Topological Complexity of Smooth Random Functions

Topological Complexity of Smooth Random Functions
Author: Robert Adler,Jonathan E. Taylor
Publsiher: Springer Science & Business Media
Total Pages: 135
Release: 2011-05-18
Genre: Mathematics
ISBN: 9783642195792

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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.

Topological Complexity of Smooth Random Functions

Topological Complexity of Smooth Random Functions
Author: Robert Adler,Jonathan E. Taylor
Publsiher: Springer
Total Pages: 122
Release: 2011-06-02
Genre: Mathematics
ISBN: 3642195814

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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.

Stochastic Geometry and Its Applications

Stochastic Geometry and Its Applications
Author: Sung Nok Chiu,Dietrich Stoyan,Wilfrid S. Kendall,Joseph Mecke
Publsiher: John Wiley & Sons
Total Pages: 561
Release: 2013-06-27
Genre: Mathematics
ISBN: 9781118658253

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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.

Scientific Visualization

Scientific Visualization
Author: Charles D. Hansen,Min Chen,Christopher R. Johnson,Arie E. Kaufman,Hans Hagen
Publsiher: Springer
Total Pages: 397
Release: 2014-09-18
Genre: Mathematics
ISBN: 9781447164975

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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.

Some Mathematical Models from Population Genetics

Some Mathematical Models from Population Genetics
Author: Alison Etheridge
Publsiher: Springer
Total Pages: 129
Release: 2011-01-05
Genre: Mathematics
ISBN: 9783642166327

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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.

Simultaneous Statistical Inference

Simultaneous Statistical Inference
Author: Thorsten Dickhaus
Publsiher: Springer Science & Business Media
Total Pages: 182
Release: 2014-01-23
Genre: Science
ISBN: 9783642451829

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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.

Theory of Random Functions

Theory of Random Functions
Author: Anonim
Publsiher: Unknown
Total Pages: 432
Release: 1965
Genre: Electronic Book
ISBN: OCLC:1056808706

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Manufacturing Systems and Technologies for the New Frontier

Manufacturing Systems and Technologies for the New Frontier
Author: Mamoru Mitsuishi,Kanji Ueda,Fumihiko Kimura
Publsiher: Springer Science & Business Media
Total Pages: 556
Release: 2008-05-14
Genre: Technology & Engineering
ISBN: 9781848002678

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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.