Complex Systems Made Simple

Transcription

1 Erasmus Mundus Masters in Complex Systems Science Complex Systems Made Simple by Agent-Based Modeling and Simulation René Doursat

2 Course Contents What this course is about (dense preview, will be repeated) an exploration of various complex systems objects: cellular automata, pattern formation, swarm intelligence, complex networks, spatial communities, structured morphogenesis and their common questions: emergence, self-organization, positive feedback, decentralization, between simple and disordered, more is different, adaptation & evolution by interactive experimentation (using NetLogo), introducing practical complex systems modeling and simulation from a computational viewpoint, in contrast with a mathematical one (i.e., formal or numerical resolution of symbolic equations), based on discrete agents moving in discrete or quasi-continuous space, and interacting with each other and their environment 2

3 What you will be doing code two exercises Research Project prepare an individual research project topics must address complex systems and may be: expanding upon examples seen here overlapping with your own interests / another project of yours both or neither project deliverables: modeling & simulation program journal-style report (but shorter) conference-style presentation, with live demo project deadlines: day x: send proposal 1-2-page & few slides presentations on x+1 day y: send final code, report & slides presentations on y+1 3

4 Complex Systems Made Simple 1. Introduction 2. A Complex Systems Sampler 3. Commonalities 4. NetLogo Tutorial 4

5 1. Introduction Complex Systems Made Simple a. What are complex systems? b. A vast archipelago c. Computational modeling 2. A Complex Systems Sampler 3. Commonalities 4. NetLogo Tutorial 5

6 Complex Systems Made Simple 1. Introduction a. What are complex systems? b. A vast archipelago Few agents Many agents CS in this course c. Computational modeling 2. A Complex Systems Sampler 3. Commonalities 4. NetLogo Tutorial 6

7 1. Introduction a. What is a system? System A group/configuration of elements/parts which are interacting/connected/joined together, and form a unified whole Types of systems Physical systems: weather, planets (solar system),... Biological systems: body (circulatory, respiratory, nervous),... Engineering systems: BE, EE, ME,... Information systems: CS, ICT,

8 Any ideas? The School of Rock (2003) Jack Black, Paramount Pictures 8

9 Few agents, simple emergent behavior ex: two-body problem fully solvable and regular trajectories for inverse-square force laws (e.g., gravitational or electrostatic) Two bodies with similar mass Wikimedia Commons Two bodies with different mass Wikimedia Commons 9

10 Few agents, complex emergent behavior ex: three-body problem generally no exact mathematical solution (even in restricted case m 1 m 2 m 3 ): must be solved numerically chaotic trajectories NetLogo model: /Chemistry & Physics/Mechanics/Unverified Transit orbit of the planar circular restricted problem Scholarpedia: Three Body Problem & Joachim Köppen Kiel s applet 10

11 Few agents, complex emergent behavior ex: more chaos (baker s/horseshoe maps, logistic map, etc.) chaos generally means a bounded, deterministic process that is aperiodic and sensitive on initial conditions small fluctuations create large variations ( butterfly effect ) even one-variable iterative functions: x n+1 = f(x n ) can be complex Baker s transformation Craig L. Zirbel, Bowling Green State University, OH Logistic map 11

12 Many agents, simple rules, simple emergent behavior ex: crystal and gas (covalent bonds or electrostatic forces) either highly ordered, regular states (crystal) or disordered, random, statistically homogeneous states (gas): a few global variables (P, V, T) suffice to describe the system NetLogo model: /Chemistry & Physics/GasLab Isothermal Piston Diamond crystal structure Tonci Balic-Zunic, University of Copenhagen 12

13 Many agents, simple rules, complex emergent behavior ex: cellular automata, pattern formation, swarm intelligence (insect colonies, neural networks), complex networks, spatial communities the clichés of complex systems: a major part of this course and NetLogo models 13

14 Many agents, complicated rules, complex emergent behavior natural ex: organisms (cells), societies (individuals + techniques) agent rules become more complicated, e.g., heterogeneous depending on the element s type and/or position in the system behavior is also complex but, paradoxically, can become more controllable, e.g., reproducible and programmable biological development & evolution termite mounds companies techno-networks cities 14

15 From statistical to morphological complex systems social insects: collective constructions cells: biological morphogenesis ant trail inert matter: pattern formation network of ant trails termite mound ant nest cells architectures without architects! termites ants grains of sand + warm air 15

16 Many agents, complicated rules, complex emergent behavior ex: self-organized artificial life : swarm chemistry, morphogenesis in swarm chemistry (Sayama 2007), mixed self-propelled particles with different flocking parameters create nontrivial formations in embryomorphic engineering (Doursat 2006), cells contain the same genetic program, but differentiate and self-assemble into specific shapes PF4 SA4 PF6 SA6 Swarm chemistry Hiroki Sayama, Binghamton University SUNY Embryomorphic engineering René Doursat, Insitut des Systèmes Complexes, Paris PF SA 16

