title: Delayed-exponential approximation of a linear homogeneous diffusion model of neuron.
abstract: The diffusion models of neuronal activity are general yet conceptually simple and flexible enough to be useful in a variety of modeling problems. Unfortunately, even simple diffusion models lead to tedious numerical calculations. Consequently, the existing neural net models use characteristics of a single neuron taken from the "pre-diffusion" era of neural modeling. Simplistic elements of neural nets forbid to incorporate a single learning neuron structure into the net model. The above drawback cannot be overcome without the use of the adequate structure of the single neuron as an element of a net. A linear (not necessarily homogeneous) diffusion model of a single neuron is a good candidate for such a structure, it must, however, be simplified. In the paper the structure of the diffusion model of neuron is discussed and a linear homogeneous model with reflection is analyzed. For this model an approximation is presented, which is based on the approximation of the first passage time distribution of the Ornstein-Uhlenbeck process by the delayed (shifted) exponential distribution. The resulting model has a simple structure and has a prospective application in neural modeling and in analysis of neural nets.
authors.affiliation: Department of Electrical and Computer Engineering, Oregon State University, Corvallis 97331.
authors.forename: A
authors.initials: A
authors.lastname: Pacut
authors.forename: L
authors.initials: L
authors.lastname: Dabrowski
mesh_terms: D008433:Mathematics; D008959:Models, Neurological; D009474:Neurons / Q000502:physiology*