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Updated: Feb 12, 2026
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Analyzing Large Protein Complexes by Structural Mass Spectrometry
Published on: June 19, 2010
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Spectral simplicity of apparent complexity. II. Exact complexities and complexity spectra
Paul M Riechers1, James P Crutchfield1
1Complexity Sciences Center, Department of Physics, University of California at Davis, One Shields Avenue, Davis, California 95616, USA.
Chaos (Woodbury, N.Y.)
|April 2, 2018
Summary
This study introduces a new spectral analysis method to analyze complex systems and stochastic processes. The approach provides analytical tractability for information processing in hidden Markov models and chaotic systems.
Area of Science:
- Complex Systems Analysis
- Information Theory
- Dynamical Systems Theory
Background:
- Nondiagonalizability of linear operators hinders analysis of complex systems' temporal evolution.
- Predicting system behavior requires robust methods for analyzing stochastic processes.
- Existing complexity measures may not fully capture distinct informational and computational properties.
Purpose of the Study:
- To develop a meromorphic functional calculus for analyzing nondiagonalizable operators.
- To derive closed-form expressions for various information-theoretic measures in stochastic processes.
- To introduce novel spectral analysis techniques for complex systems.
Main Methods:
- Meromorphic functional calculus from Part I.
- Spectral decomposition of linear operators.
- Derivation of closed-form expressions for correlation functions and entropy-rate approximates.
- Introduction of coronal spectrograms and past-future mutual information spectra.
Main Results:
- Analytical tractability for information processing in hidden Markov models, symbolic dynamics, and chaotic systems.
- Identification of mathematical similarities between distinct complexity measures.
- New spectral analysis tools for multivariate dependencies.
Conclusions:
- The developed methods enhance the analytical investigation of information processing in complex dynamical systems.
- The study bridges concepts in information theory and dynamical systems.
- Novel spectral analysis techniques offer new insights into system dynamics and information flow.
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