Topological Complexity Of Smooth Random Functions

Author : Robert Adler,Jonathan E. Taylor
Publisher : Springer Science & Business Media
Page : 135 pages
File Size : 52,9 Mb
Release : 2011-05-18
Category : Mathematics
ISBN : 9783642195792

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Topological Complexity of Smooth Random Functions by Robert Adler,Jonathan E. Taylor Pdf

These notes, based on lectures delivered in Saint Flour, provide an easy introduction to the authors’ 2007 Springer monograph “Random Fields and Geometry.” While not as exhaustive as the full monograph, they are also less exhausting, while still covering the basic material, typically at a more intuitive and less technical level. They also cover some more recent material relating to random algebraic topology and statistical applications. The notes include an introduction to the general theory of Gaussian random fields, treating classical topics such as continuity and boundedness. This is followed by a quick review of geometry, both integral and Riemannian, with an emphasis on tube formulae, to provide the reader with the material needed to understand and use the Gaussian kinematic formula, the main result of the notes. This is followed by chapters on topological inference and random algebraic topology, both of which provide applications of the main results.

Author : Robert Adler,Jonathan E. Taylor
Publisher : Springer
Page : 122 pages
File Size : 51,6 Mb
Release : 2011-06-02
Category : Mathematics
ISBN : 3642195814

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Topological Complexity of Smooth Random Functions by Robert Adler,Jonathan E. Taylor Pdf

These notes, based on lectures delivered in Saint Flour, provide an easy introduction to the authors’ 2007 Springer monograph “Random Fields and Geometry.” While not as exhaustive as the full monograph, they are also less exhausting, while still covering the basic material, typically at a more intuitive and less technical level. They also cover some more recent material relating to random algebraic topology and statistical applications. The notes include an introduction to the general theory of Gaussian random fields, treating classical topics such as continuity and boundedness. This is followed by a quick review of geometry, both integral and Riemannian, with an emphasis on tube formulae, to provide the reader with the material needed to understand and use the Gaussian kinematic formula, the main result of the notes. This is followed by chapters on topological inference and random algebraic topology, both of which provide applications of the main results.

Author : Sung Nok Chiu,Dietrich Stoyan,Wilfrid S. Kendall,Joseph Mecke
Publisher : John Wiley & Sons
Page : 561 pages
File Size : 46,7 Mb
Release : 2013-06-27
Category : Mathematics
ISBN : 9781118658253

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Stochastic Geometry and Its Applications by Sung Nok Chiu,Dietrich Stoyan,Wilfrid S. Kendall,Joseph Mecke Pdf

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 : Charles D. Hansen,Min Chen,Christopher R. Johnson,Arie E. Kaufman,Hans Hagen
Publisher : Springer
Page : 397 pages
File Size : 43,5 Mb
Release : 2014-09-18
Category : Mathematics
ISBN : 9781447164975

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Scientific Visualization by Charles D. Hansen,Min Chen,Christopher R. Johnson,Arie E. Kaufman,Hans Hagen Pdf

Based on the seminar that took place in Dagstuhl, Germany in June 2011, this contributed volume studies the four important topics within the scientific visualization field: uncertainty visualization, multifield visualization, biomedical visualization and scalable visualization. • Uncertainty visualization deals with uncertain data from simulations or sampled data, uncertainty due to the mathematical processes operating on the data, and uncertainty in the visual representation, • Multifield visualization addresses the need to depict multiple data at individual locations and the combination of multiple datasets, • Biomedical is a vast field with select subtopics addressed from scanning methodologies to structural applications to biological applications, • Scalability in scientific visualization is critical as data grows and computational devices range from hand-held mobile devices to exascale computational platforms. Scientific Visualization will be useful to practitioners of scientific visualization, students interested in both overview and advanced topics, and those interested in knowing more about the visualization process.

