa, ISA, and CEAUL, Portugal∗dsrp@fct.unl.pt

Natural hazards such as high rainfall and windstorms, arise due to physical processes and are spatialin extent. Spatial statistics deals with statistical methods in which spatial locations play an explicitrole. Classical geostatistics is mostly based on multivariate normal distributions, inappropriate formodeling tail behavior. Spatial extreme analysis joins two areas of statistics: extreme value analysisand geostatistics. A variety of statistical tools have been used for the spatial modeling of extremes,including Bayesian hierarchical models, copulas and max-stable random fields. Max-stable processesform a natural class of processes extending extreme value theory when sample maxima are observedat each site of a spatial process.

A real case of extreme spatial precipitation in Portugal is discussed. This study also intendsto show the main tools for the statistical analysis in spatial extremes using R software. Newfunctions were also defined. Maps of extreme precipitation from the fitted max-stable models arealso obtained.

Analysis of HIV integration sites in human chromosomes by genetic and statisticalmethodsInes J. Sequeira 1 Elsa Moreira 2, Joao T. Mexia, 2, Juliana Goncalves 3, Aldina Bras 3

1 FCT/UNL and CMA2 Universidade Nova de Lisboa, FCT and CMA, Portugal3 Universidade Nova de Lisboa, FCM and CIGMH, Portugal

Integration of the human immunodeficiency virus (HIV) DNA into human genome is essential forHIV-induced disease. The human genome is organized into chromosomes and within these we candefine the chromosomal fragile sites. Our aim is to contribute to help clarifying the integration sitespreferences of HIV1 and HIV2 in fragile or non-fragile regions. Here we apply statistical techniques,namely non-parametric tests and analysis of variance for analyzing two sets of data of HIV1 andHIV2 integrations in the human genome. The results show that the integrations occur significantlywith more intensity in the non-fragile regions of the human genome and that the HIV1 in particularhas the major contribution to this fact. This study could have implications in human disease.

Robust outlier testing with application to a maize data setV. Lourenco 1,∗, A. M. Pires 2

1 FCT/UNL, Dep. Mathematics and CMA, Portugal2 IST/UTL, Dep. Mathematics and CEMAT, Portugal∗vmml@fct.unl.pt

Robust multiple linear regression methods are a valuable tool when the underlying classical as-sumptions are not completely fulfilled. In this setting robust methods ensure the analysis is notsignificantly disturbed by any outlying observation. Still, knowledge of these observations may beimportant to assess the underlying mechanisms of the data. Therefore, a robust outlier test is dis-cussed together with an adequate false discovery rate correction measure, to be used in the contextof a multiple linear regression model with categorical explanatory variables, focusing in particular

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on genetic association studies of quantitative traits. The good performance of the test is validatedby means of a simulation study and a real data example application from a maize candidate genestudy.

A State Space Model Approach for Modelling the Population Dynamics of Black Scab-bardfishIsabel Natario 1, Ivone Figueiredo 2, M. Lucılia Carvalho 3

1 CEAUL; Dep. de Matematica, Faculdade de Ciencias e Tecnologia, Universidade Nova de Lisboa2 Instituto Portugues do Mar e da Atmosfera (IPMA), Portugal3 CEAUL; Faculdade de Ciencias da Universidade de Lisboa, Portugal

Black scabbardfish (Aphanopus carbo Lowe, 1839) is a widely distributed species over the oceans.In Portuguese mainland waters (ICES IXa) the existing specimens are immature (not able to repro-duce). It is admitted that they have migrated from the West of the British Isles (BI) and that theyremain in the area for some years, maturing. Later, after attaining an adequate size or physiologicalcondition, these specimens leave the area and migrate to reproduce elsewhere.

The present study aims at modelling the dynamics of the population of black scabbardfish,but only for that living in ICES IXa, for which disaggregated data is available, although withinthe context of a larger population. This dynamics is modeled through a state-space model, whichenables the estimation of the unknown abundance (latent process) by exploring its dependencerelation with the observational data on this species fishing landings in that area. For this, thepopulation is partitioned into length groups and the population evolution process is sub-dividedinto biological sub-processes that are assumed to always happen in the same order (survival tonatural death, length-class transition, displacement by migration and survival to fishery). Theestimation is achieved within a Bayesian paradigm, where all the available biological information isincorporated into the sub-processes parameters prior distributions.

Short-term trajectories of the population living in IXa are studied via simulations that are con-structed based on different management scenarios. The consequences of the scenarios are evaluatedthrough the analysis of the resulting trends and by considering the associated uncertainties.

Biological Invasions in the AzoresOrganizer: Ricardo TeixeiraDepartamento de Matematica da Universidade dos AcoresSeptember 2nd, 14:15-15:15, Auditorio 3

Marine invasions in offshore islands: a case study from the Macaronesia regionJoao Canning-Clode1,2,3,∗, Paula Chainho 3, Paul Fofonoff 2, Linda McCann 2, James T. Carlton 4, Gregory

Ruiz 2 and Ricardo Serrao Santos1

1 Centre of IMAR of the University of the Azores, Department of Oceanography and Fisheries/UAz &

LARSyS Associated Laboratory, Portugal2 Smithsonian Environmental Research Center, USA3 Center of Oceanography, Faculty of Sciences, University of Lisbon, Portugal4 Williams College - Mystic Seaport, Mystic, CT, USA∗canning-clode@uac.pt

While terrestrial introductions have been well documented on many island ecosystems and continueto be the focus of extensive work in invasion biology, studies on marine invasions on most of theworld’s islands have been poorly explored. Three island systems in the Pacific Ocean (New Zealand,Hawaiian Islands and Guam) and one in the Atlantic Ocean (Azores) are exceptions. Although theability to compare and evaluate the extent of invasions between island and mainland systems isaccompanied by a number of restraints, some studies predict that impacts of marine non-indigenousspecies (NIS) on biodiversity, as for terrestrial systems, will be greatest on islands. In contrast, otherstudies found no evidence that native marine biotas of islands are more severely affected by invasions

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compared to continental biotas. These contrasting hypotheses thus await more rigorous examinationas more data become available. To expand our understanding of the scale and diversity of foulingmarine bioinvasions on insular systems, we examine here the marine bioinvasions of Macaronesia,consisting of four archipelagos: Azores, Madeira, Canary Islands and Cape Verde. We performedthe first extensive literature review of records of fouling NIS in Macaronesia and have complementedthis search with data from ongoing field surveys in some of the islands. We recognize 54 NIS in theregion and relate these numbers with critical variables, including latitude, ship traffic, distance tomainland ports and anthropogenic activities.

Invasions versus endemisms: quantitative approaches to the study of invasive and rareplants in the AzoresLuıs Silva 1,∗

1 CIBIO, Centro de Investigacao em Biodiversidade e Recursos Geneticos, InBIO Laboratorio Associado,

Polo dos Acores, Departamento de Biologia, Universidade dos Acores, 9501-801 Ponta Delgada, Portugal∗lsilva@uac.pt

Endangered and invasive species are two faces of the ongoing biodiversity changes. In the Azores, wehave been quantifying plant biodiversity using different analytical approaches. Species lists, expertand manager knowledge was used in risk analysis of invasive and endangered species [1,2]. EcologicalNiche Factor Analysis estimated the potential distribution of invasive species and several methodsevaluated the genetic structure of endemic species [3]. A Bayesian approach quantified communitychanges along a gradient of anthropogenic disturbance and a spatial analysis estimated the potentialimpact of plant invaders in Island Natural Parks. Presently, we are addressing community assem-blages and indicator species and the conservation value of land areas. A better understanding ofthe practical and philosophical implications of using statistical methods in biology will benefit froma closer interaction between users, developers and theorists in both fields.

[1] Martın JL, MJ Arechavaleta, PAV Borges, B Faria. 2008. Top 100. Las cien especies amenazadas priori-tarias de gestion en la region europea biogeografica de la Macaronesia. Consejeria de Medio Ambiente yOrdenacion Territorial, Gobierno de Canarias.

[2] Silva L, E Ojeda Land, JL Rodrıguez Luengo. 2008. Invasive terrestrial flora and fauna of Macaronesia.Top 100 in Azores, Madeira and Canaries. ARENA, Ponta Delgada.

[3] Costa H, SC Aranda, P Lourenco, V Medeiros, EB Azevedo, L Silva. 2012. Predicting successful replace-ment of forest invaders by native species using species distribution models: The case of Pittosporumundulatum and Morella faya in the Azores. Environmental Monitoring and Assessment, 279: 90:96.

Predicting the spread of the drywood termite Cryptotermes brevis using MaximumEntropy algorithms and Agent Based Modeling approachesOrlando Guerreiro 1,∗, Miguel Ferreira 2, Jose Cascalho 3, Paulo Borges 1

1 Azorean Biodiversity Group and Plataform for Enhancing Ecological Research & Sustainability, Departa-

mento de Ciencias Agrarias, Universidade dos Acores, Angra do Heroısmo, Portugal2 Centro de Astrofısica da Universidade do Porto, R. das Estrelas, Porto3 Centro de Matematica Aplicada e Tecnologias de Informaao (CMATI), Universidade dos Acores, Portugal∗orlandogue@gmail.com

Cryptotermes brevis is a drywood termite that has recently become a pest in the major cities of theAzores Archipelago with large economical and patrimonial losses. There are important questionsthat remain to be answered. In particular, it is not known whether the species has the ability tospread to as yet unaffected towns or if its spread is limited by local climate and environmentalconditions. Also, the spatial-temporal dynamics of the propagation of the infestation, and the mostcost effective way of controlling it, are still to be determined.

We apply a maximum entropy model (Maxent) to determine the potential locations in the Azoreswhere C. brevis can spread to. This model requires local and worldwide environmental and climate

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data and the locations where the species is known to be present, to forecast the probability ofinfestation.

We have also constructed a model of the spread of the infestation in the particular urbanenvironment of Angra do Heroısmo, Azores, using an agent based modeling approach. The modelwas built in steps of increasing complexity taking into account the ecology of the species and witha continuous cross-checking of the results obtained with the field data. We have also introduceddifferent control strategies and evaluated their costs.

We find that, in general, the probability of occurrence is higher near the coast line, where themajority of the towns and villages are located so that infestation has potential to spread to yetunaffected towns and islands.

Our model of the spread of the infestation predicts a region of infestation that is similar to theknown map of infestation. The model predicts that virtually no houses inside the infested regioncan remain uninfested, even when the probability of infestation is relatively low, and this is indeedwhat is observed in the field. Some preliminary results suggest that coordination of the pest controlagents is important to provide a solution to the problem.

Dynamics, Modelling and OptimisationOrganizer: Joao Paulo AlmeidaInstituto Politecnico de BragancaSeptember 2nd, 14:15-15:15 and 15:30-16:30, Sala 1

Solving Flexible Job Shop Scheduling using Genetic AlgorithmAna I. Pereira 1,2, Ana Curralo 1, Jose Barbosa 1,3, Paulo Leitao 1,4

1 Instituto Politecnico de Braganca, Portugal.2 Algoritmi, Universidade do Minho, Portugal.3 Univ. Lille Nord de France, France & UVHC, TEMPO research center, France.4 LIACC, Portugal.

This work addresses a real assembly cell: the AIP-PRIMECA cell at the Universite de Valencienneset du Hainaut-Cambresis, in France. This system can be viewed as a Flexible Job Shop, leadingto the formulation of a Flexible Job Shop Scheduling Problem (FJSSP). This FJSSP offers thepossibility to create the products ”AIP”, ”LATE” and ”BELT” using by five workstations, eachone being able to perform a set of operations, that are linked using a conveyor system. Thetransportation between stations is achieved using a shuttle which is able to transport one productat the time, being released after the product processing conclusion.

The problem consists in finding a operations schedule on the machines, taking into account theprecedence constraints minimizing the batch makespan, i.e., the finish time of the last operationcompleted in the schedule.

To solve the flexible job shop the genetic algorithm (GA) was used to obtain the global solution.As opposed to many other optimization methods, genetic algorithm works with a population ofsolutions instead of one single solution. In the GA the solutions are combined to obtain newsolutions until obtain a satisfactory solution. The genetic algorithm is a stochastic method, whosemechanism is based on the simplifications of evolutionary process observed in nature: crossover,mutation and selection.

[1] N. Al-Hinai, T. ElMekkawy, Solving the Flexible Job Shop Scheduling Problem with Uniform ProcessingTime Uncertainty, World Academy of Science, Engineering and Technology 64, pp. 996-1001, 2012.

[2] M. Kumar, M. Husian, N. Upreti, D. Gupta, Genetic Algorithm: Review and Application, InternationalJournal of Information Technology and Knowledge Management, 2(2), pp. 451-454, 2010.

[3] C. Pach, A. Bekrar, T. Bonte, Y. Sallez, T. Berger, D. Trentesaux, P. Leitao and J. Barbosa, Benchmark-ing flexible job-shop scheduling and control systems, Control Engineering Practice 21, pp. 1204-1225,2013.

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Clustering Techniques Applied on Cross-Sectional Unemployment DataCarlos Balsa 1,∗, Alcina Nunes 1, Elisa Barros1

1 Instituto Politecnico de Braganca, Portugal∗balsa@ipb.pt

An important strategy for data classification consists in organising data points in clusters. Thek-means [1] is a traditional optimisation method but other methods, like spectral clustering [2],exist as alternative cluster methods to classify data.

Using a labour market database from diferent economic contexts (different years), we suggestthe application of alternative methods based on clustering techniques. The idea is to understand ifan approach to different economic labour market frameworks, using distinct clustering approaches,could affect the expected results.

[1] J. B. MacQueen. Some Methods for classification and Analysis of Multivariate Observations. In Proceed-ings of 5-th Berkeley Symposium on Mathematical Statistics and Probability, University of CaliforniaPress 1, 281-297, 1967.

[2] A. Y. Ng and M. I. Jordan and Y. Weiss. On spectral clustering: Analysis and an algorithm. In Advancesin Neural Information Processing Systems (NIPS) 14, 849-856, 2002.

