A heuristic approach to stochastic models of single neurons
Single neuron computation
Diffusion models of neuron activity
The handbook of brain theory and neural networks
The continuum of operating modes for a passive model neuron
Neural Computation
Numerical Recipes in C: The Art of Scientific Computing
Numerical Recipes in C: The Art of Scientific Computing
A population density approach that facilitates large-scale modeling of neural networks
A population density approach that facilitates large-scale modeling of neural networks
Impact of Correlated Inputs on the Output of the Integrate-and-Fire Model
Neural Computation
The Effect of NMDA Receptors on Gain Modulation
Neural Computation
Distortion of Neural Signals by Spike Coding
Neural Computation
Phase Transition and Hysteresis in an Ensemble of Stochastic Spiking Neurons
Neural Computation
Stochastic dynamics of a finite-size spiking neural network
Neural Computation
Stimulus-dependent correlations in threshold-crossing spiking neurons
Neural Computation
Systematic fluctuation expansion for neural network activity equations
Neural Computation
Synaptic information transfer in computer models of neocortical columns
Journal of Computational Neuroscience
Mechanisms that modulate the transfer of spiking correlations
Neural Computation
Distinguishing the causes of firing with the membrane potential slope
Neural Computation
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Neurons are sensitive to correlations among synaptic inputs. However, analytical models that explicitly include correlations are hard to solve analytically, so their influence on a neuron's response has been difficult to ascertain. To gain some intuition on this problem, we studied the firing times of two simple integrate-and-fire model neurons driven by a correlated binary variable that represents the total input current. Analytic expressions were obtained for the average firing rate and coefficient of variation (a measure of spike-train variability) as functions of the mean, variance, and correlation time of the stochastic input. The results of computer simulations were in excellent agreement with these expressions. In these models, an increase in correlation time in general produces an increase in both the average firing rate and the variability of the output spike trains. However, the magnitude of the changes depends differentially on the relative values of the input mean and variance: the increase in firing rate is higher when the variance is large relative to the mean, whereas the increase in variability is higher when the variance is relatively small. In addition, the firing rate always tends to a finite limit value as the correlation time increases toward infinity, whereas the coefficient of variation typically diverges. These results suggest that temporal correlations may play a major role in determining the variability as well as the intensity of neuronal spike trains.