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Author : Daniel Hug
Publisher : Springer Nature
ISBN 13 : 3031541049
Total Pages : 550 pages
Book Rating : 4.49/5 ( download)
Download or read book Poisson Hyperplane Tessellations written by Daniel Hug and published by Springer Nature. This book was released on with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Daniel Hug
Publisher : Springer
ISBN 13 : 9783031541032
Total Pages : 0 pages
Book Rating : 4.30/5 ( download)
Download or read book Poisson Hyperplane Tessellations written by Daniel Hug and published by Springer. This book was released on 2024-04-16 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first comprehensive presentation of a central topic of stochastic geometry: random mosaics that are generated by Poisson processes of hyperplanes. It thus connects a basic notion from probability theory, Poisson processes, with a fundamental object of geometry. The independence properties of Poisson processes and the long-range influence of hyperplanes lead to a wide range of phenomena which are of interest from both a geometric and a probabilistic point of view. A Poisson hyperplane tessellation generates many random polytopes, also a much-studied object of stochastic geometry. The book offers a variety of different perspectives and covers in detail all aspects studied in the original literature. The work will be useful to graduate students (advanced students in a Master program, PhD students), and professional mathematicians. The book can also serve as a reference for researchers in fields of physics, computer science, economics or engineering.
Author : Atsuyuki Okabe
Publisher : John Wiley & Sons
ISBN 13 : 047031785X
Total Pages : 696 pages
Book Rating : 4.53/5 ( download)
Download or read book Spatial Tessellations written by Atsuyuki Okabe and published by John Wiley & Sons. This book was released on 2009-09-25 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spatial data analysis is a fast growing area and Voronoi diagrams provide a means of naturally partitioning space into subregions to facilitate spatial data manipulation, modelling of spatial structures, pattern recognition and locational optimization. With such versatility, the Voronoi diagram and its relative, the Delaunay triangulation, provide valuable tools for the analysis of spatial data. This is a rapidly growing research area and in this fully updated second edition the authors provide an up-to-date and comprehensive unification of all the previous literature on the subject of Voronoi diagrams. Features: * Expands on the highly acclaimed first edition * Provides an up-to-date and comprehensive survey of the existing literature on Voronoi diagrams * Includes a useful compendium of applications * Contains an extensive bibliography A wide range of applications is discussed, enabling this book to serve as an important reference volume on this topic. The text will appeal to students and researchers studying spatial data in a number of areas, in particular, applied probability, computational geometry, and Geographic Information Science (GIS). This book will appeal equally to those whose interests in Voronoi diagrams are theoretical, practical or both.
Author : Volker Schmidt
Publisher : Springer
ISBN 13 : 3319100645
Total Pages : 464 pages
Book Rating : 4.47/5 ( download)
Download or read book Stochastic Geometry, Spatial Statistics and Random Fields written by Volker Schmidt and published by Springer. This book was released on 2014-10-24 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is an attempt to provide a graduate level introduction to various aspects of stochastic geometry, spatial statistics and random fields, with special emphasis placed on fundamental classes of models and algorithms as well as on their applications, e.g. in materials science, biology and genetics. This book has a strong focus on simulations and includes extensive codes in Matlab and R which are widely used in the mathematical community. It can be seen as a continuation of the recent volume 2068 of Lecture Notes in Mathematics, where other issues of stochastic geometry, spatial statistics and random fields were considered with a focus on asymptotic methods.
Author : Eva B. Vedel Jensen
Publisher : Springer
ISBN 13 : 3319519514
Total Pages : 462 pages
Book Rating : 4.17/5 ( download)
Download or read book Tensor Valuations and Their Applications in Stochastic Geometry and Imaging written by Eva B. Vedel Jensen and published by Springer. This book was released on 2017-06-10 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this volume is to give an up-to-date introduction to tensor valuations and their applications. Starting with classical results concerning scalar-valued valuations on the families of convex bodies and convex polytopes, it proceeds to the modern theory of tensor valuations. Product and Fourier-type transforms are introduced and various integral formulae are derived. New and well-known results are presented, together with generalizations in several directions, including extensions to the non-Euclidean setting and to non-convex sets. A variety of applications of tensor valuations to models in stochastic geometry, to local stereology and to imaging are also discussed.
Author : Giovanni Peccati
Publisher : Springer
ISBN 13 : 3319052330
Total Pages : 346 pages
Book Rating : 4.35/5 ( download)
Download or read book Stochastic Analysis for Poisson Point Processes written by Giovanni Peccati and published by Springer. This book was released on 2016-07-07 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic geometry is the branch of mathematics that studies geometric structures associated with random configurations, such as random graphs, tilings and mosaics. Due to its close ties with stereology and spatial statistics, the results in this area are relevant for a large number of important applications, e.g. to the mathematical modeling and statistical analysis of telecommunication networks, geostatistics and image analysis. In recent years – due mainly to the impetus of the authors and their collaborators – a powerful connection has been established between stochastic geometry and the Malliavin calculus of variations, which is a collection of probabilistic techniques based on the properties of infinite-dimensional differential operators. This has led in particular to the discovery of a large number of new quantitative limit theorems for high-dimensional geometric objects. This unique book presents an organic collection of authoritative surveys written by the principal actors in this rapidly evolving field, offering a rigorous yet lively presentation of its many facets.
