Journal
PHYSICS LETTERS A
Volume 380, Issue 9-10, Pages 998-1002Publisher
ELSEVIER
DOI: 10.1016/j.physleta.2016.01.008
Keywords
Excess entropy; Statistical complexity; Projection operator; Resolvent; Entropy rate; Predictable information
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Funding
- U.S. Army Research Laboratory
- U.S. Army Research Office [W911NF-13-1-0390, W911NF-13-1-0340, W911NF-12-1-0234]
- John Templeton Foundation
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We give exact formulae for a wide family of complexity measures that capture the organization of hidden nonlinear processes. The spectral decomposition of operator-valued functions leads to closed form expressions involving the full eigenvalue spectrum of the mixed-state presentation of a process's epsilon-machine causal-state dynamic. Measures include correlation functions, power spectra, past-future mutual information, transient and synchronization informations, and many others. As a result, a direct and complete analysis of intrinsic computation is now available for the temporal organization of finitary hidden Markov models and nonlinear dynamical systems with generating partitions and for the spatial organization in one-dimensional systems, including spin systems, cellular automata, and complex materials via chaotic crystallography. (C) 2016 Elsevier B.V. All rights reserved.
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