A periodic tree Tn consists of full n-level copies of a finite tree T . The tree Tn is labeled by random bits. The root label is chosen randomly, and the probability of two adjacent vertices to have the same label is 1− . This model simulates noisy propagation of a bit from the root, and has significance both in communication theory and in biology. Our aim is to find an algorithm which decides ...

Simple families of increasing trees have been introduced by Bergeron, Flajolet and Salvy. They include random binary search trees, random recursive trees and random plane-oriented recursive trees (PORTs) as important special cases. In this paper, we investigate the number of subtrees of size k on the fringe of some classes of increasing trees, namely generalized PORTs and d-ary increasing trees...

Stochastic trees are semi-Markov processes represented using tree diagrams. Such trees have been found useful for prescriptive modeling of temporal medical treatment choice. We consider utility functions over stochastic trees which permit recursive evaluation in a graphically intuitive manner analogous to decision tree rollback. Such rollback is computationally intractable unless a low-dimensio...

Let Tn be a random recursive tree with vertex set [n] := {1, . . . , n} and edges directed towards the root. Let degn(i) denote the number of children of vertex i ∈ [n] of Tn. Devroye and Lu [1] showed that the maximum degree ∆n of Tn satisfies ∆n/ log2 n→ 1 a.s. Here we study the distribution of the maximum degree and of the number of vertices with near-maximum degree. For any d ∈ Z, let X d =...

We present a general construction to reduce the communication cost of recent tree-based ORAMs. Contrary to trees with constant height and path lengths, our new construction r-ORAM provides varying, shorter path lengths. Accessing an element in the ORAM tree will have different communication cost depending on the location of the element. The main idea behind r-ORAM is a recursive ORAM tree struc...

Khoussainov, B. Recursive “nary algebras and trees, Annals of Pure and Applied Logic 67 (1994) 213-268. A unary algebra is an algebraic system d = (A,f,, ,L). wheref,, . ,fm are unary operations on A and n EW. In the paper we develop the theory ofeffective “nary algebras. We investigate well-known questions of constructive (recursive) model theory with respect to the class of unary algebras. In...

We consider the number of random cuts that are necessary to isolate the node with label λ, 1 ≤ λ ≤ n, in a random recursive tree of size n. At each stage of the edge-removal procedure considered an edge is chosen at random from the tree and cut, separating the tree into two subtrees. The procedure is then continued with the subtree containing the specified label λ, whereas the other subtree is ...

While tree contraction algorithms play an important role in efficient tree computation in parallel, it is difficult to develop such algorithms due to the strict conditions imposed on contracting operators. In this paper, we propose a systematic method of deriving efficient tree contraction algorithms from recursive functions on trees. We identify a general recursive form that can be parallelize...

Numerical modeling was carried out to investigate the responses of suction bucket foundations under vertical cyclic loading. Numerical results were compared with centrifuge experiment results. Before the capacity of the model suction bucket to resist cyclic loading could be investigated, the static pullout capacities had to be determined. The buckets with different aspect ratio are investigated...

ISSN: 1058-6458 (Print) 1944-950X (Online) Journal homepage: http://www.tandfonline.com/loi/uexm20 On the Asymptotic Probability of Forbidden Motifs on the Fringe of Recursive Trees Mohan Gopaladesikan, Stephan Wagner & Mark Daniel Ward To cite this article: Mohan Gopaladesikan, Stephan Wagner & Mark Daniel Ward (2016) On the Asymptotic Probability of Forbidden Motifs on the Fringe of Recursive...