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Exact Solutions for Rate and Synchrony in Recurrent Networks of Coincidence Detectors

samikula{at}ucdavis.edu Center for Neuroscience, University of California, Davis, CA 95618, U.S.A.

Ernst Niebur

niebur{at}jhu.edu Krieger Mind/Brain Institute, Johns Hopkins University, Baltimore, MD 21218, U.S.A.

We provide analytical solutions for mean firing rates and cross-correlations of coincidence detector neurons in recurrent networks with excitatory or inhibitory connectivity, with rate-modulated steady-state spiking inputs. We use discrete-time finite-state Markov chains to represent network state transition probabilities, which are subsequently used to derive exact analytical solutions for mean firing rates and cross-correlations. As illustrated in several examples, the method can be used for modeling cortical microcircuits and clarifying single-neuron and population coding mechanisms. We also demonstrate that increasing firing rates do not necessarily translate into increasing cross-correlations, though our results do support the contention that firing rates and cross-correlations are likely to be coupled. Our analytical solutions underscore the complexity of the relationship between firing rates and cross-correlations.