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Author : Tamal Krishna Dey,Yusu Wang
Publisher : Cambridge University Press
Page : 455 pages
File Size : 42,5 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 : Gunnar Carlsson,Mikael Vejdemo-Johansson
Publisher : Cambridge University Press
Page : 233 pages
File Size : 40,5 Mb
Release : 2021-12-16
Category : Computers
ISBN : 9781108838658
This timely text introduces topological data analysis from scratch, with detailed case studies.
Author : Raul Rabadan,Andrew J. Blumberg
Publisher : Cambridge University Press
Page : 522 pages
File Size : 51,9 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 : Julien Tierny
Publisher : Springer
Page : 150 pages
File Size : 45,7 Mb
Release : 2018-01-16
Category : Mathematics
ISBN : 9783319715070
Combining theoretical and practical aspects of topology, this book provides a comprehensive and self-contained introduction to topological methods for the analysis and visualization of scientific data. Theoretical concepts are presented in a painstaking but intuitive manner, with numerous high-quality color illustrations. Key algorithms for the computation and simplification of topological data representations are described in detail, and their application is carefully demonstrated in a chapter dedicated to concrete use cases. With its fine balance between theory and practice, "Topological Data Analysis for Scientific Visualization" constitutes an appealing introduction to the increasingly important topic of topological data analysis for lecturers, students and researchers.
Author : Nils A. Baas,Gunnar E. Carlsson,Gereon Quick,Markus Szymik,Marius Thaule
Publisher : Springer Nature
Page : 522 pages
File Size : 53,7 Mb
Release : 2020-06-25
Category : Mathematics
ISBN : 9783030434083
This book gathers the proceedings of the 2018 Abel Symposium, which was held in Geiranger, Norway, on June 4-8, 2018. The symposium offered an overview of the emerging field of "Topological Data Analysis". This volume presents papers on various research directions, notably including applications in neuroscience, materials science, cancer biology, and immune response. Providing an essential snapshot of the status quo, it represents a valuable asset for practitioners and those considering entering the field.
Author : Valerio Pascucci,Xavier Tricoche,Hans Hagen,Julien Tierny
Publisher : Springer Science & Business Media
Page : 265 pages
File Size : 47,9 Mb
Release : 2010-11-23
Category : Mathematics
ISBN : 9783642150142
Topology-based methods are of increasing importance in the analysis and visualization of datasets from a wide variety of scientific domains such as biology, physics, engineering, and medicine. Current challenges of topology-based techniques include the management of time-dependent data, the representation of large and complex datasets, the characterization of noise and uncertainty, the effective integration of numerical methods with robust combinatorial algorithms, etc. . The editors have brought together the most prominent and best recognized researchers in the field of topology-based data analysis and visualization for a joint discussion and scientific exchange of the latest results in the field. This book contains the best 20 peer-reviewed papers resulting from the discussions and presentations at the third workshop on "Topological Methods in Data Analysis and Visualization", held 2009 in Snowbird, Utah, US. The 2009 "TopoInVis" workshop follows the two successful workshops in 2005 (Slovakia) and 2007 (Germany).
Author : Steve Y. Oudot
Publisher : American Mathematical Soc.
Page : 218 pages
File Size : 49,8 Mb
Release : 2017-05-17
Category : Electronic
ISBN : 9781470434434
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 : Leonid Polterovich,Daniel Rosen,Karina Samvelyan,Jun Zhang
Publisher : American Mathematical Soc.
Page : 128 pages
File Size : 44,6 Mb
Release : 2020-05-11
Category : Education
ISBN : 9781470454951
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 : Hamish Carr,Christoph Garth,Tino Weinkauf
Publisher : Springer
Page : 363 pages
File Size : 50,7 Mb
Release : 2017-06-01
Category : Mathematics
ISBN : 9783319446844
This book presents contributions on topics ranging from novel applications of topological analysis for particular problems, through studies of the effectiveness of modern topological methods, algorithmic improvements on existing methods, and parallel computation of topological structures, all the way to mathematical topologies not previously applied to data analysis. Topological methods are broadly recognized as valuable tools for analyzing the ever-increasing flood of data generated by simulation or acquisition. This is particularly the case in scientific visualization, where the data sets have long since surpassed the ability of the human mind to absorb every single byte of data. The biannual TopoInVis workshop has supported researchers in this area for a decade, and continues to serve as a vital forum for the presentation and discussion of novel results in applications in the area, creating a platform to disseminate knowledge about such implementations throughout and beyond the community. The present volume, resulting from the 2015 TopoInVis workshop held in Annweiler, Germany, will appeal to researchers in the fields of scientific visualization and mathematics, domain scientists with an interest in advanced visualization methods, and developers of visualization software systems.
