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ERIC Number: ED563693
Record Type: Non-Journal
Publication Date: 2013
Pages: 91
Abstractor: As Provided
Reference Count: N/A
ISBN: 978-1-3035-3900-8
Measures and Metrics of Information Processing in Complex Systems: A Rope of Sand
James, Ryan Gregory
ProQuest LLC, Ph.D. Dissertation, University of California, Davis
How much information do natural systems store and process? In this work we attempt to answer this question in multiple ways. We first establish a mathematical framework where natural systems are represented by a canonical form of edge-labeled hidden fc models called e-machines. Then, utilizing this framework, a variety of measures are defined and algorithms for computing them from an e-machine are described. The first two measures defined are related to the length of time a system remembers. The first, the Markov order, is a well-known measure of the time one must observe a system in order to make accurate predictions. Despite its statistical nature, it is shown to be a topological property of the process's e-machine. The second, the recently defined cryptic order, quantifies the ability to retrodict a system's internal dynamics. It is also shown to be a topological property of the e-machine, and efficient algorithms for computing both quantities are given. The second batch of metrics quantify information generation and storage in a system by partitioning the observations. By considering the role of both the past and the future behavior of a system, a semantic understanding of information generation emerges, labeling some information generation as "ephemeral," having no lasting effects on the system, and the rest as "bound," playing a role temporal structure. Following through with this decomposition, other quantities of less straight-forward interpretation are also defined. This is followed by a thorough discussion of these quantities and other derived quantities. Lastly the decomposition of the entropy rate into ephemeral and bound components is applied to several standard chaotic systems through a duality between the entropy rate and the Lyapunov exponent. This exposes new structural behaviors hitherto unknown in these systems. These revolutions hint at a method for tuning natural or engineered systems so as to maximize the ability to harness their intrinsic computing abilities. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page:]
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Publication Type: Dissertations/Theses - Doctoral Dissertations
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A