Automatic filters for the detection of coherent structure in spatiotemporal systems

Cosma Rohilla Shalizi, Robert Haslinger, Jean-Baptiste Rouquier, Kristina Lisa Klinkner, and Cristopher Moore
Phys. Rev. E 73, 036104 – Published 2 March 2006

Abstract

Most current methods for identifying coherent structures in spatially extended systems rely on prior information about the form which those structures take. Here we present two approaches to automatically filter the changing configurations of spatial dynamical systems and extract coherent structures. One, local sensitivity filtering, is a modification of the local Lyapunov exponent approach suitable to cellular automata and other discrete spatial systems. The other, local statistical complexity filtering, calculates the amount of information needed for optimal prediction of the system’s behavior in the vicinity of a given point. By examining the changing spatiotemporal distributions of these quantities, we can find the coherent structures in a variety of pattern-forming cellular automata, without needing to guess or postulate the form of that structure. We apply both filters to elementary and cyclical cellular automata (ECA and CCA) and find that they readily identify particles, domains, and other more complicated structures. We compare the results from ECA with earlier ones based upon the theory of formal languages and the results from CCA with a more traditional approach based on an order parameter and free energy. While sensitivity and statistical complexity are equally adept at uncovering structure, they are based on different system properties (dynamical and probabilistic, respectively) and provide complementary information.

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  • Received 27 July 2005

DOI:https://doi.org/10.1103/PhysRevE.73.036104

©2006 American Physical Society

Authors & Affiliations

Cosma Rohilla Shalizi1,*, Robert Haslinger2,†, Jean-Baptiste Rouquier3,‡, Kristina Lisa Klinkner4,§, and Cristopher Moore5,6,7,∥

  • 1Center for the Study of Complex Systems, University of Michigan, Ann Arbor, Michigan 48109 USA
  • 2Martinos Center for Biomedical Imaging, Massachusetts General Hospital, Charlestown, Massachusetts 02129 USA
  • 3Laboratoire de l’Informatique du Parallélisme, École Normale Supérieure de Lyon, 46 Allée d’Italie, 69364 Lyon, France
  • 4Statistics Department, University of Michigan, Ann Arbor, Michigan 48109 USA
  • 5Department of Computer Science, University of New Mexico, Albuquerque, New Mexico 87131 USA
  • 6Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131 USA
  • 7Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501 USA

  • *Present address: Statistics Department, Carnegie Mellon University, Pittsburgh, PA 15213, USA. Electronic address: cshalizi@cmu.edu
  • Electronic address: robhh@nmr.mgh.harvard.edu
  • Electronic address: jean-baptiste.rouquier@ens-lyon.fr
  • §Present address: Statistics Department, Carnegie Mellon University, Pittsburgh, PA 15213, USA. Electronic address: klinkner@cmu.edu.
  • Electronic address: moore@santafe.edu

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Issue

Vol. 73, Iss. 3 — March 2006

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