Dissertation/Thesis Abstract

Structural Complexity in Stationary Stochastic Dynamical Systems
by Ellison, Christopher James, Ph.D., University of California, Davis, 2011, 182; 3482120
Abstract (Summary)

This dissertation is an information-theoretic analysis of discrete-time, discrete-valued, stationary, stochastic dynamical systems that are modeled by edge-emitting, finite-state hidden Markov models. The approach follows that of computational mechanics, a discipline which uses the optimal predictor of a dynamical system, known as the ε-machine, to uniquely characterize its structural properties. One of the primary contributions of this thesis is a closed-form expression for the excess entropy, a measure of structure which describes the amount of information that the entire past of the system shares with the entire future of the system. Generalizing away from ε-machines, we then define a number of structural measures for generic hidden Markov models through the decomposition of their state entropy. This decomposition breaks the state entropy into four components: excess entropy, crypticity, oracular information, and gauge information. Finally, this thesis utilizes optimal predictors and retrodictors in a detailed study of irreversibility. The bidirectional machine is introduced as an encompassing model of dynamical systems from which one can calculate, in closed-form, a number of well-known, and also new, measures of structural complexity.

Indexing (document details)
Advisor: Crutchfield, James P.
Commitee: D'Souza, Raissa M., Rundle, John B.
School: University of California, Davis
Department: Physics
School Location: United States -- California
Source: DAI-B 73/03, Dissertation Abstracts International
Subjects: Applied Mathematics, Theoretical physics, Computer science
Keywords: Automata, Computational mechanics, Dynamical systems, Hidden Markov models, Information theory, Stochastic processes
Publication Number: 3482120
ISBN: 978-1-267-02338-4
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