17 Many agents, complicated rules, deterministic behavior classical engineering: electronics, machinery, aviation, civil construction artifacts composed of a immense number of parts yet still designed globally to behave in a limited and predictable (reliable, controllable) number of ways "I don t want my aircraft to be creatively emergent in mid-air" not "complex" systems in the sense of: little decentralization no emergence no self-organization Systems engineering Wikimedia Commons, 17

18 Many agents, complicated rules, centralized behavior spectators, orchestras, military, administrations people reacting similarly and/or simultaneously to cues/orders coming from a central cause: event, leader, plan hardly "complex" systems: little decentralization, little emergence, little self-organization 18

19 Recap: complex systems in this course Category Agents / Parts Local Rules Emergent Behavior A "Complex System"? 2-body problem few simple simple NO 3-body problem, low-d chaos few simple complex NO too small crystal, gas many simple simple NO few params suffice to describe it patterns, swarms, complex networks many simple complex YES but mostly random and uniform structured morphogenesis many complicated complex YES reproducible and heterogeneous machines, crowds with leaders many complicated deterministic/ centralized COMPLICATED not self-organized 19

20 Recap: complex systems in this course Category Agents / Parts Local Rules Emergent Behavior A "Complex System"? 2-body problem few simple simple NO 3-body problem, low-d chaos few simple complex NO too small crystal, gas many simple simple NO few params suffice to describe it patterns, swarms, complex networks many simple complex YES but mostly random and uniform structured morphogenesis many complicated complex YES reproducible and heterogeneous machines, crowds with leaders many complicated deterministic/ centralized COMPLICATED not self-organized 20

21 Complex systems in this course large number of elementary agents interacting locally (more or less) simple individual agent behaviors creating a complex emergent, self-organized behavior decentralized dynamics: no master blueprint or grand architect physical, biological, technical, social systems (natural or artificial) pattern formation = matter biological development = cell the brain & cognition = neuron insect colonies = ant Internet & Web = host/page social networks = person 21

22 Physical pattern formation: Convection cells WHAT? T HOW? Rayleigh-Bénard convection cells in liquid heated uniformly from below (Scott Camazine, Convection cells in liquid (detail) (Manuel Velarde, Universidad Complutense, Madrid) Schematic convection dynamics (Arunn Narasimhan, Southern Methodist University, TX) Sand dunes (Scott Camazine, Solar magnetoconvection (Steven R. Lantz, Cornell Theory Center, NY) Hexagonal arrangement of sand dunes (Solé and Goodwin, Signs of Life, Perseus Books) thermal convection, due to temperature gradients, creates stripes and tilings at multiple scales, from tea cups to geo- and astrophysics 22

23 Biological pattern formation: Animal colors WHAT? ctivator HOW? nhibitor Mammal fur, seashells, and insect wings (Scott Camazine, NetLogo fur coat simulation, after David Young s model of fur spots and stripes (Michael Frame & Benoit Mandelbrot, Yale University) animal patterns (for warning, mimicry, attraction) can be caused by pigment cells trying to copy their nearest neighbors but differentiating from farther cells 23

24 Spatiotemporal synchronization: Neural networks HOW? Cortical layers WHAT? Animation of a functional MRI study (J. Ellermann, J. Strupp, K. Ugurbil, U Minnesota) the brain constantly generates patterns of activity ( the mind ) they emerge from 100 billion neurons that exchange electrical signals via a dense network of contacts Schematic neural network Pyramidal neurons & interneurons (Ramón y Cajal 1900) 24

25 Swarm intelligence: Insect colonies (ant trails, termite mounds) WHAT? archive_2003/epow _files/matabele_ants.jpg Termite mound (J. McLaughlin, Penn State University) tridentoriginal/ghana TermiteMound%20CS.gif Harvester ant (Deborah Gordon, Stanford University) Termite stigmergy (after Paul Grassé; from Solé and Goodwin, Signs of Life, Perseus Books) HOW? ants form trails by following and reinforcing each other s pheromone path termite colonies build complex mounds by stigmergy 25

26 Collective motion: flocking, schooling, herding HOW? S A C Fish school (Eric T. Schultz, University of Connecticut) WHAT? Bison herd (Center for Bison Studies, Montana State University, Bozeman) Separation, alignment and cohesion ( Boids model, Craig Reynolds, coordinated collective movement of dozens or 1000s of individuals (confuse predators, close in on prey, improve motion efficiency, etc.) each individual adjusts its position, orientation and speed according to its nearest neighbors 26

27 Complex networks and morphodynamics: human organizations organizations urban dynamics cellular automata model HOW? WHAT? (Thomas Thü Hürlimann, global connectivity SimCity ( techno-social networks NetLogo urban sprawl simulation scale-free network model NSFNet Internet (w2.eff.org) NetLogo preferential attachment simulation 27

28 Categories of complex systems by agents the brain organisms ant trails biological patterns cells termite mounds living cell molecules animals animal flocks physical patterns Internet, Web humans & tech markets, economy social networks cities, populations 28

