biologically-inspired computing luis rocha 2015 lecture 12 - - PowerPoint PPT Presentation

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Info rm atics biologically-inspired computing luis rocha 2015 lecture 12 biologically Inspired computing rocha@indiana.edu INDIANA UNIVERSITY http://informatics.indiana.edu/rocha/i-bic Info rm atics course outlook luis rocha 2015

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

biologically Inspired computing

INDIANA UNIVERSITY

Informatics luis rocha 2015

biologically-inspired computing lecture 12

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biologically Inspired computing

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

INDIANA UNIVERSITY

Informatics luis rocha 2015

course outlook

 Assignments: 35%

 Students will complete 4/5 assignments based

  • n 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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biologically Inspired computing

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

INDIANA UNIVERSITY

Informatics luis rocha 2015

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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biologically Inspired computing

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

INDIANA UNIVERSITY

Informatics luis rocha 2015

final project schedule

 Projects

 Due by May 4th in Oncourse

 ALIFE 15 (14)

 Actual conference due date: 2016  http://blogs.cornell.edu/alife14nyc/  8 pages (LNCS proceedings format)  http://www.springer.com/computer/lncs?SGWI

D=0-164-6-793341-0

 Preliminary ideas due by April 1st!

 Individual or group

 With very definite tasks assigned per

member of group

ALIFE 15

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

biologically Inspired computing

INDIANA UNIVERSITY

Informatics luis rocha 2015

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 template N

N N

K = Σ ∈ α α ,

Number of possible neighborhood states

N

K

K D =

Number of possible transition functions

Example K=8 N=5 |α|=37,768 D ≈1030,000

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biologically Inspired computing

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

INDIANA UNIVERSITY

Informatics luis rocha 2015

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

K n K − = λ

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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biologically Inspired computing

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

INDIANA UNIVERSITY

Informatics luis rocha 2015

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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biologically Inspired computing

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

INDIANA UNIVERSITY

Informatics luis rocha 2015

Computation at the edge of chaos?

Transition region

 Supports both static and propagating structures

 λ =0.4+

 Propagating waves (“signals”?) across the CA lattice

 Necessary for computation?  Signals and storage?

Computation

 Requires storage and transmission of information  Any dynamical system supporting computation must exhibit

long-range signals in space and time

Wolfram’s CA classes

 I: homogeneous state

 Steady-state

 II: periodic state

 Limit cycles

 III: chaotic  IV: complex patterns of localized structures

 Long transients  Capable of universal computation

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

biologically Inspired computing

INDIANA UNIVERSITY

Informatics luis rocha 2015 quorum sensing or what decision to take? (Density Classification)

imagine automata as agents

128 27 = =

N

K

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biologically Inspired computing

INDIANA UNIVERSITY

Informatics luis rocha 2015 density classification task

random strategies

128 27 = =

N

K

Typically chaotic behavior No convergence

= P

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

biologically Inspired computing

INDIANA UNIVERSITY

Informatics luis rocha 2015 density classification task

local strategy: majority rule

128 27 = =

N

K

= P

Isolated groups No information transmission

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

biologically Inspired computing

INDIANA UNIVERSITY

Informatics luis rocha 2015 density classification task

block expansion strategy

128 27 = =

N

K

[ ]

% 60 %, 53 ∈ P

“blind” spreading of local information No information integration Not much better than random choice

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

biologically Inspired computing

INDIANA UNIVERSITY

Informatics luis rocha 2015 density classification task

emergent computation strategies

128 27 = =

N

K

Integration and transmission of information across population

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

biologically Inspired computing

INDIANA UNIVERSITY

Informatics luis rocha 2015 for DST

best CA rules

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biologically Inspired computing

Informatics luis rocha 2015

How to characterize complex behavior?

collective (emergent) computation via computational mechanics

Crutchfield & Mitchell [1995]. PNAS 92: 10742-10746

GA to evolve rules for DCT [1994]

Das, Mitchell & Crutchfield [1994]. In: Parallel Problem Solving from Nature-III: 344-353.

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

biologically Inspired computing

INDIANA UNIVERSITY

Informatics luis rocha 2015

the game of life

John Horton Conway

2-D

x

Sum N8 1 2 3 4 5 6 7 8 xi,i= 0 0 1 0 0 0 0 xi,i= 1 1 1 0 0 0 0

Introduced in Martin Gardner’s Scientific American “Mathematical Games” Column in 1970. Conway was interested in a rule that for certain initial conditions would produce patterns that grow without limit, and some others that fade or get stable. Popularized CAs.

1)

Any living cell with fewer than two neighbors dies of loneliness.

2)

Any living cell with more than three neighbors dies of crowding.

3)

Any dead cell with exactly three neighbors comes to life.

4)

Any living cell with two or three neighbors lives, unchanged, to the next generation

{ }

1 ,

, = j i

x

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biologically Inspired computing

INDIANA UNIVERSITY

Informatics luis rocha 2015

game of life

wide dynamic range

Simple Attractors Blinkers block More complicated attractors

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biologically Inspired computing

INDIANA UNIVERSITY

Informatics luis rocha 2015

game of life

moving patterns

Glider

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biologically Inspired computing

INDIANA UNIVERSITY

Informatics luis rocha 2015

unbounded growth

a threshold of complexity?

R-pentomino runs 1103 steps before settling down into 6 gliders, 8 blocks, 4 blinkers, 4 beehives, 1 boat, 1 ship, and 1 loaf.

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biologically Inspired computing

INDIANA UNIVERSITY

Informatics luis rocha 2015

the glider gun

Unbounded growth but not complexity

Fires a glider every 30 iterations.

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biologically Inspired computing

INDIANA UNIVERSITY

Informatics luis rocha 2015

life and information

unbounded complexity requires information

1)

Patterns that can implement information, descriptions, and construction

2)

Gliders, guns, blocks, eaters

Universal Turing Machine on game of life!!!

Very brittle Built, not evolved Not evolving

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biologically Inspired computing

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

INDIANA UNIVERSITY

Informatics luis rocha 2015

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biologically Inspired computing

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

INDIANA UNIVERSITY

Informatics luis rocha 2015

Rule 110

Radius 1

 Neighborhood =3

Binary

 23 = 8 input neighborhoods  28 = 256 rules

http://mathworld.wolfram.com/Rule110.html

information in attractor patterns

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biologically Inspired computing

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

INDIANA UNIVERSITY

Informatics luis rocha 2015

computing structures in rule 110

Universal Computation

Identification of gliders, spaceships, and other long-range or self- perpetuating patterns

 On the background domain produced by rule 110

14 cells repeat every seven iterations: 00010011011111

Collisions and combinations of glider patterns are exploited for computation.

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biologically Inspired computing

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

INDIANA UNIVERSITY

Informatics luis rocha 2015

computation and the edge of chaos

Many systems biology models operate in the ordered regime

Dynamical systems capable of computation exist well before the edge

  • f chaos

A much wider transition? A “band” of chaos.

Most important information transmission and computation in Biology an altogether different process than self-organization

Turing/Von Neumann Tape

is self-organization enough?

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biologically Inspired computing

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

INDIANA UNIVERSITY

Informatics luis rocha 2015

Next lectures

 Class Book

 Nunes de Castro, Leandro [2006]. Fundamentals of

Natural Computing: Basic Concepts, Algorithms, and

  • Applications. Chapman & Hall.

 Chapter 2, 7, 8

 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