Modeling and Computing with

Multi-scale Cellular Automata

John-Thones Amenyo

jta@york.cuny.edu

York College, City University of New York (CUNY)

Multi-scale CA: Overview

z Trends in HPC (High Performance Computing)

z Research Focus

z SOCAR: Separation of Concerns, Aspects & Roles

z Quipu-charts, Q-charts: Time-Space Representation

z Temporal or Diachronic Structures: Managing Synchrony

z Spatial or Synchronic Structures: Attributed Structures

z Details of Examples

z Summary & Conclusions

CSC 2010. Multi-scale CA. J-T. Amenyo. York College, CUNY 2

Multi-scale CA: Trends in HPC

z Very Large-scale Application Development (in STEM)

z Multi-core, (Massively) Many-core Computing Platforms

z Massively Parallel, Distributed, Concurrent Computing

CSC 2010. Multi-scale CA. J-T. Amenyo. York College, CUNY

Mega-scale

(106)Giga-scale

(109)

Tera-scale

(1012)

Peta-scale

(1015)

Exa-scale

(1018)

P: Processor MIPS GFLOPS TFLOPS PFLOPS EFLOPS

M: Memory MBytes GBytes TBytes PBytes Ebytes

S: Comm. Mbps Gbps Tbps Pbps Ebps

C: Control MThrOPS GThrOPS TThrOPS PThrOPS EThrOPS

IO: Inp/Out MIOPS GIOPS TIOPS PIOPS EIOPS

3

ThrOPS: Thread Operations/Sec; FLOPS: Floating Point Oper/Sec; IPS: Instructions/Sec; bps: Bits/SecIOPS: IO operations/Sec

Multi-scale CA: SOCARSeparation of Concerns, Aspects & Roles

z Very Large-scale: Super-scale, Ultra-scale, Hyper-scale

y Modularization, Modularity

y Multi-scale

y Multi-resolution: (mega�macro�meso�micro�nano�pico)-scales

y Multi-layer, multi-level, multi-phase, multi-stage, multi-bundles

y Multi-Paradigm, Multi-STEM, Multi-science, Multi-physics

y Automatic Programming

z Direct Discrete, Digital Computing

y Lattice, Crystal, Cellular, Finite Element Methods, Network Theory

y Programmable Matter Approach to Natural Computation

y Bio-inspired, Bio-mimetic Computing

z Management of Large-scale, Organized Complexity

y Autonomic Computing: Conscious & Self-Aware AutomataCSC 2010. Multi-scale CA. J-T. Amenyo. York College, CUNY 4

Multi-scale CA: Research Focus

z EUPP (End-User Parallel Programming) Methodologiesz DSL / ASICF (Domain /Application-specific) Languages, Intelligence Formalisms

z STEM (Science, Technology, Engineering, Math) Applications

y Modeling, Simulation, Animation, Games, Interactive Play, Viz.

y Define, Specify, Understand, Analyze, Develop, Deploy, Operate, Control, Coordinate, Maintain, Repair, Evolve, Discuss, Exchange

z Integrate Parallel & Distributed Computing Paradigms:

y Many Paradigms, schemes, styles, formalisms; Most do not scale

z Reconfigurable / Self-Reconfigurable Robots

z Bioinformatics, Neuro-informatics, Sys. Biol., Comput. Biol.

z Virtual Organs, Virtual Tissues, Virtual Cells

y Virtual Prostate, Virtual Cowper’s (Bulbourethral) gland

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Multi-scale CA: Methodology

z Mapping: Application Domain � Computing Platform

z Main Computational Platform Concept: Thread

y (Temporal, diachronic) Sequence of actions, activity, transactions, operations, events, behaviors, cooperation, collaborations, competitions, scripts, workflow, rituals, rites, ceremony, procedures, routines, co-routines

y Multi-threading: Thread interleaving, Concurrent threads

y Poly-threads: Parallel threads, (spatially) distributed threads

z Main Application Domain Concept: Automata, Agent, Robot

z Main diachronic concern: Synchronization – timing coordination of

collections, ensembles of threads & domain objects.

