A rigorous formalism of information transfer between dynamical system components. I. Discrete mapping (original) (raw)
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2019
In this paper we develop the concept of information transfer between the Borel-measurable sets for a dynamical system described by a measurable space and a non-singular transformation. The concept is based on how Shannon entropy is transferred between the measurable sets, as the dynamical system evolves. We show that the proposed definition of information transfer satisfies the usual notions of information transfer and causality, namely, zero transfer and transfer asymmetry. Furthermore, we show how the information transfer measure can be used to classify ergodicity and mixing. We also develop the computational methods for information transfer computation and apply the framework for optimal placements of actuators and sensors for control of non-equilibrium dynamics.
InformatIon In DynamIcal SyStemS anD complex SyStemS Summer 2013 WorkShop
2013
exact Complexity: The spectral Decomposition of intrinsic Computation James Crutchfield, University of California, Davis I'll present exact expressions for a wide family of complexity measures for hidden Markov processes. An eigen-decomposition using the Cauchy integral formula for operator-valued functions leads to closed-form expressions involving the full eigenvalue spectrum of a process's Ɛ-machine causal state dynamic. The measures include correlation functions, power spectra, past-future mutual information (excess entropy), transient and synchronization informations, and many others. Local Complexity for Heterogeneous spatial systems David Feldman, College of the Atlantic I will begin with a quick review of the excess entropy, a well understood and broadly applicable measure of complexity that allows for a comparison of information processing abilities among very different systems. I will then present some relatively new work in which a local form of the two-dimensiona...