Pattern, Prediction and Computation in One-Dimensional Sequences

Nonlinear Time Series Analysis Seminar

Max Planck Institute for the Physics of Complex Systems

January 2005

Abstract:

Understanding and quantifying patterns in physical systems is a
significant challenge for scientists. Borrowing ideas from the formal
theory languages and information theory, computational mechanics provides
a framework to express and analyze one-dimensional patterns. The resulting
description of the pattern, called an epsilon-machine or casual state
machine, represents a complete statistical characterization of the
pattern. From the epsilon-machine, measures of computation, such as
statistical complexity and entropy, are calculable. I will consider a
specific example from condensed matter physics where epsilon-machine
reconstruction gives new insight into the structure of a layered material.