Mean exit times for particles driven by weakly colored noise
SIAM Journal on Applied Mathematics
A population density approach that facilitates large-scale modeling of neural networks
A population density approach that facilitates large-scale modeling of neural networks
Rate models for conductance-based cortical neuronal networks
Neural Computation
Firing rate of the noisy quadratic integrate-and-fire neuron
Neural Computation
Mean instantaneous firing frequency is always higher than the firing rate
Neural Computation
Computing and stability in cortical networks
Neural Computation
Minimal Models of Adapted Neuronal Response to In Vivo–lLike Input Currents
Neural Computation
Efficient Computation Based on Stochastic Spikes
Neural Computation
Stochastic dynamics of a finite-size spiking neural network
Neural Computation
Populations of tightly coupled neurons: The rgc/lgn system
Neural Computation
Anatomy of a cortical simulator
Proceedings of the 2007 ACM/IEEE conference on Supercomputing
International Journal of Computer Mathematics - Computer Mathematics in Dynamics and Control
Systematic fluctuation expansion for neural network activity equations
Neural Computation
First spiking dynamics of stochastic neuronal model with optimal control
ICONIP'08 Proceedings of the 15th international conference on Advances in neuro-information processing - Volume Part I
Journal of Computational Physics
A systematic method for configuring vlsi networks of spiking neurons
Neural Computation
First passage time problem for the ornstein-uhlenbeck neuronal model
ICONIP'06 Proceedings of the 13 international conference on Neural Information Processing - Volume Part I
First passage time problem for the ornstein-uhlenbeck neuronal model
ICONIP'06 Proceedings of the 13 international conference on Neural Information Processing - Volume Part I
Dynamic state and parameter estimation applied to neuromorphic systems
Neural Computation
Information filtering by synchronous spikes in a neural population
Journal of Computational Neuroscience
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Cortical neurons in vivo undergo a continuous bombardment due to synaptic activity, which acts as a major source of noise. Here, we investigate the effects of the noise filtering by synapses with various levels of realism on integrate-and-fire neuron dynamics. The noise input is modeled by white (for instantaneous synapses) or colored (for synapses with a finite relaxation time) noise. Analytical results for the modulation of firing probability in response to an oscillatory input current are obtained by expanding a Fokker-Planck equation for small parameters of the problem--when both the amplitude of the modulation is small compared to the background firing rate and the synaptic time constant is small compared to the membrane time constant. We report here the detailed calculations showing that if a synaptic decay time constant is included in the synaptic current model, the firing-rate modulation of the neuron due to an oscillatory input remains finite in the high-frequency limit with no phase lag. In addition, we characterize the low-frequency behavior and the behavior of the high-frequency limit for intermediate decay times. We also characterize the effects of introducing a rise time to the synaptic currents and the presence of several synaptic receptors with different kinetics. In both cases, we determine, using numerical simulations, an effective decay time constant that describes the neuronal response completely.