SHE Wei, MA Jiawei, ZHANG Shuhui et al. · SHILAP Revista de lepidopterología · 2025
A covert communication model based on a dynamic time binary tree was proposed to address the efficiency and security issues in blockchain-based covert communication. A time binary tree was dynamically generated at specific moments, and the roothash was used to extract random factors for assigning different path codes to the tree nodes. Communication information characters were mapped to the encoded paths and index fields. By embedding vacant bits of the path codes at specific moments and integrating them into blockchain transactions, covert transmission was achieved. The receiver reconstructed the time binary tree at the specific moment to complete the decoding. Experimental results show that, compared to similar models, the proposed model improves communication efficiency while ensuring security, and avoids the security risks brought by the pre-negotiation process.
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Qiang Zhang, Mike Steel · Bulletin of Mathematical Biology · 2026
Rooted phylogenetic networks allow biologists to represent evolutionary relationships between present-day species by revealing ancestral speciation and hybridization events. A convenient and well-studied class of such networks are 'tree-child networks' and a 'ranking' of such a network is a temporal ordering of the ancestral speciation and hybridization events. In this short note, we investigate the question of counting such rankings on any given binary (or semi-binary) tree-child network. We also investigate the relationship between rankable tree-child networks and the class of 'normal' networks. Finally, we provide an explicit asymptotic expression for the expected number of rankings of a tree-child network chosen uniformly at random.
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Fei Gao · 2001
This paper studies the tree based contention resolution algorithm over a random multi access channel, and proposes a new algorithm model which is named Improved Ternary tree Algorithm( ITA ). The channel throughput over blocked access reaches 0 422. The analytical expression and computer simulation results indicate that the performance of ITA is better than the basic binary and ternary tree algorithm.
Cited by 1
O. V. Rubleva · Mathematical Notes · 2016
An expression for the coarse Ricci curvature of a weighted tree with a random walk on the vertex set is obtained. As a corollary, it is shown that the structure of a binary tree can be reconstructed up to isomorphism from the matrix of pairwise Ricci curvatures of its vertices.
Cited by 2
Weijia Zhu, Andrew Segall · 2018
During the exploration of video coding technology for potential next generation standards, the Joint Video Exploration Team (JVET) has been studying quad-tree plus binary-tree (QTBT) partition structures within its Joint Exploration Model (JEM). This QTBT partition structure provides more flexibility compared with the quad-tree only partition structure in HEVC. Here, we further consider the QTBT structure and extended it to allow quad-tree partitioning to be performed both before and after a binary-tree partition. We refer to this structure as a compound split tree (CST). To show the efficacy of the approach, we implemented the method into JEM7. The method achieved 1.25%, 2.11% and 1.87% BD-bitrate savings for Y, U and V components on average under the random-access configuration, respectively.
Cited by 4
Pise, Dr. Sachin Kantilal · Zenodo (CERN European Organization for Nuclear Research) · 2023
Introduction: Stream Ordering: These numbers were first developed in hydrology by Robert E. Horton (1945) and Arthur Newell Strahler (1952, 1957); in this application, they are referred to as the Strahler stream order and are used to define stream size based on a hierarchy of tributaries. Algorithmically, these numbers may be assigned by performing a depth-first search and assigning each node's number in post order. Another equivalent definition of the Strahler number of a tree is that it is the height of the largest complete binary tree that can be homeomorphically embedded into the given tree; the Strahler number of a node in a tree is similarly the height of the largest complete binary tree that can be embedded below that node. Any node with Strahler number i must have at least two descendants with Strahler number i − 1, at least four descendants with Strahler number i − 2, etc., and at least 2 i − 1 leaf descendants. Therefore, in a tree with n nodes, the largest possible Strahler number is log2 n . However, unless the tree forms a complete binary tree its Strahler number will be less than this bound. In an n -node binary tree , chosen uniformly at random among all possible binary trees , the expected index of the root is with high probability very close to log4 n .
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S. Pushpa, P. Vinod, Jilani Abdul Khader · 2007
Summary Recently, a new version of the insert-delete pair has been proposed that maintains a random binary search tree in such a way that all the grandparents in the tree always have both of their sub-trees full. For a tree with ‘n’ nodes, if such an arrangement is made, it is straightforward that even an arbitrary sequence of insertion and deletion would not cause the tree to grow beyond n/2. Compare this with conventional insert delete algorithms where a tree may grow up to the height of n-1 reducing search to be sequential. Lesser the height of the tree, lesser would be its internal path-length, and hence faster the search would be. To study the behavior of the Binary Search tree with proposed insert delete pair, we have simulated a binary search tree with 1024 nodes. In this article we provide some empirical results to show that the proposed insert-delete pair maintains the tree in better shape, with considerable reduction in the internal path-length.