Anosov diffeomorphisms and tilingsJoao P. Almeida 1,2 and Alberto A. Pinto2,3

1 Instituto Politecnico de Braganca, Portugal.2 LIAAD - INESC TEC, Portugal.3 University of Porto, Portugal.

Inspired in the works of Y. Jiang [3] and A. Pinto and D. Sullivan [10], A. Pinto et al. [5] introducedthe notion of golden tiling and proved the existence of a natural correspondence between goldentilings, smooth conjugacy classes of Anosov diffeomorphisms with invariant measure absolutely con-tinuous with respect to Lebesgue measure and solenoid functions. Here we extend their result andintroduce the notion of γ-tiling. Like the golden tilings, the γ-tilings record the infinitesimal geo-metric structure determined by the dynamics of an Anosov diffeomorphism G along the unstableleaf that is invariant under the action of G. The properties of γ-tilings are defined using a decom-position of natural numbers that we call γ-Fibonacci decomposition. The main contribution of thiswork consists in understanding the way how this γ-Fibonacci decomposition encodes the combina-torics determined by the Markov partition of G along the unstable leaf. Our goal is to exhibit anatural correspondence between γ-tilings, smooth conjugacy classes of Anosov diffeomorphisms withinvariant measure absolutely continuous with respect to Lebesgue measure and solenoid functions.

[1] Almeida, J. P. and Pinto, A. A.: Anosov diffeomorphisms and γ-tilings. (2013), 1–25 (submitted).

[2] de Faria, E., de Melo, W. and Pinto, A.: Global hyperbolicity of renormalization for Cr unimodalmappings. Annals of Mathematics, 164, 731–824 (2006).

[3] Jiang, Y.: Metric invariants in dynamical systems. Journal of Dynamics and Differentiable Equations,Vol. 17 (1), 51–71 (2005).

[4] de Melo, W. and Pinto, A.: Rigidity of C2 infinitely renormalization for unimodal maps. Communicationsof Mathematical Physics, 208, 91–105 (1999).

[5] Pinto, A. A., Almeida, J. P. and Portela, A.: Golden tilings. Transactions of the American MathematicalSociety, 364 (2012), 2261–2280.

[6] Pinto, A. A. and Rand, D. A., Solenoid functions for hyperbolic sets on surfaces. Dynamics, ErgodicTheory and Geometry: Dedicated to Anatole Katok (ed. Boris Hasselblat) MSRI Publications, 54, (2007),145-178.

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[7] Pinto, A. A. and Rand, D. A., Rigidity of hyperbolic sets on surfaces. J. London Math. Soc., 71, 2 (2004),481-502.

[8] Pinto, A. A. and Rand, D. A., Smoothness of holonomies for codimension 1 hyperbolic dynamics. Bull.London Math. Soc., 34, (2002), 341-352.

[9] Pinto, A. A., Rand, D. A., Ferreira, F., Fine structures of hyperbolic diffeomorphisms. Springer-VerlagMonograph (2008).

[10] Pinto, A. A. and Sullivan, D., The circle and the solenoid. Dedicated to Anatole Katok On the Occasionof his 60th Birthday. DCDS -A 16, 2 (2006), 463-504.

Rivers and the Stock Market

Renato Fernandes 1, Ricardo Cruz 1, Alberto Pinto 1

1 Faculdade Ciencias, Universidade do Porto

The BHP distribution has been found to be useful in modeling various natural and human phenom-ena. We will fit flows of the Paiva river for the BHP, and apply the same tools for stock marketflows. The river flow from the first and latter decades is examined to test against climate change.

[1] R. Goncalves, H. Ferreira, A. Pinto, N. Stollenwerk. Universality in nonlinear prediction of complexsystems. In Journal of Difference Equations and Applications 15:11-12, 1067-1076, 2009.

[2] R. Goncalves, H. Ferreira, A. Pinto. Universality in the stock exchange market In Journal of DifferenceEquations and Applications 17:7, 1049-1063, 2011.

PDE’s and Calculus of VariationsOrganizer: Ana Margarida Ribeiro and Rita FerreiraFCT-UNL and IST-UTL & FCT-UNLSeptember 2nd, 14:15-15:15, Sala 2

3D-2D dimensional reduction for a nonlinear optimal design problem with perimeterpenalizationGraca Carita 1

1 Universidade de Evora

We studied the worst possible design of a two-phase mixture of elastic materials in a thin film inthe same spirit of [3] and [2] where the asymptotic analysis of a two-field minimization problem hasbeen studied as the thickness of the sample tends to zero. Having in mind the results contained in[1] and [4], we introduce a perimeter penalization in our functional in order to derive from the 3Denergy a limiting 2D model.

[1] Ambrosio, L., Buttazzo, G., “An optimal design with perimeter penalization”, Calc. Var. Partial Differ.Equ., 1, no. 1 (1993), 55-69.

[2] Braides, A., Fonseca, I., Francfort, G., “3D-2D asymptotic analysis for inhomogeneous thin films”, IndianaUniv. Math. J., 49, no. 4, (2000), 1367-1404.

[3] Fonseca, I., Francfort, G., “3D-2D asymptotic analysis of an optimal design problem for thin films”, J.Reine Angew. Math, 505, (1998), 173-202.

[4] Lin, F. H., Kohn, V., “Partial regularity for optimal design problems involving both bulk and surfaceenergies”, Chin. Ann. of Math. Ser. B 20, No. 2, (1999), 137-158.

A geometrical view of the Nehari manifoldJose Maria Gomes 1

1 Faculdade de Ciencias e Tecnologia da Universidade Nova de Lisboa

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We study the Nehari N manifold associated to the boundary value problem

−∆u = f(u), u ∈ H10 (Ω),

where Ω is a bounded regular domain in Rn. Using elementary concepts of Differential Geome-try such as the principal curvatures of an hypersurface, we provide a local description proving inparticular the existence of an exterior tangent sphere at any point in N .

Second order analysis for non local isoperimetric problems in microphase separationGiovanni Pisante 1

1 Seconda Universita di Napoli

Aim of the talk is to discuss some recent results on a non-local isoperimetric problem arising asthe sharp interface limit of the Ohta-Kawasaki free energy introduced to model microphase separa-tion of diblock copolymers. Performing a second order variational analysis is possible to provide aquantitative second order minimality condition. More precisely it can be shown that critical config-urations with positive second variation are indeed strict local minimizers of the nonlocal perimeter.Moreover, via a suitable quantitative inequality of isoperimetric type, an estimate of the deviationfrom minimality for configurations close to the minimum in the L1 topology is provided.

Chaotic Dynamics in Growth modelsOrganizer: Jose Leonel RochaInstituto Superior de Engenharia de Lisboa -ISEL, IPLSeptember 2nd, 15:30-16:30, Auditorio 3

An Extension of Gompertzian Growth Dynamics: Weibull and Frechet ModelsSandra M. Aleixo 1,∗, J. Leonel Rocha 1

1 Instituto Superior de Engenharia de Lisboa - ISEL, ADM and CEAUL, Portugal∗sandra.aleixo@adm.isel.pt

In this work a new dynamical approach to an extension of the Gompertz law is proposed. Ageneralized family of probability density functions, designated by Beta∗(p, q), which is proportionalto the right hand side of the Tsoularis-Wallace model, is studied. In particular, for p = 2, theinvestigation is extended to the extreme value models of Weibull and Frechet type. These models,described by differential equations, are proportional to the hyper-Gompertz growth model. Thedynamical analysis is performed using techniques of symbolic dynamics and the system complexityis measured using topological entropy. Generally, the natural history of a malignant tumour isreflected through bifurcation diagrams, in which are identified regions of regression, stability, perioddoubling, chaos and terminus.

Synchronizaton in Richards’ chaotic systemsAcilina Caneco 1,∗, Sandra M. Aleixo 1, J. Leonel Rocha 1

1 Instituto Superior de Engenharia de Lisboa - ISEL, ADM and CEAUL, Portugal∗acilina@adm.isel.pt

In this work we established new one-dimensional discrete dynamical systems: a family of unimodalmaps that is proportional to the right hand side of Richards’ growth equation. We investigatein detail the bifurcation structure of Richards’ functions, on the two-dimensional parameter space(β, r), where β is the shape parameter, related with the growth-retardation phenomena, and ris the intrinsic growth rate. Sufficient conditions are provided for the occurrence of extinction,stability, period doubling, chaos and non admissibility of Richards’ dynamics. We consider networkshaving in each node a Richards’ function. We prove some results about the synchronization levelwhen fixing the network topology and changing the local dynamics expressed by the Lyapunov

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exponents, which depends on the (β, r) parameters. Moreover, we fix the local dynamics and proveresults about the synchronization when the network topology change for some kind of networks.Finally, using numerical simulations, we compute the Lyapunov exponents to measure the systemcomplexity, we obtain synchronization intervals of these networks, and we discuss the evolution ofthe synchronization level in terms of the parameters Richard’s function.

Discrete-valued time seriesOrganizer: Isabel PereiraUniversidade de AveiroSeptember 2nd, 15:30-16:30, Sala 2

Multivariate models for integer-valued time seriesMaria Eduarda Silva 1

1 Center for Research and Development in Mathematics and Applications Faculdade de Economia, Univer-

sidade do Porto, Portugal

Time series of counts are available in a wide variety of fields and the need to analyse such dataadequately led to a multiplicity of approaches and a diversification of models that explicitly accountfor the discreteness of the data. One such approach consists in replacing the multiplication in theconventional ARMA models by an appropriate random operator, denominated thinning operator,originating the so called INARMA models. In the context of univariate time series of counts, theclass of INARMA models has been widely studied in the literature and applied in many differentcontexts. However, for multivariate time series of counts several difficulties arise and the literatureis not so elaborate. In this work we address the problem of modelling univariate and multivariatetime series of counts using thinning based models. The models and methods are illustrated insimulated and real data sets.

Threshold Models in Time Series of CountsIsabel Pereira 1

1 Center for Research and Development in Mathematics and Applications. Departamento de Matematica,

Universidade de Aveiro

In this work we extend the SETINAR class of self-exciting threshold integer-valued autoregressivemodels introduced by Monteiro et al (2010), considering general orders in the INAR processes ofeach regime. Basic probabilistic and statistical properties of this class of models are discussed.Moreover, parameter estimation is also addressed, considering the least squares conditional methodand likelihood methodology through EM algorithm. Using MCMC algorithm with data augmenta-tion, devised by Neal and Subba Rao (2007) for a general INARMA(p, q) process with known ordersp and q, Bayesian estimates for the parameters are obtained. Based on Enciso-Mora et al (2009)work it is considered the problem of order selection of r and s for SETINAR (2; r, s) model con-structing a Reversible Jump Markov Chain Monte Carlo algorithm (RJMCMC). Finally, in orderto assess inferential performance and RJMCMC algorithm capabilities it is conducted a simulationstudy.

[1] Enciso-Mora, V., Neal, P.J. and Subba Rao, T. (2009) Efficient order selection algorithms for integer-valued ARMA processes. Journal of Time Series Analysis, 30 1-18.

[2] Monteiro, M., Pereira, I. and Scotto, M.G. (2010). Integer-Valued Self-Exciting Threshold AutoregressiveProcesses. Communications in Statistics - Theory and Methods

[3] Neal, P.J. and Subba Rao, T. (2007). MCMC for integer valued ARMA processes. Journal of Time SeriesAnalysis, 28, 92-110.

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A periodic bivariate Integer-valued Autoregressive model - An application to fire ac-tivityMagda Monteiro1

1 Center for Research and Development in Mathematics and Applications Escola Superior de Tecnologia e

Gestao de Agueda, Universidade de Aveiro

In the last years the study of count series models has been subject of great interest with the focuscentered on univariate models. More recently Pedeli and Karlis (2011) presented a bivariate integer-valued autoregressive model (BINAR) whose generalization is carried out in this work through theintroduction and study of a BINAR(1) model with periodic structure. Basic probabilistic andstatistical properties of the model are discussed and the emphasis is placed on models with periodicbivariate Poisson innovations. Moreover, parameter estimation and forecasting are also addressed.Since Poisson distribution have equidispersion we also analyze the case where the innovations haveother bivariate periodic distribution. The work finishes with an empirical application to a set ofdata concerning the monthly number of fires in Aveiro and Coimbra districts.

[1] Pedeli, X., Karlis, D., 2011. A bivariate INAR(1) process with application. Statist. Model. 11, 325-349.

Optimal Alarm Systems and its Application to the INAPARCH modelMaria da Conceicao Lopes Costa1, Manuel G. Scotto, Isabel S. Pereira1 Center for Research and Development in Mathematics and Applications. Departamento de Matematica,

Universidade de Aveiro

An alarm system is an algorithm which, based on current information, predicts whether a level-crossing event is going to occur at a specified time in the future. In the last few decades, it hasbeen recognized the potential of optimal alarm systems in detecting and warning the occurrenceof catastrophes, and the spectrum of applications of optimal alarm systems is wide and yet tobe explored. In this work an optimal alarm system is developed, and a particular application ispresented in the econometrics area. Regarding the interesting characteristics of the APARCH(p, q)representation for financial time series, we propose the introduction of the INteger-valued Asym-metric Power ARCH, INAPARCH(p, q), as a possible counterpart for modeling time series of counts.The probabilistic properties of the INAPARCH(1, 1) model are studied and the conditional max-imum likelihood (ML) estimation method is developed. The implementation of an optimal alarmsystem to the INAPARCH(1, 1) model is done and an application is presented to two data seriesconcerning the number of transactions in stocks.

Some economic applicationsOrganizer: Alberto A. Alvarez LopezUNED, SpainSeptember 3rd, 10:30-11:30, Auditorio 3

Emancipation and Household FormationOrlando Montoro 1

1 UNED, Spain

This paper initiates a novel pathway in the estimation of the population and its trends in the typeand composition of households that form, starting with the study of young people dependent ontheir parents to be emancipated. To maximize the information available the model breaks downthe process of emancipation in three levels; fist level It is decided whether to leave the parentalhome, second level it is decided whether to form a new home or leave the country and third levelit is chosen between living alone or starting a domestic partnership. Each level is estimated with

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a binary logit of characteristics of the target population that includes gender, age, working status,average income of the individual, the family home average income and year of leaving home.

