ComplexComplex SystemsSystems MadeMade SimpleSimple 1. Introduction
2. A Complex Systems Sampler a. Cellular automata b. Pattern formation c. Swarm intelligence d. Complex networks e. Spatial communities f. Structured morphogenesis 3. Commonalities
4. NetLogo Tutorial
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 49 ComplexComplex SystemsSystems MadeMade SimpleSimple 1. Introduction
2. A Complex Systems Sampler a. Cellular automata: • Game of life • 1-D binary automata b. Pattern formation c. Swarm intelligence d. Complex networks e. Spatial communities f. Structured morphogenesis 3. Commonalities
4. NetLogo Tutorial
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 50 2. A Complex Systems Sampler a. Cellular automata – Game of life
NetLogo model: /Computer Science/Cellular Automata/Life History ¾most famous cellular automaton ¾designed by John H. Conway in 1970 ¾in an attempt to find a simpler self-replicating machine than von Neumann’s 29-state cells ¾very simple set of rules on black and white pixels ¾creates small “autonomous”, “life-like” patterns (static, repeating, translating, etc.) on Bill Gosper's Glider Gun the few-pixel scale (Wikipedia, “Conway’s Game of Life”)
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 51 2. A Complex Systems Sampler a. Cellular automata – Game of life
Rules of the game ¾survival: a live cell with 2 or 3 neighboring live cells survives for the next generation ¾death by overcrowding: a live survival death by overcrowding cell with 4 of more neighbors dies ¾death by loneliness: a live cell with 1 neighbor or less dies ¾birth: an empty cell adjacent to exactly 3 live cells becomes live
death by isolation birth
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 52 2. A Complex Systems Sampler a. Cellular automata – 1-D binary automata
History NetLogo model: /Computer Science/Cellular Automata/CA 1D Elementary ¾“elementary CAs” = black and white pixels on one row ¾like the Game of Life, simple rules depending on nearest neighbors only (here, 2) repeating: Rule 250 nesting: Rule 90 ¾total number of rules = 2^(2^3) = 256 ¾Wolfram’s attempt to classify them in four major groups: repetition randomness: Rule 30 localized structures: Rule 110 nesting [apparent] randomness localized structures (“complex”)
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 53 2. A Complex Systems Sampler a. Cellular automata
Concepts collected from these examples ¾ large number of elements = pixels ¾ ultra-simple local rules ¾ emergence of macroscopic structures (patterns >> pixels) ¾ complex & diverse patterns (self- reproducible, periodic, irregular)
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 54 ComplexComplex SystemsSystems MadeMade SimpleSimple 1. Introduction
2. A Complex Systems Sampler a. Cellular automata • Physical: convection cells b. Pattern formation: • Biological: animal colors; slime mold c. Swarm intelligence • Chemical: BZ reaction d. Complex networks e. Spatial communities f. Structured morphogenesis 3. Commonalities
4. NetLogo Tutorial
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 55 2. A Complex Systems Sampler b. Pattern formation – Physical: convection cells
Phenomenon ¾“thermal convection” is the motion of fluids caused by a temperature differential ¾observed at multiple scales, Rayleigh-Bénard convection cells Convection cells in liquid (detail) whether frying pan or in liquid heated uniformly from below (Manuel Velarde, Universidad Complutense, Madrid) (Scott Camazine, http://www.scottcamazine.com) geo/astrophysical systems ¾spontaneous symmetry- breaking of a homogeneous state ¾formation of stripes and cells, several order of magnitudes larger than molecular scale
Sand dunes Solar magnetoconvection (Scott Camazine, http://www.scottcamazine.com) (Steven R. Lantz, Cornell Theory Center, NY)
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 56 2. A Complex Systems Sampler b. Pattern formation – Physical: convection cells
Mechanism ¾warm fluid is pushed up from the bottom ΔT by surrounding higher density (buoyancy force) ¾cold fluid sinks down from the top due to surrounding lower density Schematic convection dynamics (Arunn Narasimhan, Southern Methodist University, TX) ¾accelerated motion ¾viscosity and thermal diffusion normally counteract buoyancy... ¾... but only up to a critical temperature differential ΔTc
¾beyond ΔTc buoyancy takes over and breaks up the fluid into alternating rolls Hexagonal arrangement of sand dunes (Solé and Goodwin, “Signs of Life”, Perseus Books)
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 57 2. A Complex Systems Sampler b. Pattern formation – Physical: convection cells
Modeling & simulation ¾surfaces of constant temperatures (red for hot, blue for cold) ¾visualization of ascending and descending currents ¾notice the moving cell borders at the top ¾marginal case of multi-agent modeling: top-down modeling by discretization of macroscopic differential equations
Convection dynamics (Stéphane Labrosse, Institut de Physique du Globe, Paris) extremely fine-grain and dense distribution of agents = fixed grid
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 58 2. A Complex Systems Sampler b. Pattern formation – Physical: convection cells
Concepts collected from this example ¾ large number of elementary constituents ¾ emergence of macroscopic structures (convection cells >> molecules) ¾ self-arranged patterns ¾ amplification of small fluctuations (positive feedback, symmetry breaking) ¾ phase transition ¾ far from equilibrium
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 59 2. A Complex Systems Sampler b. Pattern formation – Biological: animal colors
Phenomenon ¾rich diversity of pigment patterns across species ¾evolutionary advantage: warning camouflage, mimicry sexual attraction individual recognition etc.
