Info biologically-inspired computing · [email protected] biologically Inspired computing INDIANA UNIVERSITY Informatics luisrocha2015 biologically-inspired computing

[email protected]://informatics.indiana.edu/rocha/i-bic

biologicallyInspired

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Informatics luis rocha 2015

biologically-inspired computinglecture 11


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course outlook

Assignments: 35% Students will complete 4/5 assignments based

on algorithms presented in class Lab meets in I1 (West) 109 on Lab

Wednesdays Lab 0 : January 14th (completed)

Introduction to Python (No Assignment) Lab 1 : January 28th

Measuring Information (Assignment 1) Graded

Lab 2 : February 11th

L-Systems (Assignment 2) Graded

Lab 3: March 11th

Cellular Automata and Boolean Networks (Assignment 3)

Sections I485/H400


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Readings until now

Class Book Nunes de Castro, Leandro [2006]. Fundamentals of Natural

Computing: Basic Concepts, Algorithms, and Applications. Chapman & Hall. Chapter 2, all sections Chapter 7, sections 7.3 – Cellular Automata Chapter 8, sections 8.1, 8.2, 8.3.10

Lecture notes Chapter 1: What is Life? Chapter 2: The logical Mechanisms of Life Chapter 3: Formalizing and Modeling the World Chapter 4: Self-Organization and Emergent

Complex Behavior posted online @ http://informatics.indiana.edu/rocha/i-

bic Optional

Flake’s [1998], The Computational Beauty of Life. MIT Press. Chapters 10, 11, 14 – Dynamics, Attractors and chaos



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highlightsLab 2: L-Systems

Tyler WojcikMatthew Remmel

Darlan Farias



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Darlan Farias

Michael Sorg

Kendall Ebley



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Darlan Farias

Michael Sorg

Kendall Ebley

Rafael Paiva

Edward Lautzenhiser



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Darlan Farias

Michael Sorg

Kendall Ebley

Rafael Paiva

Edward Lautzenhiser

Jonathan Stout


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Kauffman’s statistical analysis

Random networks Started with random initial conditions

Self-organization is not a result of special initial conditions

Statistical analysis K 2

Steady state, ordered, crystallization (5 K to ) K=N

Disordered, chaotic Mean length of cycles: 0.5 x 2N/2

Mean number of cycles: N/e High reachability, sensitive to perturbation

Number of other state cycles system can reach after perturbation

K=2 Mean length: n1/2

Mean number of cycles: n1/2

Low reachability Percolation of frozen clusters (isolated subsets) Not very sensitive to perturbation

Of NK-Boolean Networks


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edge of chaos on Boolean Networks

2 K 5 Good for evolvability? Some changes with large repercussions Best capability to perform information exchange

Information can be propagated more easily Problems with analysis

Network topology is random Not scale-free, as later explored by Aldana

Real genetic networks tend to have lower values of K (in ordered regime)

Genes as simply Boolean may be oversimplification Though a few states can approximate very well continuous

data

criticality



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dynamical behavior of ensembles of networkscriticality in Boolean networks

Aldana, M. [2003]. Physica D. 185: 45–66

Random topology

scale-free topology



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Criticality in Boolean Networks

Marques-Pita, Manicka, Teuscher & Rocha, [2015]. In Prep.

Current theory

kp 211

21

Aldana, M. [2003]. Physica D. 185: 45–66



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criticality in the presence of canalizationinput redundancy, effective connectivity

kFf f

r

nxk

2

max #

|

xkxkxk re )()(

ecrit k

p 32.0

kp 211

21

Marques-Pita, Manicka, Teuscher & Rocha, [2014]. In preparation.

Current Theory (CT): No redundancy is considered, only connectivity and bias of logical functions. Green: stable ensembles of BN. Red chaotic ensembles of BN. Blue line, criticality region for CT.

New Theory (NT): Redundancy is considered, as effective connectivity (a form of canalization and dynamical redundancy). Red chaotic ensembles of BN. Blue line, criticality region for NT.



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criticality in the presence of canalizationinput redundancy, effective connectivity

kFf f

r

nxk

2

max #

|

xkxkxk re )()(

ecrit k

p 32.0

kp 211

21

Marques-Pita, Manicka, Teuscher & Rocha, [2014]. In preparation.

Current Theory (CT): No redundancy is considered, only connectivity and bias of logical functions. Green: stable ensembles of BN. Red chaotic ensembles of BN. Blue line, criticality region for CT.

