Unconventional criticality in the stochastic Wilson-Cowan model

Detalhes bibliográficos
Autor(a) principal: BASTOS, Helena Christina Piuvezam de Albuquerque
Data de Publicação: 2023
Tipo de documento: Tese
Idioma: eng
Título da fonte: Repositório Institucional da UFPE
dARK ID: ark:/64986/001300001432m
Texto Completo: https://repositorio.ufpe.br/handle/123456789/56169
Resumo: The Wilson-Cowan model serves as a classic framework for comprehending the collective neuronal dynamics within networks comprising both excitatory and inhibitory units. Extensively employed in literature, it facilitates the analysis of collective phases in neural networks at a mean-field level, i.e., when considering large fully connected networks. To study fluctuation- induced phenomena, the dynamical model alone is insufficient; to address this issue, we need to work with a stochastic rate model that is reduced to the Wilson-Cowan equations in a mean-field approach. Throughout this thesis, we analyze the resulting phase diagram of the stochastic Wilson-Cowan model near the active to quiescent phase transitions. We unveil eight possible types of transitions that depend on the relative strengths of excitatory and inhibitory couplings. Among these transitions are second-order and first-order types, as expected, as well as three transitions with a surprising mixture of behaviors. The three bona fide second- order phase transitions belong to the well-known directed percolation universality class, the tricritical directed percolation universality class, and a novel universality class called “Hopf tricritical directed percolation", which presents an unconventional behavior with the breakdown of some scaling relations. The discontinuous transitions behave as expected and the hybrid transitions have different anomalies in scaling across them. Our results broaden our knowledge and characterize the types of critical behavior in excitatory and inhibitory networks and help us understand avalanche dynamics in neuronal recordings. From a more general perspective, these results contribute to extending the theory of non-equilibrium phase transitions into quiescent or absorbing states.
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spelling BASTOS, Helena Christina Piuvezam de Albuquerquehttp://lattes.cnpq.br/6373327506505583http://lattes.cnpq.br/9400915429521069SILVA, Mauro Copelli Lopes da2024-05-02T14:03:18Z2024-05-02T14:03:18Z2023-12-15BASTOS, Helena Christina Piuvezam de Albuquerque. Unconventional criticality in the stochastic Wilson-Cowan model. 2023. Tese (Doutorado em Física) – Universidade Federal de Pernambuco, Recife, 2023.https://repositorio.ufpe.br/handle/123456789/56169ark:/64986/001300001432mThe Wilson-Cowan model serves as a classic framework for comprehending the collective neuronal dynamics within networks comprising both excitatory and inhibitory units. Extensively employed in literature, it facilitates the analysis of collective phases in neural networks at a mean-field level, i.e., when considering large fully connected networks. To study fluctuation- induced phenomena, the dynamical model alone is insufficient; to address this issue, we need to work with a stochastic rate model that is reduced to the Wilson-Cowan equations in a mean-field approach. Throughout this thesis, we analyze the resulting phase diagram of the stochastic Wilson-Cowan model near the active to quiescent phase transitions. We unveil eight possible types of transitions that depend on the relative strengths of excitatory and inhibitory couplings. Among these transitions are second-order and first-order types, as expected, as well as three transitions with a surprising mixture of behaviors. The three bona fide second- order phase transitions belong to the well-known directed percolation universality class, the tricritical directed percolation universality class, and a novel universality class called “Hopf tricritical directed percolation", which presents an unconventional behavior with the breakdown of some scaling relations. The discontinuous transitions behave as expected and the hybrid transitions have different anomalies in scaling across them. Our results broaden our knowledge and characterize the types of critical behavior in excitatory and inhibitory networks and help us understand avalanche dynamics in neuronal recordings. From a more general perspective, these results contribute to extending the theory of non-equilibrium phase transitions into quiescent or absorbing states.CAPESO modelo Wilson-Cowan é um modelo clássico para a compreensão da dinâmica coletiva de redes neurais com unidades excitatórias e inibitórias. Esse modelo foi extensivamente estu- dado na literatura, especialmente na análise de fases de redes neurais em uma aproximação de campo médio, ou seja, em grandes redes completamente conectada. Para estudar fenô- menos induzidos por flutuações, o modelo dinâmico é insuficiente. Portanto, é importante introduzirmos um modelo estocástico de taxas que se reduz às equações de Wilson-Cowan na aproximação de campo médio. Nesta tese, analisamos o diagrama de fases do modelo esto- cástico de Wilson-Cowan acerca das transições ativo-quiescente. Desvendamos oito possíveis tipos de transições dependentes do valor relativo do acoplamento entre unidades excitatorias e inibitórias. Entre essas transições estão transições de segunda e primeira ordem, e adicio- nalmente encontramos três tipos de transições que possuem uma mistura de comportamento ou hibridas. As três transições verdadeiramente críticas pertencem às classes de percolação direcionada, percolação direcionada tricrítica e uma classe nova que chamamos de “percolação direcionada Hopf tricrítica", que apresenta um comportamento não convencional com quebras de relações de escala. As transições descontínuas se comportam como esperado e as híbridas