Quantification of functional efficiency in energy futures marketsMeliyara Consuegra 1

1 UNED, Spain

This paper proposes a method to estimate the functional efficiency of energy futures markets interms of social welfare. Using a standard futures markets structural model, it can be concludedthat the error committed when using futures prices at moment t to predict spot prices at t + 1results in welfare losses through resource misallocation. Therefore, the social welfare associatedwith the presence of energy futures markets can be measured using a social loss (SL) statistic andits components. This statistic is computed for six energy futures contracts with eight maturities eachwith data from April 1992 to December 2012. The results confirm the consistency and robustnessof the method. Finally, several practical uses for the SL statistic are suggested.

Entropy and negentropy: applications in Game TheoryEduardo Oliva 1

1 UNED, Spain

Since the early works of Carnot, Clausius and Boltzmann, entropy has proven to be one of themost fruitful concepts in science. Although originally devised to study heat engines, entropy playsa fundamental role in such different fields as thermodynamics, cosmology, biology, informationtheory and, recently, economics. This talk will focus in the economic application. We will applythe entropy ordering of Cabrales, Gossner and Serrano to coordination games in which differentinformation structures are available for the agents.

Properties and comparative-static effects in models of decision under uncertainty: ap-plications to the theory of the firmAlberto A. Alvarez-Lopez 1

1 UNED, Spain

We consider a simple model of decision under uncertainty, in which a representative risk-averse agentmaximizes the expected utility of a random wealth. The wealth is postulated in a quite generalform, especially concerning the effect of the decision variable, so that other decision problems underuncertainty can be considered as particular cases of this model. In this general framework, wepropose a new method to readily obtain both properties of the optimal solution and comparative-static effects. We illustrate the usefulness of this formulation by applying it to some models fromthe theory of the firm under uncertainty. In these models we are able to easily derive their keyproperties, and also new results.

Graphs and CombinatoricsOrganizer: Domingos CardosoCIDMA, DMat, Universidade de AveiroSeptember 3rd, 10:30-11:30, 11:45-12:45 and 14:15-15:15 / September 4th, 10:30-11:30 and11:45-12:45, Sala 1

The maximum k-regular induced subgraph problemSofia J. Pinheiro 1,∗, Domingos M. Cardoso 1

1 CIDMA, DMat, Univ. de Aveiro∗spinheiro@ua.pt

Many optimization problems on graphs are reduced to the determination of a subset of vertices ofmaximum cardinality which induces a k-regular subgraph. We denote this maximum cardinality by

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αk(G). Since the determination of the order of a k-regular induced subgraph is in general a NP-hardproblem, it is crucial to find upper bounds determined in polynomial time as good approximations.In this presentation some upper bounds on αk(G) are proposed and an extension to arbitrarygraphs of the convex quadratic upper bound introduced in Cardoso, Kaminski, and Lozin [J. Comb.Optim., 14, 455-463, 2007] for regular graphs is presented. Based on this approach, new spectralupper bounds on the order of maximum size k-regular induced subgraphs are deduced. Finally afew computational experiments are presented.

(0, 2)-regular sets and applicationsMaria de Fatima Pacheco 1,∗, Domingos M. Cardoso 2, Carlos J. Luz1 Polytechnic Inst. of Braganca, CIDMA, Univ. de Aveiro2 CIDMA, DMat, Univ. de Aveiro∗pacheco@ipb.pt

A (κ, τ)-regular set in a graph is a subset of vertices inducing a κ-regular subgraph and such thateach vertex not in the set has exactly τ neighbors in it. We will present a new algorithm for thedetermination of (0, 2)-regular sets in line graphs as well as its application to the determination ofmaximum matchings in arbitrary graphs.

The construction of the poset of regular exceptional graphs using equitable partitionsInes Barbedo 1,∗, Domingos M. Cardoso 2, Paula Rama1 Polytechnic Inst. of Braganca, CIDMA, Univ. de Aveiro2 CIDMA, DMat, Univ. de Aveiro∗inesb@ipb.pt

An exceptional graph is a connected graph with least eigenvalue greater than or equal to −2 which isnot a generalized line graph. In [3] it is shown that the set of regular exceptional graphs is partitionedin three layers. A (κ, τ)-regular set is a subset of the vertices of a graph, inducing a κ-regularsubgraph such that every vertex not in the subset has τ neighbors in it [2]. In [1] a new recursiveconstruction of regular exceptional graphs is proposed, where each regular exceptional graph of thefirst and the second layer is constructed by a (0, 2)-regular set extension. In this talk we presentan algorithm based on this recursive construction and show that this technique induces a partialorder relation on the set of regular exceptional graphs. The process of extending a graph is reducedto the construction of the incidence matrix of a combinatorial 1-design, considering several rulesto prevent the production of isomorphic graphs, and we show that each regular exceptional graphhas an equitable partition which, by this construction technique, is extended with a new element,the set of the additional vertices. The recursive construction is generalized to the construction ofarbitrary families of regular graphs, by extending a regular graph G with another regular graphH such that V (H) is a (κ, τ)-regular set of the regular graph produced. This technique is used toconstruct the exceptional regular graphs of the third layer. The Hasse diagrams of the posets of thethree layers are presented.

[1] D.M. Cardoso and D. Cvetkovic.

Graphs with least eigenvalues -2 attaining a convex quadratic upper bound for the stability number., Bull.Acad. Serbe Sci. Arts, Cl. Sci. Math. Natur., Sci. Math., CXXXIII (31):41–55, 2006.

[2] D. M. Cardoso and P. Rama, Spectral results on regular graphs with (κ, τ)-regular sets, Discrete Math.(307) 1306-1316, 2007.

[3] D. Cvetkovic, P. Rowlinson and S. Simic. Spectral Generalizations of line graphs: on graphs with leasteigenvalue -2, Cambridge University Press, Cambridge, 2004.

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Matchings and orthogonality of symmetrized tensorsMaria Manuel Torres 1,∗, Jose Perdigao Dias da Silva1 CELC, DMat, Univ. de Lisboa∗mmanuel@ptmat.fc.ul.pt

Many scheduling problems are stated in terms of edge colorings on bipartite graphs, that is, decom-positions by disjoint matchings covering the entire edge set. We will show how the orthogonality ofcertain symmetrized tensors can be described by a scheduling condition.

Graph Decomposition: A blend of Turan numbers and Ramsey numbersTeresa Maria Sousa 1,∗, Henry Liu1 DMat, FCT-Univ. Nova de Lisboa∗tmjs@fct.unl.pt

Let H = (H1, . . . ,Hk) be a fixed k-tuple of graphs and let G be a graph on n vertices whose edgesare colored with k colors. A monochromatic H-decomposition of G is a partition of its edge setsuch that each part is either a single edge or a copy of Hi monochromatic in color i. The aim isto find the smallest number, denoted by f(n,H, k), such that, any k-edge colored graph with nvertices admits a monochromatic H-decomposition with at most f(n,H, k) parts. We will considerthe problem when H is a fixed k-tuple of cliques (a clique is a complete graph) for all values of k.The results presented will involve both the Turan numbers and the Ramsey numbers.

Topological Indices of graphsPaula Carvalho 1,∗, Paula Rama1 CIDMA, DMat, Univ. de Aveiro∗paula.carvalho@ua.pt

A topological index of a graph is a numerical parameter that is mathematically derived fromthe structure of the graph. Many topological indices emerged in Chemical Graph Theory in thedevelopment of new relationships between the physico-chemical properties of a molecule and itschemical structure, represented by a graph. In this talk we focus on the modified Schultz index:S∗ =

∑u,v dG(u)dG(v)distG(u, v). We consider some graph operations, namely cartesian product,

complete product, composition and subdivision, and we obtain explicit formulae for the modifiedSchultz index of a graph in terms of the number of vertices and edges as well as some other topo-logical invariants such as the Wiener index, the Schultz index and the first and second Zagrebindices.

Min-max regret robust shortest path problem in a finite multi-scenario modelM. Pascoal 1,∗, Marisa Resende1 INESC-Coimbra, DMat, Univ. de Coimbra∗marta@mat.uc.pt

The min-max regret robust shortest path problem is a classical problem based on the determinationof a path with the minimal maximum deviation from the shortest path between a pair of nodes ina given network. The research on this subject has been mainly focused on interval data models.Nevertheless, for discrete models with a bounded number of scenarios the problem has receivedlittle attention. In this talk the min-max regret robust shortest path problem is defined consideringa finite number of scenarios, and some properties of the optimal solutions are presented. Twotypes of methods are then proposed, the first is a labelling approach and the second is based onthe ranking of paths by order of cost. Two variants of the latter method are described. Oneconsists of ranking paths in every scenario and of using a stopping condition dependent on costupper bounds given by the paths that are computed, the other improves this version by includingfurther reduction techniques. The performances of the three algorithms are compared based oncomputational experiments performed on randomly generated networks.

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A Generalization of the Krein parameters and some admissibility conditions for stronglyregular graphsVasco Moco Mano 1,∗, Enide A. Martins and Luis A. Vieira1 DMat, Univ. do Porto∗vascomocomano@gmail.com

In this work, we describe a Jordan-algebraic approach to the theory of strongly regular graphs. Inparticular, we associate a three dimensional Euclidean Jordan algebra to the adjacency matrix ofa strongly regular graph. With this approach, we generalize the Krein parameters and derive thegeneralized Krein admissibility conditions for such graphs. In light of these generalizations, we wereable to extract further information over the classical Krein parameters and obtain some tight upperbounds for some of the generalized Krein parameters.

Some results on the modified Schultz indexPaula Rama 1,∗, Paula Carvalho1 CIDMA, DMat, Univ. de Aveiro∗prama@ua.pt

The topological indices are graph invariants much studied in both mathematical and chemicalliterature. The modified Schultz index, also known as the Gutman index, is defined as S∗(G) =∑u,v⊂V (G)

d(u)d(v)dist(u, v), where d(u) is the degree of vertex u and dist(u, v) is the distance

between vertices u and v. In this talk, we present several results on the modified Schultz index,in particular, we determine a lower bound of the modified Schultz index of tricyclic graphs withthree cycles and n vertices, that is, connected graphs of order n with exactly three cycles, and wecharacterize all extremal graphs which attain the lower bound.

Singleton free set partitions avoiding a 3-element setRicardo Mamede 1,∗

1 CMUC, DMat, Univ. de Coimbra∗mamede@mat.uc.pt

The definition and study of pattern avoidance for set partitions, which is an analogue of patternavoidance for permutations, begun with Klazar. Sagan continued his work by considering setpartitions which avoids a single partition of three elements, and Goyt generalized these results byconsidering partitions which avoids any family of partitions of a 3-element set. We continue this workwith the enumeration and description of set partitions, even set partitions and odd set partitionswithout singletons which avoids any family of partitions of a 3-element set. The characterizationof these families allows us to conclude that the corresponding sequences are P -recursive. We alsoconstruct Gray codes for the sets of singletons free partitions that avoids a single partition of threeelements.

Maps and hypermaps with large symmetry groupRui Duarte 1,∗

1 CIDMA, DMat, Univ. de Aveiro∗rduarte@ua.pt

Maps and hypermaps are cellular embeddings of graphs and hypergraphs into closed surfaces. Anautomorphism or symmetry of a hypermap H is an incidence-preserving permutation of each ofthe sets of vertices, edges and faces. In this talk we present some families of hypermaps with largesymmetry group. We also present some constructions of hypermaps and their properties.

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Shannon switching games and directed variantsIlda Perez da Silva 1,∗, Luıs Sequeira1 CELC, DMat, Univ. de Lisboa∗ipsilva@fc.ul.pt

Shannon switching game is a combinatorial game modeling break down repair of a network. Thegame was completely solved by Lehman in 1963. In the late 1980’s Y.O. Hamidoune and M. LasVergnas introduced and studied directed versions of the game. Despite the results obtained so far,Hamidoune-Las Vergnas directed switching games are still far from being completely understood.We will do a brief account of results and open questions on the subject.

Growth diagrams, crystal operators and Cauchy kernel expansionsOlga Azenhas 1,∗, A. Emami1 CMUC, DMat, Univ. de Coimbra∗oazenhas@mat.uc.pt

We formulate the reverse RSK and an analogue of RSK for pairs of certain combinatorial objects,in the framework of Fomin’s growth diagrams. We recall crystal operators as operators on words,introduced by Lascoux and Schutzenberger in the study of the plactic monoid, and later rediscoveredby Kashiwara and Nakashima in the theory of crystal bases to define crystal graph. These tools arethen used to regain expansions of non symmetric Cauchy kernels over Ferrers shapes in type A.

Dynamical models and data analysis in epidemiologyOrganizer: Nico StollenwerkCMAF, Universidade de LisboaSeptember 3rd, 10:30-11:30 and 11:45-12:45, Sala 2

Modelling dengue fever epidemiology: complex dynamics and its implication for dataanalysisMaira Aguiar 1

1 CMAF, Universidade de Lisboa

Dengue fever dynamics is well known to be particularly complex with large fluctuations of dis-ease incidences. Mathematical models describing the irregular behaviour of dengue epidemics areparametrized on data referring to incidence and ultimately aim to be used as a predictive tool thatcan be used by the public health authorities of disease control. In dengue fever epidemiology thereare four antigenically related but distinct serotypes, raising many complications in the analysis andinterpretation of the available incidence data. Antibodies generated by exposure to any one strainare known to be cross-reactive for other strains, but they are believed only to provide strain-specificlifelong immunity to reinfection, whereas subsequent infections by other serotypes (one of the threeheterologous serotypes) increase the risk of developing severe dengue. The high antibody titersattained after primary infection appear to generate a degree of cross-protection for a while, butif secondary exposure occurs after antibody levels begin to decline, cross-reactivity appears to actto enhance the growth rate of the new invading viral strain. This is called antibody-dependentenhancement and its occurrence in dengue has been used to explain the etiology of severe disease.Multi-strain dengue models are often modelled with SIR-type models where the SIR classes arelabelled for the hosts that have seen the individual strains. In this talk, we present a set of modelsmotivated by dengue fever epidemiology and compare different dynamical behaviours originatedwhen increasing complexity into model framework, anticipating that temporary cross-immunityand difference between primary and secondary infections appear to be the key factors determiningdisease transmission, outcome of infection and epidemics. These models are parametrized on theoficial notification dengue data from Bureau of Epidemiology, Ministry of Public Health in Thailand.The extended models show complex dynamics and qualitatively a very good result when comparingempirical data and model simulations.