x Wave synchrony (Melody) , Sequential Composition; Barrier Synchronization; Parallel Composition

x Unison synchrony (Harmony, Cacophony) (Parallel: Coordinated, Uncoordinated), Map Reduce, SIMD, MIMD

z Also temporal logic conditions (do, redo, repeat, do not) (until, as soon as, as long as, if, whenever…)(condition)

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Multi-scale CA: Q-Charts

z Time-space / Space-time (Diachronic) Representation of Computation Workflows, Behavior Processes – Quipu (Inca)

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time

non-time

Quipu Image Source: Jean-Jacques Quisquater, MIT 2007

Multi-scale CA: Quipu-Charts

z Time-space / Space-time Representation of Computation Workflows, Behavior Processes – Quipu charts (Inca)

CSC 2010. Multi-scale CA. J-T. Amenyo. York College, CUNY 8

time

non-time

Quipu Image Source: Jean-Jacques Quisquater, MIT 2007

Multi-scale CA: Quipu-Charts

z Time-space / Space-time Representation of Computation Workflows, Behavior Processes.

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Source: Jean-Jacques Quisquater, MIT 2007

Multi-scale CA: Quipu-Charts

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time

non-time

Source: Jean-Jacques Quisquater, MIT 2007

Multi-scale CA: Q-Charts

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nt

(time or) non-time

time

Multi-scale CA: Q-Charts

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non-time

time

Close-up view of the 8 × 26 hole punched cards—one card per pick

(weft) in the fabric. Used in a Jacquard loom

Source: Wikipedia.org

Multi-scale CA: Q-Charts

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time

non-time

Compare: musical notation, music scores, composition, film strip, cartoon strip, comic strip, music tape, (magnetic) data tape, punch card, message sequence charts (CSP, Occam, UML), orchestration chart, instrumentation chart, time-frequency diagrams, workflow diagrams, piano roll, punched tape

Concepts: precede, succeed, transfer, communicate, exchange, interchange, transport, anti-port, synport, pre-event, post-event, co-event, barrier synchronization, island of synchrony, cord, chord, melody, harmony, symphony, tie, bracket, map, reduce, SIMD, MIMD, MISD, pipeline, join, gather, scatter, mux, partition, allocate, interleave, interweave, superposition, shuffle, cyclic service

Multi-scale CA: Structures

z Synchronic Aspects: Grouping, Bracketing into Collections, Ensembles, Organizations, Complexes, Populations, Assemblies, Communities:

y Attributed (Spatial structures, Topological structures, Merological Structures):

compare: Attribute Grammars, Semantic Networks, Entity-Relation Models, Metadata.

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Structure Relation

Embodiment

Geometry

Associations

Non-

Functional Attributes

Functional

Attributes

FormArray, Dust

GraphCombinatorial

topology

Co-structuresAssociative structuresSemantic networks

E-R diagrams

PointsNodes

HyperedgesTiles

PolygonsPolyhedraPolytopes

ValuesVectors

Vector CodingRel. tables, DB

Arrays, MatricesTensors

Data StructuresAbstract Data

types

FunctionsOperators

CombinatorsAutomata

CA

RobotsVirtual Ants

Agents

Multi-scale CA:

