Entropy rates for Horton self-similar trees
نویسندگان
چکیده
منابع مشابه
Horton Law in Self-Similar Trees
Abstract. Self-similarity of random trees is related to the operation of pruning. Pruning R cuts the leaves and their parental edges and removes the resulting chains of degree-two nodes from a finite tree. A Horton-Strahler order of a vertex v and its parental edge is defined as the minimal number of prunings necessary to eliminate the subtree rooted at v. A branch is a group of neighboring ver...
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The Horton and Tokunaga branching laws provide a convenient framework for studying self-similarity in random trees. The Horton self-similarity is a weaker property that addresses the principal branching in a tree; it is a counterpart of the power-law size distribution for elements of a branching system. The stronger Tokunaga self-similarity addresses so-called side branching. The Horton and Tok...
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Numerical approximations of shock waves sometimes suffer from instabilities called carbuncles. Techniques for suppressing carbuncles are trialand-error and lack in reliability and generality, partly because theoretical knowledge about carbuncles is equally unsatisfactory. It is not known which numerical schemes are affected in which circumstances, what causes carbuncles to appear and whether ca...
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In a rooted infinite full binary tree, each vertex is the parent of exactly two children. Since there are exactly 2−1 vertices at level less than or equal to n, the infinite binary tree is said to have exponential growth with growth rate 2. Can we readily determine the growth rates of other self-similar infinite trees? We will see that the answer is yes for a class of trees that can be construc...
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We consider the Horton-Strahler number S, for random equiprobable binary trees with n nodes. We give a simple probabilistic proof of the well-known result that ES, = log,n + O(1) and show that for every x > 0, P{ 1 S, log,n ( > x} Q D/4x, for some constant D > 0.
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ژورنال
عنوان ژورنال: Chaos: An Interdisciplinary Journal of Nonlinear Science
سال: 2018
ISSN: 1054-1500,1089-7682
DOI: 10.1063/1.5048965