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Entropy 2018, 20(1), 34; https://doi.org/10.3390/e20010034

Information Entropy Production of Maximum Entropy Markov Chains from Spike Trains

1
Centro de Investigación y Modelamiento de Fenómenos Aleatorios, Facultad de Ingeniería, Universidad de Valparaíso, Valparaíso 2340000, Chile
2
IPICYT/División de Matemáticas Aplicadas, Instituto Potosino de Investigación Científica y Tecnológica, San Luis Potosí 78216, Mexico
*
Author to whom correspondence should be addressed.
Received: 7 November 2017 / Revised: 3 January 2018 / Accepted: 5 January 2018 / Published: 9 January 2018
(This article belongs to the Special Issue Information Theory in Neuroscience)
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Abstract

The spiking activity of neuronal networks follows laws that are not time-reversal symmetric; the notion of pre-synaptic and post-synaptic neurons, stimulus correlations and noise correlations have a clear time order. Therefore, a biologically realistic statistical model for the spiking activity should be able to capture some degree of time irreversibility. We use the thermodynamic formalism to build a framework in the context maximum entropy models to quantify the degree of time irreversibility, providing an explicit formula for the information entropy production of the inferred maximum entropy Markov chain. We provide examples to illustrate our results and discuss the importance of time irreversibility for modeling the spike train statistics. View Full-Text
Keywords: information entropy production; discrete Markov chains; spike train statistics; Gibbs measures; maximum entropy principle information entropy production; discrete Markov chains; spike train statistics; Gibbs measures; maximum entropy principle
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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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Cofré, R.; Maldonado, C. Information Entropy Production of Maximum Entropy Markov Chains from Spike Trains. Entropy 2018, 20, 34.

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