Models of neural networks with stochastic neurons and different topologies: construction and analysis.

Author(s)

Vinicius Lima Cordeiro

• Document type: Master's Dissertation
• Press: Ribeirão Preto.
• Institution: Universidade de São Paulo (USP). Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto (PCARP/BC)
• Defense date: 2019-08-29

Examining board members

Antonio Carlos Roque da Silva Filho; Ariadne de Andrade Costa; Jorge Stolfi; Renato Tinós

• Advisor: Antonio Carlos Roque da Silva Filho; Osame Kinouchi Filho

Abstract

The nervous system is submitted to several sources of noise. In general, those sources can be classified as endogenous and exogenous. Synaptic noise and ionic channel noise are the main endogenous sources of noise. The exogenous noise can be assigned to the variability existent in external stimuli. The nervous system has strategies to deal with the presence of noise, however, it has been discussed the role of noise in neuronal processing. There are at least two ways of introducing endogenous noise sources in mathematical neuron models: the first is to consider a deterministic model and add stochastic terms to the ionic or synaptic inputs received by the neuron, the second is to assume that the emission of an action potential is an intrinsically stochastic event. It is possible to model the latter by introducing a random fluctuating spike threshold, where the occurrence of an action potential is defined by means of a voltage-dependent spike probability function. In this dissertation, we have used an intrinsically stochastic neuron model, aiming to determine the influences of its noise on cellular and network scales. To do so, first, we propose a method to estimate the spike probability curves from eletrophysiological data. Then, we use those curves in the stochastic model to study the effect of the intrinsic noise on relevant natural phenomena as the spiking time reliability and stochastic resonance. We finish the dissertation studying the effect of different network topologies on the intrinsic stochasticity of individual neurons. We study topologies with random connectivity and specific connectivity of a cortical microcircuit. Using a time series of membrane potential we have estimated the spiking probability curve used in the stochastic model, showing that it has an exponential shape as observed in the literature. Among the results obtained, it can be observed the existence of stochastic resonance caused by the neurons intrinsic noise, and the reproducibility of the increasing spiking time reliability due to input synaptic noise into the neuron. Finally, studies of the network show that the influence caused by the stochastic neuron is dependent on the networks dynamical state and topology, with weaker effects on asynchronous and regular random networks (AU)

• FAPESP's process: 17/05874-0 - Models of neural networks with stochastic neurons and different topologies: construction and analysis
• Grantee: Vinícius Lima Cordeiro
• Support Opportunities: Scholarships in Brazil - Master