biologically-inspired computing lecture 9 Informatics luis rocha 2015 INDIANA UNIVERSITY biologically Inspired computing

Transcription

1 luis ocha 25 lectue 9 -inspied

2 luis ocha 25 Sections I485/H4 couse outlook Assignments: 35% Students will complete 4/5 assignments based on algoithms pesented in class Lab meets in I (West) 9 on Lab Wednesdays Lab : Januay 4 th (completed) Intoduction to Python (No Assignment) Lab : Januay 28 th Measuing Infomation (Assignment ) Gaded Lab 2 : Febuay th L-Systems (Assignment 2) Due Febuay 25 th Lab 3: Mach th Cellula Automata and Boolean Netwoks (Assignment 3)

3 luis ocha 25 Readings until now Class Book Nunes de Casto, Leando [26]. Fundamentals of Natual Computing: Basic Concepts, Algoithms, and Applications. Chapman & Hall. Chapte 2, all sections Chapte 7, sections 7.3 Cellula Automata Chapte 8, sections 8., 8.2, 8.3. Lectue notes Chapte : What is Life? Chapte 2: The logical Mechanisms of Life Chapte 3: Fomalizing and Modeling the Wold Chapte 4: Self-Oganization and Emegent Comple Behavio posted Optional Flake s [998], The Computational Beauty of Life. MIT Pess. Chaptes,, 4 Dynamics, Attactos and chaos

4 luis ocha 25 quadatic equation The logistic map Demogaphic model intoduced by Piee Fançois Vehulst in 838 Continuous state-detemined system Memoy of the pevious state only Obsevations X: population etinct X: Ovepopulation, leads to etinction Population size positive feedback negative feedback [,] [,4] ( t+ t t ) Repoduction ate

5 luis ocha 25 plot logistic map t+ f ( ) ( t+ t t ) [,] /4 [,4] f /2 ( ) ( ) f ( ) -/ t f ( ) ( 2), f ( ) f ( ) ( ( ) + ) ( ) Fied-point attactos < stable > unstable

6 Infomatics luis ocha 25 logistic map > < unstable ) ( stable ) ( ), 2 ( ) ( f f f > < unstable stable, ) 2 ( ) ( f

7 luis ocha 25 3 logistic map -/ f ( ) ( 2), f f ( ) < stable ( ) > unstable f ( ) f ( ) 2

8 luis ocha ( 3.44) logistic map f ( ) < stable f ( ) ( 2), f ( ) > unstable f ( ) 2 f ( ) Limit cycle f ( f ( ))

9 luis ocha ( ) logistic map f ( f ( f ( f ( )))) Limit cycle

10 luis ocha 25 4 logistic map Chaotic Deteministic Sensitive egodic

11 luis ocha 25 movie logistic map

12 luis ocha 25 bifucation map logistic map Peiod doubling

13 luis ocha 25 bifucation map logistic map Peiod doubling Chaotic Deteministic (not andom) Sensitive egodic

14 luis ocha 25 bifucation map: cycle of 3 logistic map f ( f ( f ( ))) Peiod doubling

15 luis ocha 25 eploing similaities acoss natue Natual design pinciples self-simila stuctues Tees, plants, clouds, mountains mophogenesis Mechanism Iteation, ecusion Unpedictability Fom limited knowledge o inheent in natue? Mechanism Chaos (sensitivity to initial conditions, egodicity) Collective behavio, emegence, and self-oganization Comple behavio fom collectives of many simple units o agents cellula automata, ant colonies, development, mophogenesis, bains, immune systems, economic makets Mechanism Paallelism, multiplicity, edundancy, attacto beghavio, emegent computation Adaptation Evolution, leaning, social evolution Mechanism Repoduction, tansmission, vaiation, selection, Tuing s tape Netwok causality (compleity) Behavio deived fom many insepaable souces Envionment, embodiment, epigenetics, cultue Mechanism Modulaity, connectivity, stigmegy

16 luis ocha 25 eamples t Cellula Automata - + discete dynamical systems NK Boolean Netwok (N3, K3) RBNLAB (Calos Geshenson):

17 luis ocha 25 Stuat Kauffman NK Boolean Netwok (N3, K3) NK-netwoks 2 2 K #nodes (Boolean vaiables) # of inputs pe node 2 K possible input combinations fo an automaton node possible Boolean functions of k inputs 2 2 p.25 K2 2 p: bias, o popotion of s (o s ) in output Self-oganization: solely dependent on its own ules

18 luis ocha 25 Small NK-netwok n and p q p q simple Boolean netwok State space n 3 n 2 o o t t+ n n 2 n 3 n n 2 n 3 p q p q

19 luis ocha 25 Eample: attactos n and t t+ n n 2 n 3 n n 2 n simple Boolean netwok n 3 n o o : 7 7 4: : 2: 5: 3: 7: 6:

20 luis ocha 25 state-space (State-tansition Gaph) : : 2: simple Boolean netwok : 5: 3: 7: 6: 2 3 In discete dynamical systems thee must always eist at least one cycle, because thee is only a finite numbe of states, eventually the system must epeat a pevious state.

21 Small Boolean netwok luis ocha 25 SimpleNet

22 luis ocha 25 dynamical landscape of SimpleNet State-tansition gaph (basins of attaction) Thee ae possible states but only a small set of attactos

23 luis ocha 25 Small Boolean netwok SimpleNet: dynamical landscape (basins of attaction) Thee ae possible states but only a small set of attactos

24 luis ocha 25 eamples discete dynamical systems NK Boolean Netwok (N3, K3) DDLab (Andy wuensche): Thee ae possible states but only a small set of attactos

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26 luis ocha 25 self-oganization attacto behavio The states in state space ae oganized into 5 basins attacto peiods anging between and 7. The numbe of states in each basin is: 68, 984, 784, 3, 264, 76,36, 2, 64, 2, 256, 2724,64, 84, 428.

27 luis ocha 25 eadings Net lectues Class Book Nunes de Casto, Leando [26]. Fundamentals of Natual Computing: Basic Concepts, Algoithms, and Applications. Chapman & Hall. Chapte 2, all sections Chapte 7, sections 7.3 Cellula Automata Chapte 8, sections 8., 8.2, 8.3. Lectue notes Chapte : What is Life? Chapte 2: The logical Mechanisms of Life Chapte 3: Fomalizing and Modeling the Wold Chapte 4: Self-Oganization and Emegent Comple Behavio posted Papes and othe mateials Optional Flake s [998], The Computational Beauty of Life. MIT Pess. Chaptes,, 4 Dynamics, Attactos and chaos