29 Categories of complex systems by range of interactions biological patterns the brain organisms ant trails termite mounds living cell animal flocks physical patterns 2D, 3D spatial range Internet, Web markets, economy non-spatial, hybrid range social networks cities, populations 29

30 Natural and human-caused categories of complex systems living cell biological patterns physical patterns the brain organisms ant trails... yet, even human-caused systems are natural in the sense of their unplanned, spontaneous emergence Internet, Web markets, economy social networks termite mounds cities, populations animal flocks 30

31 Architectured natural complex systems (without architects) living cell biological patterns physical patterns the brain organisms ant trails biology strikingly demonstrates the possibility of combining pure self-organization and elaborate architecture Internet, Web markets, economy social networks termite mounds cities, populations animal flocks 31

32 Simple/random vs. architectured natural complex systems 32

33 Complex systems can possess a strong architecture, too soldier transport royal chamber 1. Introduction a. What are complex systems? "complex" doesn t imply "homogeneous"... heterogeneous agents and diverse patterns, via positions "complex" doesn t imply "flat"... modular, hierarchical, detailed architecture "complex" doesn t imply "random"... reproducible patterns relying on programmable agents queen reproduce nursery galleries ventilation shaft architecture worker defend build fungus gardens (mockup) EA-style diagram of a termite mound but then what does it mean for a module to be an "emergence" of many fine-grain agents? cells and social insects have successfully "aligned business and infrastructure" for millions of years without any architect telling them how to 33

34 Doursat, Sanchez, Fernandez, Kowaliw & Vico (2012) 34

35 Human superstructures are "natural" CS by their unplanned, spontaneous emergence and adaptivity... geography: cities, populations people: social networks wealth: markets, economy technology: Internet, Web... arising from a multitude of traditionally designed artifacts houses, buildings address books companies, institutions computers, routers small to midscale artifacts computers, routers companies, institutions address books houses, buildings Architects overtaken by their architecture large-scale emergence Internet, Web markets, economy social networks cities, populations 35

36 Many self-organized systems exhibit random patterns... (a) "simple"/random self-organization gap to fill... while "complicated" architecture is designed by humans (d) direct design (top-down) more self-organization more architecture 36

37 Many self-organized systems exhibit random patterns... The only natural emergent and structured CS are biological Can we transfer some of their principles to human-made systems and organizations? (b) natural self-organized architecture (c) engineered self-organization (bottom-up).... self-forming robot swarm self-programming software self-connecting micro-components 1. Introduction a. What are complex systems?.... self-reconfiguring manufacturing plant self-stabilizing energy grid self-deploying emergency taskforce self-architecting enterprise artificial natural more self-organization more architecture 37

38 A Complex Systems Sampler Emergence on multiple levels of self-organization complex systems: a) a large number of elementary agents interacting locally b) simple individual behaviors creating a complex emergent collective behavior c) decentralized dynamics: no master blueprint or grand architect 38

39 A Complex Systems Sampler From genotype to phenotype, via development 39

40 A Complex Systems Sampler From cells to pattern formation, via reaction-diffusion NetLogo Fur ctivator nhibitor 40

41 A Complex Systems Sampler From social insects to swarm intelligence, via stigmergy NetLogo Ants 41

42 A Complex Systems Sampler NetLogo Flock From birds to collective motion, via flocking separation alignment cohesion 42

43 A Complex Systems Sampler From neurons to brain, via neural development... Ramón y Cajal

44 1. Introduction Complex Systems Made Simple a. What are complex systems? b. A vast archipelago c. Computational modeling Related disciplines Big questions big objects Science engineering links 2. A Complex Systems Sampler 3. Commonalities 4. NetLogo Tutorial 44

45 Common Properties of Complex Systems Emergence the system has properties that the elements do not have these properties cannot be easily inferred or deduced different properties can emerge from the same elements Self-organization order of the system increases without external intervention originates purely from interactions among the agents (possibly via cues in the environment) Counter-examples of emergence without self-organization ex: well-informed leader (orchestra conductor, military officer) ex: global plan (construction area), full instructions (program) 45

46 Common Properties of Complex Systems Positive feedback, circularity creation of structure by amplification of fluctuations (homogeneity is unstable) ex: termites bring pellets of soil where there is a heap of soil ex: cars speed up when there are fast cars in front of them ex: the media talk about what is currently talked about in the media Decentralization the invisible hand : order without a leader ex: the queen ant is not a manager ex: the first bird in a V-shaped flock is not a leader distribution: each agent carry a small piece of the global information ignorance: agents don t have explicit group-level knowledge/goals parallelism: agents act simultaneously 46

47 Common Properties of Complex Systems N O T E Decentralized processes are far more abundant than leader-guided processes, in nature and human societies... and yet, the notion of decentralization is still counterintuitive many decentralized phenomena are still poorly understood a leader-less or designer-less explanation still meets with resistance this is due to a strong human perceptual bias toward an identifiable source or primary cause 47