Propagation of spiking moments in linear hawkes networks
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- dc.contributor.author Gilson, Matthieu
- dc.contributor.author Pfister, Jean-Pascal
- dc.date.accessioned 2020-12-17T07:28:59Z
- dc.date.available 2020-12-17T07:28:59Z
- dc.date.issued 2020
- dc.description.abstract The present paper provides exact mathematical expressions for the high-order moments of spiking activity in a recurrently connected network of linear Hawkes processes. It extends previous studies that have explored the case of a (linear) Hawkes network driven by deterministic intensity functions to the case of a stimulation by external inputs (rate functions or spike trains) with arbitrary correlation structure. Our approach describes the spatio-temporal filtering induced by the afferent and recurrent connectivities (with arbitrary synaptic response kernels) using operators acting on the input moments. This algebraic viewpoint provides intuition about how the network ingredients shape the input-output mapping for moments, as well as cumulants. We also show using numerical simulation that our results hold for neurons with refractoriness implemented by self-inhibition, provided the corresponding negative feedback for each neuron only mildly alters its mean firing probability.en
- dc.description.sponsorship The work of the first author was supported by the European Union's Horizon 2020 Research and Innovation program via the Marie Sk\lodowska-Curie Actions (H2020-MSCA-656547) and under grant agreement 785907 (HBP SGA2). The work of the second author was supported by the Swiss National Science Foundation (SNSF) grants PP00P3 150637 and PP00P3 179060.
- dc.format.mimetype application/pdf
- dc.identifier.citation Gilson M, Pfister JP. Propagation of spiking moments in linear hawkes networks. SIAM J Appl Dyn Syst. 2020 Apr 20;19(2):828-59. DOI: 10.1137/18M1220030
- dc.identifier.doi http://dx.doi.org/10.1137/18M1220030
- dc.identifier.issn 1536-0040
- dc.identifier.uri http://hdl.handle.net/10230/46072
- dc.language.iso eng
- dc.publisher SIAM (Society for Industrial and Applied Mathematics)
- dc.relation.ispartof SIAM Journal on Applied Dynamical Systems. 2020 Apr 20;19(2):828-59
- dc.relation.projectID info:eu-repo/grantAgreement/EC/H2020/656547
- dc.rights © 2020 SIAM. Published by SIAM under the terms of the Creative Commons 4.0 license (https://creativecommons.org/licenses/by/4.0/)
- dc.rights.accessRights info:eu-repo/semantics/openAccess
- dc.rights.uri https://creativecommons.org/licenses/by/4.0/
- dc.subject.keyword Hawkes processen
- dc.subject.keyword Momentsen
- dc.subject.keyword Cumulantsen
- dc.subject.keyword Recurrent neural networken
- dc.subject.keyword Spiking statisticsen
- dc.title Propagation of spiking moments in linear hawkes networksen
- dc.type info:eu-repo/semantics/article
- dc.type.version info:eu-repo/semantics/publishedVersion