Conservative trees have universal segment measure distributions
type: Item
instance of: scholarly article
title: Conservative trees have universal segment measure distributions
zbMATH Open document ID: 0598.92025
DOI: 10.1016/0025-5564(86)90043-X
published in: Mathematical Biosciences
publication date: 1986-01-01T00:00:00Z
review text: It is shown that ''conservative trees'', which possess some measure that is conserved across branchpoints, generate a distribution of the measure over the segments that is approximately hyperbolic. When the trees become large, the shape of the distribution becomes independent of drastic changes in the asymmetry of the branching, in the measure distribution of the root segments, or in the valency of the branchpoints. In contrast to the invariant shape, the amplitude of the distribution does depend on the above parameters, but it can be computed numerically or, in many important cases, analytically. These results can be used to compute the distribution of related (but nonconserved) quantities of the trees, to solve the scaling problem of large trees, and to gain insight into the relations between local and global consequences of dendritic growth.
Mathematics Subject Classification ID: 92F05
Mathematics Subject Classification ID: 92B05
zbMATH DE Number: 3965888
zbMATH Keywords: segment measure distributions
zbMATH Keywords: hyperbolic distribution
zbMATH Keywords: broken stick model
zbMATH Keywords: conservative trees
zbMATH Keywords: scaling problem
zbMATH Keywords: dendritic growth
author: André J. Noest
MaRDI profile type: Publication
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full work available at URL: 0025-5564(86)90043-x
OpenAlex ID: W2016247704
description: scientific article; zbMATH DE number 3965888