biologically-inspired computing lecture 12 Informatics luis rocha 2015 INDIANA UNIVERSITY biologically Inspired computing

Transcription

1 lecture 12 -inspired

2 Sections I485/H400 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 14 th (completed) Introduction to Python (No Assignment) Lab 1 : January 28 th Measuring Information (Assignment 1) Graded Lab 2 : February 11 th L-Systems (Assignment 2) Graded Lab 3: March 11 th Cellular Automata and Boolean Networks (Assignment 3)

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

4 final project schedule ALIFE 15 Projects Due by May 4 th in Oncourse ALIFE 15 (14) Actual conference due date: pages (LNCS proceedings format) D= Preliminary ideas due by April 1 st! Individual or group With very definite tasks assigned per member of group

5 more formally D-dimensional lattice L with a finite automaton in each lattice site (cell) What s a CA? Neighborhood template N 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 Example K=8 N=5 α =37,768 D 10 30,000 N α Σ, α = K N D = K Number of possible neighborhood states K N Number of possible transition functions

6 Finding the structure of all possible transition functions 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: s q Usually 0 A particular function Δ has n transitions to this state and (K N -n) transitions to other states s of Σ (1-λ) is the probability of having a s q in every position of the rule table λ = N K n K N Range: from most homogeneous to most heterogeneous Langton, C.G. [1990]. Computation at the edge of chaos: phase transitions and emergent computation. Artificial Life II. Addison-Wesley. λ = 0: all transitions lead to s q (n =K N ) λ = 1: no transitions lead to s q (n =0) λ = 1-1/K: equally probable states ( n=1/k. K N )

7 A phase transition? 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

8 Transition region Computation at the edge of chaos? 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

9 imagine automata as agents quorum sensing or what decision to take? (Density Classification) K N = 2 7 =128

10 density classification task random strategies K N = 2 7 =128 P = 0 Typically chaotic behavior No convergence

11 density classification task local strategy: majority rule K N = 2 7 =128 P = 0 Isolated groups No information transmission

12 density classification task block expansion strategy K N = 2 7 =128 P [ 53%,60% ] blind spreading of local information No information integration Not much better than random choice

13 density classification task emergent computation strategies K N = 2 7 =128 Integration and transmission of information across population

14 for DST best CA rules

15 How to characterize complex behavior? collective (emergent) computation via computational mechanics Crutchfield & Mitchell [1995]. PNAS 92: GA to evolve rules for DCT [1994] Das, Mitchell & Crutchfield [1994]. In: Parallel Problem Solving from Nature-III:

16 John Horton Conway 2-D the game of life x x i, j = { 0,1} Sum N x i,i = x i,i = ) 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 Introduced in Martin Gardner s Scientific American Mathematical Games Column in 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.

17 wide dynamic range game of life Simple Attractors Blinkers block More complicated attractors

18 moving patterns game of life Glider

19 a threshold of complexity? unbounded growth R-pentomino runs 1103 steps before settling down into 6 gliders, 8 blocks, 4 blinkers, 4 beehives, 1 boat, 1 ship, and 1 loaf.

20 Unbounded growth but not complexity the glider gun Fires a glider every 30 iterations.

21 unbounded complexity requires information 1) Patterns that can implement information, descriptions, and construction 2) Gliders, guns, blocks, eaters life and information Very brittle Built, not evolved Not evolving Universal Turing Machine on game of life!!!

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23 information in attractor patterns Radius 1 Neighborhood =3 Binary 2 3 = 8 input neighborhoods 2 8 = 256 rules Rule 110

24 structures in rule 110 Universal Computation Identification of gliders, spaceships, and other long-range or selfperpetuating patterns On the background domain produced by rule cells repeat every seven iterations: Collisions and combinations of glider patterns are exploited for computation.

25 is self-organization enough? 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 of 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

26 readings 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 Papers and other materials Optional Flake s [1998], The Computational Beauty of Life. MIT Press. Chapters 10, 11, 14 Dynamics, Attractors and chaos