Topological Persistence In Geometry And Analysis PDF Download
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Author | : Leonid Polterovich |
Publisher | : American Mathematical Soc. |
Total Pages | : 128 |
Release | : 2020-05-11 |
Genre | : Education |
ISBN | : 1470454955 |
Download Topological Persistence in Geometry and Analysis Book in PDF, ePub and Kindle
The theory of persistence modules originated in topological data analysis and became an active area of research in algebraic topology. This book provides a concise and self-contained introduction to persistence modules and focuses on their interactions with pure mathematics, bringing the reader to the cutting edge of current research. In particular, the authors present applications of persistence to symplectic topology, including the geometry of symplectomorphism groups and embedding problems. Furthermore, they discuss topological function theory, which provides new insight into oscillation of functions. The book is accessible to readers with a basic background in algebraic and differential topology.
Author | : Tamal Krishna Dey |
Publisher | : Cambridge University Press |
Total Pages | : 456 |
Release | : 2022-03-10 |
Genre | : Mathematics |
ISBN | : 1009103199 |
Download Computational Topology for Data Analysis Book in PDF, ePub and Kindle
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 | : Steve Y. Oudot |
Publisher | : American Mathematical Soc. |
Total Pages | : 218 |
Release | : 2017-05-17 |
Genre | : |
ISBN | : 1470434431 |
Download Persistence Theory: From Quiver Representations to Data Analysis Book in PDF, ePub and Kindle
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.
Author | : Jean-Daniel Boissonnat |
Publisher | : Cambridge University Press |
Total Pages | : 247 |
Release | : 2018-09-27 |
Genre | : Computers |
ISBN | : 1108419399 |
Download Geometric and Topological Inference Book in PDF, ePub and Kindle
A rigorous introduction to geometric and topological inference, for anyone interested in a geometric approach to data science.
Author | : Herbert Edelsbrunner |
Publisher | : American Mathematical Society |
Total Pages | : 241 |
Release | : 2022-01-31 |
Genre | : Mathematics |
ISBN | : 1470467690 |
Download Computational Topology Book in PDF, ePub and Kindle
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 | : Robert W. Ghrist |
Publisher | : Createspace Independent Publishing Platform |
Total Pages | : 0 |
Release | : 2014 |
Genre | : Mathematics |
ISBN | : 9781502880857 |
Download Elementary Applied Topology Book in PDF, ePub and Kindle
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.
Author | : Gunnar Carlsson |
Publisher | : Cambridge University Press |
Total Pages | : 233 |
Release | : 2021-12-16 |
Genre | : Computers |
ISBN | : 1108838650 |
Download Topological Data Analysis with Applications Book in PDF, ePub and Kindle
This timely text introduces topological data analysis from scratch, with detailed case studies.
Author | : Herbert Edelsbrunner |
Publisher | : Springer Science & Business |
Total Pages | : 105 |
Release | : 2014-04-28 |
Genre | : Computers |
ISBN | : 3319059572 |
Download A Short Course in Computational Geometry and Topology Book in PDF, ePub and Kindle
This monograph presents a short course in computational geometry and topology. In the first part the book covers Voronoi diagrams and Delaunay triangulations, then it presents the theory of alpha complexes which play a crucial role in biology. The central part of the book is the homology theory and their computation, including the theory of persistence which is indispensable for applications, e.g. shape reconstruction. The target audience comprises researchers and practitioners in mathematics, biology, neuroscience and computer science, but the book may also be beneficial to graduate students of these fields.
Author | : Isao Tanaka |
Publisher | : Springer |
Total Pages | : 298 |
Release | : 2018-01-15 |
Genre | : Technology & Engineering |
ISBN | : 9811076170 |
Download Nanoinformatics Book in PDF, ePub and Kindle
This open access book brings out the state of the art on how informatics-based tools are used and expected to be used in nanomaterials research. There has been great progress in the area in which “big-data” generated by experiments or computations are fully utilized to accelerate discovery of new materials, key factors, and design rules. Data-intensive approaches play indispensable roles in advanced materials characterization. "Materials informatics" is the central paradigm in the new trend. "Nanoinformatics" is its essential subset, which focuses on nanostructures of materials such as surfaces, interfaces, dopants, and point defects, playing a critical role in determining materials properties. There have been significant advances in experimental and computational techniques to characterize individual atoms in nanostructures and to gain quantitative information. The collaboration of researchers in materials science and information science is growing actively and is creating a new trend in materials science and engineering.
Author | : Ronald Peikert |
Publisher | : Springer Science & Business Media |
Total Pages | : 299 |
Release | : 2012-01-10 |
Genre | : Mathematics |
ISBN | : 3642231756 |
Download Topological Methods in Data Analysis and Visualization II Book in PDF, ePub and Kindle
When scientists analyze datasets in a search for underlying phenomena, patterns or causal factors, their first step is often an automatic or semi-automatic search for structures in the data. Of these feature-extraction methods, topological ones stand out due to their solid mathematical foundation. Topologically defined structures—as found in scalar, vector and tensor fields—have proven their merit in a wide range of scientific domains, and scientists have found them to be revealing in subjects such as physics, engineering, and medicine. Full of state-of-the-art research and contemporary hot topics in the subject, this volume is a selection of peer-reviewed papers originally presented at the fourth Workshop on Topology-Based Methods in Data Analysis and Visualization, TopoInVis 2011, held in Zurich, Switzerland. The workshop brought together many of the leading lights in the field for a mixture of formal presentations and discussion. One topic currently generating a great deal of interest, and explored in several chapters here, is the search for topological structures in time-dependent flows, and their relationship with Lagrangian coherent structures. Contributors also focus on discrete topologies of scalar and vector fields, and on persistence-based simplification, among other issues of note. The new research results included in this volume relate to all three key areas in data analysis—theory, algorithms and applications.