Topological Complexity Of Smooth Random Functions
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Author |
: Robert Adler |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 135 |
Release |
: 2011-05-18 |
ISBN-10 |
: 9783642195792 |
ISBN-13 |
: 3642195792 |
Rating |
: 4/5 (92 Downloads) |
Synopsis Topological Complexity of Smooth Random Functions by : Robert Adler
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 |
Publisher |
: Springer |
Total Pages |
: 122 |
Release |
: 2011-06-02 |
ISBN-10 |
: 3642195814 |
ISBN-13 |
: 9783642195815 |
Rating |
: 4/5 (14 Downloads) |
Synopsis Topological Complexity of Smooth Random Functions by : Robert Adler
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 |
Publisher |
: John Wiley & Sons |
Total Pages |
: 561 |
Release |
: 2013-06-27 |
ISBN-10 |
: 9781118658253 |
ISBN-13 |
: 1118658256 |
Rating |
: 4/5 (53 Downloads) |
Synopsis Stochastic Geometry and Its Applications by : Sung Nok Chiu
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 |
Publisher |
: Springer |
Total Pages |
: 397 |
Release |
: 2014-09-18 |
ISBN-10 |
: 9781447164975 |
ISBN-13 |
: 1447164970 |
Rating |
: 4/5 (75 Downloads) |
Synopsis Scientific Visualization by : Charles D. Hansen
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 |
Total Pages |
: 129 |
Release |
: 2011-01-05 |
ISBN-10 |
: 9783642166327 |
ISBN-13 |
: 3642166326 |
Rating |
: 4/5 (27 Downloads) |
Synopsis Some Mathematical Models from Population Genetics by : Alison Etheridge
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 |
Total Pages |
: 182 |
Release |
: 2014-01-23 |
ISBN-10 |
: 9783642451829 |
ISBN-13 |
: 3642451829 |
Rating |
: 4/5 (29 Downloads) |
Synopsis Simultaneous Statistical Inference by : Thorsten Dickhaus
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 |
: |
Publisher |
: |
Total Pages |
: 432 |
Release |
: 1965 |
ISBN-10 |
: OCLC:1056808706 |
ISBN-13 |
: |
Rating |
: 4/5 (06 Downloads) |
Synopsis Theory of Random Functions by :
Author |
: Robert A. Meyers |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 1885 |
Release |
: 2011-10-05 |
ISBN-10 |
: 9781461418054 |
ISBN-13 |
: 1461418054 |
Rating |
: 4/5 (54 Downloads) |
Synopsis Mathematics of Complexity and Dynamical Systems by : Robert A. Meyers
Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.
Author |
: V. I. Arnold |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 170 |
Release |
: 2015-07-14 |
ISBN-10 |
: 9780821894163 |
ISBN-13 |
: 0821894161 |
Rating |
: 4/5 (63 Downloads) |
Synopsis Experimental Mathematics by : V. I. Arnold
One of the traditional ways mathematical ideas and even new areas of mathematics are created is from experiments. One of the best-known examples is that of the Fermat hypothesis, which was conjectured by Fermat in his attempts to find integer solutions for the famous Fermat equation. This hypothesis led to the creation of a whole field of knowledge, but it was proved only after several hundred years. This book, based on the author's lectures, presents several new directions of mathematical research. All of these directions are based on numerical experiments conducted by the author, which led to new hypotheses that currently remain open, i.e., are neither proved nor disproved. The hypotheses range from geometry and topology (statistics of plane curves and smooth functions) to combinatorics (combinatorial complexity and random permutations) to algebra and number theory (continuous fractions and Galois groups). For each subject, the author describes the problem and presents numerical results that led him to a particular conjecture. In the majority of cases there is an indication of how the readers can approach the formulated conjectures (at least by conducting more numerical experiments). Written in Arnold's unique style, the book is intended for a wide range of mathematicians, from high school students interested in exploring unusual areas of mathematics on their own, to college and graduate students, to researchers interested in gaining a new, somewhat nontraditional perspective on doing mathematics. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession. Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI).
Author |
: Vladimir Semenovich Pugachev |
Publisher |
: Pergamon |
Total Pages |
: 833 |
Release |
: 1965-06 |
ISBN-10 |
: 0080104215 |
ISBN-13 |
: 9780080104218 |
Rating |
: 4/5 (15 Downloads) |
Synopsis Theory of Random Functions by : Vladimir Semenovich Pugachev