apresentam diferentes anomalias entres elas. Nossos resultados ampliam o conhecimento sobre e caracterizam os tipos de comportamento crítico em redes excitatórias e inibitórias, alén de ajudar a compreender a dinâmica de avalanches em registros neuronais experimentais. De uma perspectiva mais geral, estes resultados contribuem para estender a teoria de transições de fase de não-equilíbrio entre estados quiescentes e absorventes.engUniversidade Federal de PernambucoPrograma de Pos Graduacao em Educacao FisicaUFPEBrasilAttribution-NonCommercial-NoDerivs 3.0 Brazilhttp://creativecommons.org/licenses/by-nc-nd/3.0/br/info:eu-repo/semantics/openAccessFísica teórica e computacionalModelo de Wilson-CowanAvalanches neuronaisUnconventional criticality in the stochastic Wilson-Cowan modelinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisdoutoradoreponame:Repositório Institucional da UFPEinstname:Universidade Federal de Pernambuco (UFPE)instacron:UFPEORIGINALTESE Helena Christina Piuvezam de Albuquerque Bastos.pdfTESE Helena Christina Piuvezam de Albuquerque Bastos.pdfapplication/pdf7539358https://repositorio.ufpe.br/bitstream/123456789/56169/1/TESE%20Helena%20Christina%20Piuvezam%20de%20Albuquerque%20Bastos.pdfde3408336726e94f1789d7bb6546f9edMD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; 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dc.title.pt_BR.fl_str_mv Unconventional criticality in the stochastic Wilson-Cowan model
title Unconventional criticality in the stochastic Wilson-Cowan model
spellingShingle Unconventional criticality in the stochastic Wilson-Cowan model
BASTOS, Helena Christina Piuvezam de Albuquerque
Física teórica e computacional
Modelo de Wilson-Cowan
Avalanches neuronais
title_short Unconventional criticality in the stochastic Wilson-Cowan model
title_full Unconventional criticality in the stochastic Wilson-Cowan model
title_fullStr Unconventional criticality in the stochastic Wilson-Cowan model
title_full_unstemmed Unconventional criticality in the stochastic Wilson-Cowan model
title_sort Unconventional criticality in the stochastic Wilson-Cowan model
author BASTOS, Helena Christina Piuvezam de Albuquerque
author_facet BASTOS, Helena Christina Piuvezam de Albuquerque
author_role author
dc.contributor.authorLattes.pt_BR.fl_str_mv http://lattes.cnpq.br/6373327506505583
dc.contributor.advisorLattes.pt_BR.fl_str_mv http://lattes.cnpq.br/9400915429521069
dc.contributor.author.fl_str_mv BASTOS, Helena Christina Piuvezam de Albuquerque
dc.contributor.advisor1.fl_str_mv SILVA, Mauro Copelli Lopes da
contributor_str_mv SILVA, Mauro Copelli Lopes da
dc.subject.por.fl_str_mv Física teórica e computacional
Modelo de Wilson-Cowan
Avalanches neuronais
topic Física teórica e computacional
Modelo de Wilson-Cowan
Avalanches neuronais
description The Wilson-Cowan model serves as a classic framework for comprehending the collective neuronal dynamics within networks comprising both excitatory and inhibitory units. Extensively employed in literature, it facilitates the analysis of collective phases in neural networks at a mean-field level, i.e., when considering large fully connected networks. To study fluctuation- induced phenomena, the dynamical model alone is insufficient; to address this issue, we need to work with a stochastic rate model that is reduced to the Wilson-Cowan equations in a mean-field approach. Throughout this thesis, we analyze the resulting phase diagram of the stochastic Wilson-Cowan model near the active to quiescent phase transitions. We unveil eight possible types of transitions that depend on the relative strengths of excitatory and inhibitory couplings. Among these transitions are second-order and first-order types, as expected, as well as three transitions with a surprising mixture of behaviors. The three bona fide second- order phase transitions belong to the well-known directed percolation universality class, the tricritical directed percolation universality class, and a novel universality class called “Hopf tricritical directed percolation", which presents an unconventional behavior with the breakdown of some scaling relations. The discontinuous transitions behave as expected and the hybrid transitions have different anomalies in scaling across them. Our results broaden our knowledge and characterize the types of critical behavior in excitatory and inhibitory networks and help us understand avalanche dynamics in neuronal recordings. From a more general perspective, these results contribute to extending the theory of non-equilibrium phase transitions into quiescent or absorbing states.
publishDate 2023
dc.date.issued.fl_str_mv 2023-12-15
dc.date.accessioned.fl_str_mv 2024-05-02T14:03:18Z
dc.date.available.fl_str_mv 2024-05-02T14:03:18Z
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dc.identifier.citation.fl_str_mv BASTOS, Helena Christina Piuvezam de Albuquerque. Unconventional criticality in the stochastic Wilson-Cowan model. 2023. Tese (Doutorado em Física) – Universidade Federal de Pernambuco, Recife, 2023.
dc.identifier.uri.fl_str_mv https://repositorio.ufpe.br/handle/123456789/56169
dc.identifier.dark.fl_str_mv ark:/64986/001300001432m
identifier_str_mv BASTOS, Helena Christina Piuvezam de Albuquerque. Unconventional criticality in the stochastic Wilson-Cowan model. 2023. Tese (Doutorado em Física) – Universidade Federal de Pernambuco, Recife, 2023.
ark:/64986/001300001432m
url https://repositorio.ufpe.br/handle/123456789/56169
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dc.publisher.none.fl_str_mv Universidade Federal de Pernambuco
dc.publisher.program.fl_str_mv Programa de Pos Graduacao em Educacao Fisica
dc.publisher.initials.fl_str_mv UFPE
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publisher.none.fl_str_mv Universidade Federal de Pernambuco
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