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Overview 111111111111111111111333333333333333333333222222222222222222222 I Introduction II Cartesian genetic programming Cell Programming: French III Developmental Cartesian genetic programming IV Evolving growing 2-D maps Flags/Boolean

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SLIDE 1

Cell Programming: French Flags/Boolean Circuits

Murray Bratland CPSC607 February 3, 2005

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Overview

I Introduction II Cartesian genetic programming III Developmental Cartesian genetic programming IV Evolving growing 2-D maps

  • A. How cells and chemicals are represented
  • B. How a cell program is encoded into a genotype
  • C. experimental parameters
  • D. Tasks for the cellular maps

V Experiment and results

  • A. Analysis of the genotype

VI Discussion

Introduction

  • Life: single cell complete organism
  • Cell: unit of life (1013 in humans)

– self renewal (life and death cycle), self repair, adaptation to/interaction with the environment

  • Developmental biologists’ view:

– How do cells self regulate? – What is the underlying structure?

  • Computer Scientists’ view:

– cell = mini robot that can: eat food, interact with the environment, and replicate. – What developmental processes are incidental? fundamental? – What is the underlying structure of cell processes?

Introduction (con’t)

  • Two reasons for studying cell-related development:
  • 1. help understand developmental biology
  • 2. see if developmental approaches can help solve computer

science problems Two questions being asked:

– If each cell has the same program, how can complex structures be created? – How can self-regulated structures be made?

Cartesian Genetic Programming (CGP)

x4 + 2x3 + x2 + x

The above drawing is an example of a Boolean Circuit where f0 is addition and f1 is multiplication Graph resulting from above nodes

001102113… 001112113…

CGP (con’t)

The 6 steps in chromosome evolution/fitness 3. Generate 5 chromosomes randomly to form the population 4. Evaluate the fitness of all the chromosomes on the population 5. Determine the best of all the chromosomes in the population 6. Generate 4 more chromosomes (offspring) by mutation the current_best 7. The current_best and the four offspring become the new population 8. Unless stopping criterion reached return to 2. Note: “+” evolutionary strategy; mutation/duplication exercised

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SLIDE 2

Developmental CGP

  • 4 Inputs to cell:

– 2 connections (A,B) – a function (F) – it’s position (P)

  • 4 Outputs from cell:

– 2 new connections

(A',B')

– new function (F') – Divide? Y/N (D) – Outputs produced from the program inside the node (previous) – Goal: evolve smaller programs and use them to create larger ones

A “cell”

Evolving growing 2-D maps

  • Plan: create a 2-D world of cells of different types, each with

identical GT

How cells and chemicals are represented

  • The GT represents a Boolean circuit : maps input ->
  • utput
  • Cell sees (Clockwise):

– Its own state: 2 bits (cell type) + 8 bits (chemical) – state of 8 neighbours: 2 bits x 8 – chemical amount of 8 neighbours: 8 bits x 8

  • Cell determines (Counterclockwise):

– amount of chemical to produce (8 bits) – Whether to live or die (1 bit) – If it should change into a different cell (2 bits) – how it will grow (8 bits)

  • (1 = blue, 2 = red, 3 = white cell, 0 = empty/dead

cell)

How cells and chemicals are represented (con’t)

  • Chemicals: 8-bit binary code

4 types: dead (none), blue, white, red

  • Diffusion rule ensures dead cells will not alter chemical landscape

(cij)new = 1/2(cij)old + 1/16k,lN(ckl)old

  • Program cycle:

scan a cell growth/differentiation/death update landscape

  • Later cells overwrite previous cells, therefore, bias to bottom right

cells

72 68 44 84 76 64 92 83 75

How cells and chemicals are represented (con’t)

  • Three questions of interest:
  • 1. How can collections of independent cells interact/coordinate

to build an organism?

  • 2. What is importance of direct cell interaction and global

chemical signaling?

  • 3. How can we regulate growth?

How a cell program is encoded into a GT

  • GT = 400 integers (only ~ the nodes are active)

– Each group of 4 integers represents one of four 2:1 multiplexers and its three connections – “2:1 multiplexer” – 3-input Boolean logic gate

  • i.e. f(A,B,C) = A.C + B.C = (A AND NOT C) OR (B AND C)
  • Experimental Parameters

– Algorithm used to evolve the GTs described previously – Mutation rate = 1% / generation – 30,000 generations

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SLIDE 3

Tasks for the cellular maps

FRENCH FLAG (Lewis Wolpert, 1998) MODEL

  • Goals:
  • 1. Construct a French Flag through cell programmed evolution
  • condition: must always look like a French Flag
  • 2. Grow French Flag to specified size and remain at that size
  • How will the cell/flag map behave when damaged?