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Understanding dengue fever dynamics: study of seasonality in the modelsFilipe Rocha 1

1 CMAF, Universidade de Lisboa

The dengue fever dynamics present seasonality being more active during the warmer seasons. Inthis paper we analyse seasonally forced epidemic models with and without vector dynamics. Wefind out the analytic solution for the real response of each state variable and also the respectiveamplitude and phase. The analysis started by the simplest SIS, followed by the simplest model withvectors dynamic SISUV. Finally we compare the more complicated SIR and SIRUV models and weconcluded that the models give basically the same information when we multiply the infection rateof humans by the infection rate of mosquitos over their life span in the SIR model.

Spatial epidemiological models, superdiffusionUrszula Skwara 1

1 CMAF, Universidade de Lisboa∗urszula@ptmat.fc.ul.pt

Spreading of disease does not only happen from person to its geografical neighbour but often overwide distances when infected but asymptomatic people travel and carry infection to others overwide distances. Therefore superdiffusion has been suggested to model such spreading in spatiallyrestricted contact networks, i.e. there is still a notion of geographical distance, but spreadinghappens with high probability for large distances. From fractional calculus several ways of describingsuperdiffusion are know. Laplace operator can be generalized to super-diffusive case using fractionalcalculus. We apply the integral representation of the fractional Laplace operator to epidemiologicalmodels, especially to spatial SIS model.

Bayesian Model Comparison and Semiclassical Approximations in Population BiologyLuis Mateus 1

1 CMAF, Universidade de Lisboa

We begin by presenting two simple stochastic epidemiological models which have the advantage ofbeing analytically treatable in full up to the point where the major quantity for model comparison,the Bayes factor, can be computed. We then compare one model against the other in the Bayesianframework, both models performing on the same simulated data. The concepts illustrated withthese models can be applied to more complex ones, even if most of the steps have to be performednumerically.

In cases where analytical solutions cannot be given easily we approximate Markovian stochasticprocesses, also called master equations in theoretical physics. Several schemes have been proposed,among which the so called semiclassical approximations. We will describe such approximations fora still simple, yet not analytically treatable, SIS model.

Evolution towards critical fluctuations and Self-Organized Criticality (SOC) in a sys-tem of accidental pathogensPeyman Ghaffari 1,2,∗ and Nico Stollenwerk 1

1 CMAF, Universidade de Lisboa2 Complexity and Networks Group, Imperial College London, United Kingdom∗peyman@ptmat.fc.ul.pt

In models for accidental pathogens, with the paradigmatic epidemiological system of bacterialmeningitis, evolution towards states exhibiting critical fluctuations with power law behavior wasobserved [5]. This is a model with many possibly pathogenenic strains evolving independently to lowpathogenicity. Previous study had shown that in the limit of vanishing pathogenicity there are crit-ical fluctuations with power law distributions, even when only two strains interact [4]. The earlier

43

version of a two strain model was very recently reinvestigated [1]and named as Stollenwerk-Jansen(SJ) model. Munoz et al. demonstrated recently that this two-strain model for accidental pathogensis in the universality class of the so-called voter model. Though this model clearly shows signs ofcriticality, its control parameter, the pathogenicity, is not self-tuning towards criticality. However,the multi-strain version mentioned above is well evolving towards criticality [5], as well as a spatiallyexplicit version of this [6]. The models of multi- strain type including explicitly mutations of thepathogenicity are called SJ-models of type II [7, 8]. Since the original epidemiological model is ofSIRYX-type the evolution to zero pathogenicity is slow and perturbed by large population noise.In the present work we show based on the motion of the voter-model universality classes the evolu-tion of n-voter models with mutation towards criticality, now much less perturbed by populationnoise. In this we find the system to evolve to low pathogenicity causing large critical fluctuationsleading to a power-law distributed behaviour without tuning the control parameter meaning thepathogenicity ”, a self- organization of critcality [2]. This model has wide implications for manydiseases in which a large proportion of infections is asymptomic. This holds not only for the originalparadigmatic case of bacterial meningitis, but was also suggested for instance also for dengue fever.

[1] Pinto, O.A., & Munoz, M.A. (2011) Quasi-neutral theory of epidemic outbreaks, PLoS ONE 6, e21946.

[2] Jensen, H.J. (1998) Self-organized criticality, emergent complex behaviour in physical and biological sys-tems (Cambridge University Press, Cambridge).

[3] Stollenwerk, N., & Jansen, V. (2010) Population biology and criticality (Imperial Col- lege Press, London).

[4] Stollenwerk, N., & Jansen, V.A.A. (2003, a) Meningitis, pathogenicity near criticality: the epidemiologyof meningococcal disease as a model for accidental pathogens. Journal of Theoretical Biology 222, 347–359.

[5] Stollenwerk, N., & Jansen, V.A.A. (2003, b) Evolution towards criticality in an epi- demiological modelfor meningococcal disease. Physics Letters A 317, 87–96.

[6] N. Stollenwerk and V. Jansen (2011) Population Biology and Criticality: From critical birth-death pro-cesses to self-organized criticality in mutation pathogen systems (Imperial Colledge Press, World Scientific,London)

[7] P. Ghaffari, V. Jansen and N. Stollenwerk, Evolution towards critical fluctua- tions in a systemof accidental pathogenes, ICNAAM 2011, Chalkidiki, 1263–1266 (Numerical Analysis and AppliedMathematics ICNAAM 2011 AIP Conf. Proc. 1389, 1224–1227 (2011); doi: 10.1063/1.3637837

[8] P. Ghaffari and N. Stollenwerk, Evolution of N-species Kimura/Voter models towards criticality,surrogate for general models of accidental pathogens, AIP Conf. Proc. 1479, 1331 (2012);doi:10.1063/1.4756401

Parameter estimation in complex systemsNico Stollenwerk 1

1 CMAF, Universidade de Lisboa

To describe fluctuations in dengue long term fever time series from Thailand and neighbouringSouth East Asian countries where dengue is endemic, multi-strain models with temporary cross-immunity and differences in primary versus secondary infection turned out to be adequate (Aguiaret al., JTB, 2011, and references therein). For such systems with deterministically chaotic skeletonand complex interplay between population stochasticity and chaoticity, characterized by Lyapunovexponents, including coexistences of several attractors, methods from parameter estimation andmodel comparison have been developed recently, namely iterated (Stollenwerk et al., Interface Focus2012, and references therein). We investigate several approximation schemes, among which Fokker-Planck- and Hamilton-Jacobi-approximations to speed up the notoriously computationally intensivestochastic simulation for such filtering methods to make them feasable for e.g. the complex dengue

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models to finally (i) predict future outbreaks in endemic areas and (ii) to transfer the knowledge todescribe present and future invasion scenarios of dengue fever into new world areas (as part of theEU-project DENFREE).

Multiscale tales in epidemiologyMax Souza 1

1 Universidade Federal Fluminense, Brazil

We shall concentrate on two problems: the first one is the dynamics of a SIR-SI model for ar-boviruses. In this case, we shall show how a natural dichotomy in time-scales appear and leads toa reduced model that fully approximates the original one. The second problem is the study of astochastic SIS model for large, but finite populations. We shall obtain a PDE that contains all therelevant information of the model and, in the infinity population limit, recovers the classical SISmodel. If time allows we may discuss further applications to ecological and evolutionary models.

[1] Fabio A. C. C. Chalub & Max O. Souza, From discrete to continuous evolution models: A unifyingapproach to drift-diffusion and replicator dynamics, Theoretical Population Biology, 76 (4) 268–277,2009.

Dynamical Systems and BifurcationsOrganizer: Alexandre RodriguesFCUP, CMUPSeptember 3rd, 11:45-12:45, Auditorio 3

Global Dynamics for Symmetric Planar MapsSofia B. S. D. Castro 1,∗

1 Faculdade de Economia and Centro de Matematica, Universidade do Porto∗sdcastro@fep.up.pt

We consider sufficient conditions to determine the global dynamics for equivariant maps of the planewith a unique fixed point which is also hyperbolic. When the map is equivariant under the action ofa compact Lie group, it is possible to describe the local dynamics and – from this – also the globaldynamics. In particular, if the group contains a reflection, there is a line invariant by the map.This allows us to use results based on the theory of free homeomorphisms to describe the globaldynamical behaviour. In the absence of reflections, we use equivariant examples to show that globaldynamics may not follow from local dynamics near the unique fixed point.

This is joint work with Begona Alarcon (Department of Mathematics, University of Oviedo)and Isabel S. Labouriau (Centro de Matematica, Universidade do Porto), reported in [1] and [2].

[1] B. Alarcon, S.B.S.D. Castro and I.S. Labouriau, Global Dynamics for Symmetric Planar Maps, Discreteand Continuous Dynamical Systems – series A, Vol. 33 (6), 2241 – 2251 (2013)

[2] B. Alarcon, S.B.S.D Castro and I. Labouriau. A local but not global attractor for a Zn-symmetric map,

Proceedings of the 2nd Workshop on Generic Geometry and Applications — Journal of Singularities, vol.6, 1–14 (2012)

Splitting of separatrices near a Hamiltonian-Hopf bifurcationJose Pedro Gaivao 1,∗

1 CEMAPRE, ISEG, Universidade Tecnica de Lisboa∗jpgaivao@iseg.utl.pt

45

We study the splitting of separatrices near a subcritical Hamiltonian-Hopf bifurcation. It is wellknown that the normal form of the Hamiltonian describing this bifurcation is integrable. Therefore,to measure the splitting of separatrices we need to devise a method capable of detecting exponen-tially small phenomena. Our main result is an asymptotic expansion for a homoclinic invariantwhich quantitatively describes the splitting of separatrices.

Rotation numbers for planar attractors of equivariant homeomorphismsBegona Alarcon 1,∗

1 Departamanto de Matematicas, Universidad de Oviedo, Spain∗alarconbegona@uniovi.es

This work is motivated by the study of the global behavior of a planar map having a fixed pointwhich is asymptotically stable but is not a global attractor.

Let f : R2 → R2 be an orientation preserving homeomorphism with a fixed point which is nota global attractor and its basin of attraction is unbounded. In that case, the theory of Prime Endsdue to Caratheodory is applied and f induces an orientation preserving homeomorphism f? in thespace of prime ends. Since this space is homeomorphic to the circle, it is possible to associate arotation number to f being the rotation number of f?.

Under these condition periodic orbits different from the fixed point will appear when the rotationnumber is rational. However the converse seems to be a very difficult problem with interesting andstrong applications. One way to tackle this problem is assuming that f has some symmetry.

Actually, we might think that the presence of the Zm–symmetry implies that the rotation numberof the homeomorphism should be rational. One consequence would be that the asymptotically stablefixed point is a global attractor if and only if there are no periodic points different from the fixedpoint.

In this talk we will prove the existence of Zm–equivariant and dissipative homeomorphismswith an asymptotically stable fixed point such that the induced map in the space of prime ends isconjugated to a Denjoy map, which is also Zm–equivariant.

[1] B. Alarcon, Rotation number for planar attractors of equivariant ho- meomorphisms, To appear in Topo-logical Methods in Nonlinear Analysis.

On C2-stability of HamiltoniansMaria Joana Torres 1, Mario Bessa 2, Jorge Rocha 31 CMAT, Univ. Minho2 Univ. Beira Interior3 Univ. Porto

We consider the setting of Hamiltonian systems H ∈ C2(M,R), defined on a 2d-dimensional sym-plectic manifold M (d ≥ 2). We address the following results, that we proved recently:

• A Hamiltonian star system is Anosov. As a consequence we obtain the proof of the stabilityconjecture for Hamiltonians. This generalizes the 4-dimensional results in [1].

• A Hamiltonian system H is Anosov if any of the following statements holds: H is robustlytopologically stable; H is stably shadowable; H is stably expansive; and H has the stable weakspecification property. Moreover, for a C2-generic Hamiltonian H, the union of the partiallyhyperbolic regular energy hypersurfaces and the closed elliptic orbits, forms a dense subset ofM . As a consequence, any robustly transitive regular energy hypersurface of a C2-Hamiltonianis partially hyperbolic. Finally, stably weakly shadowable regular energy hypersurfaces arepartially hyperbolic.

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[1] M. Bessa, C. Ferreira and J. Rocha, On the stability of the set of hyperbolic closed orbits of a Hamiltonian,Math. Proc. Cambridge Philos. Soc., 149 (2) (2010), 373–383.

[2] M. Bessa, J. Rocha and M. J. Torres, Hyperbolicity and Stability for Hamiltonian flows, Jr. Diff. Eq., 254(1) (2013), 309–322.

[3] M. Bessa, J. Rocha and M. J. Torres, Shades of Hyperbolicity for Hamiltonians, arXiv 2012.

Evolutionary games and economyOrganizer: Elvio AccinelliFacultad de Economia de la UASLPSeptember 3rd, 14:15-15:15, Auditorio 3

Migrant behavior by imitationEdgar J. Sanchez Carrera 1,∗, Elvio Accinelli 1, Osvaldo Salas 2

1 Facultad de Economıa, UASLP Mexico2 School of Public Administration, University of Gothenburg∗edgar.carrera@uaslp.mx

Migration has an important impact in the economic development and in social welfare both indeveloping countries as in developed countries. While the number of empirical studies on migrationis relatively large, the literature that considers formal models describing migration behavior ofincreasing importance in the world, is scarce. Hence this paper aims to introduce a theoreticalapproach to explain the strategic foundations of the migrant behavior. We claim that a preferencefor migration is transmitted through imitation, and then we study the evolutionary dynamics ofthis imitation process. We show that there exists a threshold value of the share of innovative firmsexisting in a given country, such that if in a given country, this percentage is below to the thresholdvalue, then a process of emigration of skilled workers to outside is observed, while inside of thecountry we find a process of imitation of the behavior followed by unskilled workers. To reverse thistwofold process the central planner need to develop a economic policy tending to lower the cost ofeducation and at the same time, to encourage the growth of the share of innovative firms in thecountry.

