title: Exact solutions for rate and synchrony in recurrent networks of coincidence detectors.
abstract: 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.
authors.affiliation: Center for Neuroscience, University of California, Davis, CA 95618, USA. samikula@ucdavis.edu
authors.forename: Shawn
authors.initials: S
authors.lastname: Mikula
authors.forename: Ernst
authors.initials: E
authors.lastname: Niebur
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D000818:Animals; D008390:Markov Chains; D008959:Models, Neurological; D009433:Neural Inhibition; D016571:Neural Networks, Computer; D009474:Neurons / Q000502:physiology*; D013223:Statistics as Topic