Author : Alison Etheridge
Publisher : Springer
Page : 129 pages
File Size : 44,8 Mb
Release : 2011-01-05
Category : Mathematics
ISBN : 9783642166327

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Some Mathematical Models from Population Genetics by Alison Etheridge Pdf

This work reflects sixteen hours of lectures delivered by the author at the 2009 St Flour summer school in probability. It provides a rapid introduction to a range of mathematical models that have their origins in theoretical population genetics. The models fall into two classes: forwards in time models for the evolution of frequencies of different genetic types in a population; and backwards in time (coalescent) models that trace out the genealogical relationships between individuals in a sample from the population. Some, like the classical Wright-Fisher model, date right back to the origins of the subject. Others, like the multiple merger coalescents or the spatial Lambda-Fleming-Viot process are much more recent. All share a rich mathematical structure. Biological terms are explained, the models are carefully motivated and tools for their study are presented systematically.

Author : Thorsten Dickhaus
Publisher : Springer Science & Business Media
Page : 182 pages
File Size : 44,8 Mb
Release : 2014-01-23
Category : Science
ISBN : 9783642451829

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Simultaneous Statistical Inference by Thorsten Dickhaus Pdf

This monograph will provide an in-depth mathematical treatment of modern multiple test procedures controlling the false discovery rate (FDR) and related error measures, particularly addressing applications to fields such as genetics, proteomics, neuroscience and general biology. The book will also include a detailed description how to implement these methods in practice. Moreover new developments focusing on non-standard assumptions are also included, especially multiple tests for discrete data. The book primarily addresses researchers and practitioners but will also be beneficial for graduate students.

Author : Anonim
Publisher : Unknown
Page : 432 pages
File Size : 43,5 Mb
Release : 1965
Category : Electronic
ISBN : OCLC:1056808706

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Theory of Random Functions by Anonim Pdf

Author : Mamoru Mitsuishi,Kanji Ueda,Fumihiko Kimura
Publisher : Springer Science & Business Media
Page : 556 pages
File Size : 47,9 Mb
Release : 2008-05-14
Category : Technology & Engineering
ISBN : 9781848002678

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Manufacturing Systems and Technologies for the New Frontier by Mamoru Mitsuishi,Kanji Ueda,Fumihiko Kimura Pdf

Collected here are 112 papers concerned with all manner of new directions in manufacturing systems given at the 41st CIRP Conference on Manufacturing Systems. The high-quality material presented in this volume includes reports of work from both scientific and engineering standpoints and several invited and keynote papers addressing the current cutting edge and likely future trends in manufacturing systems. The book’s subjects include: (1) new trends in manufacturing systems design: sustainable design, ubiquitous manufacturing, emergent synthesis, service engineering, value creation, cost engineering, human and social aspects of manufacturing, etc.; (2) new applications for manufacturing systems – medical, life-science, optics, NEMS, etc.; (3) intelligent use of advanced methods and new materials – new manufacturing process technologies, high-hardness materials, bio-medical materials, etc.; (4) integration and control for new machines – compound machine tools, rapid prototyping, printing process integration, etc.

Author : R. J. Adler,Jonathan E. Taylor
Publisher : Springer Science & Business Media
Page : 455 pages
File Size : 46,7 Mb
Release : 2009-01-29
Category : Mathematics
ISBN : 9780387481166

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Random Fields and Geometry by R. J. Adler,Jonathan E. Taylor Pdf

This monograph is devoted to a completely new approach to geometric problems arising in the study of random fields. The groundbreaking material in Part III, for which the background is carefully prepared in Parts I and II, is of both theoretical and practical importance, and striking in the way in which problems arising in geometry and probability are beautifully intertwined. "Random Fields and Geometry" will be useful for probabilists and statisticians, and for theoretical and applied mathematicians who wish to learn about new relationships between geometry and probability. It will be helpful for graduate students in a classroom setting, or for self-study. Finally, this text will serve as a basic reference for all those interested in the companion volume of the applications of the theory.

Author : Ronald A. DeVore,Arieh Iserles,Endre Süli
Publisher : Cambridge University Press
Page : 418 pages
File Size : 49,6 Mb
Release : 2001-05-17
Category : Mathematics
ISBN : 0521003490

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Foundations of Computational Mathematics by Ronald A. DeVore,Arieh Iserles,Endre Süli Pdf

Collection of papers by leading researchers in computational mathematics, suitable for graduate students and researchers.

