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Topological properties of binary trees grown with order-dependent branching probabilities

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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.

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Authors and Affiliations

  1. Netherlands Institute for Brain Research, Meibergdreef 33, 1105 AZ, Amsterdam, The Netherlands

    J. Van Pelt & R. W. H. Verwer

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  1. J. Van Pelt
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  2. R. W. H. Verwer
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Van Pelt, J., Verwer, R.W.H. Topological properties of binary trees grown with order-dependent branching probabilities. Bltn Mathcal Biology 48, 197–211 (1986). https://doi.org/10.1007/BF02460023

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  • DOI: https://doi.org/10.1007/BF02460023

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