Francesco Bonilauri — University of Parma #
Dynamical Mean Field Theory of Sparse Inhibitory-Excitatory Networks #
A realistic model of a real world biological neural network would need to be both sparse and comprised of separate inhibitory and excitatory neuron populations. While dynamical mean field theory (DMFT) approaches exist separately for networks in the very sparse regime (degree $c \ll N$) and for diluted I-E networks, in our work we combine the two, using a population dynamics algorithm to sample the mean field path probability of very sparse I-E networks. We find that this approach correctly predicts the neuron currents, whereas the gaussian approximation fails. Moreover, this approach makes no assumptions about the degree distribution, and we show that even in the high connectivity limit $c \to \infty$, the network is affected by the degree fluctuations of an inhomogeneous distribution, diverging from the usual dense gaussian theory.