A. M. Zubkov, Vasiliy I. Kruglov · Discrete Mathematics and Applications · 2016
Abstract Let all vertices of a complete binary tree of finite height be independently and equiprobably labeled by the elements of some finite alphabet. We consider the numbers of pairs of identical tuples of labels on chains of subsequent vertices in the tree. Exact formulae for the expectations of these numbers are obtained. Convergence to the compound Poisson distribution is proved.
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Matthew I. Roberts · 2010
We consider a (random permutation model) binary search tree with n nodes and give asymptotics on the log log scale for the height Hn and saturation level hn of the tree as n→∞, both almost surely and in probability. We then consider the number Fn of particles at level Hn at time n, and show that Fn is unbounded almost surely. This is a work in progress — we hope to give further results on the asymp-totics of Fn. 1 Introduction and main results Consider the complete rooted binary tree T. We construct a sequence Tn, n = 1, 2,... of subtrees of T recursively as follows. T1 consists only of the root. Given Tn, we choose a leaf u uniformly at random from the set of all leaves of Tn and add its two children to the tree to create Tn+1. Thus Tn+1 consists of
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Pitman, Matthias Winkel · 2008
We use a natural ordered extension of the Chinese Restaurant Process to grow a two-parameter family of binary self-similar continuum fragmentation trees. We provide an explicit embedding of Ford’s sequence of alpha model trees in the continuum tree which we identified in a previous article as a distributional scaling limit of Ford’s trees. In general, the Markov branching trees induced by the two-parameter growth rule are not sampling consistent, so the existence of compact limiting trees cannot be deduced from previous work on the sampling consistent case. We develop here a new approach to establish such limits, based on regenerative interval partitions and the urnmodel description of sampling from Dirichlet random distributions. 1. Introduction. We
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Fuqing Gao, Zhi Qu, Youzhou Zhou · Journal of Statistical Physics · 2025
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Luo Sun, Joseph Mathew, Samuel Pagliarini et al. · Journal of Low Power Electronics · 2014
In the modern portable applications, the embedded systems are required to have low power dissipation. Therefore, SRAM designs are required to achieve both high-performance and low-power for the microprocessors. However, low power design of these memories is highly challenging due to conflicting design requirements of high-performance and robustness under process-voltagetemperature (PVT) variations. In this paper, an architectural-level methodology is proposed for lowpower SRAMs (LPSRAM). In the proposed LPSRAM architecture, the SRAM subsystem is divided into modules, with inter-module connections organized in a binary tree. Due to such organization LPSRAM can achieve low power consumption and dynamic reconfiguration during normal operation mode. We formulate the read/write power, performance and area models of the proposed memory design, which are then substantiated and validated through a number of experiments using CAD tools and HSPICE simulations. We show that LPSRAM can significantly reduce power consumption (by up to 30% in normal operation mode) when compared with traditional SRAM designs at the expense of reasonable area overheads. Moreover, we demonstrate that due to efficient switching architecture LPSRAM offers better robustness under process variations, while retaining high performance. Furthermore, the LPSRAM structure has strong potential to be built with testability. The memory nodes can be tested in parallel, since all the memory modules are located in the bottom level of the binary tree. Within the proposed testable LPSRAM architecture, a reduction in testing time and power can be achieved.
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P. Vidhya Saraswathi · Journal of Computer Science · 2012
Many people consume multimedia content (images, music, movie) on portable devices like DVD player, MP3 player, Portable Multimedia Player and also through Internet. Problem statement: The conventional algorithms such as DES and AES cannot be used directly in multimedia data, since multimedia data are repeatedly have high redundancy, large-volumes and require real-time operations, such as displaying, cutting, copying, bit-rate conversion and so forth. A block cipher is usually used to encrypt multimedia content because of its reasonable security and performance. Approach: In this study, we introduce a naive approach of efficient multimedia content encryption scheme which uses a block of bits rather than bytes or pixels. The proposed block cipher encrypts any type of compressed multimedia content by random substitution using binary tree traversal, row shifting and column shifting. Results: Experimental results show that the new algorithm has better performance than DES algorithm, encrypting multimedia content by dividing the plaintext by blocks. Conclusion: The proposed algorithm is implemented for all types of multimedia files like audio, video, images and text data and this algorithm can be used to multimedia data during transmisson through Internet or through any communication channels.
