Phys. Rev. Lett. 93, 118701 (2004) [4 pages]Quantifying Self-Organization with Optimal Predictors |
PRL Celebrates 50 Years
This Week's Milestone Letters are from 1984: |
Cosma Rohilla Shalizi1 *, Kristina Lisa Shalizi2 †, and Robert Haslinger3,4 ‡
1Center for the Study of Complex Systems, University of Michigan, Ann Arbor, Michigan 48109, USA
2Statistics Department, University of Michigan, Ann Arbor, Michigan 48109, USA
3MGH-NMR Center, Department of Radiology, Massachusetts General Hospital, Charlestown, Massachusetts 02129, USA
4Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
See Also: Publisher's Note
Received 22 July 2003; revised 21 January 2004; published 10 September 2004; corrected 21 September 2004
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.
©2004 The American Physical Society
URL: http://link.aps.org/abstract/PRL/v93/e118701
DOI: 10.1103/PhysRevLett.93.118701
PACS: 05.65.+b, 02.50.Tt, 89.75.Fb, 89.75.Kd
* Electronic address: cshalizi@umich.edu
† Electronic address: kshalizi@umich.edu
‡ Electronic address: robhh@nmr.mgh.harvard.edu
See Also
Publisher's Note: Cosma Rohilla Shalizi, Kristina Lisa Shalizi, and Robert Haslinger, Publisher's Note: Quantifying Self-Organization with Optimal Predictors [Phys. Rev. Lett. 93, 118701 (2004)], Phys. Rev. Lett. 93, 149902 (2004)
[ Abstract | Previous article | Next article | Issue 11 ]
About PROLA | Terms and Conditions | Subscriptions | Search | Help
Content in PROLA © 2008 by The American Physical Society All rights reserved. PROLA™ is a trademark of The American Physical Society. Use of APS online journals implies that the user has read and agrees to the Terms and Conditions in the Subscription Agreement.