Author : Jean-Daniel Boissonnat,Frédéric Chazal,Mariette Yvinec
Publisher : Cambridge University Press
Page : 247 pages
File Size : 49,7 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 : Peer-Timo Bremer,Ingrid Hotz,Valerio Pascucci,Ronald Peikert
Publisher : Springer Science & Business
Page : 279 pages
File Size : 42,6 Mb
Release : 2014-04-22
Category : Mathematics
ISBN : 9783319040998
This collection of peer-reviewed conference papers provides comprehensive coverage of cutting-edge research in 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 volume also features material on core research challenges such as the representation of large and complex datasets and integrating numerical methods with robust combinatorial algorithms. Reflecting the focus of the TopoInVis 2013 conference, the contributions evince the progress currently being made on finding experimental solutions to open problems in the sector. They provide an inclusive snapshot of state-of-the-art research that enables researchers to keep abreast of the latest developments and provides a foundation for future progress. With papers by some of the world’s leading experts in topological techniques, this volume is a major contribution to the literature in a field of growing importance with applications in disciplines that range from engineering to medicine.
Author : Robert W. Ghrist
Publisher : Createspace Independent Publishing Platform
Page : 0 pages
File Size : 51,5 Mb
Release : 2014
Category : Mathematics
ISBN : 1502880857
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 : Robert L. Devaney,Kit C. Chan,P.B. Vinod Kumar
Publisher : Springer Nature
Page : 278 pages
File Size : 55,6 Mb
Release : 2021-09-23
Category : Mathematics
ISBN : 9789811601743
This book collects select papers presented at the International Workshop and Conference on Topology & Applications, held in Kochi, India, from 9–11 December 2018. The book discusses topics on topological dynamical systems and topological data analysis. Topics are ranging from general topology, algebraic topology, differential topology, fuzzy topology, topological dynamical systems, topological groups, linear dynamics, dynamics of operator network topology, iterated function systems and applications of topology. All contributing authors are eminent academicians, scientists, researchers and scholars in their respective fields, hailing from around the world. The book is a valuable resource for researchers, scientists and engineers from both academia and industry.
Author : Afra J. Zomorodian
Publisher : Cambridge University Press
Page : 264 pages
File Size : 42,6 Mb
Release : 2005-01-10
Category : Computers
ISBN : 1139442635
The emerging field of computational topology utilizes theory from topology and the power of computing to solve problems in diverse fields. Recent applications include computer graphics, computer-aided design (CAD), and structural biology, all of which involve understanding the intrinsic shape of some real or abstract space. A primary goal of this book is to present basic concepts from topology and Morse theory to enable a non-specialist to grasp and participate in current research in computational topology. The author gives a self-contained presentation of the mathematical concepts from a computer scientist's point of view, combining point set topology, algebraic topology, group theory, differential manifolds, and Morse theory. He also presents some recent advances in the area, including topological persistence and hierarchical Morse complexes. Throughout, the focus is on computational challenges and on presenting algorithms and data structures when appropriate.
Author : Ingrid Hotz,Talha Bin Masood,Filip Sadlo,Julien Tierny
Publisher : Springer Nature
Page : 372 pages
File Size : 50,5 Mb
Release : 2021-09-28
Category : Mathematics
ISBN : 9783030835002
This book is a result of a workshop, the 8th of the successful TopoInVis workshop series, held in 2019 in Nyköping, Sweden. The workshop regularly gathers some of the world’s leading experts in this field. Thereby, it provides a forum for discussions on the latest advances in the field with a focus on finding practical solutions to open problems in topological data analysis for visualization. The contributions provide introductory and novel research articles including new concepts for the analysis of multivariate and time-dependent data, robust computational approaches for the extraction and approximations of topological structures with theoretical guarantees, and applications of topological scalar and vector field analysis for visualization. The applications span a wide range of scientific areas comprising climate science, material sciences, fluid dynamics, and astronomy. In addition, community efforts with respect to joint software development are reported and discussed.