Detection of dynamical states of neuronal networks with persistent homology tools

The Brunel network is a neuronal network model composed of excitatory and inhibitory leaky integrate-and-fire spiking neurons. This network is known to present four distinguished activity states, which can be mainly described by the synchronicity and regularity of the firing of its neurons. Topologi...

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Detalles Bibliográficos
Autor: Gutiérrez Von Porat, Nils
Tipo de recurso: tesis de maestría
Fecha de publicación:2021
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/349590
Acceso en línea:https://hdl.handle.net/2117/349590
Access Level:acceso abierto
Palabra clave:Algebra, Homological
Categories (Mathematics)
Topological data analysis
Computational neuroscience
Persistent homology
Neuronal networks
Persistence diagrams
Neuronal activity patterns
Synaptic plasticity
Àlgebra homològica
Categories (Matemàtica)
Classificació AMS::55 Algebraic topology::55U Applied homological algebra and category theory
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria
Descripción
Sumario:The Brunel network is a neuronal network model composed of excitatory and inhibitory leaky integrate-and-fire spiking neurons. This network is known to present four distinguished activity states, which can be mainly described by the synchronicity and regularity of the firing of its neurons. Topological data analysis (TDA) is a field from algebraic topology and computational geometry developed during the 2000s, designed to study the topological structure of datasets. The main tool of TDA is persistent homology. This algebraic method allows to study the topological structure of a network by monitoring how its cavities or holes at different dimensions evolve. The aim of this project is to show that persistent homology can be useful to identify the dynamics of neuronal networks. In order to do so, we apply persistent homology to identify the four activity states produced by the Brunel network. Moreover, we use persistent homology to identify the dynamics induced by the presence of synaptic plasticity (specifically short-time depression) in the Brunel network.