English

Quantifying Self-Organization with Optimal Predictors

Adaptation and Self-Organizing Systems 2011-11-10 v1 Statistical Mechanics Statistics Theory Cellular Automata and Lattice Gases Data Analysis, Statistics and Probability Statistics Theory

Abstract

Despite broad interest in self-organizing systems, there are few quantitative, experimentally-applicable criteria for self-organization. The existing criteria all give counter-intuitive results for important cases. In this Letter, we propose a new criterion, namely an internally-generated increase in the statistical complexity, the amount of information required for optimal prediction of the system's dynamics. We precisely define this complexity for spatially-extended dynamical systems, using the probabilistic ideas of mutual information and minimal sufficient statistics. This leads to a general method for predicting such systems, and a simple algorithm for estimating statistical complexity. The results of applying this algorithm to a class of models of excitable media (cyclic cellular automata) strongly support our proposal.

Keywords

Cite

@article{arxiv.nlin/0409024,
  title  = {Quantifying Self-Organization with Optimal Predictors},
  author = {Cosma Rohilla Shalizi and Kristina Lisa Shalizi and Robert Haslinger},
  journal= {arXiv preprint arXiv:nlin/0409024},
  year   = {2011}
}

Comments

Four pages, two color figures