CMU talk: Automatic Filters for the Detection of Coherent Structure in Spatiotemporal Systems

Cosma Shalizi
November 29, 2005
Abstract: Current methods for identifying coherent structures in spatially-extended systems rely on prior information about the form which those structures take. This talk describes two new approaches to automatically filter the changing configurations of spatial dynamical systems and extract coherent structures. One, local sensitivity filtering, gauges the ability of locally-applied perturbations to produce large-scale changes in the system configuration. 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 systems, without needing to guess or postulate the form of that structure. The results are at least comparable to those obtained with older techniques based on formal language theory or the statistical- mechanical theory of order parameters. Paper URL: http://arxiv.org/abs/nlin.CG/0508001