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| Author | : Jean-Daniel Boissonnat |
| Publisher | : Cambridge University Press |
| Total Pages | : 247 |
| Release | : 2018-09-27 |
| Genre | : Computers |
| ISBN | : 1108419399 |
A rigorous introduction to geometric and topological inference, for anyone interested in a geometric approach to data science.
| Author | : Robert Adler |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 135 |
| Release | : 2011-05-18 |
| Genre | : Mathematics |
| ISBN | : 3642195792 |
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 | : Tamal Krishna Dey |
| Publisher | : Cambridge University Press |
| Total Pages | : 456 |
| Release | : 2022-03-10 |
| Genre | : Mathematics |
| ISBN | : 1009103199 |
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.
| Author | : R. James Milgram |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 330 |
| Release | : 1978 |
| Genre | : Mathematics |
| ISBN | : 0821814338 |
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.
| Author | : Michael H. Freedman |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 93 |
| Release | : 1990 |
| Genre | : Mathematics |
| ISBN | : 0821870009 |
Based on lectures presented at Pennsylvania State University in February 1987, this work begins with the notions of manifold and smooth structures and the Gauss-Bonnet theorem, and proceeds to the topology and geometry of foliated 3-manifolds. It also explains why four-dimensional space has special attributes.
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| Publisher | : |
| Total Pages | : |
| Release | : 1970 |
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| ISBN | : |
| Author | : Raul Rabadan |
| Publisher | : Cambridge University Press |
| Total Pages | : 522 |
| Release | : 2019-12-19 |
| Genre | : Science |
| ISBN | : 1108757499 |
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.
| Author | : William Hilal Kazez |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 622 |
| Release | : 1996-10-22 |
| Genre | : Mathematics |
| ISBN | : 9780821806548 |
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.
| Author | : Kathryn Hess |
| Publisher | : Frontiers Media SA |
| Total Pages | : 229 |
| Release | : 2022-11-07 |
| Genre | : Science |
| ISBN | : 2832504124 |
| Author | : De Witt L. Sumners |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 266 |
| Release | : 1992 |
| Genre | : Mathematics |
| ISBN | : 9780821855027 |
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.
