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Author: Jean-Daniel Boissonnat
Publisher: Cambridge University Press
Published: 2018-09-27
Total Pages: 247
ISBN-13: 1108419399
DOWNLOAD EBOOKA rigorous introduction to geometric and topological inference, for anyone interested in a geometric approach to data science.
Author: Tamal Krishna Dey
Publisher: Cambridge University Press
Published: 2022-03-10
Total Pages: 456
ISBN-13: 1009103199
DOWNLOAD EBOOKTopological 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: Raúl Rabadán
Publisher: Cambridge University Press
Published: 2019-10-31
Total Pages: 521
ISBN-13: 1108753396
DOWNLOAD EBOOKBiology has entered the age of Big Data. The 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 questions to a comparison of algebraic invariants, such as numbers, which are typically easier to solve. 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 alongside mathematicians interested in applied topology.
Author: Gunnar Carlsson
Publisher: Cambridge University Press
Published: 2021-12-16
Total Pages: 233
ISBN-13: 1108838650
DOWNLOAD EBOOKThis timely text introduces topological data analysis from scratch, with detailed case studies.
Author: Frank Nielsen
Publisher: Springer Nature
Published: 2021-07-14
Total Pages: 929
ISBN-13: 3030802094
DOWNLOAD EBOOKThis 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.
Author: Steve Y. Oudot
Publisher: American Mathematical Soc.
Published: 2017-05-17
Total Pages: 229
ISBN-13: 1470434431
DOWNLOAD EBOOKPersistence 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.
Author: Robert W. Ghrist
Publisher: Createspace Independent Publishing Platform
Published: 2014
Total Pages: 0
ISBN-13: 9781502880857
DOWNLOAD EBOOKThis 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.
Author: Steven G. Krantz
Publisher: Springer Science & Business Media
Published: 2008-12-15
Total Pages: 344
ISBN-13: 0817646795
DOWNLOAD EBOOKThis textbook introduces geometric measure theory through the notion of currents. Currents, continuous linear functionals on spaces of differential forms, are a natural language in which to formulate types of extremal problems arising in geometry, and can be used to study generalized versions of the Plateau problem and related questions in geometric analysis. Motivating key ideas with examples and figures, this book is a comprehensive introduction ideal for both self-study and for use in the classroom. The exposition demands minimal background, is self-contained and accessible, and thus is ideal for both graduate students and researchers.
Author: Cornelius Evers
Publisher:
Published: 1926
Total Pages: 38
ISBN-13:
DOWNLOAD EBOOKAuthor: Herbert Edelsbrunner
Publisher: American Mathematical Soc.
Published: 2010
Total Pages: 256
ISBN-13: 0821849255
DOWNLOAD EBOOKCombining 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.
