Nonnegative matrices and other topics in linear algebra
Nonnegative matrices and other topics in linear algebra
Neural networks: a systematic introduction
Neural networks: a systematic introduction
Queueing networks and Markov chains: modeling and performance evaluation with computer science applications
Finite Automata, Pattern Recognition and Perceptrons
Journal of the ACM (JACM)
Introduction to Algorithms
Generation of Synthetic Spike Trains with Defined Pairwise Correlations
Neural Computation
Correlated inhibitory and excitatory inputs to the coincidence detector: analytical solution
IEEE Transactions on Neural Networks
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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.