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 Sections I485/H400 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 biologically (Assignment 3) Inspired computing rocha@indiana.edu INDIANA UNIVERSITY http://informatics.indiana.edu/rocha/i-bic
Info rm atics Readings until now luis rocha 2015 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. biologically Chapters 10, 11, 14 – Dynamics, Attractors and chaos Inspired computing rocha@indiana.edu INDIANA UNIVERSITY http://informatics.indiana.edu/rocha/i-bic
Info rm atics final project schedule luis rocha 2015 ALIFE 15 Projects Due by May 4 th 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 1 st ! Individual or group With very definite tasks assigned per biologically Inspired member of group computing rocha@indiana.edu INDIANA UNIVERSITY http://informatics.indiana.edu/rocha/i-bic
Info rm atics What’s a CA? luis rocha 2015 more formally D -dimensional lattice L with a finite Neighborhood template automaton in each lattice site (cell) N State-determined system Example finite number of states Σ : K=| Σ | K=8 E.g. Σ = {0,1} N=5 finite input alphabet α | α |=37,768 transition function Δ : α→Σ D ≈ 10 30,000 uniquely ascribes state s in Σ to input patterns α α ∈ Σ α = N N D = N , K K K biologically Number of possible Inspired Number of possible transition functions computing neighborhood states rocha@indiana.edu INDIANA UNIVERSITY http://informatics.indiana.edu/rocha/i-bic
Info rm atics Langton’s parameter luis rocha 2015 Finding the structure of all possible transition functions 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 = 0: all transitions lead to s q (n =K N ) − N K n λ = λ = 1: no transitions lead to s q (n =0) λ = 1-1/K: equally probable states ( n=1/K . K N ) N K biologically Range: from most homogeneous to most Inspired heterogeneous computing Langton, C.G. [1990]. “Computation at the edge of chaos: phase transitions and emergent computation”. Artificial Life II . Addison-Wesley. rocha@indiana.edu INDIANA UNIVERSITY http://informatics.indiana.edu/rocha/i-bic
Info rm atics Edge of chaos luis rocha 2015 A phase transition? 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 biologically Patterns that move across the lattice Inspired computing rocha@indiana.edu INDIANA UNIVERSITY http://informatics.indiana.edu/rocha/i-bic
Info rm atics Computation at the edge of chaos? luis rocha 2015 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 biologically Capable of universal computation Inspired computing rocha@indiana.edu INDIANA UNIVERSITY http://informatics.indiana.edu/rocha/i-bic
Info rm atics imagine automata as agents luis rocha 2015 quorum sensing or what decision to take? (Density Classification) 2 7 = = N 128 K biologically Inspired computing rocha@indiana.edu INDIANA UNIVERSITY http://informatics.indiana.edu/rocha/i-bic
Info rm atics random strategies luis rocha 2015 density classification task 2 7 = = N 128 K = P 0 Typically chaotic behavior biologically No convergence Inspired computing rocha@indiana.edu INDIANA UNIVERSITY http://informatics.indiana.edu/rocha/i-bic
Info rm atics local strategy: majority rule luis rocha 2015 density classification task 2 7 = = N 128 K = P 0 Isolated groups biologically No information transmission Inspired computing rocha@indiana.edu INDIANA UNIVERSITY http://informatics.indiana.edu/rocha/i-bic
Info rm atics block expansion strategy luis rocha 2015 density classification task 2 7 = = N 128 K [ ] ∈ P 53 %, 60 % “blind” spreading of local information No information integration biologically Inspired Not much better than random choice computing rocha@indiana.edu INDIANA UNIVERSITY http://informatics.indiana.edu/rocha/i-bic
Info rm atics emergent computation strategies luis rocha 2015 density classification task 2 7 = = N 128 K Integration and transmission of biologically information across population Inspired computing rocha@indiana.edu INDIANA UNIVERSITY http://informatics.indiana.edu/rocha/i-bic
Info rm atics best CA rules luis rocha 2015 for DST biologically Inspired computing rocha@indiana.edu INDIANA UNIVERSITY http://informatics.indiana.edu/rocha/i-bic
Info rm atics How to characterize complex behavior? luis rocha 2015 collective (emergent) computation via computational mechanics Crutchfield & Mitchell [1995]. PNAS GA to evolve rules for DCT [1994] 92 : 10742-10746 Das, Mitchell & Crutchfield [1994]. In: Parallel Problem Solving from Nature-III : 344-353. biologically Inspired computing rocha@indiana.edu http://informatics.indiana.edu/rocha/i-bic
Info rm atics the game of life luis rocha 2015 John Horton Conway 2-D Sum N 8 0 1 2 3 4 5 6 7 8 x i,i = 0 0 0 0 1 0 0 0 0 0 x i,i = 1 0 0 1 1 0 0 0 0 0 x Any living cell with fewer than two neighbors 1) dies of loneliness. Any living cell with more than three neighbors 2) dies of crowding. Any dead cell with exactly three neighbors 3) comes to life. Any living cell with two or three neighbors lives, { } 4) , = unchanged, to the next generation 0 , 1 x i j 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 biologically Inspired that fade or get stable. computing Popularized CAs. rocha@indiana.edu INDIANA UNIVERSITY http://informatics.indiana.edu/rocha/i-bic
Info rm atics game of life luis rocha 2015 wide dynamic range Simple Attractors Blinkers block More complicated attractors biologically Inspired computing rocha@indiana.edu INDIANA UNIVERSITY http://informatics.indiana.edu/rocha/i-bic
Info rm atics game of life luis rocha 2015 moving patterns biologically Inspired computing Glider rocha@indiana.edu INDIANA UNIVERSITY http://informatics.indiana.edu/rocha/i-bic
Info rm atics unbounded growth luis rocha 2015 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. biologically Inspired computing rocha@indiana.edu INDIANA UNIVERSITY http://informatics.indiana.edu/rocha/i-bic
Info rm atics the glider gun luis rocha 2015 Unbounded growth but not complexity Fires a glider every 30 biologically iterations. Inspired computing rocha@indiana.edu INDIANA UNIVERSITY http://informatics.indiana.edu/rocha/i-bic
Info rm atics life and information luis rocha 2015 unbounded complexity requires information Patterns that can implement information, 1) descriptions, and construction Gliders, guns, blocks, eaters 2) Very brittle Built, not evolved Not evolving Universal Turing Machine on game of biologically life!!! Inspired computing rocha@indiana.edu INDIANA UNIVERSITY http://informatics.indiana.edu/rocha/i-bic
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