Mammal fur, seashells, and insect wings (Scott Camazine, http://www.scottcamazine.com)
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 60 2. A Complex Systems Sampler b. Pattern formation – Biological: animal colors
Possible mechanism (schematic) ctivator ¾development of spots and stripes on nhibitor mammal fur ¾melanocytes (pigment cells) can be undifferentiated “U”, or differentiated “D” ¾only D cells produce color → they diffuse two morphogens, activator “A” and inhibitor “I” ¾neighboring cells differentiate or not according to: short-range activation long-range inhibition
David Young’s model of fur spots and stripes ¾a classical case of reaction-diffusion (Michael Frame & Benoit Mandelbrot, Yale University)
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 61 2. A Complex Systems Sampler b. Pattern formation – Biological: animal colors
NetLogo model: /Biology/Fur
NetLogo fur coat simulation, after David Young’s model (Uri Wilensky, Northwestern University, IL)
Modeling & simulation ¾each cell’s state is updated by: ¾example of cellular counting pigmented neighbors within radius 3 (they contribute to automaton activation) ¾each cell has 2 states: counting pigmented neighbors “pigmented” (black) between radius 3 and 6 (they contribute to inhibition) “undifferentiated” (white) calculating weighted vote
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 62 2. A Complex Systems Sampler b. Pattern formation – Biological: animal colors
Concepts collected from this example ¾ simple microscopic rules ¾ emergence of macroscopic structures (spots >> cells) ¾ self-arranged patterns (random, unique) ¾ amplification of small fluctuations (positive feedback, symmetry breaking) ¾ local cooperation, distant competition (cell ↔ cell)
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 63 2. A Complex Systems Sampler b. Pattern formation – Biological: slime mold
Phenomenon ¾unicellular organisms (amoebae) clump together into multicellular “slugs” ¾with enough food, they grow and divide independently ¾under starvation, they synchronize (chemical waves), aggregate and differentiate ¾aggregation phase shows same concentric wave patterns as BZ reaction ¾a famous example of “excitable medium” and self-organization Synchronization, breakup and aggregation of slime mold amoebae on an agar plate (P. C. Newell; from Brian Goodwin, “How the leopard changed its spots”, Princeton U. Press)
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 64 2. A Complex Systems Sampler b. Pattern formation – Biological: slime mold
Mechanism ¾life cycle of slime mold amoebae (Dictyostelium): independent amoebae (A) → aggregation
(A) → clump → slug → growth → body & fruit → spore release & germination
Life cycle of Dictyostelium slime mold → amoebae (A) (Ivy Livingstone, BIODIDAC, University of Ottawa)
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 65 2. A Complex Systems Sampler b. Pattern formation – Biological: slime mold
Mechanism ¾life cycle of slime mold amoebae (Dictyostelium): independent amoebae (A) → aggregation stage 1: oscillatory secretion of (A) chemical (cAMP) by each cell stage 2: local coupling of secretion signal, forming spiral waves stage 3: pulsatile motion toward spiral centers → clump
Life cycle of Dictyostelium slime mold (Ivy Livingstone, BIODIDAC, University of Ottawa) → ...
