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"Spike trains and chain systems with variable order memory" Eva Löcherbach (Video)
Mini-course
Introduction and study of a simple model in discrete time for the generation of spikes in a system with an infinity of interacting neurons.
In this model, each neuron emits a discharge (= spike) with a probability that depends on its past since its last spike and interactions with other neurons. We discuss this model as well as various associated theoretical results (existence of a stationary solution, perfect simulation...).
In a second time, we study a version in continuous time of the same model. A description by a Markovian particle system will be discussed as well as its behavior in long time. Finally, we study the property of propagation of chaos in a model of interactions of average field type.
Video 1 Video 2
In a second time, we study a version in continuous time of the same model. A description by a Markovian particle system will be discussed as well as its behavior in long time. Finally, we study the property of propagation of chaos in a model of interactions of average field type.
Video 1 Video 2
Dates
Created on April 16, 2015