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Pise, Dr. Sachin Kantilal · Zenodo (CERN European Organization for Nuclear Research) · 2023
Introduction: Stream Ordering: These numbers were first developed in hydrology by Robert E. Horton (1945) and Arthur Newell Strahler (1952, 1957); in this application, they are referred to as the Strahler stream order and are used to define stream size based on a hierarchy of tributaries. Algorithmically, these numbers may be assigned by performing a depth-first search and assigning each node's number in post order. Another equivalent definition of the Strahler number of a tree is that it is the height of the largest complete binary tree that can be homeomorphically embedded into the given tree; the Strahler number of a node in a tree is similarly the height of the largest complete binary tree that can be embedded below that node. Any node with Strahler number i must have at least two descendants with Strahler number i − 1, at least four descendants with Strahler number i − 2, etc., and at least 2 i − 1 leaf descendants. Therefore, in a tree with n nodes, the largest possible Strahler number is log2 n . However, unless the tree forms a complete binary tree its Strahler number will be less than this bound. In an n -node binary tree , chosen uniformly at random among all possible binary trees , the expected index of the root is with high probability very close to log4 n .
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Yoshiaki Itoh, Hosam M. Mahmoud · Journal of Applied Probability · 2003
The binary interval tree is a random structure that underlies interval division and parking problems. Five incomplete one-sided variants of binary interval trees are considered, providing additional flavors and variations on the main applications. The size of each variant is studied, and a Gaussian tendency is proved in each case via an analytic approach. Differential equations on half scale and delayed differential equations arise and can be solved asymptotically by local expansions and Tauberian theorems. Unlike the binary case, in an incomplete interval tree the size determines most other parameters of interest, such as the height or the internal path length.
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David M. Hillis, John P. Huelsenbeck · Journal of Heredity · 1992
DNA sequences and other molecular data compared among organisms may contain phylogenetic signal, or they may be randomized with respect to phylogenetic history. Some method is needed to distinguish phylogenetic signal from random noise to avoid analysis of data that have been randomized with respect to the historical relationships of the taxa being compared. We analyzed 8,000 random data matrices consisting of 10-500 binary or four-state characters and 5-25 taxa to study several options for detecting signal in systematic data bases. Analysis of random data often yields a single most-parsimonious tree, especially if the number of characters examined is large and the number of taxa examined is small (both often true in molecular studies). The most-parsimonious tree inferred from random data may also be considerably shorter than the second-best alternative. The distribution of tree lengths of all tree topologies (or a random sample thereof) provides a sensitive measure of phylogenetic signal: data matrices with phylogenetic signal produce tree-length distributions that are strongly skewed to the left, whereas those composed of random noise are closer to symmetrical. In simulations of phylogeny with varying rates of mutation (up to levels that produce random variation among taxa), the skewness of tree-length distributions is closely related to the success of parsimony in finding the true phylogeny. Tables of critical values of a skewness test statistic, g1, are provided for binary and four-state characters for 10-500 characters and 5-25 taxa. These tables can be used in a rapid and efficient test for significant structure in data matrices for phylogenetic analysis.
Cited by 1,322
Alice Contat, Lucile Laulin · arXiv (Cornell University) · 2025
We study the parking process on the random recursive tree. We first prove that although the random recursive tree has a non-degenerate Benjamini--Schramm limit, the phase transition for the parking process appears at density $0$. We then identify the critical window for appearance of a positive flux of cars with high probability. In the case of binary car arrivals, this happens at density $ \log (n)^{-2+o(1)}$ where $n$ is the size of the tree. This is the first work that studies the parking process on trees with possibly large degree vertices.
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Michael Albert, Cecilia Holmgren, Tony Johansson et al. · Bristol Research (University of Bristol)
We investigate the number of permutations that occur in random labellings of trees. This is a generalisation of the number of subpermutations occurring in a random permutation. It also generalises some recent results on the number of inversions in randomly labelled trees. We consider complete binary trees as well as random split trees a large class of random trees of logarithmic height introduced by Devroye in 1998. Split trees consist of nodes (bags) which can contain balls and are generated by a random trickle down process of balls through the nodes. For complete binary trees we show that asymptotically the cumulants of the number of occurrences of a fixed permutation in the random node labelling have explicit formulas. Our other main theorem is to show that for a random split tree, with high probability the cumulants of the number of occurrences are asymptotically an explicit parameter of the split tree. For the proof of the second theorem we show some results on the number of embeddings of digraphs into split trees which may be of independent interest.
