Interplay between Graph Topology and Correlations of Third Order in Spiking Neuronal Networks
Fig 1
Hawkes process theory reproduces rates, correlations and third cumulants in a simulated network with Erdős-Rényi type random connectivity.
Network parameters are N = 1000, NE = 800, NI = 200, p = 0.1, gE = 0.015 and gI = −0.075. Top left: Fluctuating firing rates of 50 randomly chosen neurons (gray traces) and their average (red line). The average rate only rarely goes below 0 (dashed line). Top right: Estimated temporal averages of firing rates scattered vs. rates predicted by Hawkes theory. The diagonal (green line) indicates a perfect match. Note that there is a slight discrepancy between theory and simulation for very low rates. Bottom left: Estimated integrated pairwise covariances (of all possible neuron pairs) scattered vs. integrated covariances predicted by Hawkes theory. Bottom right: Estimated integrated joint third cumulants (see the following sections for a definition) of a 100 randomly chosen neurons, scattered vs. integrated joint cumulants computed from Hawkes theory. The larger discrepancies are due to finite simulation time and a relatively small sample size.