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Linear Response of General Observables in Spiking Neuronal Network Models

1
Biovision Team, INRIA and Neuromod Institute, Université Côte d’Azur, 06902 Sophia Antipolis, France
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Departamento de Informática, Universidad Técnica Federico Santa María, 2340000 Valparaíso, Chile
3
CIMFAV-Ingemat, Facultad de Ingeniería Universidad de Valparaíso, 2340000 Valparaíso, Chile
*
Author to whom correspondence should be addressed.
Academic Editor: David Holcman
Entropy 2021, 23(2), 155; https://doi.org/10.3390/e23020155
Received: 10 December 2020 / Revised: 20 January 2021 / Accepted: 21 January 2021 / Published: 27 January 2021
(This article belongs to the Section Multidisciplinary Applications)
We establish a general linear response relation for spiking neuronal networks, based on chains with unbounded memory. This relation allow us to predict the influence of a weak amplitude time dependent external stimuli on spatio-temporal spike correlations, from the spontaneous statistics (without stimulus) in a general context where the memory in spike dynamics can extend arbitrarily far in the past. Using this approach, we show how the linear response is explicitly related to the collective effect of the stimuli, intrinsic neuronal dynamics, and network connectivity on spike train statistics. We illustrate our results with numerical simulations performed over a discrete time integrate and fire model. View Full-Text
Keywords: neuronal network dynamics; spike train statistics; linear response; non-Markovian dynamics; Gibbs distributions; maximum entropy principle neuronal network dynamics; spike train statistics; linear response; non-Markovian dynamics; Gibbs distributions; maximum entropy principle
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MDPI and ACS Style

Cessac, B.; Ampuero, I.; Cofré, R. Linear Response of General Observables in Spiking Neuronal Network Models. Entropy 2021, 23, 155. https://doi.org/10.3390/e23020155

AMA Style

Cessac B, Ampuero I, Cofré R. Linear Response of General Observables in Spiking Neuronal Network Models. Entropy. 2021; 23(2):155. https://doi.org/10.3390/e23020155

Chicago/Turabian Style

Cessac, Bruno, Ignacio Ampuero, and Rodrigo Cofré. 2021. "Linear Response of General Observables in Spiking Neuronal Network Models" Entropy 23, no. 2: 155. https://doi.org/10.3390/e23020155

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