Neural Networks and Mathematical Modeling of Cortex’s Circuits

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Tahvili, Farzin | 2020

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 53042 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Razvan, Mohammad Reza; Safari, MirShahram
Abstract:
In this thesis, we review some models for mathematical modeling of neuronal circuits of brain and especially, the main aim of this thesis is chapter two that we review a rigorous model for cortical microcir-cuits which is called liquid state machine. The structure of this thesis is as follows, first in the introduction we give some prerequisites that are essential for understanding contents of this thesis and also, one of the first mathematical model for neural computations, attractor neural networks, has been mentioned. In chapter one, we introduce feedforward neural networks equipped with dynamical synapses. In fact in this chapter we review two experimental models for dynam-ical synapses and then prove some important theorems which show feedforward networks equipped with these synaptic models, have general computational abilities. In chapter two we review liquid state machine that is a very good model for cortical microcircuits and does not have problems of previous models
Keywords:
Dynamical Synapse ; Feed Forward Neural Network ; Liquid State Machine ; Microcircuit ; Cortex ; Attractor Neural Network