# 06.10.2020 Mean-field techniques for Neuroscience - Mini-course by Gianluigi Mongillo

## Mean-field techniques for Neuroscience

### Abstract:

Cognitive functions, such as memory and decision-making, are thought to emerge from the collective dynamics of relatively large, and heterogeneous, neuronal networks. The pattern and strengths of the synaptic connections in these networks, as well as the parameters characterizing the single cell (e.g., spiking threshold) and single synapse (e.g., probability of release) dynamics, are only known statistically. In order to compare with experiments, then, one seeks predictions about the “typical” dynamical behavior of the “typical” network (i.e., for “typical” realizations of the synaptic connectivity and of the constitutive parameters), assuming that such a typical behavior is indeed well defined and relevant for the description of the real system. A similar necessity arises in the physics of disordered systems, where a collection of powerful techniques, which go collectively under the name of mean-field techniques, have been developed in order to cope with the problem. In this minicourse, I will describe how one such technique – the cavity method – can be naturally, and usefully, extended to the case of neuronal networks. In particular, using the cavity method, I will derive self-consistent equations that describe the statistics of the activity in the fixed point of a partially symmetric, balanced network. I will also show how the cavity method can be used to investigate the stability of the fixed points, besides finding them.

*Please confirm your participation : chloe.bourgeois@univ-cotedazur.fr *