Spiking Neuron Models: An Introduction
Spiking Neuron Models: An Introduction
A population study of integrate-and-fire-or-burst neurons
Neural Computation
Dynamics of the firing probability of noisy integrate-and-fire neurons
Neural Computation
Firing rate of the noisy quadratic integrate-and-fire neuron
Neural Computation
A Review of the Integrate-and-fire Neuron Model: I. Homogeneous Synaptic Input
Biological Cybernetics
Numerical methods for solving moment equations in kinetic theory of neuronal network dynamics
Journal of Computational Physics
Stochastic dynamics of a finite-size spiking neural network
Neural Computation
Populations of tightly coupled neurons: The rgc/lgn system
Neural Computation
Journal of Computational Physics
Improved dimensionally-reduced visual cortical network using stochastic noise modeling
Journal of Computational Neuroscience
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The population density approach to neural network modeling has been utilized in a variety of contexts. The idea is to group many similar noisy neurons into populations and track the probability density function for each population that encompasses the proportion of neurons with a particular state rather than simulating individual neurons i.e., Monte Carlo. It is commonly used for both analytic insight and as a time-saving computational tool. The main shortcoming of this method is that when realistic attributes are incorporated in the underlying neuron model, the dimension of the probability density function increases, leading to intractable equations or, at best, computationally intensive simulations. Thus, developing principled dimension-reduction methods is essential for the robustness of these powerful methods. As a more pragmatic tool, it would be of great value for the larger theoretical neuroscience community. For exposition of this method, we consider a single uncoupled population of leaky integrate-and-fire neurons receiving external excitatory synaptic input only. We present a dimension-reduction method that reduces a two-dimensional partial differential-integral equation to a computationally efficient one-dimensional system and gives qualitatively accurate results in both the steady-state and nonequilibrium regimes. The method, termed modified mean-field method, is based entirely on the governing equations and not on any auxiliary variables or parameters, and it does not require fine-tuning. The principles of the modified mean-field method have potential applicability to more realistic i.e., higher-dimensional neural networks.