288 pp. per issue
6 x 9, illustrated
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Neural Computation

November 2008, Vol. 20, No. 11, Pages 2637-2661
(doi: 10.1162/neco.2008.07-07-570)
© 2008 Massachusetts Institute of Technology
Exact Solutions for Rate and Synchrony in Recurrent Networks of Coincidence Detectors
Article PDF (553.65 KB)

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.