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Naga Raju C, Vijaya Kumar · i-manager’s Journal on Software Engineering · 2007
i-manager's Journal on Future Engineering and Technology, i-manager's Journal on Software Engineering, i-manager's Journal on Electrical Engineering, i-manager's Journal on Electronics Engineering, i-manager's Journal of Educational Technology, i-manager's Journal on Educational Psychology, i-manager's Journal on School Educational Technology, i-manager's Journal on English Language Teaching, i-manager's Journal on Mechanical Engineering, i-manager's Journal on Civil Engineering, i-manager's Journal on Embedded Systems, i-manager's Journal on Information Technology, i-manager's Journal on Structural Engineering, i-manager's Journal on Communication Engineering and Systems, i-manager's Journal on Wireless Communication Networks, i-manager's Journal on Instrumentation and Control Engineering, i-manager's Journal on Circuits and Systems, i-manager's Journal on Digital Signal Processing, i-manager's Journal on Power Systems Engineering, i-manager's Journal on Computer Science, i-manager's Journal on Material Science, i-manager's Journal on Cloud Computing, i-manager's Journal on Image Processing, i-manager's Journal on Mobile Applications and Technologies, i-manager's Journal on Pattern Recognition, i-manager's Journal on Mathematics, i-manager's Journal on Management, i-manager's Journal on Nursing, i-manager's Journal on Physical Sciences, i-manager's Journal on Chemical Sciences, i-manager's Journal on Economics & Commerce , i-manager's Journal on Humanities & Social Sciences, i-manager's Journal on Life Sciences , i-manager's Journal on Construction Management, i-manager's Oyla , ,India best Journal Publication Website,World Best Plication SIte,Free atrticle published website,Journal Publised,Published Journal,Research Paper Published,indian research paper publications,how to published your article/research paper in india for free,journal’s instructions for authors
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Jing Nan · WIT transactions on information and communication technologies · 2014
Welcome to the WIT Press eLibrary - the home of the Transactions of the Wessex Institute collection, providing on-line access to papers presented at the Institute's prestigious international conferences and from its State-of-the-Art in Science & Engineering publications.
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Guo Yingying, Hongwei Ding, Zhao Yi-fan et al. · Advances in intelligent systems research/Advances in Intelligent Systems Research · 2013
This paper proposed a new type of discrete random contention system based on the literature [1], researched it using the average cycle method, then get the formu la of the systemic throughput for the new random access protocol by building mathematical modeling; but the uncertainty of random mult iple access on frequency and time resulting in the conflict probability increases as the higher loading, therefore, introducing binary tree conflict resolution algorithm is very important to improve the channel utilizat ion. The paper analyzed the isolated binary tree conflict resolution algorithm and then got the average length of t imeslot of the algorithm; on the basis, the paper puts forward a new type of discrete random contention system based on binary tree conflict resolution algorith m. Analytic formulate for throughput of the new d iscrete random contention system and the system based on the conflict resolution algorith m are derived by build ing mathematical model and using the average cycle method. Finally, the computer simu lation experiments show that the correctness of the theoretical, at the same t ime, show that the new discrete random contention system protocol based on binary tree conflict resolution algorithm is effective to further improve the system performance.
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Janson, Svante · arXiv (Cornell University) · 2024
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Hendrick S., Lie, Ignatius · Unika Repositor (Unika) · 2017
Creating visualization in binary tree is intended for users to learn and \nunderstand the concept of binary tree. Based on its definition binary tree is a tree \nthat only has two children. The visualization can be used to create, search, and \ndelete node from the tree. \nThe process of this system divided into 4 parts i.e. users entry the number \nof data, and data entered into the system. All data saved to txt file, program will \ntakes all values from txt and display binary tree in to browser. \nThe advantages of this program are, create a binary tree by a lot of value, \nthat has been inputted from users with random system. For the random process \nuser input minimum value and maximum value. Then system can search data from \nthe binary tree. and the last is user can delete node by system. \nKeyword: visualization, binary tree, visualization binary tree php.
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Salvador Roura · 1998
Abstract. In this paper, we present randomized algorithms over binary search trees such that: (a) the insertion of a set of keys, in any fixed order, into an initially empty tree always produces a random binary search tree; (b) the deletion of any key from a random binary search tree results in a random binary search tree; (c) the random choices made by the algorithms are based upon the sizes of the subtrees of the tree; this implies that we can support accesses by rank without additional storage requirements or modification of the data structures; and (d) the cost of any elementary operation, measured as the number of visited nodes, is the same as the expected cost of its standard deterministic counterpart; hence, all search and update operations have guaranteed expected cost 2(log n), but now irrespective of any assumption on the input distribution.
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Jiaqi Huang, Chongyang Zheng, Guohuan Feng · 2024
The binary classification problem is a fundamental and core problem type in machine learning, and many machine learning algorithms, such as logistic regression and tree models, are widely used to solve binary classification problems. Based on the Kaggle open-source binary classification dataset, a prediction model for binary classification data was established using five different machine learning algorithms, namely KNN, decision tree, gradient boosting tree, random forest, and extreme random decision tree integration. The parameters of the models were determined through relevant theoretical analysis cross-validation methods, and the test accuracy of the five integrated learning models were compared, and the experimental results showed that the test accuracy of the gradient boosting tree and random forest models reached 93.23%, which indicated that these two models had the best prediction performance in solving the binary classification problem. In addition, these two models also have high stability. Therefore, this study provides strong support to the field of machine learning and demonstrates the potential of gradient boosted trees and random forests in solving real-world problems.