Author : Robert J. Adler
Publisher : SIAM
Page : 295 pages
File Size : 40,9 Mb
Release : 2010-01-28
Category : Mathematics
ISBN : 9780898716931

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The Geometry of Random Fields by Robert J. Adler Pdf

An important treatment of the geometric properties of sets generated by random fields, including a comprehensive treatment of the mathematical basics of random fields in general. It is a standard reference for all researchers with an interest in random fields, whether they be theoreticians or come from applied areas.

Author : Jean-Marc Azais,Mario Wschebor
Publisher : John Wiley & Sons
Page : 407 pages
File Size : 44,5 Mb
Release : 2009-02-17
Category : Mathematics
ISBN : 9780470434635

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Level Sets and Extrema of Random Processes and Fields by Jean-Marc Azais,Mario Wschebor Pdf

A timely and comprehensive treatment of random field theory with applications across diverse areas of study Level Sets and Extrema of Random Processes and Fields discusses how to understand the properties of the level sets of paths as well as how to compute the probability distribution of its extremal values, which are two general classes of problems that arise in the study of random processes and fields and in related applications. This book provides a unified and accessible approach to these two topics and their relationship to classical theory and Gaussian processes and fields, and the most modern research findings are also discussed. The authors begin with an introduction to the basic concepts of stochastic processes, including a modern review of Gaussian fields and their classical inequalities. Subsequent chapters are devoted to Rice formulas, regularity properties, and recent results on the tails of the distribution of the maximum. Finally, applications of random fields to various areas of mathematics are provided, specifically to systems of random equations and condition numbers of random matrices. Throughout the book, applications are illustrated from various areas of study such as statistics, genomics, and oceanography while other results are relevant to econometrics, engineering, and mathematical physics. The presented material is reinforced by end-of-chapter exercises that range in varying degrees of difficulty. Most fundamental topics are addressed in the book, and an extensive, up-to-date bibliography directs readers to existing literature for further study. Level Sets and Extrema of Random Processes and Fields is an excellent book for courses on probability theory, spatial statistics, Gaussian fields, and probabilistic methods in real computation at the upper-undergraduate and graduate levels. It is also a valuable reference for professionals in mathematics and applied fields such as statistics, engineering, econometrics, mathematical physics, and biology.

Author : Tamal Krishna Dey,Yusu Wang
Publisher : Cambridge University Press
Page : 455 pages
File Size : 42,7 Mb
Release : 2022-03-10
Category : Computers
ISBN : 9781009098168

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Computational Topology for Data Analysis by Tamal Krishna Dey,Yusu Wang Pdf

This book provides a computational and algorithmic foundation for techniques in topological data analysis, with examples and exercises.

Author : Herbert Edelsbrunner,John L. Harer
Publisher : American Mathematical Society
Page : 241 pages
File Size : 55,9 Mb
Release : 2022-01-31
Category : Mathematics
ISBN : 9781470467692

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Computational Topology by Herbert Edelsbrunner,John L. Harer Pdf

Combining concepts from topology and algorithms, this book delivers what its title promises: an introduction to the field of computational topology. Starting with motivating problems in both mathematics and computer science and building up from classic topics in geometric and algebraic topology, the third part of the text advances to persistent homology. This point of view is critically important in turning a mostly theoretical field of mathematics into one that is relevant to a multitude of disciplines in the sciences and engineering. The main approach is the discovery of topology through algorithms. The book is ideal for teaching a graduate or advanced undergraduate course in computational topology, as it develops all the background of both the mathematical and algorithmic aspects of the subject from first principles. Thus the text could serve equally well in a course taught in a mathematics department or computer science department.

Author : Anonim
Publisher : Unknown
Page : 860 pages
File Size : 47,6 Mb
Release : 2007
Category : Mathematics
ISBN : UOM:39015076649899

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Mathematical Reviews by Anonim Pdf