Κατεύθυνση Στατιστική και Επιχειρησιακή Έρευνα
Library of the School of Science

2023-11-03

2023

Mandilaris Kyriakos

Σάμης Τρέβεζας, Επίκουρος Καθηγητής, Τμήμα Μαθηματικών ΕΚΠΑ

Piecewise Deterministic Markov Processes with Applications in Modeling Neuronal Activity

English

Piecewise Deterministic Markov Processes with Applications in Modeling Neuronal Activity

In this thesis we investigate the nature and the mechanisms of the fundamental units of our brain and our nervous system; the neurons. Our main tool for this purpose is Piecewise deterministic Markov processes (PDMPs), a class of stochastic models that have been widely used as a framework in the study of single neuron dynamics.

We begin by introducing the basic concepts of PDMPs, including their definition, properties, and relationship to other types of stochastic processes. We then present the biological features of a neuron and link their stochastic behaviour with different types of PDMPs, mainly focusing on the Hogdkin-Huxley model, which constitutes a milestone for neuroscience.

By simulating different types of PDMPs, we demonstrate how they can be used to accurately gain insight into a wide range of single neuron mechanisms, including the generation of an action potential, spiking ratio and inter-spike intervals.

Overall, this thesis provides an overview of the use of PDMPs for single neuron modeling, and demonstrates their utility as a tool for understanding the complex dynamics of individual neurons.

Science

Piecewise Deterministic Markov Process, Stochastic simulation, Neuron, Gillespie, Markov process, action potential, stochastic modelling, Hodgkin-Huxley

Yes

2

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File access is restricted only to the intranet of UoA.

https://pergamos.lib.uoa.gr/uoa/dl/object/3363714