Stochastic formulation of neural interaction
type: Item
instance of: scholarly article
title: Stochastic formulation of neural interaction
zbMATH Open document ID: 0571.92007
DOI: 10.1007/BF00052461
published in: Acta Applicandae Mathematicae
publication date: 1985-01-01T00:00:00Z
review text: Starting from basic physiological evidence, stochastic equations are formulated for the description of neural interaction. The formulation is based upon the deterministic linear spatio-temporal integration of action potentials into generator potentials. On the other hand, the action potentials are considered as stochastic all-or-none variables whose probability of generation depends only on the local instantaneous value of generator potential and generator current. For a model in continuous time, the action potentials can be appropriately modelled by a point process; for the description in discrete time, a switching process appears more suitable. Properties of the trajectories representing neural dynamics in state space are indicated. A neural partition function is defined and shown to be related to a statistical description of the neural activity pattern. The relevance of the mathematical formulation is indicated for the relation of neural correlation and synaptic connectivity.
Mathematics Subject Classification ID: 92Cxx
Mathematics Subject Classification ID: 60G55
Mathematics Subject Classification ID: 94A99
zbMATH DE Number: 3912162
zbMATH Keywords: nervous system
zbMATH Keywords: somatic potential
zbMATH Keywords: interaction
zbMATH Keywords: Markov process
zbMATH Keywords: neural interaction
zbMATH Keywords: action potentials
zbMATH Keywords: generator potentials
zbMATH Keywords: generator current
zbMATH Keywords: switching process
zbMATH Keywords: neural dynamics
zbMATH Keywords: state space
zbMATH Keywords: neural partition function
zbMATH Keywords: neural correlation
zbMATH Keywords: synaptic connectivity
author: Peter I. M. Johannesma
author: Henk F. P. van den Boogaard
MaRDI profile type: Publication
cites work: The spectro-temporal receptive field. A functional characteristic of auditory neurons
cites work: Q4404098
cites work: Methods of analysis of neural nets
cites work: Diffusion approximation and first passage time problem for a model neuron
cites work: On the inverse of the first passage time probability problem
cites work: Q5630908
cites work: Temporal oscillations in neuronal nets
cites work: Large-scale activity in neural nets. I: Theory with application to motoneuron pool responses
cites work: Numerical studies of the laminar boundary layer for Mach numbers up to 15
cites work: Integral Decomposition of Hermitian Forms
cites work: A field theory of neural nets: I: Derivation of field equations
cites work: A field theory of neural nets: II. Properties of the field equations
cites work: Q5684870
cites work: Q3859612
cites work: Q4124657
cites work: A logical calculus of the ideas immanent in nervous activity
cites work: Q3941232
cites work: Q4182307
cites work: Q4161130
cites work: Informationsverarbeitung in homogenen Netzen von Neuronenmodellen
cites work: Analysis of neuronal networks in the visual system of the cat using statistical signals
cites work: Q4166000
cites work: Q4401783
cites work: Improved neuronal models for studying neural networks
full work available at URL: https://doi.org/10.1007/bf00052461
OpenAlex ID: W4248698977
description: scientific article; zbMATH DE number 3912162