On the dynamics of corruption and polluting firmsElvio Accinelli 1,∗, Laura Policardo 2, Edgar J. Sanchez Carrera 1

1 Facultad de Economıa, UASLP Mexico2 Department of Economics, University of Siena, Italy∗elvio.accinell@eco.uaslp.mx

We develop a model of briber’ firm facing a pollution standard and bribed official inspecting theirpollution level. Officials follow an imitative behavior of the most successful to decide whetherto be corrupt or not. Instead firms maximize inter-temporal profits. We study the evolutionarydynamics of corrupt officers by imitation while firms maximize profits with/without compromisingenvironmental quality. We show that a multiplicity of equilibria exist from stable corruption,through officer controlled corruption, via multiple equilibria to honesty by imitation on behalf ofreviewing officers and the share of nonpolluting firms. The main parameters to get a good outcomeare fines, bribes and environmental cost of production (together with the discount rate).

Extremes and other statistical properties of dynamical systemsOrganizer: Jorge FreitasUniversidade do portoSeptember 3rd, 14:15-15:15, Sala 2

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Limiting behaviour of high order quantiles estimatorsLaura Cavalcante 1

1 CMUP and FCUP, Portugal

The study of extreme or rare events is of great relevance in a wide variety of fields. The adequateestimation of high order quantiles is one of the most important problems as it allows a robust statisti-cal inference. We consider here the problem of estimating high order quantiles using geometric-typeestimators and show, in particular, the asymptotic normality of the resulting estimators. We ap-ply the proposed estimators to the analysis of real data sets and illustrate the performance of theestimators using simulated data.

Rare events for random dynamicsHale Aytac 1

1 CMUP and FCUP, Portugal

In this talk, we will explain how we get laws of rare events for randomly perturbed dynamicalsystems using the link between Extreme Value Laws (EVL) and Hitting/Return Time Statistics(HTS/RTS). Mainly, we will consider random perturbations of uniformly expanding systems, suchas piecewise expanding maps of the circle, and show that for additive absolutely continuous (w.r.t.Lebesgue) noise, the limiting distribution is standard exponential for any point. Our main ingredientwill be decay of correlations against all L1 observables in a suitable Banach space and due to theabove link we get our results by means of the first return time from a set to itself.

Piecewise smooth dynamicsOrganizer: Jose Pedro GaivaoISEG, UTLSeptember 3rd, 15:30-16:30, Auditorio 3

Invisibility and retro-reflection in billiardsAlexander Plakhov 1

1 Universidade de Aveiro

We consider the problem of invisibility for bodies with mirror surface within the scope of geometricaloptics. The problem amounts to studying billiards in the exterior of bounded regions. Examplesof bodies invisible in 1, 2, and 3 directions and bodies invisible from 1 and 2 points are providedin the talk. It is proved that there do not exist bodies invisible in all directions. The questionof maximum number of directions and/or points of invisibility of a body remains open. Further,we consider retro-reflecting bodies with mirror surface. A body is called a perfect retroreflector, ifthe direction of any beam of light incident on it is changed to the opposite. We provide severalexamples of asymptotically retro-reflecting sequences of bodies. On the other hand, it is not knownif there exist perfect billiard retroreflectors.

A joint discontinuity and singularity induced bifurcation arising in a Cournot-RamseymodelPaulo Brito 1

1 ISEG-UTL

Piecewise smooth dynamical systems and singular dynamical are studies in different literaturesand using different approaches. In particular, there does not seems to exist a bifurcation theoryencompassing both discontinuity and singularity induced bifurcations. In this paper, we present aCournot-Ramsey model in which both types of bifurcations can jointly occur and present a methodto characterize it locally.

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Complex dynamics in pendulum-type equations with variable lengthAlessandro Margheri 1

1 FCUL

We prove the existence of complex dynamics for a generalized pendulum type equation with variablelength. The solutions we find switch from an oscillatory behavior around the stable vertical positionto a rotational type behavior crossing the unstable position with positive or negative velocity follow-ing any prescribed two-sided sequence of symbols. Moreover, to any periodic sequence of symbolscorresponds a periodic solution of the equation. The proof is based on a topological approach andthe results are robust with respect to small perturbations. In particular a small friction term canbe added to the equation.

BiomathematicsOrganizer: Jose MartinsSchool of Technology and Management, Polytechnic Institute of Leiria; LIAAD-INESC TECSeptember 3rd, 15:30-16:30, Sala 1

A recursive approximation to the quasi-stationary distribution in epidemiological mod-elsJ. Martins 1, A. Pinto, N. Stollenwerk1 Polytechnic Institute of Leiria and LIAAD-INESC TEC

For the stochastic SIS model, we derive recursively the dynamic equations for all the moments,through cumulant neglection, and we develop a recursive method to compute the equilibria manifoldof the moment closure ODE’s. We observe that the stable equilibria in moment closure can be usedto give a good approximation of the quasi-stationary mean value of infected. The approximationsobtained through this method are crucial when the quasi-stationary distribution is highly skewed,which is more likely the case when either the population size is small or the infection rate is smallor both.

An adaptive approach for skin lesion segmentation in dermoscopy images using a multi-scale Local NormalizationJorge Pereira 1

1 Instituto de Telecomunicacoes - Leiria

Skin cancer is one of the most common malignancy in humans. Early detection of suspicious skinsigns is critical to prevent this kind of malignancies. Dermatologists uses dermatoscopy to performearly diagnosis of melanocytic lesions, and to track the progression thereof.

The classification of some melanocytic lesions is sometimes difficult, even for experienced spe-cialists. The lesion border is especially relevant for diagnosis since it allows to gather informationabout the shape of the lesion, growth path, and growth rate. Digital image processing methodscan be used to perform automatic lesion border detection, nonetheless, the presence of artifactsmay induce artificial borders, thereby jeopardizing the efficiency of automatic detection algorithms.Artifact removal is a required pre-processing step to improve the quality of the border accurateidentification.

The present method starts removing this non-desirable data right on the color transformationfrom RGB to gray scale, by using a weighted average of all three channels, allowing with this amore accurate separation on the image histogram of the skin lesion data and other image typicaldata, like some artifacts.

This process is then based on several applications of the Local Normalization, which is a methodthat increases the local contrast between local pixels, improving the overall quality of the image,especially with non-uniform illumination. Being a scale sensitive method it allows, by using different

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order scales to create ROI for all images and then using a multi-scale approach that can adaptsuccessfully to every skin lesion shape and size.

An Overview of Quantitative Compound TestsRui Santos 1

1 School of Technology and Management, Polytechnic Institute of Leiria; CEAUL - Center of Statistics and

Applications of University of Lisbon

Economic dynamics and computationOrganizer: Paulo B. VasconcelosFaculdade Economia Porto and Centro Matematica da UPSeptember 3rd, 15:30-16:30, Sala 2

The dynamics of a cycle smoothing policy in a discrete stochastic growth model withtaxesTiago Pinheiro1

1 Faculdade Economia Porto

Growth economic models play a crucial role in understanding countries development, inter-countrymacroeconomic relationship, and, ultimately, to anticipate the effects on endogenous variables dueto political shocks on model parameters or exogenous variables. The ability to simulate, underinitial assumptions, is, assuredly, a priceless tool for policy makers to take decisions and to adaptthem along the time. We present a discrete stochastic growth model to assess fiscal policy goals,namely, those of government spending stability. This framework is well suited for the Europeancountries under the Stability and Growth Pact (SGP), a rule-based framework for the coordinationof national fiscal policies in the economic and monetary union (EMU). Reference to the steadystate of the model as well as to the required stability conditions for the convergence of the iterativeprocess will be undertaken. Illustrative computer simulations will be provided, allowing for a clearunderstanding on the magnitude of the effects over economic recession or expansion.

The Macrodynamics of Employment under UncertaintyPaulo Mota1

1 Faculdade Economia Porto and NIFIP

This paper analyses the effect of uncertainty in the macrodynamics of employment. This topic is ofmajor importance in the context of the current euro zone crisis. At a first step a Non-Ideal Relay-type microeconomic model of employment adjustment with uncertainty is presented. Then, anaggregation mechanism is explicitly considered in order to analyse the aggregate level of employment.Finally, as a new feature, uncertainty is considered endogenously determined by the actual state ofthe economy. Aggregate time-series built from micro monthly data on a representative sample ofPortuguese manufacturing firms is used on a computational implementation of the linear play modelof hysteresis. Results show that uncertainty enhances the hysteretic behaviour of employment insmall firms, but this effect is not significant for large ones.

Dynamic Political Effects in a Neoclassic Growth Model with Healthcare and CreativeActivitiesOscar Afonso1

1 Faculdade Economia Porto and CEF.UP

By considering microeconomic foundations, the Ramsey-Cass-Koopmans (RCK) model has made agreat impact in the economic growth literature; however, the long-term economic growth remainsunexplained (e.g., Acemoglu 2009). In the original RCK model, agents maximize their lifetime

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utility, dependent on the consumption level, and their labour supply is assumed to be constant.These assumptions are restrictive; for example, the number of hours worked by each individualis not constant through time and leisure, in which healthcare and creative activities are included,affects positively the utility (e.g., Fogel 2000, Ramey and Francis 2009). The paper extends theRCK model to cope with its weakness, allowing that a well-known and established model be usedto analyse the economic growth effects arising from governmental policies (e.g., Irmen and Kuehnel,2009). In line with Fogel (2000) and Ramey and Francis (2009), among others, the utility function ismodified to consider the fraction of time each individual devotes to healthcare and creative activities.In this context, governmental expenditures financed by lump-sum taxes and inefficient expenditureslead to a decrease in the short, medium and long-run economic growth.

Industry Dynamics and Aggregate StabilityPedro Mazeda Gil1

1 Faculdade Economia Porto and CEF.UP

This paper presents an endogenous growth model of directed technical change with vertical andhorizontal R&D to study an analytical mechanism that is consistent with the coexistence of ag-gregate stability and structural change. We focus on changes in the share of the high- versusthe low-tech sectors in the context of a slow, but flexible, transitional dynamics that arises froma dynamic system with a three-dimensional stable manifold. Under the hypothesis of a positiveshock in the proportion of high-skilled labour, the technological-knowledge bias channel leads tononbalanced sectoral growth, while the aggregate variables remain approximately constant and thusconsistent with the Kaldor facts. With prevailing market-scale effects, a calibration exercise showsthat the model is able to account for around two-thirds of the increase in the share of the high-techmanufacturing sectors observed in European data from 1995 to 2007.

Bio-DynamicsOrganizer: Bruno OliveiraFCNA, University of PortoSeptember 3rd, 17:00-18:00, Sala 1

Equilibria when considering asymmetric death rates for active and inactive T cells andTregsIsabel Figueiredo 1

1 FC - University of Porto and ISEP - Polythecnic Institue of Porto.

We analyse a model of immune response by T cells (CD4), where regulatory T cells (Tregs) actby inhibiting IL-2 secretion. We introduced an asymmetry reflecting that the difference betweenthe growth and death rates can be higher for the active T cells and the active Tregs than for theinactive T cells and inactive Tregs. This asymmetry can mimic the effect of memory T cells. Wepresent an explicit formula that give the concentration of T cells as a function of the concentrationof Tregs and an explicit formula that relate the antigenic stimulation of T cells, the concentrationof T cells and the concentration of Tregs.

Immune response dynamics by T cells with asymmetry in the death ratesBruno Oliveira 1

1 FCNA and INESC TEC - University of Porto

We analyse a model of immune response by T cells (CD4), where regulatory T cells (Tregs) act byinhibiting IL-2 secretion. We introduced an asymmetry reflecting that the difference between thegrowth and death rates can be higher for the active T cells and the active Tregs than for the inactiveT cells and inactive Tregs. This asymmetry can mimic the effect of memory T cells. The presenceof the asymmetry enhances the immune response by the T cells, in particular in the bystander

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proliferation case. When considering a tuning between the antigenic stimulation of T cells and the(self) antigenic stimulation of Tregs, we find a transcritical bifurcation, for some parameter values.The presence of this transcritical bifurcation can play a role on the appearance of autoimmunityfor low values of the antigenic stimulation of T cells.

A mathematical model of carbon life in vineyardsJoao Coelho 1,∗, A. A. Pinto 1, P.B. Vasconcelos 2

1 Department of Mathematics, Faculty of Science, U. Porto, PT.2 Department of Mathematics and Information Systems, Faculty of Economy, U. Porto, PT.∗up200804736@fc.up.pt

In this presentation will be shown a model of the behaviour of Carbon in the different structures of avine, based on reference [1], with some stochastic modifications. How is the development of shoots,leaves and grapes? How much Carbon they consume? Which are the probabilities associated withstructures growth? This model answers these questions and some results will be shown with realdata collected in the Douro vineyards region that is UNESCO World Heritage Site.

[1] Wermelinger, B., Baumgartner, J., Gutierrez, A.P. A demographic model of assimilation and allocationof carbon and nitrogen in grapevines Ecological Modelling, 53 (1991) 1-26 1990;

Investing to reduce the production costs in a Cournot duopolyJoana Becker 1

1 FC - University of Porto

We analyse a duopolistic Cournot competition model, where both firms can invest to reduce theirproduction costs according to the Ferreira, Oliveira e Pinto R&D investment function. We char-acterize the associated game and study the economical effects derived from using this new R&Dinvestment function. We find regions with one, two and three Nash equilibria of the investmentin the reduction of the production costs. Changing the values of the parameters can dramaticallychange the size of the regions with multiple Nash equilibria.

Coupled Cell NetworksOrganizer: Celia MoreiraUniversity of Porto (CMUP)September 4th, 10:30-11:30, Auditorio 3

Exploring coupled cell networksC.S. Moreira 1,∗

1 Centro de Matematica da Universidade do Porto∗celiasofiamoreira@gmail.com

In this talk we motivate and introduce the theory of coupled cell networks. We also consider thecellular splitting process and present a result that is useful to compare the dynamics in the originalnetwork and in the network resulting from a splitting.

