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  • 1
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    Two Generalized Topological Models of Stream Network Growth (1989)
    University of Chicago Press
    Details
    Publication Date: 1989-05-01
    Print ISSN: 0022-1376
    Electronic ISSN: 1537-5269
    Topics: Geosciences
    Published by University of Chicago Press
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  • 2
    Electronic Resource
    Electronic Resource
    Topological properties of binary trees grown with order-dependent branching probabilities (1986)
    Springer
    Bulletin of mathematical biology 48 (1986), S. 197-211 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This paper describes a growth model for binary topological trees. The model defines the branching probability of all segments in the tree. The branching probability of a segment is formulated as a function of two variables, one indicating its type (intermediate or terminal), the other representing its order, i.e. the topological distance to the root segment. The function is determined by two parameters, namely the ratio of branching probabilities of intermediate and terminal segments and the strength of the order dependency, implemented in an exponential form. Expressions are derived for the calculation of symmetry properties of the partitions and it is indicated which part of the parameter domain results in predominantly symmetrical trees.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460023
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Cuttrees in the topological analysis of branching patterns (1984)
    Springer
    Bulletin of mathematical biology 46 (1984), S. 283-294 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In this paper the effects of the occurrence of cut trees in the topological analysis of branching patterns have been studied. It is assumed that branches are removed at random from the trees. We prove that, for both the segmental and terminal growth models, the probability distributions of the cut trees are identical to those of complete trees.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460075
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  • 4
    Electronic Resource
    Electronic Resource
    Centrifugal-order distributions in binary topological trees (1989)
    Springer
    Bulletin of mathematical biology 51 (1989), S. 511-536 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Statistical properties of topological binary trees are studied on the basis of the distribution of segments in relation to centrifugal order. Special attention is paid to the mean of this distribution in a tree as it will be used as a measure of tree topology. It will be shown how the expectation of the mean centrifugal order depends both on the size of the tree and on the mode of growth in the context of modelling the growth of tree structures. Observed trees can be characterized by their mean orders and procedures are described to find the growth mode that optimally corresponds to these data. The variance structure of the mean-order measure appears to be a crucial factor in these fitting procedures. Examples indicate that mean-order analysis is an accurate alternative to partition analysis that is based on the partitioning of segments over sub-tree pairs at branching points.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460088
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  • 5
    Electronic Resource
    Electronic Resource
    Growth models (including terminal and segmental branching) for topological binary trees (1985)
    Springer
    Bulletin of mathematical biology 47 (1985), S. 323-336 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A growth model for topological trees is formulated as a generalization of the terminal and segmental growth model. For this parameterized growth model, expressions are derived for the partition probabilities (probabilities of subtree pairs of certain degrees). The probabilities of complete trees are easily derived from these partition probabilities.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459919
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  • 6
    Electronic Resource
    Electronic Resource
    The exact probabilities of branching patterns under terminal and segmental growth hypotheses (1983)
    Springer
    Bulletin of mathematical biology 45 (1983), S. 269-285 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Information about the way of branching of dendritic arborizations may be obtained by comparing the frequency distributions of observed branching patterns with theoretical distributions based on well-defined growth models. Two models usually get much attention in geomorphological and (neuro)biological studies, viz. terminal growth and segmental growth. Formulae to construct the exact probability distributions for both growth models are presented. It is shown that ranking and lumping of the individual branching patterns enable the analysis of very large arborizations with relatively few data. The application of the Kolmogorov goodness-of-fit test for discrete distributions to the analysis is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462361
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