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Microscopic approach of a time elapsed neural model Julien Chevallier 4e1ee78accc7217e8e6615a29e6802a3 univ-grenoble-alpes.fr julien-chevallier 7536 37726-7536 https://arxiv.org/a/chevallier_j_1 https://scholar.google.fr/citations?user=PLia_KwAAAAJ&hl=fr https://www.idref.fr/197670377 https://orcid.org/0000-0002-0736-8487 Maria J. Caceres 741788-0 Marie Doumic 88437e12457e1068a53b7b690e38082f inria.fr marie-doumic-jauffret 2247 27552-2247 https://www.idref.fr/155592181 https://orcid.org/0000-0002-3183-8215 Patricia Reynaud-Bouret 7c0552269302cb6b71a0ae1145ef1864 gmail.com patricia-reynaud-bouret 8239 14705-8239 https://www.idref.fr/083750266 https://orcid.org/0000-0002-3054-1137 Marie Doumic 55e57919364d1a779d13e7c1922fb2e2 inria.fr 2015-06-07 21:08:36 2015-06-02 2025-06-23 11:29:48 2015-06-08 08:41:38 2015-12-25 2015-06-08 contributor Marie Doumic 55e57919364d1a779d13e7c1922fb2e2 inria.fr CCSD hal-01159215 https://hal.sorbonne-universite.fr/hal-01159215 chevallier:hal-01159215 <i>Mathematical Models and Methods in Applied Sciences</i>, 2015, http://www.worldscientific.com/doi/10.1142/S021820251550058X. <a target="_blank" href="https://dx.doi.org/10.1142/S021820251550058X">⟨10.1142/S021820251550058X⟩</a> Mathematical Models and Methods in Applied Sciences, 2015, http://www.worldscientific.com/doi/10.1142/S021820251550058X. ⟨10.1142/S021820251550058X⟩ HAL Authorization Université Nice Sophia Antipolis Université Denis Diderot - Paris VII Université Pierre et Marie Curie CNRS - Centre national de la recherche scientifique INRIA - Institut National de Recherche en Informatique et en Automatique INRIA Paris - Rocquencourt CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions Laboratoire Jean-Alexandre Dieudonné Laboratoire Jacques-Louis Lions OpenAIRE INRIA - Institut National de Recherche en Informatique et en Automatique TESTALAIN1 INRIA 2 Laboratoire J.A. Dieudonné - UMR 7351 - Probabilités et Statistiques UPMC Pôle 1 Université Côte d'Azur Sorbonne Université Faculté des Sciences de Sorbonne Université Université Paris Cité Sorbonne Université - Texte Intégral ANR Alliance Sorbonne Université TEST3-HALCNRS UNIV-COTEDAZUR_COLLECTION_DEFAUT test nice International No Yes Microscopic approach of a time elapsed neural model Julien Chevallier 4e1ee78accc7217e8e6615a29e6802a3 univ-grenoble-alpes.fr julien-chevallier 7536 37726-7536 https://arxiv.org/a/chevallier_j_1 https://scholar.google.fr/citations?user=PLia_KwAAAAJ&hl=fr https://www.idref.fr/197670377 https://orcid.org/0000-0002-0736-8487 Maria J. Caceres 741788-0 Marie Doumic 88437e12457e1068a53b7b690e38082f inria.fr marie-doumic-jauffret 2247 27552-2247 https://www.idref.fr/155592181 https://orcid.org/0000-0002-3183-8215 Patricia Reynaud-Bouret 7c0552269302cb6b71a0ae1145ef1864 gmail.com patricia-reynaud-bouret 8239 14705-8239 https://www.idref.fr/083750266 https://orcid.org/0000-0002-3054-1137 16924 0218-2025 1793-6314 Mathematical Models and Methods in Applied Sciences World Scientific Publishing http://www.worldscientific.com/doi/10.1142/S021820251550058X 2015-12-25 1506.02361 10.1142/S021820251550058X English population dynamics neural network AMS Subject Classification:35F15 renewal equation Wold process Hawkes process Structured equations 35B10, 92B20, 60G57, 60K15 Computer Science [cs]/Numerical Analysis [cs.NA] Journal articles Journal articles Journal articles

The spike trains are the main components of the information processing in the brain. To model spike trains several point processes have been investigated in the literature. And more macroscopic approaches have also been studied, using partial differential equation models. The main aim of the present article is to build a bridge between several point processes models (Poisson, Wold, Hawkes) that have been proved to statistically fit real spike trains data and age-structured partial differential equations as introduced by Pakdaman, Perthame and Salort.

MTM2014-52056-P P08-FQM-04267 Laboratoire Jean Alexandre Dieudonné JAD 1996-01-01 2011-12-31

Université de Nice - Sophia Antipolis U.M.R. no 6621 du C.N.R.S. Parc Valrose 06108 Nice Cedex 02 France

http://math.unice.fr/ https://ror.org/04njjy449 Universidad de Granada = University of Granada UGR

Avda. del Hospicio, s/n C.P. 18010 Granada

http://www.ugr.es 199712644L Laboratoire Jacques-Louis Lions LJLL

Université Pierre et Marie Curie, Boîte courrier 187 - 75252 Paris Cedex 05

https://www.ljll.math.upmc.fr 201421109N Modelling and Analysis for Medical and Biological Applications MAMBA 2015-06-04 2016-12-07

http://www.inria.fr/equipes/mamba 060325887 201220430J https://ror.org/0274zdr66 Laboratoire Jean Alexandre Dieudonné LJAD 2012-01-01

Université Côte d'Azur U.M.R. no 7351 du C.N.R.S. Parc Valrose 06108 Nice Cedex 02 France

http://math.unice.fr/ 026403498 0000000123372892 https://ror.org/02k9vew78 Université Nice Sophia Antipolis (1965 - 2019) UNS 1965-10-23 2019-12-31

Parc Valrose, 06100 Nice

http://unice.fr/ 02636817X 0000000122597504 https://ror.org/02feahw73 Centre National de la Recherche Scientifique CNRS 1939-10-19

https://www.cnrs.fr/ https://ror.org/02en5vm52 Université Pierre et Marie Curie - Paris 6 UPMC 2017-12-31

4 place Jussieu - 75005 Paris

http://www.upmc.fr/ 027542084 0000000121514068 https://ror.org/02n7qrg46 Université Paris Diderot - Paris 7 UPD7 2019-12-31

5 rue Thomas-Mann - 75205 Paris cedex 13

http://www.univ-paris-diderot.fr Inria Paris-Rocquencourt 2016-03-30

INRIA Rocquencourt : Domaine de Voluceau, Rocquencourt B.P. 105 78153 le Chesnay Cedex

http://www.inria.fr/centre/paris-rocquencourt https://ror.org/02kvxyf05 Institut National de Recherche en Informatique et en Automatique Inria

Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex

http://www.inria.fr/en/ 241035694 https://ror.org/019tgvf94 Université Côte d'Azur UniCA 2020-01-01

Parc Valrose, 28, avenue Valrose 06108 Nice Cedex 2

https://univ-cotedazur.fr ANR-11-BS01-0010 BLANC Calibration Calibration statistique 2011 306321 ERC-2012-StG_20111012 ERC-2012-StG_20111012 SKIPPERAD Simulation of the Kinetics and Inverse Problem for the Protein PolymERization in Amyloid Diseases (Prion, Alzheimer’s) 2012-01-12 2018-07-31