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Automating Aggregate Quantification in Caenorhabditis elegans
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Identification of probabilistic cellular automata.

S A Billings1, Yingxu Yang

  • 1Dept. of Autom. Control & Syst. Eng., Univ. of Sheffield, UK.

IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics : a Publication of the IEEE Systems, Man, and Cybernetics Society
|February 2, 2008
PubMed
Summary

A new algorithm efficiently identifies probabilistic cellular automata (PCA) neighborhoods. This method refines polynomial models for binary probabilistic cellular automata (BPCA), enabling accurate rule determination.

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Area of Science:

  • Computational Science
  • Complex Systems
  • Theoretical Computer Science

Background:

  • Probabilistic Cellular Automata (PCA) are complex systems with applications in various scientific fields.
  • Identifying the rules governing PCA, especially binary probabilistic cellular automata (BPCA), is challenging due to inherent noise and vast rule spaces.
  • Existing methods often struggle with the probabilistic nature and large search spaces involved in PCA rule discovery.

Purpose of the Study:

  • To develop and validate a novel two-stage algorithm for the efficient identification of probabilistic cellular automata (PCA) neighborhoods.
  • To demonstrate that a binary probabilistic cellular automaton (BPCA) can be modeled as a noisy polynomial, simplifying the neighborhood search.
  • To establish a method for accurately determining the probability table of a BPCA by identifying its equivalent polynomial rule.

Main Methods:

  • A two-stage neighborhood detection algorithm is introduced for identifying PCA.
  • The algorithm leverages the concept of a noisy polynomial representation for binary probabilistic cellular automata (BPCA).
  • A multiobjective genetic algorithm (GA) with integer constraints is employed to refine the neighborhood and identify the polynomial rule.

Main Results:

  • The study proves that correct term contributions in the polynomial model can be calculated independently of noise terms.
  • A neighborhood detection technique, adapted from deterministic rules, is successfully applied with a larger cutoff for initial BPCA neighborhood presearch.
  • The genetic algorithm effectively refines the reduced neighborhood and identifies the polynomial rule equivalent to the probabilistic rule with the highest probability.

Conclusions:

  • The developed algorithm provides an efficient and effective method for identifying probabilistic cellular automata (PCA) neighborhoods and rules.
  • The noise-independent calculation of polynomial terms significantly enhances the search for BPCA rules.
  • The method's efficiency is validated across various dimensions (1D, 2D, 3D) of binary probabilistic cellular automata (BPCA).