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Geometric And Topological Inference
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Book Synopsis Geometric and Topological Inference by : Jean-Daniel Boissonnat
Download or read book Geometric and Topological Inference written by Jean-Daniel Boissonnat and published by Cambridge University Press. This book was released on 2018-09-27 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous introduction to geometric and topological inference, for anyone interested in a geometric approach to data science.
Book Synopsis Topological Complexity of Smooth Random Functions by : Robert Adler
Download or read book Topological Complexity of Smooth Random Functions written by Robert Adler and published by Springer Science & Business Media. This book was released on 2011-05-18 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Computational Topology for Data Analysis by : Tamal Krishna Dey
Download or read book Computational Topology for Data Analysis written by Tamal Krishna Dey and published by Cambridge University Press. This book was released on 2022-03-10 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological data analysis (TDA) has emerged recently as a viable tool for analyzing complex data, and the area has grown substantially both in its methodologies and applicability. Providing a computational and algorithmic foundation for techniques in TDA, this comprehensive, self-contained text introduces students and researchers in mathematics and computer science to the current state of the field. The book features a description of mathematical objects and constructs behind recent advances, the algorithms involved, computational considerations, as well as examples of topological structures or ideas that can be used in applications. It provides a thorough treatment of persistent homology together with various extensions – like zigzag persistence and multiparameter persistence – and their applications to different types of data, like point clouds, triangulations, or graph data. Other important topics covered include discrete Morse theory, the Mapper structure, optimal generating cycles, as well as recent advances in embedding TDA within machine learning frameworks.
Book Synopsis Topological Data Analysis for Genomics and Evolution by : Raul Rabadan
Download or read book Topological Data Analysis for Genomics and Evolution written by Raul Rabadan and published by Cambridge University Press. This book was released on 2019-12-19 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: Biology has entered the age of Big Data. A technical revolution has transformed the field, and extracting meaningful information from large biological data sets is now a central methodological challenge. Algebraic topology is a well-established branch of pure mathematics that studies qualitative descriptors of the shape of geometric objects. It aims to reduce comparisons of shape to a comparison of algebraic invariants, such as numbers, which are typically easier to work with. Topological data analysis is a rapidly developing subfield that leverages the tools of algebraic topology to provide robust multiscale analysis of data sets. This book introduces the central ideas and techniques of topological data analysis and its specific applications to biology, including the evolution of viruses, bacteria and humans, genomics of cancer, and single cell characterization of developmental processes. Bridging two disciplines, the book is for researchers and graduate students in genomics and evolutionary biology as well as mathematicians interested in applied topology.
Book Synopsis Algebraic and Geometric Topology by : R. James Milgram
Download or read book Algebraic and Geometric Topology written by R. James Milgram and published by American Mathematical Soc.. This book was released on 1978 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains sections on Structure of topological manifolds, Low dimensional manifolds, Geometry of differential manifolds and algebraic varieties, $H$-spaces, loop spaces and $CW$ complexes, Problems.
Book Synopsis Selected Applications of Geometry to Low-dimensional Topology by : Michael H. Freedman
Download or read book Selected Applications of Geometry to Low-dimensional Topology written by Michael H. Freedman and published by American Mathematical Soc.. This book was released on 1989 with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt: The inaugural volume in the popular AMS softcover series designed to make more widely available some of the outstanding lectures presented by various faculty in North America.
Download or read book Topology and Geometry written by and published by . This book was released on 1970 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geometric topology by : William Hilal Kazez
Download or read book Geometric topology written by William Hilal Kazez and published by American Mathematical Soc.. This book was released on 1996-10-22 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is Part 1 of a two-part volume reflecting the proceedings of the 1993 Georgia International Topology Conference held at the University of Georgia during the month of August. The texts include research and expository articles and problem sets. The conference covered a wide variety of topics in geometric topology. Features: Kirby's problem list, which contains a thorough description of the progress made on each of the problems and includes a very complete bibliography, makes the work useful for specialists and non-specialists who want to learn about the progress made in many areas of topology. This list may serve as a reference work for decades to come. Gabai's problem list, which focuses on foliations and laminations of 3-manifolds, collects for the first time in one paper definitions, results, and problems that may serve as a defining source in the subject area.