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 66 2. A Complex Systems Sampler b. Pattern formation – Biological: slime mold
NetLogo model: /Biology/Slime
NetLogo simulation of slime mold aggregation, after Mitchel Resnick (Uri Wilensky, Northwestern University, IL)
Modeling & simulation ¾for clumping (stage 3 of aggregation), ¾for wave formation (stages 1 three simplified rules: & 2 of aggregation) each cell (red) secretes a chemical (shades of green) → see B-Z reaction model each cell moves towards greater concentration of chemical chemical evaporates
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 67 2. A Complex Systems Sampler b. Pattern formation – Biological: slime mold
Concepts collected from this example ¾ simple, “blind” individual behavior ¾ emergence of aggregates ¾ cluster centers are not already differentiated cells (decentralization) ¾ local interactions (cell ↔ chemical) ¾ phase transition (critical mass)
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 68 2. A Complex Systems Sampler b. Pattern formation – Chemical: BZ reaction
Phenomenon ¾Belousov-Zhabotinsky reaction: “chemical clock” ¾if well stirred, it oscillates ¾if spread on a plate, it creates waves (reaction- diffusion) ¾example of an “excitable medium” ¾often cited in self-
The Belousov-Zhabotinsky reaction Spiral and circular traveling waves organization (a) well-stirred tank; (b) Petri dish in the Belousov-Zhabotinsky reaction (Gabriel Peterson, College of the Redwoods, CA) (Arthur Winfree, University of Arizona)
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 69 2. A Complex Systems Sampler b. Pattern formation – Chemical: BZ reaction
Mechanism
(A) ¾in each elementary volume of solution, there is competition between two reaction branches, A and B ¾A is faster than B, but B is autocatalytic ¾when A runs out of reactants, B takes over and regenerates them (B) ¾a color indicator signals the oscillation between A and B through iron ions 2+ 3+ Simplified diagram of the Belousov-Zhabotinsky reaction (Fe /Fe ) (Gabriel Peterson, College of the Redwoods, CA)
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 70 2. A Complex Systems Sampler b. Pattern formation – Chemical: BZ reaction
NetLogo model: /Chemistry & Physics/Chemical Reactions/B-Z Reaction
NetLogo B-Z reaction simulation, after A. K. Dewdney’s “hodgepodge machine” (Uri Wilensky, Northwestern University, IL)
Modeling & simulation ¾abstract, simplified rules ¾each cell follows 3 rules that create a cycle: ¾each cell has 3 states: if “healthy, become “infected” as a function of neighbors “healthy” (x = 0, black) if “infected”, increase infection “infected” (0 < x < 1, red) level as a function of neighbors “sick” (x = 1, white) if “sick”, become “healthy”
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 71 2. A Complex Systems Sampler b. Pattern formation – Chemical: BZ reaction
Concepts collected from this example ¾ simple individual rules (modeling a less simple, but small set of reactions) ¾ emergence of long-range spatiotemporal correlations ¾ no impurities; spiral centers are not specialized (decentralization) ¾ local interactions by reaction and diffusion
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 72 ComplexComplex SystemsSystems MadeMade SimpleSimple 1. Introduction
2. A Complex Systems Sampler a. Cellular automata b. Pattern formation • Insect colonies: ant trails; termites c. Swarm intelligence: • Collective motion: flocking; traffic jams d. Complex networks • Synchronization: fireflies; neurons e. Spatial communities f. Structured morphogenesis 3. Commonalities
4. NetLogo Tutorial
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 73 2. A Complex Systems Sampler c. Swarm intelligence – Insect colonies: ant trails
Phenomenon ¾insect colonies are the epitome of complex systems, self-organization and emergence ¾one striking example of collective behavior: spontaneous trail formation by ants, without anyone having a map ¾two-way trails appear between nest and food source, brooding area or cemetery
White-footed ants trailing on a wall ¾ants carry various items back and (J. Warner, University of Florida) forth on these trails ¾the colony performs collective optimization of distance and productivity without a leader
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 74 2. A Complex Systems Sampler c. Swarm intelligence – Insect colonies: ant trails
Basic mechanism ¾while moving, each ant deposits a chemical (“pheromone”) to signal the path to other ants ¾each ant also “smells” and follows the pheromone gradient laid down by others
Harvester ant (Deborah Gordon, Stanford University)
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 75 2. A Complex Systems Sampler c. Swarm intelligence – Insect colonies: ant trails
NetLogo model: /Biology/Ants
StarLogo ant foraging simulation, after Mitchel Resnick (StarLogo Project, MIT Media Laboratory, MA)
