Statistics of spike trains in conductance-based neural networks: Rigorous results

We consider a conductance-based neural network inspired by the generalized Integrate and Fire model introduced by Rudolph and Destexhe in 1996. We show the existence and uniqueness of a unique Gibbs distribution characterizing spike train statistics. The corresponding Gibbs potential is explicitly c...

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Detalles Bibliográficos
Autor principal: Cessac, Bruno
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer 2011
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3496623/
https://www.ncbi.nlm.nih.gov/pubmed/22657160
http://dx.doi.org/10.1186/2190-8567-1-8
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author Cessac, Bruno
author_facet Cessac, Bruno
author_sort Cessac, Bruno
collection PubMed
description We consider a conductance-based neural network inspired by the generalized Integrate and Fire model introduced by Rudolph and Destexhe in 1996. We show the existence and uniqueness of a unique Gibbs distribution characterizing spike train statistics. The corresponding Gibbs potential is explicitly computed. These results hold in the presence of a time-dependent stimulus and apply therefore to non-stationary dynamics.
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spelling pubmed-34966232012-11-16 Statistics of spike trains in conductance-based neural networks: Rigorous results Cessac, Bruno J Math Neurosci Research We consider a conductance-based neural network inspired by the generalized Integrate and Fire model introduced by Rudolph and Destexhe in 1996. We show the existence and uniqueness of a unique Gibbs distribution characterizing spike train statistics. The corresponding Gibbs potential is explicitly computed. These results hold in the presence of a time-dependent stimulus and apply therefore to non-stationary dynamics. Springer 2011-08-25 /pmc/articles/PMC3496623/ /pubmed/22657160 http://dx.doi.org/10.1186/2190-8567-1-8 Text en Copyright © 2011 Cessac; licensee Springer https://creativecommons.org/licenses/by/2.0/This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0 (https://creativecommons.org/licenses/by/2.0/) ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research
Cessac, Bruno
Statistics of spike trains in conductance-based neural networks: Rigorous results
title Statistics of spike trains in conductance-based neural networks: Rigorous results
title_full Statistics of spike trains in conductance-based neural networks: Rigorous results
title_fullStr Statistics of spike trains in conductance-based neural networks: Rigorous results
title_full_unstemmed Statistics of spike trains in conductance-based neural networks: Rigorous results
title_short Statistics of spike trains in conductance-based neural networks: Rigorous results
title_sort statistics of spike trains in conductance-based neural networks: rigorous results
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3496623/
https://www.ncbi.nlm.nih.gov/pubmed/22657160
http://dx.doi.org/10.1186/2190-8567-1-8
work_keys_str_mv AT cessacbruno statisticsofspiketrainsinconductancebasedneuralnetworksrigorousresults

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