Coupled cell networks and the synchrony latticeM. A. D. Aguiar 1, Ana Paula S. Dias 2,∗

1 Faculdade de Economia, Centro de Matematica, Universidade do Porto2 Departamento de Matematica da Faculdade de Ciencias, Centro de Matematica, Universidade do Porto∗apdias@fc.up.pt

A coupled cell network is a finite set of nodes (or cells) linked together by a finite number ofarrows. Dynamical systems (systems of ordinary differential equations) that are consistent with

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this network structure are called the coupled cell systems. The existence of certain flow-invariantsubspaces, defined in terms of equalities of certain cell coordinates (the synchrony subspaces) for allthe associated coupled cell systems is forced by the coupled cell network. We show how to obtainthe lattice of synchrony subspaces of a network based on the eigenvalue structure of the networkadjacency matrices and we present an algorithm that generates the lattice.

[1] M.A.D. Aguiar and A.P.S. Dias. Synchrony in Coupled Cell Networks. In Journal of Nonlinear Scienceaccepted for publication pending minor revisions (2013).

Synchrony and graph operations on coupled cell networksM.A.D. Aguiar 1,∗, A.P.S. Dias 2, H. Ruan 3

1 Centro de Matematica & Faculdade de Economia, Universidade do Porto2 Centro de Matematica & Departamento de Matematica, Universidade do Porto3 Fachbereich Mathematik, Universitat Hamburg∗maguiar@fep.up.pt

A network is a set of units that are organized by mutual interactions. Networks are utilized inmodeling many real world problems in a wide range of scientific fields and have become a subject ofvast research interest in recent years. Among others, networks can be used to graphically representcoupled dynamical systems, where time evolution of individual systems influence one another.

Most real world networks are evolving networks, that is, their topology evolves with time, eitherdue to a rewiring of a link, the appearance or disappearance of a link or node, or by a merging ofsmall networks into a larger one. The dynamics of network topology reflects frequent changes in theinteractions among network components and translates into a rich variety of evolutionary patterns.

One widely observed and most studied collective dynamics in coupled dynamical systems is thesynchronization, where phase trajectories of two or more coupled units coincide over time. Thesubspaces that are defined by equalities of cell coordinates and left invariant under every coupledcell system respecting the given network structure are called synchrony subspaces. These form acomplete lattice under set-inclusions.

As the lattice of synchrony subspaces of a coupled cell system can be determined solely by theunderlying network structure, it is natural and of interest to ask how the lattice evolves as theunderlying topology of the network changes. In this perspective, in [1] we consider non-productbinary operations on networks such as the join and the coalescence. Classification results areobtained for synchrony subspaces of the combined network, which clarify the relation between thelattice of synchrony subspaces of the combined network and its components.

In [2] we evaluate the impact of structural changes in network topology on the lattice of balancedequivalence relations of the network, through elementary graph operations such as addition and/ordeletion of cells and/or edges, and/or rewiring of edges. As one can expect, the lattice of balancedequivalence relations changes in general: some relations persist, some disappear and some emerge.In particular, we describe necessary and sufficient conditions for balanced equivalence relations topersist or disappear.

[1] M.A.D. Aguiar and H. Ruan. Evolution of Synchrony under Combination of Coupled Cell Networks.Nonlinearity 25, 3155-3187, 2012.

[2] M.A.D. Aguiar, A.P.S. Dias and H. Ruan. Synchrony and Elementary Operations on Coupled Cell Net-works. CMUP-Preprint 2013-7, 2013.

Hopf bifurcation in coupled cell networks with abelian symmetryRui C. Paiva 1,∗, Ana Paula S. Dias 2

1 Escola Superior de Tecnologia e Gestao do Instituto Politecnico de Leiria, Morro do Lena - Alto do Vieiro

2411-901 Leiria Apartado 4163.

Centro de Matematica da Universidade do Porto, Rua do Campo Alegre, 687, 4169-007 Porto, Portugal.

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2 Departamento de Matematica Pura, Faculdade de Ciencias da Universidade do Porto, Centro de Matematica

da Universidade do Porto, Rua do Campo Alegre, 687, 4169-007 Porto, Portugal.∗rui.paiva@ipleiria.pt

We consider symmetric coupled cell networks of differential equations. We show that already at thelevel of Abelian symmetry, very degenerate codimension-one bifurcations can occur. This degeneratebehaviour occurs due to the restrictions that the symmetry group of the network and the networkstructure impose at the associated coupled cell networks of differential equations. Our results arebased at the properties of the complex irreducible characters of abelian groups. We determinegeneric conditions involving the complex characters of the symmetry group that permit in oneparameter the occurrence of Hopf bifurcation associated to the crossings with the imaginary axis oftwo or more distinct pairs of complex eigenvalues of linearization.

[1] F. Antoneli and I. Stewart. Symmetry and synchrony in coupled cell networks 1: fixed-point spaces, Int.J. Bif. Chaos 16 (3), 559-577, 2006.

[2] F. Antoneli and I. Stewart. Symmetry and synchrony in coupled cell networks 2: group networks, Int. J.Bif. Chaos 17 (3), 935-951, 2007.

[3] A.P.S. Dias and J.S.W. Lamb. Local bifurcation in symmetric coupled cell networks: linear theory, PhysicaD 223, 93-108, 2006.

[4] J.B. Fraleight. A First Course in Abstract Algebra (Fourth Edition), Addison-Wesley, New York 1989.

[5] M. Golubitsky and R. Lauterbach. Bifurcations from synchrony in homogeneous networks: linear theory,SIAM J. Appl. Dyn. Syst. 8 (1) (2009).

[6] G. James and M. Liebeck. Representations and Characters of Groups, 2nd ed. Cambridge UniversityPress, New York 2001.

[7] I. Stewart, M. Golubitsky and M. Pivato. Symmetry groupoids and patterns of synchrony in coupled cellnetworks, SIAM J. Appl. Dynam. Sys. 2 (4), 609-646, 2003.

Marine Systems for Ocean Exploration and Exploitation: Theory and PracticeOrganizer: Fatima Leite and Antonio PascoalUniversidade de Coimbra and Universidade Tecnica de LisboaSeptember 4th, 10:30-11:30 and 11:45-12:45, Sala 2

Cooperative Motion Control of Multiple Autonomous Marine Vehicles: Science andTechnologyA. Pascoal 1

1 LARSyS/ISR-Lisbon, IST, Lisbon, PT,

This talk addresses the general topic of cooperative motion control of marine vehicles, both froma theoretical and a practical standpoint. The presentation is rooted in practical developments andexperiments. Examples of scientific mission scenarios with autonomous surface vehicles (ASVs) andautonomous underwater vehicles (AUVs), acting alone or in cooperation, set the stage for the maincontents of the presentation. From a theoretical standpoint, special attention is given to a numberof challenging problems that include cooperative motion control of fleets of autonomous vehicles.The efficacy of the systems developed has been shown during real tests at sea. Recent resultson cooperative motion control with applications to the development of devices for robot-assisteddiving operations are also described. The results are illustrated with videos from actual field testswith multiple marine robots. The core material presented in the talk was obtained in the scopeof the GREX (http://www.grex-project.eu), CO3AUVs (http://www.co3-auvs.org), and MORPH(http://morph-project.eu/) projects of the EC.

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Dynamic Optimization Control for Autonomous Vehicle SystemsFernando Lobo Pereira 1

1 ISR-Porto and FEUP, Porto, PT

Systems involving multiple networked autonomous vehicles interacting with one another, with otherdevices, and with human operators are increasingly being considered in order to address the, typi-cally, large scale and long term challenging issues that humankind is bound to face. The sophisti-cation of data gathering and actuation requirements implies a huge diversity of state and controlconstraints - such as the ones arising in the specifcation of formations of vehicles, or induced bycommunication processes, etc. - that have to be considered in the formulation of control problems.Moreover, resources onboardthe vehicles, such power, space, communication and computational ca-pabilities are at a premium and therefore, these vehicle systems have to be controlled so that theoverall resources are optimized. Thus, optimal control is a paradigm of choice to support the syn-thesis of control strategies for autonomous vehicle systems. Moreover, the rich body of theory thathas been consolidated over the years provides not only insight into solutions but also mechanismsfor their characterization and computation. Maximum principles, value function based control, andmodel predictive control are some of the results and techniques that will be considered in this pre-sentation reporting some of the research undertaken at Porto University to address optimal controlchallenges arising in the control of autonomous vehicles and in the coordinated control of teams ofthese vehicles.

Potential Field Inverse Problems: from Geophysical Prospecting to Autonomous Un-derwater NavigationF. Curado 1

1 Centre for Environmental and Marine Studies (CESAM) & Geosciences Dept. University of Aveiro, PT

This talk describes novel methods for 3D localization of robotic underwater vehicles based on theobservation of magnetic field anomalies present in the surveyed environment. The approach pro-posed borrows from the theories of classical electrodynamics and geopotential field inversion. Thework discusses the relative advantages and limitations of the deterministic inversion methods versusthe stochastic approach for this particular application and introduces a new analytic formulationdesigned to stabilize the solution of the inverse problem in real-time. Using similar inversion meth-ods a procedure is developed to track a moving object based on its associated disturbance of theenvironmental magnetic field. We envision the integration of these methods in underwater navi-gation and tracking systems. The theoretical developments described are complemented with theresults of computer simulations using realistic scenarios.

Ocean acoustic propagation modeling and communication in the vicinity of submergedstructuresA.J. Silva 1, O.C. Rodrıguez 1, and S.M. Jesus1

1 SiPLAB, FCT - Univ. of Algarve, Campus de Gambelas, Faro, PT

Autonomous underwater vehicle (AUV) navigation relies heavily on point-to point acoustic com-munications with a surface ship or with underwater companions. Transmission and reception ofacoustic packets depends significantly on the impulse response of the acoustic channel which, asrelative distances increase, can be described by acoustic propagation models well designed for theunderwater environment. In complex environments, as near submerged structures, underwatercanyons or sea mountains the reflection of sound energy from the bottom, walls, and sea surface in-duces a complex behaviour of the impulse response, whose anticipation is of the utmost importancefor the prediction of communications performance and for mission planning.

The communication performance of two AUVs, navigating in formation for the inspection ofan underwater canyon, is evaluated through simulations over a real bathymetry, using a two-dimensional (2D) and a three-dimensional (3D) acoustic propagation model. The behaviour of2D and 3D models is analysed in terms of eigenrays and corresponding impulse responses, and the

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communication performance is evaluated considering the resulting intersymbolic interference andimpulse response length.

Range-based localization of nodes in underwater acoustic networks through convexrelaxationJ. Gomes 1

1 LARSyS/ISR-Lisbon, IST, Lisbon, PT

Similarly to terrestrial applications, there is currently a strong emphasis on networked operation ofmultiple assests to efficiently carry out missions in underwater scenarios. Importantly, because GPSis unavailable in the ocean, absolute or relative positions must be determined by other means, oftenthrough time-of-flight measurements of acoustic transmissions between assets. The present workfocuses on acoustic positioning techniques based on pairwise range or range-difference measurementsthat enable the locations of several unknown nodes in an acoustic network (e.g., underwater vehiclesoperating in coordination) to be jointly determined. This differs from GPS-like systems where asingle node is to be located relative to a set of known reference points (anchors). The approachis based on reconstruction and factorization of Euclidean Distance Matrices (EDM), which offers asolid framework to deal with noisy measurements and partial loss of data, while providing a compactmathematical formulation. When absolute range measurements are available EDM reconstructionis formulated as a convex optimization problem that can be handled by general-purpose solvers withlittle a priori information on the spatial configuration of the network. This approach can handleeither squared ranges (the most common option) or plain ranges, for improved tolerance to outliermeasurements.

Ranges can be inferred from round-trip times between pairs of nodes, complemented by observeddifferences between arrival times of packets broadcast over the network. The latter are key forefficent usage of very limited communication resources, but incorporating them into the EDMreconstruction framework destroys the convexity when some of the measurements are not available.This work discusses strategies for handling the non-convexity of the joint node localization problem,and characterizes the performance of efficient interrogation schemes that can be used in practiceto obtain the required ranges or range differences. Algorithms are tested with simulated data formulti-node networks, as well as experimental data for a simple three-node network.

Cooperative Marine Vehicle NavigationA. Pedro Aguiar 1

1 LARSyS/ISR-Lisbon and FEUP, Porto, PT

This talk presents the last results obtained in the scope of the European projects CO3AUVs andMORPH in the general topic of single and cooperative navigation of marine autonomous roboticvehicles. In particular, special attention is given to a number of challenging problems that includeobservability analysis and observer design to solve the localization problem of an Autonomous Un-derwater Vehicle using relative range measurements to beacons whose locations are also unknown.This is done by taking explicitly into account the presence of complex vehicle dynamics and severeacoustic-based navigation and communication constraints, where the latter are imposed by inter-mittent failures and latency. Experimental results with a Medusa-type robotic vehicle are presentedand discussed.

Interest Rate, Credit Risk and Investment ModelsOrganizer: Claudia NunesIST/CEMATSeptember 4th, 11:45-12:45, Auditorio 3

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Investment, suspension or exit from the market, in a declining marketClaudia Nunes 1

1 IST/CEMAT

We study the problem of a firm that produces with a current technology for which it faces a decliningsales volume. It has three options: it can either exit this industry, suspend production or invest ina new technology with which it can produce an innovative product. We distinguish between twoscenarios in the sense that the resulting new market can be booming or ends up to be smaller thanthe old market used to be. We analise both the inflexible capacity-case, as the flexible one.

Ensemble predictions of recovery ratesJoao Bastos 1

1 ISEG/CEMAPRE

In many domains, the combined opinion of a committee of experts provides better decisions thanthe judgment of a single expert. This paper shows how to implement a successful ensemble strategyfor predicting recovery rates on defaulted debts. Using data from Moody’s Ultimate RecoveryDatabase, it is shown that committees of models derived from the same regression method presentbetter forecasts of recovery rates than a single model. More accurate predictions are observedwhether we forecast bond or loan recoveries, and across the entire range of actual recovery values.

Price Modelling in Carbon Emission and Electricity MarketsDaniel Schwarz 1

1 CMU and IST/CEMAT

We present a model to explain the joint dynamics of the prices of electricity and carbon emissionallowance certificates as a function of exogenously given fuel prices and power demand. The modelfor the electricity price consists of an explicit construction of the electricity supply curve; the modelfor the allowance price takes the form of a coupled forward-backward stochastic differential equa-tion (FBSDE) with random coefficients. Reflecting typical properties of emissions trading schemesthe terminal condition of this FBSDE exhibits a gradient singularity. Appealing to compactnessarguments we prove the existence of a unique solution to this equation.

