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Entropy 2015, 17(4), 2432-2458; doi:10.3390/e17042432

Information Geometry on Complexity and Stochastic Interaction

1,2,3
1
Max Planck Institute for Mathematics in the Sciences, Inselstraße 22, 04103 Leipzig, Germany
2
Faculty of Mathematics and Computer Science, University of Leipzig, PF 100920, 04009 Leipzig, Germany
3
Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA 
Academic Editors: Christoph Salge, Georg Martius, Keyan Ghazi-Zahedi and Daniel Polani
Received: 28 February 2015 / Revised: 2 April 2015 / Accepted: 8 April 2015 / Published: 21 April 2015
(This article belongs to the Special Issue Information Theoretic Incentives for Cognitive Systems)
View Full-Text   |   Download PDF [380 KB, uploaded 21 April 2015]   |  

Abstract

Interdependencies of stochastically interacting units are usually quantified by the Kullback-Leibler divergence of a stationary joint probability distribution on the set of all configurations from the corresponding factorized distribution. This is a spatial approach which does not describe the intrinsically temporal aspects of interaction. In the present paper, the setting is extended to a dynamical version where temporal interdependencies are also captured by using information geometry of Markov chain manifolds. View Full-Text
Keywords: stochastic interaction; complexity; information geometry; Kullback-Leibler divergence; separability; Markov chains; random fields stochastic interaction; complexity; information geometry; Kullback-Leibler divergence; separability; Markov chains; random fields
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Ay, N. Information Geometry on Complexity and Stochastic Interaction. Entropy 2015, 17, 2432-2458.

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