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Theses

Plasticity in networks of spiking neurons in interaction

Abstract : In this thesis, we study a phenomenon that may be responsible for our memory capacity: the synaptic plasticity. It modifies the links between neurons over time. This phenomenon is stochastic: it is the result of a series of diverse and numerous chemical processes. The aim of the thesis is to propose a model of plasticity for interacting spiking neurons. The main difficulty is to find a model that satisfies the following conditions: it must be both consistent with the biological results of the field and simple enough to be studied mathematically and simulated with a large number of neurons.In a first step, from a rather simple model of plasticity, we study the learning of external signals by a neural network as well as the forgetting time of this signal when the network is subjected to other signals (noise). The mathematical analysis allows us to control the probability to misevaluate the signal. From this, we deduce explicit bounds on the time during which a given signal is kept in memory.Next, we propose a model based on stochastic rules of plasticity as a function of the occurrence time of the neural electrical discharges (Spike Timing Dependent Plasticity, STDP). This model is described by a Piecewise Deterministic Markov Process (PDMP). The long time behaviour of such a neural network is studied using a slow-fast analysis. In particular, sufficient conditions are established under which the process associated with synaptic weights is ergodic. Finally, we make the link between two levels of modelling: the microscopic and the macroscopic approaches. Starting from the dynamics presented at a microscopic level (neuron model and its interaction with other neurons), we derive an asymptotic dynamics which represents the evolution of a typical neuron and its incoming synaptic weights: this is the mean field analysis of the model. We thus condense the information on the dynamics of the weights and that of the neurons into a single equation, that of a typical neuron.
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https://hal.archives-ouvertes.fr/tel-03200979
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Submitted on : Tuesday, June 8, 2021 - 12:01:08 PM
Last modification on : Monday, October 11, 2021 - 5:11:01 PM

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  • HAL Id : tel-03200979, version 2

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Pascal Helson. Plasticity in networks of spiking neurons in interaction. Neuroscience. Université Côte d'Azur, 2021. English. ⟨NNT : 2021COAZ4013⟩. ⟨tel-03200979v2⟩

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