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Doctoral Thesis
DOI
https://doi.org/10.11606/T.45.2020.tde-01032021-124843
Document
Author
Full name
Morgan Florian Thibault Andre
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2020
Supervisor
Committee
Galves, Jefferson Antonio (President)
Ferrari, Pablo Augusto
Locherbach, Eva
Pouzat, Christophe
Reynaud-Bouret, Patricia Marie Pierre
Title in English
Phase transition and metastability in a stochastic system of spiking neurons
Keywords in English
Interacting particle systems
Metastability
Neural networks
Phase transition
Stochastic models
Abstract in English
We study a continuous-time stochastic system of spiking neurons from the perspective of phase transition and metastability, using mathematical concepts and techniques borrowed from statistical physics. The model we consider is a continuous-time version of the Galves-Löcherbach model, in which the interaction beetwen the components is given by the one-dimensional lattice. It has already been proven to be subject to a phase transition with respect to the leakage parameter. In this work we show that the system is metastable in one of the phase, while it is not in the other. We then consider the same model with different graphs of interaction and we obtain various results of phase transition and mestability.
Title in Portuguese
Transição de fase e metaestabilidade num modelo estocástico de rede de neurônios gerando disparos
Keywords in Portuguese
Metaestabilidade
Modelos estocásticos de redes de neurônios biológicos
Sistemas de partículas em interação
Transição de fase
Abstract in Portuguese
Nessa tese, estudamos um sistema estocástico em tempo continuo de neurônios gerando disparos, do ponto de vista dos fenômenos de transição de fase e de metaestabilidade, usando conceitos matemáticos e técnicas emprestado da física estatística.
 
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TeseMorgan.pdf (1.24 Mbytes)
Publishing Date
2021-03-02
 
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