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Author : Jean-Daniel Boissonnat,Frédéric Chazal,Mariette Yvinec
Publisher : Cambridge University Press
Page : 247 pages
File Size : 44,6 Mb
Release : 2018-09-27
Category : Computers
ISBN : 9781108419390
A rigorous introduction to geometric and topological inference, for anyone interested in a geometric approach to data science.
Author : Robert Adler,Jonathan E. Taylor
Publisher : Springer Science & Business Media
Page : 135 pages
File Size : 54,5 Mb
Release : 2011-05-18
Category : Mathematics
ISBN : 9783642195792
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 : R. James Milgram
Publisher : American Mathematical Soc.
Page : 412 pages
File Size : 51,7 Mb
Release : 1978
Category : Mathematics
ISBN : 9780821814321
Contains sections on Algebraic $K$- and $L$-theory, Surgery and its applications, Group actions.
Author : Tamal Krishna Dey,Yusu Wang
Publisher : Cambridge University Press
Page : 455 pages
File Size : 51,8 Mb
Release : 2022-03-10
Category : Computers
ISBN : 9781009098168
This book provides a computational and algorithmic foundation for techniques in topological data analysis, with examples and exercises.
Author : Robert Adler,Jonathan E. Taylor
Publisher : Springer
Page : 122 pages
File Size : 51,7 Mb
Release : 2011-06-02
Category : Mathematics
ISBN : 3642195814
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 : Kathryn Hess,Frédéric Chazal,Umberto Lupo
Publisher : Frontiers Media SA
Page : 229 pages
File Size : 52,8 Mb
Release : 2022-11-07
Category : Science
ISBN : 9782832504123
Author : S. Buoncristiano,Colin Patrick Rourke,Brian Joseph Sanderson
Publisher : Cambridge University Press
Page : 157 pages
File Size : 45,6 Mb
Release : 1976-04
Category : Mathematics
ISBN : 9780521209403
The purpose of these notes is to give a geometrical treatment of generalized homology and cohomology theories. The central idea is that of a 'mock bundle', which is the geometric cocycle of a general cobordism theory, and the main new result is that any homology theory is a generalized bordism theory. The book will interest mathematicians working in both piecewise linear and algebraic topology especially homology theory as it reaches the frontiers of current research in the topic. The book is also suitable for use as a graduate course in homology theory.
Author : Yaiza Canzani,Linan Chen,Dmitry Jakobson
Publisher : American Mathematical Soc.
Page : 197 pages
File Size : 44,8 Mb
Release : 2019-11-20
Category : Education
ISBN : 9781470441456
This volume contains the proceedings of the CRM Workshops on Probabilistic Methods in Spectral Geometry and PDE, held from August 22–26, 2016 and Probabilistic Methods in Topology, held from November 14–18, 2016 at the Centre de Recherches Mathématiques, Université de Montréal, Montréal, Quebec, Canada. Probabilistic methods have played an increasingly important role in many areas of mathematics, from the study of random groups and random simplicial complexes in topology, to the theory of random Schrödinger operators in mathematical physics. The workshop on Probabilistic Methods in Spectral Geometry and PDE brought together some of the leading researchers in quantum chaos, semi-classical theory, ergodic theory and dynamical systems, partial differential equations, probability, random matrix theory, mathematical physics, conformal field theory, and random graph theory. Its emphasis was on the use of ideas and methods from probability in different areas, such as quantum chaos (study of spectra and eigenstates of chaotic systems at high energy); geometry of random metrics and related problems in quantum gravity; solutions of partial differential equations with random initial conditions. The workshop Probabilistic Methods in Topology brought together researchers working on random simplicial complexes and geometry of spaces of triangulations (with connections to manifold learning); topological statistics, and geometric probability; theory of random groups and their properties; random knots; and other problems. This volume covers recent developments in several active research areas at the interface of Probability, Semiclassical Analysis, Mathematical Physics, Theory of Automorphic Forms and Graph Theory.
Author : Frank Nielsen,Frédéric Barbaresco
Publisher : Springer
Page : 879 pages
File Size : 40,9 Mb
Release : 2013-08-19
Category : Computers
ISBN : 9783642400209
This book constitutes the refereed proceedings of the First International Conference on Geometric Science of Information, GSI 2013, held in Paris, France, in August 2013. The nearly 100 papers presented were carefully reviewed and selected from numerous submissions and are organized into the following thematic sessions: Geometric Statistics on Manifolds and Lie Groups, Deformations in Shape Spaces, Differential Geometry in Signal Processing, Relational Metric, Discrete Metric Spaces, Computational Information Geometry, Hessian Information Geometry I and II, Computational Aspects of Information Geometry in Statistics, Optimization on Matrix Manifolds, Optimal Transport Theory, Probability on Manifolds, Divergence Geometry and Ancillarity, Entropic Geometry, Tensor-Valued Mathematical Morphology, Machine/Manifold/Topology Learning, Geometry of Audio Processing, Geometry of Inverse Problems, Algebraic/Infinite dimensional/Banach Information Manifolds, Information Geometry Manifolds, and Algorithms on Manifolds.
Author : Michael H. Freedman,Feng Luo
Publisher : American Mathematical Soc.
Page : 79 pages
File Size : 51,9 Mb
Release : 1989
Category : Mathematics
ISBN : 9780821870006
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.
Author : Herbert Edelsbrunner,John Harer
Publisher : American Mathematical Soc.
Page : 241 pages
File Size : 48,6 Mb
Release : 2010
Category : Mathematics
ISBN : 9780821849255
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 : De Witt L. Sumners,Nicholas R. Cozzarelli
Publisher : American Mathematical Soc.
Page : 266 pages
File Size : 48,7 Mb
Release : 1992
Category : Mathematics
ISBN : 0821855026
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.
Author : Raul Rabadan,Andrew J. Blumberg
Publisher : Cambridge University Press
Page : 522 pages
File Size : 54,6 Mb
Release : 2019-12-19
Category : Science
ISBN : 9781108757492
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 : Ramin Madarshahian,François Hemez
Publisher : Springer Nature
Page : 185 pages
File Size : 45,6 Mb
Release : 2023-12-07
Category : Computers
ISBN : 9783031349461
Data Science in Engineering, Volume 10: Proceedings of the 41st IMAC, A Conference and Exposition on Structural Dynamics, 2023, the tenth volume of ten from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Data Science in Engineering, including papers on: Novel Data-driven Analysis Methods Deep Learning Gaussian Process Analysis Real-time Video-based Analysis Applications to Nonlinear Dynamics and Damage Detection High-rate Structural Monitoring and Prognostics
Author : Piervincenzo Rizzo,Alberto Milazzo
Publisher : Springer Nature
Page : 1129 pages
File Size : 53,6 Mb
Release : 2022-06-15
Category : Technology & Engineering
ISBN : 9783031072581
This volume gathers the latest advances, innovations, and applications in the field of structural health monitoring (SHM) and more broadly in the fields of smart materials and intelligent systems, as presented by leading international researchers and engineers at the 10th European Workshop on Structural Health Monitoring (EWSHM), held in Palermo, Italy on July 4-7, 2022. The volume covers highly diverse topics, including signal processing, smart sensors, autonomous systems, remote sensing and support, UAV platforms for SHM, Internet of Things, Industry 4.0, and SHM for civil structures and infrastructures. The contributions, which are published after a rigorous international peer-review process, highlight numerous exciting ideas that will spur novel research directions and foster multidisciplinary collaboration among different specialists.