Growth models for topological binary branching patterns

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Abstract

Binary branching patterns have been studied from a topological point of view. The central question is how the frequency distributions of the topologies of observed branching patterns can be understood in terms of growth of these patterns. For this purpose techniques have been developed to analyze the topological properties and growth models have been worked out mathematically to calculate the expectation values for these properties. The topologies of the branching patterns are described by the set of partitions (degrees of subtree pairs) for all branching points in all the trees. The model defines for each segment in a growing tree the probability of branching which depends of the type of segment (intermediate or terminal) and of its order (topological distance to the root). Two parameters in the model define the strength of these dependencies. Good fits to sets of observed neuronal dendrites could be obtained on basis of maximum likelihood criteria.

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Over : Jaap Van Pelt

Over : Ronald W.H. Verwer