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dc.contributorAlberich Carramiñana, Maria
dc.contributorCortes Monforte, Jorge
dc.contributor.authorPlanas Casadevall, Robert
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.coverage.spatialeast=-117.2340135; north=32.8800604; name=413 Lyman Ln, La Jolla, CA 92093, Estats Units d'Amèrica
dc.description.abstractOscillations in the brain are one of the most pervasive and robust patterns found in the neural activity and they can be directly correlated with numerous cognitive phenomena. In this work, we study the structural network characteristics, in simple mean-field models of brain activity with bounded linear-threshold rate dynamics, that will ensure the lack of equilibria, and numerically show that this approach is, indeed, a tight proxy for the existence of oscillatory behavior. Through a geometrical approach to the linear constructs intrinsic in the dynamics of the system, we provide multiple sets of sufficient conditions for the lack of equilibria in arbitrary multidimensional excitatory-inhibitory network (nE-mI). We further extend this characterization for the fully inhibitory. We also discuss the concept of degenerate oscillations, a trade off between competitive and cooperative behaviors involving different nodes or regions of the brain and we numerically compare prevalence of degenerate oscillations for all sets of sufficient conditions. Lastly, in the case of pairwise-unstable fully inhibitory networks, we further provide analytical characterizations of the degenerate oscill
dc.publisherUniversitat Politècnica de Catalunya
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències
dc.subject.otherBrain Networks
dc.subject.otherExcitatory-Inhibitory networks
dc.subject.otherFully inhibitory networks
dc.subject.otherDegenerate Oscillations
dc.titleStructural characterization of oscillatory behavior in the brain
dc.typeBachelor thesis
dc.rights.accessOpen Access
dc.audience.mediatorUniversitat Politècnica de Catalunya. Centre de Formació Interdisciplinària Superior
dc.audience.mediatorEscola Superior d'Enginyeries Industrial, Aeroespacial i Audiovisual de Terrassa
dc.audience.mediatorUniversitat Politècnica de Catalunya. Facultat de Matemàtiques i Estadística
dc.contributor.covenanteeUniversity of California, San Diego

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