Calculating the Hausdorff dimension of tree structures |
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| Authors: | Lorraine M. Rellick Gerald A. Edgar Michael H. Klapper |
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| Affiliation: | (1) Department of Chemistry, Ohio State University, 43210 Columbus, Ohio;(2) Department of Biochemistry, Ohio State University, 43210 Columbus, Ohio;(3) Department of Mathematics, Ohio State University, 43210 Columbus, Ohio |
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| Abstract: | The dimension of certain tree structures is of importance in percolation theory, as well as in the theoretical treatment of many other branching processes. We present a method of determining the Hausdorff dimension of such structures by employing the technique of Mauldin and Williams. The dimension is calculated based on the probability of generation of each branch from its parent on the tree representing the process. We use this method to analyze the dimension of tree structures representing two-directional linear bonding between equally weighted monomers, and show how it can be used to model enzymatic reaction pathways. |
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| Keywords: | Branching process enzyme reaction kinetics Hausdorff dimension Mauldin-Williams graph percolation theory tree representations |
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