Topological Persistence In Geometry And Analysis
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Topological Persistence In Geometry And Analysis
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Author : Leonid Polterovich
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-05-11
Topological Persistence In Geometry And Analysis written by Leonid Polterovich and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-11 with Education categories.
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.
Computational Topology For Data Analysis
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Author : Tamal Krishna Dey
language : en
Publisher: Cambridge University Press
Release Date : 2022-03-10
Computational Topology For Data Analysis written by Tamal Krishna Dey and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-10 with Computers categories.
This book provides a computational and algorithmic foundation for techniques in topological data analysis, with examples and exercises.
Geometric And Topological Inference
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Author : Jean-Daniel Boissonnat
language : en
Publisher: Cambridge University Press
Release Date : 2018-09-27
Geometric And Topological Inference written by Jean-Daniel Boissonnat and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-27 with Computers categories.
A rigorous introduction to geometric and topological inference, for anyone interested in a geometric approach to data science.
Topological Data Analysis With Applications
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Author : Gunnar Carlsson
language : en
Publisher: Cambridge University Press
Release Date : 2021-12-16
Topological Data Analysis With Applications written by Gunnar Carlsson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-16 with Computers categories.
This timely text introduces topological data analysis from scratch, with detailed case studies.
Nanoinformatics
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Author : Isao Tanaka
language : en
Publisher: Springer
Release Date : 2018-01-15
Nanoinformatics written by Isao Tanaka and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-15 with Technology & Engineering categories.
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.
Topological Methods In Data Analysis And Visualization V
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Author : Hamish Carr
language : en
Publisher: Springer Nature
Release Date : 2020-12-10
Topological Methods In Data Analysis And Visualization V written by Hamish Carr and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-10 with Mathematics categories.
This collection of peer-reviewed workshop papers provides comprehensive coverage of cutting-edge research into topological approaches to data analysis and visualization. It encompasses the full range of new algorithms and insights, including fast homology computation, comparative analysis of simplification techniques, and key applications in materials and medical science. The book also addresses core research challenges such as the representation of large and complex datasets, and integrating numerical methods with robust combinatorial algorithms. In keeping with the focus of the TopoInVis 2017 Workshop, the contributions reflect the latest advances in finding experimental solutions to open problems in the sector. They provide an essential snapshot of state-of-the-art research, helping researchers to keep abreast of the latest developments and providing a basis for future work. Gathering papers by some of the world’s leading experts on topological techniques, the book represents a valuable contribution to a field of growing importance, with applications in disciplines ranging from engineering to medicine.
Topological Methods In Data Analysis And Visualization Ii
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Author : Ronald Peikert
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-01-10
Topological Methods In Data Analysis And Visualization Ii written by Ronald Peikert and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-10 with Mathematics categories.
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.
Mathematical Principles Of Topological And Geometric Data Analysis
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Author : Parvaneh Joharinad
language : en
Publisher: Springer Nature
Release Date : 2023-07-29
Mathematical Principles Of Topological And Geometric Data Analysis written by Parvaneh Joharinad and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-29 with Mathematics categories.
This book explores and demonstrates how geometric tools can be used in data analysis. Beginning with a systematic exposition of the mathematical prerequisites, covering topics ranging from category theory to algebraic topology, Riemannian geometry, operator theory and network analysis, it goes on to describe and analyze some of the most important machine learning techniques for dimension reduction, including the different types of manifold learning and kernel methods. It also develops a new notion of curvature of generalized metric spaces, based on the notion of hyperconvexity, which can be used for the topological representation of geometric information. In recent years there has been a fascinating development: concepts and methods originally created in the context of research in pure mathematics, and in particular in geometry, have become powerful tools in machine learning for the analysis of data. The underlying reason for this is that data are typically equipped with some kind of notion of distance, quantifying the differences between data points. Of course, to be successfully applied, the geometric tools usually need to be redefined, generalized, or extended appropriately. Primarily aimed at mathematicians seeking an overview of the geometric concepts and methods that are useful for data analysis, the book will also be of interest to researchers in machine learning and data analysis who want to see a systematic mathematical foundation of the methods that they use.
Computational Topology
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Author : Herbert Edelsbrunner
language : en
Publisher: American Mathematical Society
Release Date : 2022-01-31
Computational Topology written by Herbert Edelsbrunner and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-31 with Mathematics categories.
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.
Mathematical Software Icms 2014
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Author : Hoon Hong
language : en
Publisher: Springer
Release Date : 2014-07-15
Mathematical Software Icms 2014 written by Hoon Hong and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-15 with Computers categories.
This book constitutes the proceedings of the 4th International Conference on Mathematical Software, ICMS 2014, held in Seoul, South Korea, in August 2014. The 108 papers included in this volume were carefully reviewed and selected from 150 submissions. The papers are organized in topical sections named: invited; exploration; group; coding; topology; algebraic; geometry; surfaces; reasoning; special; Groebner; triangular; parametric; interfaces and general.