Topic: spectral condition

Relating connectivity features to the function of a recurrent neuronal network is a longstanding problem that still remains at large. To this end we describe the combinatorics of equilibria and steady states of neurons in recurrent networks that satisfy the Dale’s law. It turns out that the combinatorial code of a Dale network can be characterized in terms of two properties: (i) the network connectivity graph, and (ii) a spectral condition on the synaptic matrix. We find that in the weak coupling regime the combinatorial code depends only on the connectivity graph, and not on the particulars o