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An essential step toward understanding neural circuits is linking theirstructure and their dynamics. In general, this relationship can be almostarbitrarily complex. Recent theoretical work has, however, begun to identifysome broad principles underlying collective spiking activity in neuralcircuits. The first is that local features of network connectivity can besurprisingly effective in predicting global statistics of activity across anetwork. The second is that, for the important case of large networks withexcitatory-inhibitory balance, correlated spiking persists or vanishesdepending on the spatial scales of recurrent and feedforward connectivity. Weclose by showing how these ideas, together with plasticity rules, can help toclose the loop between network structure and activity statistics.

From the statistics of connectivity to the statistics of spike times in neuronal networks