Combinatorial Topology

z Network Models, Diakoptics: G. Kron, Roth, Branin, Tonti

z Graphs, digraphs, trees, MINs, hyper-cubes, meshes, grids, hypergraphs, logical connectivity graphs, compound graphs, poly-graphs, geons, generalized cones, active contours

z 0-spaces, 1-spaces, 2-spaces, 3-spaces, …, p-spaces

z p-chains, p-cochains, p-circuits, p-cycles, p-cocycles,

z p-boundaries, p-coboundaries, p-complexes, p-polytopes

z Biology: Atom�Molecule�Cell�Organ�Organismz +Meso-structures: molecular networks, organelles, tissues, societies, ecologies

z 2 styles for specifying inter-level / inter-scale relations:

y Embedding, Nesting, Constituency, Composition, Decomposition, Merology

y Inter-Linking, Correspondence, Mapping, Morphism, Relation Embodiments, Semantic Networks, Concept Maps, Co-structures, p-poly-complexes, Link Classes / Types

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Multi-scale CA:

Attributed Structures

z Algebraic Topology, Differential Topology: Co-Chains

z Attribute Grammars: (Attributes = metadata)

y Inherited Attributes (macro-scale � micro-scale) influences

y Synthesized Attributes (micro-scale � macro-scale) influences

y (I/O & Communications) Interfacing & Interactions: Push attributes, Pull attributes; Pull – on demand/select; Push – publish & subscribe

z Attribute inter-relations: co-dependency or data dependency networks:

y Arithmetic circuits, Logic circuits, spreadsheet data models

y Vector coding, AI frames and schemas

y Inter-level / Inter-scale Balance, Conservations laws: KCL, KVL, Stokes’ Theorem, Maxwell’s Equations: Energy vs. Information flows

z Repr.: 2p-trees (extend: quad-trees, octrees), 8 < p < 32

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Multi-scale CA: Applications:

Virtual Gland

z Cowper’s gland / Bulbourethral gland:

y Compound tubuloalveolar secretory structure

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Alveolar

Compound branching: main duct,ducts, ductules Broccoli, Cauliflower

Tubular

Source: SIUMED.EDU

time

AttributesMetadata Structure

Multi-scale CA: Applications:

Virtual Biology (In Silico Biology)

z Barely able to handle the combinatorial complexity:

y How many cells does a prostate gland have? O(105)?

y How many molecules does a prostate gland cell have? O(1010)?

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Diagram of a typical animal (eukaryotic) cell, showing subcellular components.

Organelles:(1) nucleolus(2) nucleus

(3) ribosome(4) vesicle

(5) rough endoplasmic reticulum (ER)(6) Golgi apparatus

(7) Cytoskeleton(8) smooth endoplasmic reticulum

(9) mitochondria(10) vacuole

(11) cytoplasm(12) lysosome

(13) centrioles within centrosome

Source: Wikipedia.org

Onion layers, flower petals , artichoke, cabbage

Multi-scale CA: Applications:

Self-Reconfigurable Robots

z Self-Reconfiguration via the trick of virtual leaderless coord.

y Remove the scaffolding: Hide the infrastructure support

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Initial, Beginning, Starting Configuration

Procurement, Gathering, Acquisition of New Additions / Removal of Exclusions

Existing Configuration Deconstruction

Final, Ending, Terminal Configuration

New Configuration Assembly, Integration, Re-engineering, Recombination

New Configuration Testing, Deployment, Installation

timeDominant, Necessary, Primary

Recessive, Optional, Secondary

Multi-scale CA: Summary

z Modern High Performance Computing (HPC) applications from Computational STEM are invariably and increasingly very large scale, in all aspects and dimensions of the PMSCIO computer architecture.

y Modular approaches � Multi-scale systems

y Distributed Multi-core and Massively Many-core platforms are increasingly available as computational resources for Discrete STEM

y Systematic Methodologies are needed for Non-Professional Programmers, who are expert in their fields

y Cope with DSL / ASICF (Domain Specific Languages) / (Application Specific Intelligence and Computational Formalisms) that integrate ideas about Structure + Function:

x Combinatorial Topology, Algebraic Topology, Attribute Grammars,Network Theory, Functional Programming, Workflows, ApplicativeProgramming � Create a Methodology for Using Multi-scale CA

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Multi-scale CA

Thank You!!!

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