title: A Diffusion Approximation and Numerical Methods for Adaptive Neuron Models with Stochastic Inputs.
abstract: Characterizing the spiking statistics of neurons receiving noisy synaptic input is a central problem in computational neuroscience. Monte Carlo approaches to this problem are computationally expensive and often fail to provide mechanistic insight. Thus, the field has seen the development of mathematical and numerical approaches, often relying on a Fokker-Planck formalism. These approaches force a compromise between biological realism, accuracy and computational efficiency. In this article we develop an extension of existing diffusion approximations to more accurately approximate the response of neurons with adaptation currents and noisy synaptic currents. The implementation refines existing numerical schemes for solving the associated Fokker-Planck equations to improve computationally efficiency and accuracy. Computer code implementing the developed algorithms is made available to the public.
authors.affiliation: Applied and Computational Mathematics and Statistics, University of Notre Dame Notre Dame, IN, USA.
authors.forename: Robert
authors.initials: R
authors.lastname: Rosenbaum
keywords: Fokker-Planck equation; diffusion approximation; linear response; numerical analysis; spike frequency adaptation; stochastic modeling