modeling and computing with multi-scale cellular automata
TRANSCRIPT
Modeling and Computing with
Multi-scale Cellular Automata
John-Thones Amenyo
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
CSC 2010. Multi-scale CA. J-T. Amenyo. York College, CUNY 5
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)
CSC 2010. Multi-scale CA. J-T. Amenyo. York College, CUNY 6
Multi-scale CA: Q-Charts
z Time-space / Space-time (Diachronic) Representation of Computation Workflows, Behavior Processes – Quipu (Inca)
CSC 2010. Multi-scale CA. J-T. Amenyo. York College, CUNY 7
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.
CSC 2010. Multi-scale CA. J-T. Amenyo. York College, CUNY 9
Source: Jean-Jacques Quisquater, MIT 2007
Multi-scale CA: Quipu-Charts
CSC 2010. Multi-scale CA. J-T. Amenyo. York College, CUNY 10
time
non-time
Source: Jean-Jacques Quisquater, MIT 2007
Multi-scale CA: Q-Charts
CSC 2010. Multi-scale CA. J-T. Amenyo. York College, CUNY 11
nt
(time or) non-time
time
Multi-scale CA: Q-Charts
CSC 2010. Multi-scale CA. J-T. Amenyo. York College, CUNY 12
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
CSC 2010. Multi-scale CA. J-T. Amenyo. York College, CUNY 13
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.
CSC 2010. Multi-scale CA. J-T. Amenyo. York College, CUNY 14
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
CSC 2010. Multi-scale CA. J-T. Amenyo. York College, CUNY 15
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
CSC 2010. Multi-scale CA. J-T. Amenyo. York College, CUNY 16
Multi-scale CA: Applications:
Virtual Gland
z Cowper’s gland / Bulbourethral gland:
y Compound tubuloalveolar secretory structure
CSC 2010. Multi-scale CA. J-T. Amenyo. York College, CUNY 17
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)?
CSC 2010. Multi-scale CA. J-T. Amenyo. York College, CUNY 18
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
CSC 2010. Multi-scale CA. J-T. Amenyo. York College, CUNY 19
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
CSC 2010. Multi-scale CA. J-T. Amenyo. York College, CUNY 20