The role of degree distributions in shaping the dynamics in networks of sparsely connected spiking neurons

Abstract:

Most work on sparsely connected networks of spiking neurons has made use of the assumption that there is a fixed probability of connection between any two neurons. This results in narrow in-degree and out-degree distributions, i.e. all neurons receive and send out about the same number of connections. This allows for powerful mean field techniques to be applied making such standard random networks attractive for analytical work. However, recent electrophysiological work indicates that local cortical circuits exhibit statistical regularities not consistent with a standard random network. I will discuss how changes in the network connectivity, specifically in the degree distributions, affect the dynamics in networks of sparsely connected spiking neurons. For the case of the incoming connections, the effect of degree distribution can be accounted for in a modified rate equation in which the degree is treated as a continuous, pseudo-spatial variable. This allows one to calculate fixed point solutions and their stability using standard techniques.

I will show how varying the degree distribution shifts stability boundaries of the asynchronous state to oscillations and compare analytical results to full network simulations.

I will show how broadening the out-degree increases pairwise correlations in subthreshold currents. In the asynchronous regime, fluctuations in the excitatory and inhibitory currents dynamically balance leading to near-zero spike correlations, independent of out-degree. When oscillations are present however, the out-degree has a significant effect on spiking correlations and can qualitatively alter the dynamical state of the network.

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