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Random Generation of Trees

Random Generation of Trees
Author: Laurent Alonso
Publisher: Springer Science & Business Media
Total Pages: 217
Release: 2013-03-09
Genre: Computers
ISBN: 1475763530

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Random Generation of Trees is about a field on the crossroads between computer science, combinatorics and probability theory. Computer scientists need random generators for performance analysis, simulation, image synthesis, etc. In this context random generation of trees is of particular interest. The algorithms presented here are efficient and easy to code. Some aspects of Horton--Strahler numbers, programs written in C and pictures are presented in the appendices. The complexity analysis is done rigorously both in the worst and average cases. Random Generation of Trees is intended for students in computer science and applied mathematics as well as researchers interested in random generation.


Random Trees

Random Trees
Author: Michael Drmota
Publisher: Springer Science & Business Media
Total Pages: 466
Release: 2009-04-16
Genre: Mathematics
ISBN: 3211753575

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The aim of this book is to provide a thorough introduction to various aspects of trees in random settings and a systematic treatment of the mathematical analysis techniques involved. It should serve as a reference book as well as a basis for future research.


Algorithms for Random Generation and Counting: A Markov Chain Approach

Algorithms for Random Generation and Counting: A Markov Chain Approach
Author: A. Sinclair
Publisher: Springer Science & Business Media
Total Pages: 156
Release: 2012-12-06
Genre: Computers
ISBN: 1461203236

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This monograph is a slightly revised version of my PhD thesis [86], com pleted in the Department of Computer Science at the University of Edin burgh in June 1988, with an additional chapter summarising more recent developments. Some of the material has appeared in the form of papers [50,88]. The underlying theme of the monograph is the study of two classical problems: counting the elements of a finite set of combinatorial structures, and generating them uniformly at random. In their exact form, these prob lems appear to be intractable for many important structures, so interest has focused on finding efficient randomised algorithms that solve them ap proxim~ly, with a small probability of error. For most natural structures the two problems are intimately connected at this level of approximation, so it is natural to study them together. At the heart of the monograph is a single algorithmic paradigm: sim ulate a Markov chain whose states are combinatorial structures and which converges to a known probability distribution over them. This technique has applications not only in combinatorial counting and generation, but also in several other areas such as statistical physics and combinatorial optimi sation. The efficiency of the technique in any application depends crucially on the rate of convergence of the Markov chain.


Random Number Generation and Monte Carlo Methods

Random Number Generation and Monte Carlo Methods
Author: James E. Gentle
Publisher: Springer Science & Business Media
Total Pages: 252
Release: 2013-03-14
Genre: Computers
ISBN: 147572960X

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Monte Carlo simulation has become one of the most important tools in all fields of science. This book surveys the basic techniques and principles of the subject, as well as general techniques useful in more complicated models and in novel settings. The emphasis throughout is on practical methods that work well in current computing environments.


Proceedings of the Ninth Annual ACM-SIAM Symposium on Discrete Algorithms

Proceedings of the Ninth Annual ACM-SIAM Symposium on Discrete Algorithms
Author: Howard Karloff
Publisher: SIAM
Total Pages: 726
Release: 1998-01-01
Genre: Mathematics
ISBN: 9780898714104

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This symposium is jointly sponsored by the ACM Special Interest Group on Algorithms and Computation Theory and the SIAM Activity Group on Discrete Mathematics.


Topics in Cryptology - CT-RSA 2009

Topics in Cryptology - CT-RSA 2009
Author: Marc Fischlin
Publisher: Springer
Total Pages: 492
Release: 2009-04-29
Genre: Computers
ISBN: 3642008623

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This book constitutes the refereed proceedings of the Cryptographers' Track at the RSA Conference 2009, CT-RSA 2009, held in San Francisco, CA, USA in April 2009. The 31 revised full papers presented were carefully reviewed and selected from 93 submissions. The papers are organized in topical sections on identity-based encryption, protocol analysis, two-party protocols, more than signatures, collisions for hash functions, cryptanalysis, alternative encryption, privacy and anonymity, efficiency improvements, multi-party protocols, security of encryption schemes as well as countermeasures and faults.