We illustrate the relevance of the model at the example of pricing clean spread options, contractsthat are frequently used to value power plants in the spirit of real option theory.

Wave Interaction with Floating BodiesOrganizer: Juha Videman and Goncalo DiasInstituto Superior Tecnico/CAMGSD and CAMGSD/ISTSeptember 4th, 14:15-15:15, Auditorio 3

Interaction of water waves with freely floating structuresGoncalo Dias 1

1 CAMGSD/IST, Lisbon

We derive a linear system of equations governing the interaction of water waves with partially ortotally submerged freely floating structures in a non-homogeneous fluid. We establish conditions forthe stability of equilibrium, translated in the positive definiteness of the reduced flotation matrixK’. By considering time-harmonic motions, we rewrite the problem as a spectral boundary-valueproblem consisting of a differential equation and an algebraic system, coupled through boundaryconditions. We also give the problem a suitable variational formulation and provide examples offloating structures for which the problem admits only the trivial solution, i.e. no trapped modescan be generated.

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Trapped modes around freely floating bodiesFilipe Cal 1

1 ISEL/CAMGSD, Lisbon

We consider the spectral boundary-value problem that describes the time-harmonic motion of themechanical system consisting of a three-dimensional rigid body floating freely in a two-layer fluid.Unlike the trapping of water waves by fixed obstacles, the interaction of time-harmonic waveswith freely floating objects gives rise to a quadratic operator pencil. Under certain symmetryassumptions, we reduce the quadratic pencil to a linear spectral problem for a self-adjoint operatorin a Hilbert space and derive a sufficient condition for the nonemptiness of its discrete spectrum.Examples of floating bodies supporting trapped modes are given.

Edge waves along a sloping beachBruno Pereira 1

1 ISEL/CAMGSD, Lisbon

Based on variational techniques and spectral theory, we derive a simple geometric condition onthe nearshore slope which guarantees the existence of edge waves along a sloping beach in a non-homogeneous ocean. Edge waves correspond to waves propagating alongshore but decaying in theoffshore direction. We extend our results to shelf and indented coast profiles as well as to overhangingcliff coasts.

Stochastic ModelsOrganizer: Alberto PintoUniversity of PortoSeptember 4th, 14:15-15:15 and 15:30-16:30, Sala 1

Optimal consumption, life insurance and investment strategies in a general financialmarketFilipe Martins1

1 Universidade do Porto

We analyse a stochastic optimal control problem of consumption, life insurance and investment ina general financial market with stochastic coefficients. We derive the optimal strategies for the casewhere the coefficients are deterministic and utility have constant relative risk aversion. (CRRA)

Semi-stationarity under the prisoner’s dilemmaRicardo Cruz 1,∗, Renato Fernandes 1, Alberto Pinto 1

1 Faculdade Ciencias, Universidade do Porto∗rpmcruz@fc.up.pt

We analyse convergence among strategies under the iterated Prisoner’s Dilemma to find cases when conver-gence is so sluggish, it is almost stationary. We will call that semi-stationarity. For that, we will take allpossible strategies implemented using 2-state automata into round-robin tournaments. The automata areprone to stochastic errors.

[1] E. Maskin. Evolution, Cooperation, and Repeated Games. In Journal of Difference Equations and Appli-cations 15:11-12, 1067-1076, 2009.

[2] Martin A. Nowak, Karl Sigmund, Esam EI-Sedy. Automata, repeated games and noise In Journal ofMathemtical Biology 703-722, 1995.

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Games, Groundwater and GovernanceMikhail Smilovic1,∗

1Department of Civil Engineering, McGill University

Groundwater is a common-pool resource (CPR). CPR systems that are subject to suboptimal,or potentially exhaustive outcomes as a result of users pursuing individual strategies are CPRdilemmas. Such CPR dilemmas without regulations (at any level of governance, local to largeexternal, and any level of recognition, local agreeance to established laws) related to extraction,are highly susceptible to overextraction and the classical synopsis of “the tragedy of the commons”[1]. Even with regulations, the continued use of CPRs is heavily dependent upon both internaland external factors of the local community of appropriators. Rather than focus on the classicallysuggested approaches to governance, namely that of an external government or private enterprise,we will work to understand certain aspects of an alternative, namely cooperative self-governance[2]. In particular, we will explore aspects of institutional set-up, conflict resolution, and communitybuilding. We will explore the role of games and game-theory in these aspects of self-governance.We present commonalities underlying several case studies of cooperative groundwater managementand, building on the design-principles as proposed by Elinor Ostrom for long-enduring common-poolresource institutions, rationalize a more specified set of guidelines with respect to groundwater. Weillustrate such guidelines in the context of a case study in Northern India.

[1] Hardin, G. (1968). The Tragedy of the Commons. Science 162 (3859): 1243–1248.

[2] Ostrom, E. (1990). Governing the Commons. Cambridge University Press: Cambridge.

Survival analysis under a Markov model of diseaseMichal Krzeminski1,∗

1 Department of Probability and Biomathematics, Gdansk University of Technology, Poland∗mkrzeminski@mif.pg.gda.pl

Markov models are commonly used to simulate diseases and allow modelling of multiple health statesand outcomes. Multistate models with age-independent transitions can be used for describing theage pattern of the mortality rate at the interval of human aging. We will first see how Markovmortality models may be pressed into service of survival and event history analysis. Then, we willconsider more complex models which will be able to take into account remission, recovery or otheroutcomes of therapy.

We will discuss both explicit, analytical solutions and some sophisticated mathematical tools toobtain asymptotic behaviour of the model when such solutions are presently unobtainable.

Asymptotic stability of quadratic stochastic operators and their applications in popu-lation geneticsMalgorzata Pulka1,∗, Wojciech Bartoszek 1

1 Department of Probability and Biomathematics, Gdansk University of Technology, Poland∗mpulka@mif.pg.gda.pl

Nonlinear Markov evolution has become a subject of interest due to its immense range of appli-cations. In population genetics, so-called quadratic stochastic operators are used in modelling thedynamics of a distribution of a population trait. One of the fundamental issues is the study ofthe limit behaviour of iterates of such operators. In this talk we present conditions for asymptoticstability of quadratic stochastic operators. We also discuss a prevalence problem in the class ofquadratic stochastic operators.

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Dynamic Optimization: Applications to Economics and ManagementOrganizer: Orlando Costa GomesISCAL / IPLSeptember 4th, 14:15-15:15, Sala 2

Dairy Farming Systems’ adaptation to climate changeArmando Mendes 1, Emiliana Silva, 2, Henrique Rosa 3

1 University of Azores, DM - CEEAplA2 University of Azores, DCA - CEEAplA3 University of Azores, DCA - CITA

The climate changes as well as the food security are targets of the environmental policy in theEuropean Union for the next years. The recent proposal of agricultural policy is very dependenton the environmental policy and adds a new measure: the greening. This measure quantifies thediversity areas like forest and permanent grazing. The possible measure of climate change in dairyfarms can be achieved by using the emissions of methane by the ruminants (bovines) converted inCO2 equivalent (CO2−eq). The general European policies are very straight about carbon sequesterand a CO2 quote is already in place for the European countries. The bovine (ruminants) dairyproduction in the intensive systems has great impact in the production of methane. For the Azores’islands economy, dairy production is the main activity and it is important to get impact scenariosin the income of farmers. If the European Union creates a methane quote (CO2−eq) for agriculture,that could change the income and even the use of the land. In Azores’ islands we produce mainlymilk (in 2010 it was about 30% of Portuguese milk production), but also meat. And there aredifferent systems from extensive to intensive grazing systems. The milk production in the intensivegrazing system was the one chosen for this work, because it is the system that causes the biggestmethane emissions. To know the impact of possible future quotes of methane in the dairy milk farms,a decision model was built (a linear programming model developed by Silva and Mendes, 2011), tothe Azorean intensive grazing system of dairy farms. Then some scenarios of reductions of 10, 25,50 and 75% in the level of methane will be studied, in which the impacts of methane levels reductionin the dairy farms income is evaluated, as well as the level of CO2 equivalent (CO2−eq) emissions,intensity level of grazing system and the number of dairy animals. The linear programming modelhas 154 decision variables, and an objective of profit maximization, and restrictions of land, labor,food balance and CO2−eq emissions. The methane was estimated by Tier II method (IPPC, 2009),and in the Azorean dairy farms it reaches the value of 115.5kg per cow and year (about 2.89 tonCO2−eq per cow and year). The main results show that if there is no limitation of the methanelevel, dairy farms can reach an income of over 55721AC per year, producing 5611kg of methane or2.89 ton of CO2−eq, and about 3.1 animals per hectare as the level of intensification resulting inapproximately 49 animals for the farm being studied. If the reduction is about 50% of the methanelevel (2.6kg per cow) the profit would decrease to 27241AC (48.8% of the maximum income) andthe level of intensification would be approximately 1.6 animals per hectare (about 24 animals) and,also, the total agricultural area would not be fully used. If those levels were reduced by 75% of themethane level 2.6 CO2−eq, the income would drop drastically to 13366AC (23.9%) and would haveonly approximately 14 animals in the farm. The level of the intensity grazing system would decreaseto 0.9 animals per hectare. Any reduction of the methane level always implies a consequent decreasein income, and this must be taken into account by the politicians and farmers. If the CO2−eq hasto be limited than there is the need to find alternative income activities for farmers in order topreserve economic sustainability.

Efficiency measurement in Economics and ManagementJorge Azevedo Santos 1,∗ Palmira Caseiro 1 Elsa Rosario Negas 2

1 Centro de Investigacao em Matematica Aplicada; Departamento de Matematica da Universidade de Evora

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Portugal2 Planning of Territory, Architecture and Design Research Center (CITAD); Architecture and Arts Depart-

ments Universidade Lusıada. Lisbon-Portugal∗jmas@uevora.pt

This presentation introduces the basics of Data Envelopment Analysis techniques, with a short his-torical introduction and examples of the Constant Returns to Scale model, (CRS) and the VariableReturns to Scale (VRS) Model. The ratio models are linearized and for both orientations (inputminimization or output maximization) primal and dual models are presented, and its economicmeaning discussed on a managerial point of view. Some screenshots of specific freely availablesoftware will be explained.

Strong and Weak Ties in Social NetworksLuıs Cavique Santos 1

1 Universidade Aberta

In social networks two types of measures can be identified, the structural measures and communitystructure based on diameter and centrality. The community structure usually deals with networkpartition into communities. The key idea of this work is to explore the concept of strong andweak ties by finding brokers within communities. The strict partition problem is relaxed into a bi-objective set covering problem with k-cliques which allows over-covered and uncovered nodes. Theinformation extracted from social networking goes beyond cohesive groups, allowing the finding ofbrokers that interact between groups.

A Budget Setting ProblemOrlando Gomes 1,2,∗

1 Instituto Superior de Contabilidade e Administracao de Lisboa (ISCAL/IPL)2 UNIDE/ISCTE-IUL∗omgomes@iscal.ipl.pt

Consider a typical agency relation involving a capital owner and a manager. The principal (i.e.,the capital owner) has a potential budget to assign to investment projects. The effective amount ofinvestment will be a share of the potential level, given the specific form of interaction that will beestablished between the principal and the agent (i.e., the manager). The budget setting problemoriginating from this relation is evaluated from the point of view of the manager, who wants tomaximize the profits arising from the implementation of projects, in an intertemporal basis. Profitsare defined, in this context, as the value generated by the use of the available budgetary resourcesless the costs the agent needs to incur to obtain the funds (project proposal costs). The optimalcontrol problem is subject to a constraint, which indicates how the assigned budget evolves overtime. In this constraint, a matching function takes a central role; the arguments of the function arethe agent’s effort to absorb new funds and the financial resources the principal has available buthas not yet assigned to the manager.

Lyapunov Exponents and ApplicationsOrganizer: Mario BessaUniversidade da Beira interiorSeptember 4th, 15:30-16:30, Auditorio 3

Positive Lyapunov exponents for higher dimensional quasiperiodic cocyclesSilvius Klein 1

1 CMAF

Consider an m-dimensional analytic cocycle with underlying dynamics given by an irrational trans-lation on the circle. Assuming that the d-dimensional upper left corner of the cocycle is typically

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large enough, we prove that the d largest Lyapunov exponents associated with this cocycle arebounded away from zero. The result is uniform relative to certain measurements on the matrixblocks forming the cocycle. As an application of this result, we obtain nonperturbative (in thespirit of Sorets-Spencer theorem) positive lower bounds of the nonnegative Lyapunov exponents forvarious models of band lattice Schrodinger operators. [This is joint work with Pedro Duarte.]

On the spectrum of Lp cocyclesHelder Vilarinho 1

1 UBI

We discuss the Lp-abundance of trivial and simple spectrum for a wide class of cocycles, eitherfor discrete time case as for linear differential system. In particular, we give fine properties forthe Lp-denseness of simple spectrum and Lp-residuality of one-point spectrum. We also give someapplications. [This is a joint work with Mario Bessa.]

General dichotomic behavior for trajectories of nonautonomous difference equationsCesar M. Silva1

1 UBI

For nonautonomous linear difference equations in a Banach space and admitting a very generaltype of dichotomic behavior, we discuss the existence of invariant manifolds for small Lipschitzand C1 perturbations of the linear equation. Additionally, we also present some recent resultson the existence of some of these dichotomies using a generalized concept of Lyapunov exponent,the robustness of these dichotomies and give some examples. In the particular case of nonuniformexponential dichotomies, nonuniform polynomial dichotomies and more generally (µ, ν)-dichotomiesour results are new or improve previous known results. [This talk is based on joint work with A.Bento.]

The Lyapunov exponents of toral maps with a reversing symmetryAlexandre Rodrigues1

1 FCUP

We study the set of C1 area-preserving maps on the torus displaying a linear reversing symmetry ofdegree 2 (involution). We show that within these maps the ones exhibiting zero Lyapunov exponents,for Lebesgue almost every point, are generic. This result generalizes Bochi-Mane Theorem for theclass of reversing-symmetric maps. [This is a joint work with Mario Bessa.]

