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Title: Averaging principles for Markovian models of synaptic plasticity

Abstract: In neuroscience, synaptic plasticity refers to the set of mechanisms driving the dynamics of neuronal connections, called synapses and represented by a scalar value, the synaptic weight. In this talk I will consider a stochastic system with two connected neurons, with a variable synaptic weight that depends on point processes associated to each neuron. The input neuron is represented by an homogeneous Poisson process, whereas the output neuron jumps with an intensity that depends on the jumps of the input node and the connection intensity. I will study a scaling regime where the rate of both point processes is large compared to the dynamics of the connection, that corresponds to a classical assumption in computational neuroscience where cellular processes evolve much more rapidly than the synaptic weight. I will present an averaging principle for the time evolution of the connection intensity, and a sketch of its proof, which involves a detailed analysis of several of unbounded additive functionals in the slow-fast limit, and technical results on interacting shot-noise processes.

To attend Zoom meeting please contact elliot.paquette! [at] mcgill.ca

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