Clustering And Classification

Clustering And Classification
Author: Phips Arabie
Publisher: World Scientific
Total Pages: 501
Release: 1996-01-29
Genre: Computers
ISBN: 981450453X

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At a moderately advanced level, this book seeks to cover the areas of clustering and related methods of data analysis where major advances are being made. Topics include: hierarchical clustering, variable selection and weighting, additive trees and other network models, relevance of neural network models to clustering, the role of computational complexity in cluster analysis, latent class approaches to cluster analysis, theory and method with applications of a hierarchical classes model in psychology and psychopathology, combinatorial data analysis, clusterwise aggregation of relations, review of the Japanese-language results on clustering, review of the Russian-language results on clustering and multidimensional scaling, practical advances, and significance tests.


Algorithms for Random Generation and Counting: A Markov Chain Approach

Algorithms for Random Generation and Counting: A Markov Chain Approach
Author: A. Sinclair
Publisher: Springer Science & Business Media
Total Pages: 161
Release: 1993-02
Genre: Computers
ISBN: 0817636587

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This monograph is a slightly revised version of my PhD thesis [86], com pleted in the Department of Computer Science at the University of Edin burgh in June 1988, with an additional chapter summarising more recent developments. Some of the material has appeared in the form of papers [50,88]. The underlying theme of the monograph is the study of two classical problems: counting the elements of a finite set of combinatorial structures, and generating them uniformly at random. In their exact form, these prob lems appear to be intractable for many important structures, so interest has focused on finding efficient randomised algorithms that solve them ap proxim~ly, with a small probability of error. For most natural structures the two problems are intimately connected at this level of approximation, so it is natural to study them together. At the heart of the monograph is a single algorithmic paradigm: sim ulate a Markov chain whose states are combinatorial structures and which converges to a known probability distribution over them. This technique has applications not only in combinatorial counting and generation, but also in several other areas such as statistical physics and combinatorial optimi sation. The efficiency of the technique in any application depends crucially on the rate of convergence of the Markov chain.


Mathematics and Computer Science II

Mathematics and Computer Science II
Author: Brigitte Chauvin
Publisher: Birkhäuser
Total Pages: 526
Release: 2012-12-06
Genre: Mathematics
ISBN: 3034882114

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This is the second volume in a series of innovative proceedings entirely devoted to the connections between mathematics and computer science. Here mathematics and computer science are directly confronted and joined to tackle intricate problems in computer science with deep and innovative mathematical approaches. The book serves as an outstanding tool and a main information source for a large public in applied mathematics, discrete mathematics and computer science, including researchers, teachers, graduate students and engineers. It provides an overview of the current questions in computer science and the related modern and powerful mathematical methods. The range of applications is very wide and reaches beyond computer science.


Pattern Theory

Pattern Theory
Author: Ulf Grenander
Publisher: Oxford University Press
Total Pages: 633
Release: 2007
Genre: Computers
ISBN: 0198505701

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Pattern Theory provides a comprehensive and accessible overview of the modern challenges in signal, data, and pattern analysis in speech recognition, computational linguistics, image analysis and computer vision. Aimed at graduate students in biomedical engineering, mathematics, computer science, and electrical engineering with a good background in mathematics and probability, the text includes numerous exercises and an extensive bibliography. Additional resources including extended proofs, selected solutions and examples are available on a companion website. The book commences with a short overview of pattern theory and the basics of statistics and estimation theory. Chapters 3-6 discuss the role of representation of patterns via condition structure. Chapters 7 and 8 examine the second central component of pattern theory: groups of geometric transformation applied to the representation of geometric objects. Chapter 9 moves into probabilistic structures in the continuum, studying random processes and random fields indexed over subsets of Rn. Chapters 10 and 11 continue with transformations and patterns indexed over the continuum. Chapters 12-14 extend from the pure representations of shapes to the Bayes estimation of shapes and their parametric representation. Chapters 15 and 16 study the estimation of infinite dimensional shape in the newly emergent field of Computational Anatomy. Finally, Chapters 17 and 18 look at inference, exploring random sampling approaches for estimation of model order and parametric representing of shapes.