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Doctoral Thesis
DOI
10.11606/T.45.2014.tde-22092014-090046
Document
Author
Full name
Karina Yuriko Yaginuma
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2014
Supervisor
Committee
Galves, Jefferson Antonio (President)
Abadi, Miguel Natalio
Coletti, Cristian Favio
García, Jesús Enrique
Garcia, Nancy Lopes
Title in Portuguese
Modelagem estocástica de uma população de neurônios
Keywords in Portuguese
redes neurais biológicas
simulação perfeita
sistemas markovianos de partículas
Abstract in Portuguese
Nesta tese consideramos uma nova classe de sistemas markovianos de partículas com infinitas componentes interagentes. O sistema representa a evolução temporal dos potenciais de membrana de um conjunto infinito de neurônios interagentes. Provamos a existência e unicidade do processo construindo um pseudo-algoritmo de simulação perfeita e mostrando que este algoritmo roda em um número finito de passos quase certamente. Estudamos também o comportamento do sistema quando consideramos apenas um conjunto finito de neurônios. Neste caso, construímos um procedimento de simulação perfeita para o acoplamento entre o processo limitado a um conjunto finito de neurônios e o processo que considera todos os neurônios do sistema. Como consequência encontramos um limitante superior para a probabilidade de discrepância entre os processos.
Title in English
Stochastic modelling of a population of neurons
Keywords in English
Markovian particle systems
neural nets
perfect simulation
Abstract in English
We consider a new class of interacting particle systems with a countable number of interacting components. The system represents the time evolution of the membrane potentials of an infinite set of interacting neurons. We prove the existence and uniqueness of the process, by the construction of a perfect simulation procedure. We show that this algorithm is successful, that is, we show that the number of steps of the algorithm is finite almost surely. We also study the behaviour of the system when we consider only a finite number of neurons. In this case, we construct a perfect simulation procedure for the coupling of the process with a finite number of neurons and the process with a infinite number of neurons. As a consequence we obtain an upper bound for the error we make when sampling from a finite set of neurons instead of the infinite set of neurons.
 
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Publishing Date
2014-09-23
 
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