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Quantifying self-organization with optimal predictors.

Cosma Rohilla Shalizi1, Kristina Lisa Shalizi, Robert Haslinger

  • 1Center for the Study of Complex Systems, University of Michigan, Ann Arbor, Michigan 48109, USA. cshalizi@umich.edu

Physical Review Letters
|September 28, 2004
PubMed
Summary
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Researchers propose a new criterion for self-organizing systems: increased statistical complexity. This measure quantifies the information needed to predict system dynamics, offering a more intuitive approach for complex systems.

Area of Science:

  • Complex systems
  • Dynamical systems theory
  • Information theory

Background:

  • Self-organizing systems lack quantitative, experimentally applicable criteria for their study.
  • Existing criteria yield counter-intuitive results in significant scenarios.

Purpose of the Study:

  • To introduce a novel, quantitative criterion for self-organization.
  • To define statistical complexity for spatially extended dynamical systems.
  • To develop a predictive method and estimation algorithm for system complexity.

Main Methods:

  • Defining statistical complexity using mutual information and minimal sufficient statistics.
  • Developing a general method for predicting system dynamics.
  • Creating a simple algorithm for estimating statistical complexity.

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Main Results:

  • The proposed criterion, increased statistical complexity, offers a more intuitive measure.
  • The developed algorithm effectively estimates statistical complexity.
  • Application to cyclic cellular automata models validates the proposed criterion.

Conclusions:

  • Statistical complexity provides a robust and experimentally applicable criterion for self-organization.
  • The proposed method enhances the prediction and understanding of complex dynamical systems.