When cells are translated to other regions?

  • Set up: place one initial cell on an existing chemical map
  • Success is measured as “Fitness” – at random generations,

compare current map to desired map; sum those cells in agreement

French Flag analogy1

1Gilbert, S.F. (2003)

Experiments and results Experiments

  • 1. Create the French Flag with no deformations
  • 2. If remove parts of the French Flag, what will happen?
  • 3. If cut a large hole in the French Flag at iteration 9, what happens?
  • 4. If cut the French Flag diagonally at iteration 9, what happens?
  • 5. How can the French Flag be made to grow to a set size and stop?

(growth, stasis)

  • 6. What happens if a cell’s initial chemical level is set to zero?
  • 7. Extra: Want to obtain a regular series of spots
  • 1. Create the French Flag with

no deformations

  • Requirements: cells develop medium flag at iteration 7 and large

flag at iteration 9.

Experiment 1 (con’t)

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SLIDE 4

Experiment 1 (con’t)

  • 2. If remove parts of the French

Flag, what will happen?

  • Remove White and red cells at iteration 9 and continue to grow map
  • The blue region tries to grow into French Flag again (FAILED) rather

than just making a blue map

Experiment 2 (con’t)

  • 3. If cut a large hole in the French

Flag at iteration 9, what happens?

  • Map at 15 has red section identical to that of original map
  • Cells try to rebuild map
  • 4. If cut the French Flag diagonally

at iteration 9, what happens?

  • Blue region is not cut
  • This region returns to “normal” (Looks almost like original map)
  • Cells try to rebuild map

Experiment 4 (con’t)

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SLIDE 5
  • 5. How can the French Flag be made to

grow to a set size and stop? (growth, stasis)

  • Note that chemicals help slow down growth “naturally,” but do not

stop growth

  • Note! Vertical stripes maintained to iteration 29, even to 46, though

looks “interesting” Iteration 46 Iteration 22

  • 6. What happens if a cell’s initial

chemical level is set to zero?

  • Cells still grow at same rate as unaltered map
  • Iterations 0->2 exact same as unaltered growth
  • Forms triangle
  • Shows chemical influence is important for high fitness
  • Compare: with chemicals: average fitness: 438 dev 26

without chemicals: average fitness: 400 dev 14

Experiment 6 (con’t)

  • 7. Extra: Want to obtain a

regular series of spots

  • Perfect possible fitness = 196 (needed by iteration 5)
  • 3/10 obtained a perfect score (different ways to do so)

– Average fitness = 191

  • without chemical influence the result was not favourable

– Best fitness = 192 – Average fitness = 182

Results Summary

  • Can grow French Flag with given parameters
  • Self-repair works only on minor deformations
  • Self-repair attempted in all cases
  • Chemical landscape important to development
  • Ability to use underlying chemical structure to produce

“other” structures

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SLIDE 6

Problems

  • Cell update procedure may cause problems with end result

– Cells can override one another, in logical course – DOESN’T HAPPEN IN LIFE!!

  • This can perhaps be fixed by adding in GT judgment on how to grow

based on chemical demands of neighbouring cells

  • In this series of experiments all cells are stem cells

– Could create an experiment so most cells are not stem cells, with introduction of a rare few stem cells to evolve the map – Or, allow a number of different chemicals to be emitted by cells

  • This allows for orientation-independent fitness function, if possible
  • This would allow for electronic circuit design, since orientation doesn’t matter

(just function)

  • Bias in growth: all 8 neighbouring cells must be zero for zero growth

to occur

0 0 76 0 0 16

Future Work

  • Work on a better self-repair mechanism may allow the

French Flag to undergo more recognizable repair – Application: Self-repairing circuits

  • Chemotaxis: add a point where cells could grow to

instead of simply “outward”

  • Try starting with multiple seed cells in initial map
  • Debate: Direct encodings versus Developmental

encodings?

References and interesting Web pages

  • Morgan, D.E. (Ed.). (2003). On Growth, Form and Computers: Chapter 15:

by Miller, J., & Banzhaf, W. (2003). London: Elsevier Academic Press.

  • Gilbert, S.F. (2003). Developmental Biology, 7th ed. Sunderland,

Massachusetts: Sinauer Associates, Inc.

  • Wolfgang Banzhaf’s homepage: http://www.cs.mun.ca/~banzhaf/
  • Jullian F. Miller’s Web page: http://www.cs.bham.ac.uk/~jfm/french-flag/

Questions?

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