New Theory (NT): Redundancy is considered, as effective connectivity (a form of canalization and dynamical redundancy). Red chaotic ensembles of BN. Blue line, criticality region for NT.



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Boolean networks, sound, art, and educationself-organization and the cybernetics of life

Chaos et al [2006]. “From Genes to Flower Patterns and Evolution: Dynamic Models of Gene Regulatory Networks”. Journal of Plant Growth Regulation. 25(4): 278-289.



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Cellular automatahomogenous lattice of state-determined systems

xx-1 x+1

Cellular Automata

xt

2-D

},...2,1,0{

,...,..., 1

sxxxxfx t

riiriti

1-D

x

1,,,, ,...,..., t

rjrijirjrit

ji yxyxxxxfx

Toroidal LatticeToroidal LatticeToroidal Lattice

Space-time diagram


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cellular automata

Parallel updating Artificial physics

Local interactions only No actions at a distance

Homogeneous Unpredictable global behavior

Emergence 2-levels: rules (micro-level) and

attractor behavior (macro-level) Irreversible

Self-organization Example rules

Rug (diffusion) 256 states Average of 8 neighbors in 2-d grid, if

state is 255 -> 0. Vote/majority

binary


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elementary CA rules Radius 1

Neighborhood =3 Binary

23 = 8 input neighborhoods 28 = 256 rules

http://mathworld.wolfram.com/CellularAutomaton.html

xx-1 x+1

Cellular Automata

xt



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state-determined transitionsCellular automata


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Living patterns easily replicated in CA



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What’s a CA?more formally

D-dimensional lattice L with a finite automaton in each lattice site (cell)

State-determined system finite number of states Σ: K=| Σ|

E.g. Σ = {0,1} finite input alphabet α transition function Δ: α→Σ

uniquely ascribes state s in Σ to input patterns α

Neighborhood templateN

NN K ,Number of possible

neighborhood states

NKKD Number of possible

transition functions

ExampleK=8N=5|α|=37,768D 1030,000


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Langton’s parameter

Statistical analysis Identify classes of transition functions with similar behavior

Similar dynamics (statistically) Via Higher level statistical observables

Like Kauffman The Lambda Parameter (similar to bias in BN)

Select a subset of D characterized by λ Arbitrary quiescent state: sq

Usually 0 A particular function Δ has n transitions to this state and (KN-n)

transitions to other states s of Σ (1-λ) is the probability of having a sq in every position of the rule table

Finding the structure of all possible transition functions

Langton, C.G. [1990]. “Computation at the edge of chaos: phase transitions and emergent computation”. Artificial Life II. Addison-Wesley.

N

N

KnK

λ = 0: all transitions lead to sq (n =KN)λ = 1: no transitions lead to sq (n =0)λ = 1-1/K: equally probable states ( n=1/K . KN)

Range: from most homogeneous to most heterogeneous


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Langton’s observations λ only correlates well with dynamic behavior for fairly large values

of K and N E.g. K≥4 and N≥5

Experiments K=4, N=5


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Langton’s results


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Langton’s results

Approximate time when density is within 1% of long-term behavior


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Langton’s results



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Langton’s results



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Edge of chaos

Transient growth in the vicinity of phase transitions Length of CA lattice only relevant around phase transition (λ=0.5)

Conclusion: more complicated behavior found in the phase transition between order and chaos Patterns that move across the lattice

A phase transition?


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Next lectures

Class Book Nunes de Castro, Leandro [2006]. Fundamentals of Natural

Computing: Basic Concepts, Algorithms, and Applications. Chapman & Hall. Chapter 2, all sections Chapter 7, sections 7.3 – Cellular Automata Chapter 8, sections 8.1, 8.2, 8.3.10

Lecture notes Chapter 1: What is Life? Chapter 2: The logical Mechanisms of Life Chapter 3: Formalizing and Modeling the World Chapter 4: Self-Organization and Emergent Complex

Behavior posted online @ http://informatics.indiana.edu/rocha/i-bic

Papers and other materials Optional

Flake’s [1998], The Computational Beauty of Life. MIT Press. Chapters 10, 11, 14 – Dynamics, Attractors and chaos

readings

Documents

Info biologically-inspired computing · [email protected] biologically Inspired computing INDIANA UNIVERSITY Informatics luisrocha2015 biologically-inspired computing