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I. Kessler, Maawiya Ould Sidi · IEEE Transactions on Information Theory · 1993
A class of binary trees that grow in a random environment, where the state of the environment can change at every vertex of the trees, is studied. The trees considered are single-type and two-type binary trees that grow in a two-state Markovian environment. For each kind of tree, the conditions on the environment process for extinction of the tree are determined, and the problem of calculating the expected number of vertices of the tree is addressed. Different ways of growing the trees are compared.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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Dayue Chen, Yueyun Hu, Shen Lin · Greater South Information System · 2018
Consider a rooted infinite Galton-Watson tree with mean offspring number m > 1, and a collection of i.i.d.positive random variables ξe indexed by all the edges in the tree.We assign the resistance m d ξe to each edge e at distance d from the root.In this random electric network, we study the asymptotic behavior of the effective resistance and conductance between the root and the vertices at depth n.Our results generalize an existing work of Addario-Berry, Broutin and Lugosi on the binary tree to random branching networks.
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Zhongheng Zhang · Annals of Translational Medicine · 2016
In machine learning field, decision tree learner is powerful and easy to interpret. It employs recursive binary partitioning algorithm that splits the sample in partitioning variable with the strongest association with the response variable. The process continues until some stopping criteria are met. In the example I focus on conditional inference tree, which incorporates tree-structured regression models into conditional inference procedures. While growing a single tree is subject to small changes in the training data, random forests procedure is introduced to address this problem. The sources of diversity for random forests come from the random sampling and restricted set of input variables to be selected. Finally, I introduce R functions to perform model based recursive partitioning. This method incorporates recursive partitioning into conventional parametric model building.
Cited by 41Open access
Massoud Sokouti · Indian Journal of Science and Technology · 2009
Transposition ciphers are stronger than simple substitution ciphers. However, if the key is short and the message is long, then various cryptanalysis techniques can be applied to break such ciphers. By adding 8 bits (one byte) for each byte using a function and another mathematical function to position the bits in a binary tree and using its in-order tour, this cipher can be made protected. Using an in-order tour of binary tree can diffuse the eight bits (includes 7 bits produced by the function and 1 random bit) and eight bits of the plaintext. This can highly protect the cipher. However, if the key management processes are not secured the strongest ciphers can easily be broken. Keywords: Cryptography, binary tree, cipher protection, transposition cipher.
Cited by 21Open access
Alessandra Caraceni, Nicolas Curien, Robin Stephenson · arXiv (Cornell University) · 2024
We study a model of random binary trees grown "by the leaves" in the style of Luczak and Winkler. If $τ_n$ is a uniform plane binary tree of size $n$, Luczak and Winkler, and later explicitly Caraceni and Stauffer, constructed a measure $ν_{τ_n}$ such that the tree obtained by adding a cherry on a leaf sampled according to $ν_{τ_n}$ is still uniformly distributed on the set of all plane binary trees with size $n+1$. It turns out that the measure $ν_{τ_n}$, which we call the leaf-growth measure, is noticeably different from the uniform measure on the leaves of the tree $τ_n$. In fact, we prove that, as $n \to \infty$, with high probability it is almost entirely supported by a subset of only $n^{3 ( 2 - \sqrt{3})+o(1)} \approx n^{0.8038...}$ leaves. In the continuous setting, we construct the scaling limit of this measure, which is a probability measure on the Brownian Continuum Random Tree supported by a fractal set of dimension $ 6 (2 - \sqrt{3})$. We also compute the full (discrete) multifractal spectrum. This work is a first step towards understanding the diffusion limit of the discrete leaf-growth procedure.
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Li, Qingqing, Yang, Hui, Wang, Peipei et al. · Figshare · 2022
Additional file 1: Figure S1. The PR (precision-recall) curves of (a) Optimized XGBoost, (b) XGBoost, (c) support vector machine, (d) decision tree, (e) K-nearest neighbor, (f) logistic regression, and (g) random forest binary classifiers.
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Li, Qingqing, Yang, Hui, Wang, Peipei et al. · Figshare · 2022
Additional file 1: Figure S1. The PR (precision-recall) curves of (a) Optimized XGBoost, (b) XGBoost, (c) support vector machine, (d) decision tree, (e) K-nearest neighbor, (f) logistic regression, and (g) random forest binary classifiers.
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Hsien-kuei Hwang · 2008
We summarize several limit results for the profile of random plane-oriented recursive trees. These include the limit distribution of the normalized profile, asymptotic bimodality of the variance, asymptotic approximations of the expected width and the correlation coefficients of two level sizes. We also unveil an unexpected connection between the profile of plane-oriented recursive trees (with logarithmic height) and that of random binary trees (with height proportional to the square root of tree size). Keywords: Plane-oriented recursive trees, profile of trees, limit distribution, convergence of all moments, total path length, random binary trees 1
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