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G Thippanna · Indian Journal of Image Processing and Recognition · 2024
Image analysis plays a pivotal role in computer vision, with image segmentation and classification being fundamental tasks in this domain. This abstract presents a novel approach to image processing that leverages Binary Random Fields (BRF) with a foundation in planar graphs and neighborhood spanning trees. This innovative methodology seeks to enhance the accuracy and efficiency of image segmentation and classification, addressing key challenges in computer vision applications. Binary Random Fields (BRF) is probabilistic graphical models that have proven effective in capturing spatial dependencies and contextual information within images. Our proposed method extends the utility of BRF by incorporating planar graph theory and neighborhood spanning trees to refine the segmentation and classification processes. Planar graphs offer a structured representation of image data, preserving topological relationships among pixels, while neighborhood spanning trees provide a hierarchical framework for modeling image regions
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Binti Sholihah · 2008
Splay tree dan AVI- tree merupakan varian dari Binary Search Tree. Dua tipe struktur data ini sering digunakan untuk mendukung berbagai operasi set dinamis, seperti pencarian, penyisipan dan penghapusan. Pada operasi dengan distribusi zipfo, AVI- tree lebih baik dibanding splay tree. Namun belum diketahui efisiensi splay tree pada mode operasi random dimana tidak ada pengaksesan seragam pada tree. Eksperimen dilakukan untuk mengetahui efisiensi kedua struktur binary tree tersebut pada kondisi pengaksesan key secara random pada operasi penyisipan dan pencarian. Efisiensi tree pada operasi delete diprediksikan dari operasi insert. Hasil perbandingan menunjukkan bahwa untuk operasi pada pengaksesan random pada rasio akses 0:100 keduanya memiliki efisiensi sama, namun pada operasi dengan akses rasio 20:80, 50:50 dan 80:20 secara umum splay tree lebih baik dibandingkan AVL tree.
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Alois Panholzer · 2008
We consider extended binary trees and study the common right and left depth of leaf j, where the leaves are labelled from left to right by 0, 1,..., n, and the common right and left external pathlength of binary trees of size n. Under the random tree model, i.e., the Catalan model, we characterize the common limiting distribution of the suitably scaled left depth and the difference between the right and the left depth of leaf j in a random size-n binary tree when j ∼ ρn with 0 < ρ < 1, as well as the common limiting distribution of the suitably scaled left external pathlength and the difference between the right and the left external pathlength of a random size-n binary tree.
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Alois Panholzery · 2016
We consider extended binary trees and study the common right and left depth of leaf j, where the leaves are labelled from left to right by 0; 1; : : : ; n, and the common right and left external pathlength of binary trees of size n. Under the random tree model, i.e., the Catalan model, we characterize the common limiting distribution of the suitably scaled left depth and the difference between the right and the left depth of leaf j in a random size-n binary tree when j » n with 0 < < 1, as well as the common limiting distribution of the suitably scaled left external pathlength and the difference between the right and the left external pathlength of a random size-n binary tree.
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Lug Devroyet, John, Michael Robsont · 2008
Abstract. We consider the computer generation of random binary search trees with n nodes for the standard random permutation model. The algorithms discussed here output the number of external nodes at each level, but not the shape of the tree. This is important, for example, when one wishes to simulate the height of the binary search tree. Various paradigms are proposed, including depth-first search with pruning, incremental methods in which the tree grows with random-sized jumps, and a tree growing procedure gleaned from birth--and-death processes. The last method takes O (logo n) expected time.
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Alois Panholzer · Discrete Mathematics & Theoretical Computer Science · 2006
We consider extended binary trees and study the common right and left depth of leaf $j$, where the leaves are labelled from left to right by $0, 1, \ldots, n$, and the common right and left external pathlength of binary trees of size $n$. Under the random tree model, i.e., the Catalan model, we characterize the common limiting distribution of the suitably scaled left depth and the difference between the right and the left depth of leaf $j$ in a random size-$n$ binary tree when $j \sim \rho n$ with $0< \rho < 1$, as well as the common limiting distribution of the suitably scaled left external pathlength and the difference between the right and the left external pathlength of a random size-$n$ binary tree.
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David A. Croydon · arXiv (Cornell University) · 2024
The $λ$-biased random walk on a binary tree of depth $n$ is the continuous-time Markov chain that has unit mean holding times and, when at a vertex other than the root or a leaf of the tree in question, has a probability of jumping to the parent vertex that is $λ$ times the probability of jumping to a particular child. (From the root, it chooses one of the two children with equal probability.) For this process, when $λ<1$, we derive an $n\rightarrow \infty$ scaling limit for the cover time, that is, the time taken to visit every vertex. The distributional limit is described in terms of a jump process on a Cantor set that can be seen as the asymptotic boundary of the tree. This conclusion complements previous results obtained when $λ\geq 1$.
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