Modeling & simulation ¾ant’s behavioral repertoire: ¾typical result: food sources are exploited ¾setup: walk around randomly if bump into food, pick it and in order of increasing 1 nest (purple) return to nest distance and 3 food sources if carrying food, deposit decreasing richness (blue spots) pheromone (green) 100 to 200 ants ¾emergence of a if not carrying food, follow (moving red dots) collective “intelligent” pheromone gradient decision 7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 76 2. A Complex Systems Sampler c. Swarm intelligence – Insect colonies: ant trails
Concepts collected from this example ¾ simple individual rules ¾ emergence of collective computation ¾ no leader, no map (decentralization) ¾ amplification of small fluctuations (positive feedback) ¾ local interactions (ant ↔ environment) ¾ phase transition (critical mass = minimal number of ants)
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 77 2. A Complex Systems Sampler c. Swarm intelligence – Insect colonies: termite mounds
Phenomenon ¾another spectacular example of insect self-organization: mound building by termites ¾remarkable size and detailed architecture ¾essentially made of tiny pellets of soil glued together ¾starts with one underground chamber and grows up like a plant
Termite mound Inside of a termite mound (J. McLaughlin, Penn State University) (Lüscher, 1961)
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 78 2. A Complex Systems Sampler c. Swarm intelligence – Insect colonies: termite mounds
Mechanism ¾no plan or central control ¾termites interact indirectly, through the environment they are modifying ¾“stigmergy” is a set of stimulus- response pairs: pattern A in environment triggers behavior R in termite behavior R changes A into A1 pattern A1 triggers behavior R1 behavior R1 changes A1 into A2 etc. ¾for example, a small heap develops into an arch Termite stigmergy (after Paul Grassé; from Solé and Goodwin, “Signs of Life”, Perseus Books)
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 79 2. A Complex Systems Sampler c. Swarm intelligence – Insect colonies: termite mounds
NetLogo model: /Biology/Termites
StarLogo termite mound building simulation, after Mitchel Resnick (StarLogo Project, MIT Media Laboratory, MA)
Modeling & simulation ¾simplified setup: ¾virtual termite’s repertoire: ¾result: wood chips randomly scattered walk around randomly are stacked in piles of wood chips (or soil if bump into wood chip, pick growing size pellets) it up and move away ¾explains one aspect termites moving if carrying wood chip, drop it of mound formation among the chips where other wood chips are
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 80 2. A Complex Systems Sampler c. Swarm intelligence – Insect colonies: termite mounds
Concepts collected from this example ¾ simple individual rules ¾ emergence of macroscopic structure ¾ no architect, no blueprint ¾ amplification of small fluctuations (positive feedback) ¾ local interactions (termite ↔ environment)
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 81 2. A Complex Systems Sampler c. Swarm intelligence – Collective motion: flocking
Giant flock of flamingos Fish school (John E. Estes, UC Santa Barbara, CA) (Eric T. Schultz, University of Connecticut) Phenomenon ¾coordinated collective movement of dozens or thousands of individuals ¾adaptive significance: prey groups confuse predators predator groups close in on prey Bison herd (Center for Bison Studies, Montana State University, Bozeman) increased aero/hydrodynamic efficiency
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 82 2. A Complex Systems Sampler c. Swarm intelligence – Collective motion: flocking
S Mechanism ¾Reynolds’ “boids” model ¾each individual adjusts its position, A orientation and speed according to its nearest neighbors ¾steering rules: separation: avoid crowding local interaction flockmates potential C cohesion: move toward average position of local flockmates alignment: adopt average heading of local flockmates
Separation, alignment and cohesion (“Boids” model, Craig Reynolds, http://www.red3d.com/cwr/boids)
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 83 2. A Complex Systems Sampler c. Swarm intelligence – Collective motion: flocking
NetLogo model: /Biology/Flocking
NetLogo flocking simulation, after Craig Reynolds’ “boids” model (Uri Wilensky, Northwestern University, IL)
Modeling & simulation
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 84 2. A Complex Systems Sampler c. Swarm intelligence – Collective motion: flocking
Concepts collected from this example ¾ simple individual rules ¾ emergence of coordinated collective motion ¾ no leader, no external reference point (decentralization) ¾ local interactions (animal ↔ animal) ¾ cooperation
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 85 2. A Complex Systems Sampler c. Swarm intelligence – Collective motion: traffic jams