Author : Sung Nok Chiu
Publisher : John Wiley & Sons
ISBN 13 : 1118658256
Total Pages : 561 pages
Book Rating : 4.53/5 ( download)
Download or read book Stochastic Geometry and Its Applications written by Sung Nok Chiu and published by John Wiley & Sons. This book was released on 2013-06-27 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: An extensive update to a classic text Stochastic geometry and spatial statistics play a fundamental role in many modern branches of physics, materials sciences, engineering, biology and environmental sciences. They offer successful models for the description of random two- and three-dimensional micro and macro structures and statistical methods for their analysis. The previous edition of this book has served as the key reference in its field for over 18 years and is regarded as the best treatment of the subject of stochastic geometry, both as a subject with vital applications to spatial statistics and as a very interesting field of mathematics in its own right. This edition: Presents a wealth of models for spatial patterns and related statistical methods. Provides a great survey of the modern theory of random tessellations, including many new models that became tractable only in the last few years. Includes new sections on random networks and random graphs to review the recent ever growing interest in these areas. Provides an excellent introduction to theory and modelling of point processes, which covers some very latest developments. Illustrate the forefront theory of random sets, with many applications. Adds new results to the discussion of fibre and surface processes. Offers an updated collection of useful stereological methods. Includes 700 new references. Is written in an accessible style enabling non-mathematicians to benefit from this book. Provides a companion website hosting information on recent developments in the field www.wiley.com/go/cskm Stochastic Geometry and its Applications is ideally suited for researchers in physics, materials science, biology and ecological sciences as well as mathematicians and statisticians. It should also serve as a valuable introduction to the subject for students of mathematics and statistics.
Author : Evgeny Spodarev
Publisher : Springer
ISBN 13 : 3642333052
Total Pages : 470 pages
Book Rating : 4.57/5 ( download)
Download or read book Stochastic Geometry, Spatial Statistics and Random Fields written by Evgeny Spodarev and published by Springer. This book was released on 2013-02-11 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a modern introduction to stochastic geometry, random fields and spatial statistics at a (post)graduate level. It is focused on asymptotic methods in geometric probability including weak and strong limit theorems for random spatial structures (point processes, sets, graphs, fields) with applications to statistics. Written as a contributed volume of lecture notes, it will be useful not only for students but also for lecturers and researchers interested in geometric probability and related subjects.
Author : Csaba D. Toth
Publisher : CRC Press
ISBN 13 : 1420035312
Total Pages : 1557 pages
Book Rating : 4.15/5 ( download)
Download or read book Handbook of Discrete and Computational Geometry, Second Edition written by Csaba D. Toth and published by CRC Press. This book was released on 2004-04-13 with total page 1557 pages. Available in PDF, EPUB and Kindle. Book excerpt: While high-quality books and journals in this field continue to proliferate, none has yet come close to matching the Handbook of Discrete and Computational Geometry, which in its first edition, quickly became the definitive reference work in its field. But with the rapid growth of the discipline and the many advances made over the past seven years, it's time to bring this standard-setting reference up to date. Editors Jacob E. Goodman and Joseph O'Rourke reassembled their stellar panel of contributors, added manymore, and together thoroughly revised their work to make the most important results and methods, both classic and cutting-edge, accessible in one convenient volume. Now over more then 1500 pages, the Handbook of Discrete and Computational Geometry, Second Edition once again provides unparalleled, authoritative coverage of theory, methods, and applications. Highlights of the Second Edition: Thirteen new chapters: Five on applications and others on collision detection, nearest neighbors in high-dimensional spaces, curve and surface reconstruction, embeddings of finite metric spaces, polygonal linkages, the discrepancy method, and geometric graph theory Thorough revisions of all remaining chapters Extended coverage of computational geometry software, now comprising two chapters: one on the LEDA and CGAL libraries, the other on additional software Two indices: An Index of Defined Terms and an Index of Cited Authors Greatly expanded bibliographies
Author : Rolf Schneider
Publisher : Springer Science & Business Media
ISBN 13 : 354078859X
Total Pages : 692 pages
Book Rating : 4.91/5 ( download)
Download or read book Stochastic and Integral Geometry written by Rolf Schneider and published by Springer Science & Business Media. This book was released on 2008-09-08 with total page 692 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic geometry deals with models for random geometric structures. Its early beginnings are found in playful geometric probability questions, and it has vigorously developed during recent decades, when an increasing number of real-world applications in various sciences required solid mathematical foundations. Integral geometry studies geometric mean values with respect to invariant measures and is, therefore, the appropriate tool for the investigation of random geometric structures that exhibit invariance under translations or motions. Stochastic and Integral Geometry provides the mathematically oriented reader with a rigorous and detailed introduction to the basic stationary models used in stochastic geometry – random sets, point processes, random mosaics – and to the integral geometry that is needed for their investigation. The interplay between both disciplines is demonstrated by various fundamental results. A chapter on selected problems about geometric probabilities and an outlook to non-stationary models are included, and much additional information is given in the section notes.