Symbolic dynamics and Lorenz-like knotsOrganizer: Luıs SilvaISEL and CIMA-UESeptember 4th, 15:30-16:30, Sala 2

Invariants of templates, knots and links generated by renormalizable Lorenz mapsLuıs Silva 1

1 ISEL and CIMA-UE

We describe the sub-Lorenz templates generated by renormalizable Lorenz maps, in terms of thetemplates generated by the renormalized map and by the map that determines the renormalizationtype. Consequently we obtain explicit formulas for the Williams ζ function of renormalizable sub-Lorenz templates and also for the genus and the braid index of renormalizable Lorenz knots andlinks.

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Thurston’s classification of a family of Lorenz knotsNuno Franco 1

1 University of Evora and CIMA-UE

Thurston [2] established that all knots that are not torus knots neither satellite knots are necessarilyhyperbolic. We have characterized braids corresponding to families of symbolic sequences, thatresult from syllable permutation of an irreducible sequence. As a consequence we generate a familyof hyperbolic Lorenz knots from a torus knot. We revisit and update the status of some relatedpreviously stated conjectures.

[1] Thurston, E.: Three-dimensional manifolds, Kleinian groups and hyperbolic geometry. Bull. Amer. Math.Soc. (N. S.) 6, 357–381 (1982)

Lorenz braids, symbolic dynamics and hyperbolic knotsPaulo Gomes 1

1 ISEL and University of Evora

Birman and Williams [1] established a correspondence between Lorenz knots, Lorenz braids andsymbolic dynamics. Thurston [2] had previously shown that all knots that are not torus knotsneither satellite knots are necessarily hyperbolic. We have characterized braids correspondent tofamilies of symbolic sequences, in particular those associated with satellite knots and others thatresult from permutations on torus knot’s sequences. We used this to compute knot invariants forthese families and used the results, together with Thurston’s classification theorem, to show thatsome of these families of symbolic sequences always correspond to hyperbolic knots.

[1] Birman, J., Williams, R.: Knotted periodic orbits in dynamical systems–I: Lorenz’s equations. Topol. 22,47–82 (1983)

[2] Thurston, E.: Three-dimensional manifolds, Kleinian groups and hyperbolic geometry. Bull. Amer. Math.Soc. (N. S.) 6, 357–381 (1982)

Genus for knots and links in renormalizable templates with several branch nodesPedro Simoes 1

1 University of Evora

We aplly kneading theory to describe the knots and links generated by the iteration of renormal-izable nonautonomous dynamical systems with reducible kneading invariants, in terms of the linkscorresponding to each factor. As a consequence we obtain explicit formulas for the genus for thiskind of knots and links.

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Advanced School

Reducibility of quasi-periodically forced linear flowsJoao Lopes DiasUniversidade Tecnica de Lisboa, PortugalAugust 28th, 11:30-13:00 / August 29th, 11:30-13:00, Auditorio CGD, ISEG-UTL

We will show the existence of a coordinate change that reduces a quasi-periodically forced linearflow into the flow of a constant vector field. This is an example of a ’small divisors’ problem, acommon difficulty for many systems first dealt by Kolmogorov, Arnold and Moser in the 1960’s.Other approaches include the use of renormalization schemes, which we will adopt in these lectures.Its main tool is the use of a multidimensional continued fractions expansion method, that we willdescribe in detail.

Replicator and Lotka-Volterra SystemsPedro DuarteUniversidade de Lisboa, PortugalAugust 28th, 14:30-16:30 / August 29th, 14:30-16:30, Auditorio CGD, ISEG-UTL

This mini course will be a survey on the Replicator and the Lotka-Volterra differential equations,which play a central role in Evolutionary Game Theory.

Geometric Invariant Measures and Teichmuller StructuresYunping JiangCity University of New York, USAAugust 28th, 17:00-18:30 / August 29th, 17:00-18:30 / August 30th, 17:00-18:30, Auditorio CGD,ISEG-UTL

In this three two-hour lectures, I will discuss the existence and uniqueness of a smooth invariantprobability measure for a smooth expanding dynamical system on a compact smooth Riemannianmanifold. After that I will define the Techmuller metric on the space of all smooth invariantmeasures on the circle and discuss its completion which we call symmetric invariant measures. Wefurther show that each symmetric invariant probability measure is an invariant probability measurefor a uniformly symmetric circle endomorphism. Furthermore, we will discuss the uniqueness of asymmetric invariant probability measure as an invariant measure of a uniformly symmetric circleendomorphism.

On interaction gamesSatoru TakahashiPrinceton University, USAAugust 30th, 11:30-13:00 / 14:30-16:30, Auditorio CGD, ISEG-UTL

Interaction games are games in which a type or player interacts with various subsets of the set of alltypes/players, and total payoffs are given by the payoffs from different interactions with differentweights. The class of interaction games includes incomplete information games, network games, andperfect foresight dynamics (dynamic population game with inertia). In my lecture, I will reviewthese subclasses and explain how techniques and results in one subclass of games readily translateinto another.

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Learning in games and stochastic approximationMichel BenaimUniversite de Neuchatel, SwitzerlandSeptember 5th, 11:30-13:00, Auditorio CGD, ISEG-UTL

I will describe techniques of stochastic approximation and dynamical systems theory that are rele-vant for analyzing the long term behavior of several models of learning arising in game theory

Evolution, Crisis and General EquilibriumElvio AccinelliUASLP, MexicoSeptember 5th, 14:30-16:30, Auditorio CGD, ISEG-UTL

This paper is concerned with the continuous-time replicator dynamics of a production economy withtwo types of firms. At each moment,the profit for each type of firms is determined by a Walrasianequilibrium. Then the replicator dynamics are defined according to which type of firms earns thehigher profit. We assume that managers have not complete information at the moment to choose thetechnology for the next period, and the we introduce a process of imitation of the most successfulagent. We obtain a sufficient condition for a stationary point of the dynamics to be asymptoticallystable, and also a sufficient condition for it to be unstable.

Discrete time models for the population and evolutionary dynamics of structured pop-ulationsJim CushingUniversity of Arizona, USASeptember 5th, 17:00-18:30 / September 6th, 17:00-18:30, Auditorio CGD, ISEG-UTL

The lectures will focus on the Fundamental Bifurcation Theorem (FBT) for nonlinear discrete time,matrix models for structured populations. The theorem will be applied to several examples toillustrate various topics, including stability versus direction of bifurcation and strong Allee effectsas a backward bifurcation phenomenon. The basic FBT for primitive projection matrices will beextended to an evolutionary setting by using evolutionary game theory methodology. SemelparousLeslie models are an example of a matrix model with a non-primitive projection matrix. Thenature of the FBT in this case leads to a biologically significant dynamic dichotomy at bifurcationfor populations with a semelparous life history.

Discrete and continuous models in evolutionary dynamicsFabio Chalub / Max SousaUniversidade Nova de Lisboa, Portugal / Universidade Federal Fluminense, Niteroi, BrasilSeptember 6th, 11:30-13:00, Auditorio CGD, ISEG-UTL

In this course, we will consider two different approaches to the study of evolution: discrete (finite)populations modeled by Markov processes and continuous (infinite) populations modeled by dif-ferential equations. We will initially discuss the differences between these two models and showthat these differences are due to the fact that the differential equation capture only one of the tworelevant time scales of the discrete process. Starting from the discrete process we will find a familyof continuous approximations, These approximations, depending on the scalings, can be of diffusiveor non-diffusive type, the latter being equivalent to the Replicator Dynamics. We then study thesmall diffusion limit, and show how the Replicator Dynamics can be consistently fitted in a diffusiveapproximation.

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Optimal Stochastic Control of Life insurance and investment in a financial marketAlberto A. Pinto / Filipe MartinsUniversidade do Porto, PortugalSeptember 6th, 14:30-16:30, Auditorio CGD, ISEG-UTL

In this work we analyse a consumption, investment and life insurance purchase problem, in a verygeneral model of a financial market with stochastic coefficients that are not necessarily Markovprocesses, and that we assume to be complete. We use duality tools from convex analysis to obtainoptimal consumption, investment and life insurance purchase under very general utility functions.We analyse the case of deterministic coefficients, deducing a mutual fund result, and the Hamilton-Jacobi-Belmann equation on that case, and we obtain explicit solutions for utility functions withconstant relative risk aversion (CRRA).

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Conference Schedule

Keynote Speakers

Room: Auditorio 2

September 2nd September 3rd September 4th

9:00-10:00Satoru Takahashi Alberto A. Pinto Jim Cushing

National University of Singapore Universidade do Porto University of ArizonaCoffee Break

10:30-11:30Jose Martins Marta Faias Bruno Oliveira

I.P.Leiria Universidade Nova de Lisboa Universidade do PortoBreak

11:45-12:45Jorge Pacheco Jorge Zubelli Joana Pais

Universidade do Minho IMPA ISEG/UTLBreak

14:15-15:15Fabio Chalub Lorens Imhof Elvio Accinelli

Universidade Nova de Lisboa University of Bonn UASLPBreak

15:30-16:30Joao Lopes Dias Pedro Duarte Renato Soeiro

Universidade Tecnica de Lisboa Universidade de Lisboa Universidade do PortoCoffee Break

17:00-18:00Yunping Jiang Martin Shubik Michel Benaim

City University of New York Yale University Universite de Neuchatel(video lecture)

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Thematic Sessions

Room: Auditorio 3

September 2nd September 3rd September 4th

10:30-11:30

Bayesian Statistics: Some economic applications Coupled Cell NetworksApplications in Biology and Ecology

Joao Casaca Orlando Montoro Peinado Celia MoreiraGiovani L. Silva Meliyara Consuegra Ana Dias

Luıs Silva Eduardo Oliva Manuela Aguiar

Francesco Minunno Alberto A. Alvarez-Lopez Rui PaivaBreak

11:45-12:45

Marine Life Dynamical Systems Interest Rate, Credit Riskin the Wild Wider Ocean and Bifurcations and Investment Models

Telmo Morato Sofia Castro Claudia NunesFernando Tempera Jose Pedro Gaivao Raquel Gaspar

Pedro Afonso Begona Alarcon Joao BastosMaria Joana Torres Daniel Schwarz

Break

14:15-15:15

Biological Invasions Evolutionary games Wave Interactionin the Azores and economy with Floating Bodies

Joao Canning-Clode Edgar Carrera Goncalo DiasLuıs Silva Elvio Accinelli Filipe Cal

Orlando Guerreiro Bruno PereiraBreak

15:30-16:30Chaotic Dynamics Piecewise smooth dynamics Lyapunov Exponentsin Growth models and ApplicationsSandra M. Aleixo Alexandre Plakhov Silvius Klein

Acilina Caneco Paulo Brito Helder VilarinhoAlessandro Margheri Cesar M. Silva

Alexandre Rodrigues

Room: Sala1

September 2nd September 3rd September 4th

10:30-11:30

Discrete Dynamics Graphs and Combinatorics (I) Graphs and Combinatorics (IV)and Numerical Semigroups

Clara Gracio Sofia Pinheiro Paula RamaSusana Santos Fatima Pacheco Ricardo MamedeTeresa Silva Ines Barbedo Rui Duarte

Denise TorraoBreak

11:45-12:45

Synchronization Graphs and Combinatorics (II) Graphs and Combinatorics (V)and Discrete Dynamics

Sara Fernandes Maria Manuel Torres Ilda PerezLuıs Lopes Teresa Sousa Olga Azenhas

Andre AlbinoBreak

14:15-15:15

Dynamics, Graphs and Combinatorics (III) Stochastic Models (I)Modelling and Optimisation

Ana I. Pereira Paula Carvalho Filipe MartinsCarlos Balsa Marta Pascoal Ricardo Cruz

Joao P. Almeida Vasco Mano Mikhail SmilovicRenato Fernandes

Break

15:30-16:30Bio-Dynamics Biomathematics Stochastic Models (II)

Isabel Figueiredo Jose Martins Michal KrzeminskiBruno Oliveira Jorge Pereira Malgorzata Pulka

Joao Coelho Rui SantosJoana Becker

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Room: Sala2

September 2nd September 3rd September 4th

10:30-11:30

Mean-Field Models, Dynamical models Marine Systems for OceanOptimal Control and and data analysis Exploration and Exploitation:

Calculus of Variations in epidemiology (I) Theory and Practice (I)Gabriele Terrone Maira Aguiar A. PascoalEdgard Pimentel Filipe Rocha F. Lobo Pereira

Rita Ferreira Urszula Skwara F. CuradoBreak

11:45-12:45

Statistics in Environmental Dynamical models Marine Systems for Oceanand Life Sciences and data analysis Exploration and Exploitation:

in epidemiology (II) Theory and Practice (II)Dora Prata Gomes Luis Mateus A. Silva

Ines J. Sequeira Peyman Ghaffari J. GomesVanda Lourenco Nico Stollenwerk A. AguiarIsabel Natario Max Souza

Break

14:15-15:15

PDE’s and Extremes and other Dynamic Optimization:Calculus of Variations statistical properties Applications to Economics

of dynamical systems and ManagementGraca Carita Laura Cavalcante Armando Mendes

Jose Maria Gomes Hale Aytac Jorge SantosGiovanni Pisante Luıs Cavique Santos

Orlando GomesBreak

15:30-16:30

Discrete-valued Economic dynamics Symbolic dynamicstime series and computation and Lorenz-like knots

Maria Eduarda Silva Tiago Pinheiro Luıs SilvaIsabel Pereira Paulo Mota Nuno Franco

Magda Monteiro Oscar Afonso Paulo GomesMaria da Conceicao Costa Pedro Mazeda Gil Pedro Simoes

Advanced School

Room: Auditorio CGD, ISEG

August 28th August 28th August 30th September 5th September 6th

11:30-13:00Joao Lopes Dias Joao Lopes Dias Satoru Takahashi Michel Benaim Fabio Chalub

Max SouzaBreak

14:30-16:30Pedro Duarte Pedro Duarte Satoru Takahashi Elvio Accinelli Alberto A. Pinto

Filipe MartinsCoffee Break

17:00-18:30Yunping Jiang Yunping Jiang Yunping Jiang Jim Cushing Jim Cushing

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