Phenomenon ¾stream of cars breaks down into dense clumps and empty stretches ¾spontaneous symmetry-breaking of initially uniform density and speed ¾no need for a central cause (such as slow vehicle, stop light or Traffic jam (Department of Physics, University of Illinois at Urbana-Champaign) accident)
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 86 2. A Complex Systems Sampler c. Swarm intelligence – Collective motion: traffic jams
NetLogo model: /Social Science/Traffic Basic
Modeling & simulation ¾each car: slows down if there is another car close ahead speeds up if there is no car close ahead ¾traffic nodes move in the direction opposite to cars ¾emergence of group behavior qualitatively different from individual behavior
NetLogo traffic basic simulation, after Mitchel Resnick (Uri Wilensky, Northwestern University, IL)
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 87 2. A Complex Systems Sampler c. Swarm intelligence – Collective motion: traffic jams
Concepts collected from this example ¾ simple individual reactions ¾ emergence of moving superstructures ¾ no accident, no light, no police radar (decentralization) ¾ amplification of small fluctuations (positive feedback) ¾ local interactions (car ↔ car)
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 88 2. A Complex Systems Sampler c. Swarm intelligence – Synchronization: fireflies
Phenomenon ¾a swarm of male fireflies (beetles) synchronize their flashes ¾starting from random scattered flashing, pockets of sync grow and merge ¾adaptive significance: still unclear... cooperative behavior amplifies signal visibility to attract females (share the reward)? cooperative behavior helps blending in and avoiding predators (share the risk)? ... or competition to be the first to flash? ¾famous example of synchronization among independently sustained oscillators Fireflies flashing in sync on the river banks of Malaysia
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 89 2. A Complex Systems Sampler c. Swarm intelligence – Synchronization: fireflies
Mechanism ¾light-emitting cells (photocytes) located in the abdomen ¾1. each firefly maintains an internal regular cycle of flashing: Say's firefly, in the US (Arwin Provonsha, Purdue Dept of Entomology, IN) physiological mechanism still unclear... pacemaker cluster of neurons controlling the photocytes? autonomous oscillatory metabolism? ... or just the movie in repeat mode? :-) ¾2. each firefly adjusts its flashing cycle to its neighbors: pushing/pulling or resetting phase increasing/decreasing frequency Firefly flashing (slow motion) (Biology Department, Tufts University, MA)
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 90 2. A Complex Systems Sampler c. Swarm intelligence – Synchronization: fireflies
NetLogo model: /Biology/Fireflies
NetLogo fireflies simulation (Uri Wilensky, Northwestern University, IL)
Modeling & simulation ¾each firefly “cell”: ¾distributed system coordinates hovers around randomly itself without a central leader cycles through an internal flashing clock resets its clock upon seeing flashing in the vicinity
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 91 2. A Complex Systems Sampler c. Swarm intelligence – Synchronization: fireflies
Concepts collected from this example ¾ simple individual rules ¾ emergence of collective synchronization ¾ no conductor, no external pacemaker (decentralization) ¾ local interactions (insect ↔ insect) ¾ cooperation
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 92 2. A Complex Systems Sampler c. Swarm intelligence – Synchronization: neurons
Phenomenon ¾neurons together form... the brain! (+ peripheral nervous system) perception, cognition, action emotions, consciousness behavior, learning Medial surface of the brain (Virtual Hospital, University of Iowa) autonomic regulation: organs, glands ¾~1011 neurons in humans ¾communicate with each other through electrical potentials ¾neural activity exhibits specific patterns of spatial and temporal synchronization (“temporal code”) Pyramidal neurons and interneurons, precentral gyrus (Ramón y Cajal 1900)
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 93 2. A Complex Systems Sampler c. Swarm intelligence – Synchronization: neurons
Schematic neurons A binary neural network (adapted from CS 791S “Neural Networks”, Dr. George Bebis, UNR)
Mechanism ¾each neuron receives signals from many other neurons through its dendrites ¾the signals converge to the soma (cell body) and are integrated ¾if the integration exceeds a threshold, the neuron fires a signal on its axon
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 94 2. A Complex Systems Sampler c. Swarm intelligence – Synchronization: neurons
high activity rate
high activity rate
high activity rate
low activity rate
low activity rate
low activity rate
¾ 1 and 2 more in sync than 1 and 3
¾ 4, 5 and 6 correlated through delays
7/16-18/2008 IXXI / ISC-PIF Summer School 2008 - René Doursat: "Complex Systems Made Simple" 95