Logarithmic Combinatorial Structures
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Logarithmic Combinatorial Structures
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Author : Richard Arratia
language : en
Publisher: European Mathematical Society
Release Date : 2003
Logarithmic Combinatorial Structures written by Richard Arratia and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
This book explains similarities in asymptotic behavior as the result of two basic properties shared by the structures: the conditioning relation and the logarithmic condition. The discussion is conducted in the language of probability, enabling the theory to be developed under rather general and explicit conditions; for the finer conclusions, Stein's method emerges as the key ingredient.
Logarithmic Combinatorial Structures A Probabilistic Approach
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Author : R. Arratia (Barbour, A.D., Tavare, S.)
language : en
Publisher:
Release Date : 2013
Logarithmic Combinatorial Structures A Probabilistic Approach written by R. Arratia (Barbour, A.D., Tavare, S.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
Combinatorics And Finite Fields
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Author : Kai-Uwe Schmidt
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2019-07-08
Combinatorics And Finite Fields written by Kai-Uwe Schmidt and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-08 with Mathematics categories.
Combinatorics and finite fields are of great importance in modern applications such as in the analysis of algorithms, in information and communication theory, and in signal processing and coding theory. This book contains survey articles on topics such as difference sets, polynomials, and pseudorandomness.
Nonarchimedean And Tropical Geometry
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Author : Matthew Baker
language : en
Publisher: Springer
Release Date : 2016-08-18
Nonarchimedean And Tropical Geometry written by Matthew Baker and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-18 with Mathematics categories.
This volume grew out of two Simons Symposia on "Nonarchimedean and tropical geometry" which took place on the island of St. John in April 2013 and in Puerto Rico in February 2015. Each meeting gathered a small group of experts working near the interface between tropical geometry and nonarchimedean analytic spaces for a series of inspiring and provocative lectures on cutting edge research, interspersed with lively discussions and collaborative work in small groups. The articles collected here, which include high-level surveys as well as original research, mirror the main themes of the two Symposia. Topics covered in this volume include: Differential forms and currents, and solutions of Monge-Ampere type differential equations on Berkovich spaces and their skeletons; The homotopy types of nonarchimedean analytifications; The existence of "faithful tropicalizations" which encode the topology and geometry of analytifications; Relations between nonarchimedean analytic spaces and algebraic geometry, including logarithmic schemes, birational geometry, and the geometry of algebraic curves; Extended notions of tropical varieties which relate to Huber's theory of adic spaces analogously to the way that usual tropical varieties relate to Berkovich spaces; and Relations between nonarchimedean geometry and combinatorics, including deep and fascinating connections between matroid theory, tropical geometry, and Hodge theory.
Contemporary Combinatorics
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Author : Bela Bollobas
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-05-28
Contemporary Combinatorics written by Bela Bollobas and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-05-28 with Mathematics categories.
This volume is a collection of survey papers in combinatorics that have grown out of lectures given in the workshop on Probabilistic Combinatorics at the Paul Erdös Summer Research Center in Mathematics in Budapest. The papers, reflecting the many facets of modern-day combinatorics, will be appreciated by specialists and general mathematicians alike: assuming relatively little background, each paper gives a quick introduction to an active area, enabling the reader to learn about the fundamental results and appreciate some of the latest developments. An important feature of the articles, very much in the spirit of Erdös, is the abundance of open problems.
Analytic Combinatorics
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Author : Philippe Flajolet
language : en
Publisher: Cambridge University Press
Release Date : 2009-01-15
Analytic Combinatorics written by Philippe Flajolet and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-15 with Mathematics categories.
Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.
Pioneering Works On Distribution Theory
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Author : Nobuaki Hoshino
language : en
Publisher: Springer Nature
Release Date : 2021-01-04
Pioneering Works On Distribution Theory written by Nobuaki Hoshino and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-04 with Mathematics categories.
This book highlights the forefront of research on statistical distribution theory, with a focus on unconventional random quantities, and on phenomena such as random partitioning. The respective papers reflect the continuing appeal of distribution theory and the lively interest in this classic field, which owes much of its expansion since the 1960s to Professor Masaaki Sibuya, to whom this book is dedicated. The topics addressed include a test procedure for discriminating the (multivariate) Ewens distribution from the Pitman Sampling Formula, approximation to the length of the Ewens distribution by discrete distributions and the normal distribution, and the distribution of the number of levels in [s]-specified random permutations. Also included are distributions associated with orthogonal polynomials with a symmetric matrix argument and the characterization of the Jeffreys prior.
Partitions Hypergeometric Systems And Dirichlet Processes In Statistics
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Author : Shuhei Mano
language : en
Publisher: Springer
Release Date : 2018-07-12
Partitions Hypergeometric Systems And Dirichlet Processes In Statistics written by Shuhei Mano and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-12 with Mathematics categories.
This book focuses on statistical inferences related to various combinatorial stochastic processes. Specifically, it discusses the intersection of three subjects that are generally studied independently of each other: partitions, hypergeometric systems, and Dirichlet processes. The Gibbs partition is a family of measures on integer partition, and several prior processes, such as the Dirichlet process, naturally appear in connection with infinite exchangeable Gibbs partitions. Examples include the distribution on a contingency table with fixed marginal sums and the conditional distribution of Gibbs partition given the length. The A-hypergeometric distribution is a class of discrete exponential families and appears as the conditional distribution of a multinomial sample from log-affine models. The normalizing constant is the A-hypergeometric polynomial, which is a solution of a system of linear differential equations of multiple variables determined by a matrix A, called A-hypergeometric system. The book presents inference methods based on the algebraic nature of the A-hypergeometric system, and introduces the holonomic gradient methods, which numerically solve holonomic systems without combinatorial enumeration, to compute the normalizing constant. Furher, it discusses Markov chain Monte Carlo and direct samplers from A-hypergeometric distribution, as well as the maximum likelihood estimation of the A-hypergeometric distribution of two-row matrix using properties of polytopes and information geometry. The topics discussed are simple problems, but the interdisciplinary approach of this book appeals to a wide audience with an interest in statistical inference on combinatorial stochastic processes, including statisticians who are developing statistical theories and methodologies, mathematicians wanting to discover applications of their theoretical results, and researchers working in various fields of data sciences.
Combinatorics Geometry And Probability
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Author : Béla Bollobás
language : en
Publisher: Cambridge University Press
Release Date : 1997-05-22
Combinatorics Geometry And Probability written by Béla Bollobás and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-05-22 with Mathematics categories.
A panorama of combinatorics by the world's experts.
Combinatorics And Probability
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Author : Graham Brightwell
language : en
Publisher: Cambridge University Press
Release Date : 2007-03-08
Combinatorics And Probability written by Graham Brightwell and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-03-08 with Mathematics categories.
This volume celebrating the 60th birthday of Béla Bollobás presents the state of the art in combinatorics.