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Number of hours
Lectures : 18.0
ECTS : 1.5
Contact Adeline LECLERC SAMSON
Biophysical processes observed in neurosciences are very complex. The activity of neurons in the brain and the code used by these neurons is described by mathematical neuron models at different levels of detail. This course gives an introduction to the field of theoretical and computational neuroscience with a focus on models of single neurons. Neurons encode information about stimuli in a sequence of short electrical pulses (spikes). Mathematical tools such as differential equations, point processes, separation of time scales and stochastic processes will be presented to understand the dynamics of neurons and the neural code; especially integrate-and-fire neural models, Hodgkin-Huxley models and biophysical modeling, Poisson and Hawkes processes. Then estimation methods for neuron coding and decoding will be introduced, with parametric or non-parametric approaches. These statistical methods are based on EM algorithm, Markov chain Monte Carlo, sequential Monte Carlo and particle filtering, model selection.