Book Synopsis Topology in Real-World Machine Learning and Data Analysis by : Kathryn Hess
Download or read book Topology in Real-World Machine Learning and Data Analysis written by Kathryn Hess and published by Frontiers Media SA. This book was released on 2022-11-07 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Computational Topology by : Herbert Edelsbrunner
Download or read book Computational Topology written by Herbert Edelsbrunner and published by American Mathematical Soc.. This book was released on 2010 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis New Scientific Applications of Geometry and Topology by : De Witt L. Sumners
Download or read book New Scientific Applications of Geometry and Topology written by De Witt L. Sumners and published by American Mathematical Soc.. This book was released on 1992 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometry and topology are subjects generally considered to be "pure" mathematics. Recently, however, some of the methods and results in these two areas have found new utility in both wet-lab science (biology and chemistry) and theoretical physics. Conversely, science is influencing mathematics, from posing questions that call for the construction of mathematical models to exporting theoretical methods of attack on long-standing problems of mathematical interest. Based on an AMS Short Course held in January 1992, this book contains six introductory articles on these intriguing new connections. There are articles by a chemist and a biologist about mathematics, and four articles by mathematicians writing about science and mathematics involved. Because this book communicates the excitement and utility of mathematics research at an elementary level, it is an excellent textbook in an advanced undergraduate mathematics course.
Book Synopsis Persistence Theory: From Quiver Representations to Data Analysis by : Steve Y. Oudot
Download or read book Persistence Theory: From Quiver Representations to Data Analysis written by Steve Y. Oudot and published by American Mathematical Soc.. This book was released on 2017-05-17 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: Persistence theory emerged in the early 2000s as a new theory in the area of applied and computational topology. This book provides a broad and modern view of the subject, including its algebraic, topological, and algorithmic aspects. It also elaborates on applications in data analysis. The level of detail of the exposition has been set so as to keep a survey style, while providing sufficient insights into the proofs so the reader can understand the mechanisms at work. The book is organized into three parts. The first part is dedicated to the foundations of persistence and emphasizes its connection to quiver representation theory. The second part focuses on its connection to applications through a few selected topics. The third part provides perspectives for both the theory and its applications. The book can be used as a text for a course on applied topology or data analysis.
Book Synopsis Geometric Science of Information by : Frank Nielsen
Download or read book Geometric Science of Information written by Frank Nielsen and published by Springer Nature. This book was released on 2021-07-14 with total page 929 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 5th International Conference on Geometric Science of Information, GSI 2021, held in Paris, France, in July 2021. The 98 papers presented in this volume were carefully reviewed and selected from 125 submissions. They cover all the main topics and highlights in the domain of geometric science of information, including information geometry manifolds of structured data/information and their advanced applications. The papers are organized in the following topics: Probability and statistics on Riemannian Manifolds; sub-Riemannian geometry and neuromathematics; shapes spaces; geometry of quantum states; geometric and structure preserving discretizations; information geometry in physics; Lie group machine learning; geometric and symplectic methods for hydrodynamical models; harmonic analysis on Lie groups; statistical manifold and Hessian information geometry; geometric mechanics; deformed entropy, cross-entropy, and relative entropy; transformation information geometry; statistics, information and topology; geometric deep learning; topological and geometrical structures in neurosciences; computational information geometry; manifold and optimization; divergence statistics; optimal transport and learning; and geometric structures in thermodynamics and statistical physics.
Book Synopsis Topological Geometry by : Ian R. Porteous
Download or read book Topological Geometry written by Ian R. Porteous and published by . This book was released on 1969 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Topological Data Analysis with Applications by : Gunnar Carlsson
Download or read book Topological Data Analysis with Applications written by Gunnar Carlsson and published by Cambridge University Press. This book was released on 2021-12-16 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: This timely text introduces topological data analysis from scratch, with detailed case studies.
Book Synopsis Elementary Applied Topology by : Robert W. Ghrist
Download or read book Elementary Applied Topology written by Robert W. Ghrist and published by Createspace Independent Publishing Platform. This book was released on 2014 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an introduction to the mathematics and applications comprising the new field of applied topology. The elements of this subject are surveyed in the context of applications drawn from the biological, economic, engineering, physical, and statistical sciences.
Book Synopsis Geometry and Topology by : James C. Alexander
Download or read book Geometry and Topology written by James C. Alexander and published by . This book was released on 2014-01-15 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt:
