Research In Computational Topology
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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.
Research In Computational Topology
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Author : Erin Wolf Chambers
language : en
Publisher: Springer
Release Date : 2018-07-30
Research In Computational Topology written by Erin Wolf Chambers and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-30 with Mathematics categories.
Based on the first Workshop for Women in Computational Topology that took place in 2016, this volume assembles new research and applications in computational topology. Featured articles range over the breadth of the discipline, including topics such as surface reconstruction, topological data analysis, persistent homology, algorithms, and surface-embedded graphs. Applications in graphics, medical imaging, and GIS are discussed throughout the book. Four of the papers in this volume are the product of working groups that were established and developed during the workshop. Additional papers were also solicited from the broader Women in Computational Topology network. The volume is accessible to a broad range of researchers, both within the field of computational topology and in related disciplines such as statistics, computational biology, and machine learning.
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.
Research In Computational Topology 2
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Author : Ellen Gasparovic
language : en
Publisher: Springer Nature
Release Date : 2022-05-10
Research In Computational Topology 2 written by Ellen Gasparovic and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-10 with Mathematics categories.
This second volume of Research in Computational Topology is a celebration and promotion of research by women in applied and computational topology, containing the proceedings of the second workshop for Women in Computational Topology (WinCompTop) as well as papers solicited from the broader WinCompTop community. The multidisciplinary and international WinCompTop workshop provided an exciting and unique opportunity for women in diverse locations and research specializations to interact extensively and collectively contribute to new and active research directions in the field. The prestigious senior researchers that signed on to head projects at the workshop are global leaders in the discipline, and two of them were authors on some of the first papers in the field. Some of the featured topics include topological data analysis of power law structure in neural data; a nerve theorem for directional graph covers; topological or homotopical invariants for directed graphs encoding connections among a network of neurons; and the issue of approximation of objects by digital grids, including precise relations between the persistent homology of dual cubical complexes.
A Short Course In Computational Geometry And Topology
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Author : Herbert Edelsbrunner
language : en
Publisher: Springer Science & Business
Release Date : 2014-04-28
A Short Course In Computational Geometry And Topology written by Herbert Edelsbrunner and has been published by Springer Science & Business this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-28 with Computers categories.
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.
Computational Homology
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Author : Tomasz Kaczynski
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-18
Computational Homology written by Tomasz Kaczynski 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 2006-04-18 with Mathematics categories.
Homology is a powerful tool used by mathematicians to study the properties of spaces and maps that are insensitive to small perturbations. This book uses a computer to develop a combinatorial computational approach to the subject. The core of the book deals with homology theory and its computation. Following this is a section containing extensions to further developments in algebraic topology, applications to computational dynamics, and applications to image processing. Included are exercises and software that can be used to compute homology groups and maps. The book will appeal to researchers and graduate students in mathematics, computer science, engineering, and nonlinear dynamics.
Combinatorial Algebraic Topology
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Author : Dimitry Kozlov
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-24
Combinatorial Algebraic Topology written by Dimitry Kozlov 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 2007-10-24 with Mathematics categories.
This volume is the first comprehensive treatment of combinatorial algebraic topology in book form. The first part of the book constitutes a swift walk through the main tools of algebraic topology. Readers - graduate students and working mathematicians alike - will probably find particularly useful the second part, which contains an in-depth discussion of the major research techniques of combinatorial algebraic topology. Although applications are sprinkled throughout the second part, they are principal focus of the third part, which is entirely devoted to developing the topological structure theory for graph homomorphisms.
Topology For Computing
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Author : Afra J. Zomorodian
language : en
Publisher: Cambridge University Press
Release Date : 2005-01-10
Topology For Computing written by Afra J. Zomorodian 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 2005-01-10 with Computers categories.
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.
Introduction To Topological Quantum Computation
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Author : Jiannis K. Pachos
language : en
Publisher: Cambridge University Press
Release Date : 2012-04-12
Introduction To Topological Quantum Computation written by Jiannis K. Pachos 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 2012-04-12 with Computers categories.
Ideal for graduate students and researchers from various sub-disciplines, this book provides an excellent introduction to topological quantum computation.
Geometry And Topology For Mesh Generation
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Author : Herbert Edelsbrunner
language : en
Publisher: Cambridge University Press
Release Date : 2001-05-28
Geometry And Topology For Mesh Generation written by Herbert Edelsbrunner 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 2001-05-28 with Computers categories.
The book combines topics in mathematics (geometry and topology), computer science (algorithms), and engineering (mesh generation). The original motivation for these topics was the difficulty faced (both conceptually and in the technical execution) in any attempt to combine elements of combinatorial and of numerical algorithms. Mesh generation is a topic where a meaningful combination of these different approaches to problem solving is inevitable. The book develops methods from both areas that are amenable to combination, and explains recent breakthrough solutions to meshing that fit into this category.The book should be an ideal graduate text for courses on mesh generation. The specific material is selected giving preference to topics that are elementary, attractive, lend themselves to teaching, useful, and interesting.