A stochastic dynamical model for the characterization of the geometrical structure of dendritic processes
type: Item
instance of: scholarly article
title: A stochastic dynamical model for the characterization of the geometrical structure of dendritic processes
zbMATH Open document ID: 0615.92022
DOI: 10.1007/BF02459695
author: Wolfgang Kliemann
published in: Bulletin of Mathematical Biology
publication date: 1987-01-01T00:00:00Z
review text: Under certain basic assumptions the branching pattern of dendrites can be modeled as a Galton-Watson process in varying environment. Using results from graph theory we compute the probability distributions, expectations and variances for biologically significant variables such as the number of (intermediate and terminal) branches, the maximum number of orders, etc., together with the limit behavior of these quantities. Furthermore, the probability measure induced by the Galton-Watson process on the set of all trees is calculated. The measure assigns to any set of branching patterns the probability that it is realized by a certain process, which is completely described through the bifurcation probabilities.
Mathematics Subject Classification ID: 92F05
Mathematics Subject Classification ID: 60J85
Mathematics Subject Classification ID: 05C05
Mathematics Subject Classification ID: 92Cxx
Mathematics Subject Classification ID: 60J80
zbMATH DE Number: 3997610
zbMATH Keywords: neuronal cells
zbMATH Keywords: branching pattern of dendrites
zbMATH Keywords: Galton-Watson process in varying environment
zbMATH Keywords: distributions
zbMATH Keywords: expectations
zbMATH Keywords: variances
zbMATH Keywords: limit behavior
zbMATH Keywords: bifurcation probabilities
Wikidata QID: Q52610774
MaRDI profile type: Publication
cites work: Q5674726
cites work: Q4127752
cites work: Q4275398
cites work: The exact probabilities of branching patterns under terminal and segmental growth hypotheses
full work available at URL: https://doi.org/10.1007/bf02459695
OpenAlex ID: W4252335021
description: scientific article; zbMATH DE number 3997610