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Macroscopic description for networks of spiking neurons

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dc.contributor.author Montbrió, Ernest, 1974-
dc.contributor.author Pazó, Diego
dc.contributor.author Roxin, Alex
dc.date.accessioned 2016-05-18T14:57:04Z
dc.date.available 2016-05-18T14:57:04Z
dc.date.issued 2015
dc.identifier.citation Montbrio E, Pazo D, Roxin A. Macroscopic description for networks of spiking neurons. Phys Rev X. 2015;5(2):021028. doi: 10.1103/PhysRevX.5.021028
dc.identifier.issn 2160-3308
dc.identifier.uri http://hdl.handle.net/10230/26296
dc.description.abstract A major goal of neuroscience, statistical physics, and nonlinear dynamics is to understand how brain function arises from the collective dynamics of networks of spiking neurons. This challenge has been chiefly addressed through large-scale numerical simulations. Alternatively, researchers have formulated mean-field theories to gain insight into macroscopic states of large neuronal networks in terms of the collective firing activity of the neurons, or the firing rate. However, these theories have not succeeded in establishing an exact correspondence between the firing rate of the network and the underlying microscopic state of the spiking neurons. This has largely constrained the range of applicability of such macroscopic descriptions, particularly when trying to describe neuronal synchronization. Here, we provide the derivation of a set of exact macroscopic equations for a network of spiking neurons. Our results reveal that the spike generation mechanism of individual neurons introduces an effective coupling between two biophysically relevant macroscopic quantities, the firing rate and the mean membrane potential, which together govern the evolution of the neuronal network. The resulting equations exactly describe all possible macroscopic dynamical states of the network, including states of synchronous spiking activity. Finally, we show that the firing-rate description is related, via a conformal map, to a low-dimensional description in terms of the Kuramoto order parameter, called Ott-Antonsen theory. We anticipate that our results will be an important tool in investigating how large networks of spiking neurons self-organize in time to process and encode information in the brain.
dc.description.sponsorship D. P. and A. R. acknowledge support by MINECO (Spain) under the Ramón y Cajal program. E. M. and A. R. acknowledge support from a grants from the Spanish Ministry of Economics and Competitiveness PSI2013-42091 and BFU2012-33413.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.publisher American Physical Society
dc.relation.ispartof Physical Review X. 2015;5(2):021028
dc.rights Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
dc.rights.uri http://creativecommons.org/licenses/by/3.0/
dc.title Macroscopic description for networks of spiking neurons
dc.type info:eu-repo/semantics/article
dc.identifier.doi http://dx.doi.org/10.1103/PhysRevX.5.021028
dc.subject.keyword Biological physics
dc.subject.keyword Interdisciplinary physics
dc.subject.keyword Nonlinear dynamics
dc.relation.projectID info:eu-repo/grantAgreement/ES/1PE/PSI2013-42091
dc.relation.projectID info:eu-repo/grantAgreement/ES/3PN/BFU2012-33413
dc.rights.accessRights info:eu-repo/semantics/openAccess
dc.type.version info:eu-repo/semantics/publishedVersion

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