Research In Computational Topology

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Research in Computational Topology

Erin Wolf Chambers,Brittany Terese Fasy,Lori Ziegelmeier
Research in Computational Topology Book PDF

Author : Erin Wolf Chambers,Brittany Terese Fasy,Lori Ziegelmeier
Publisher : Springer
Page : 0 pages
File Size : 53,9 Mb
Release : 2019-01-26
Category : Mathematics
ISBN : 3030078108

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Research in Computational Topology by Erin Wolf Chambers,Brittany Terese Fasy,Lori Ziegelmeier Pdf

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.

Research in Computational Topology

Erin Wolf Chambers,Brittany Terese Fasy,Lori Ziegelmeier
Research in Computational Topology Book PDF

Author : Erin Wolf Chambers,Brittany Terese Fasy,Lori Ziegelmeier
Publisher : Springer
Page : 202 pages
File Size : 49,7 Mb
Release : 2018-07-30
Category : Mathematics
ISBN : 9783319895932

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Research in Computational Topology by Erin Wolf Chambers,Brittany Terese Fasy,Lori Ziegelmeier Pdf

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

Herbert Edelsbrunner,John L. Harer
Computational Topology Book PDF

Author : Herbert Edelsbrunner,John L. Harer
Publisher : American Mathematical Society
Page : 241 pages
File Size : 54,9 Mb
Release : 2022-01-31
Category : Mathematics
ISBN : 9781470467692

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Computational Topology by Herbert Edelsbrunner,John L. Harer Pdf

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.

Computational Topology for Data Analysis

Tamal Krishna Dey,Yusu Wang
Computational Topology for Data Analysis Book PDF

Author : Tamal Krishna Dey,Yusu Wang
Publisher : Cambridge University Press
Page : 455 pages
File Size : 54,5 Mb
Release : 2022-03-10
Category : Computers
ISBN : 9781009098168

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Computational Topology for Data Analysis by Tamal Krishna Dey,Yusu Wang Pdf

This book provides a computational and algorithmic foundation for techniques in topological data analysis, with examples and exercises.

Computational Topology for Biomedical Image and Data Analysis

Rodrigo Rojas Moraleda,Nektarios A. Valous,Wei Xiong,Niels Halama
Computational Topology for Biomedical Image and Data Analysis Book PDF

Author : Rodrigo Rojas Moraleda,Nektarios A. Valous,Wei Xiong,Niels Halama
Publisher : CRC Press
Page : 116 pages
File Size : 44,5 Mb
Release : 2019-07-12
Category : Medical
ISBN : 9780429810992

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Computational Topology for Biomedical Image and Data Analysis by Rodrigo Rojas Moraleda,Nektarios A. Valous,Wei Xiong,Niels Halama Pdf

This book provides an accessible yet rigorous introduction to topology and homology focused on the simplicial space. It presents a compact pipeline from the foundations of topology to biomedical applications. It will be of interest to medical physicists, computer scientists, and engineers, as well as undergraduate and graduate students interested in this topic. Features: Presents a practical guide to algebraic topology as well as persistence homology Contains application examples in the field of biomedicine, including the analysis of histological images and point cloud data

A Short Course in Computational Geometry and Topology

Herbert Edelsbrunner
A Short Course in Computational Geometry and Topology Book PDF

Author : Herbert Edelsbrunner
Publisher : Springer Science & Business
Page : 110 pages
File Size : 51,8 Mb
Release : 2014-04-28
Category : Computers
ISBN : 9783319059570

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A Short Course in Computational Geometry and Topology by Herbert Edelsbrunner Pdf

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.

Research in Computational Topology 2

Ellen Gasparovic,Vanessa Robins,Katharine Turner
Research in Computational Topology 2 Book PDF

Author : Ellen Gasparovic,Vanessa Robins,Katharine Turner
Publisher : Springer Nature
Page : 304 pages
File Size : 53,9 Mb
Release : 2022-05-10
Category : Mathematics
ISBN : 9783030955199

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Research in Computational Topology 2 by Ellen Gasparovic,Vanessa Robins,Katharine Turner Pdf

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.

Topology for Computing

Afra J. Zomorodian
Topology for Computing Book PDF

Author : Afra J. Zomorodian
Publisher : Cambridge University Press
Page : 264 pages
File Size : 47,6 Mb
Release : 2005-01-10
Category : Computers
ISBN : 1139442635

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Topology for Computing by Afra J. Zomorodian Pdf

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.

Computational Geometry, Topology and Physics of Digital Images with Applications

James F. Peters
Computational Geometry Topology and Physics of Digital Images with Applications Book PDF

Author : James F. Peters
Publisher : Springer Nature
Page : 440 pages
File Size : 45,8 Mb
Release : 2019-10-03
Category : Technology & Engineering
ISBN : 9783030221928

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Computational Geometry, Topology and Physics of Digital Images with Applications by James F. Peters Pdf

This book discusses the computational geometry, topology and physics of digital images and video frame sequences. This trio of computational approaches encompasses the study of shape complexes, optical vortex nerves and proximities embedded in triangulated video frames and single images, while computational geometry focuses on the geometric structures that infuse triangulated visual scenes. The book first addresses the topology of cellular complexes to provide a basis for an introductory study of the computational topology of visual scenes, exploring the fabric, shapes and structures typically found in visual scenes. The book then examines the inherent geometry and topology of visual scenes, and the fine structure of light and light caustics of visual scenes, which bring into play catastrophe theory and the appearance of light caustic folds and cusps. Following on from this, the book introduces optical vortex nerves in triangulated digital images. In this context, computational physics is synonymous with the study of the fine structure of light choreographed in video frames. This choreography appears as a sequence of snapshots of light reflected and refracted from surface shapes, providing a solid foundation for detecting, analyzing and classifying visual scene shapes.

Open Problems in Topology II

Elliott M. Pearl
Open Problems in Topology II Book PDF

Author : Elliott M. Pearl
Publisher : Elsevier
Page : 776 pages
File Size : 55,6 Mb
Release : 2011-08-11
Category : Mathematics
ISBN : 0080475299

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Open Problems in Topology II by Elliott M. Pearl Pdf

This volume is a collection of surveys of research problems in topology and its applications. The topics covered include general topology, set-theoretic topology, continuum theory, topological algebra, dynamical systems, computational topology and functional analysis. * New surveys of research problems in topology * New perspectives on classic problems * Representative surveys of research groups from all around the world

Combinatorial Algebraic Topology

Dimitry Kozlov
Combinatorial Algebraic Topology Book PDF

Author : Dimitry Kozlov
Publisher : Springer Science & Business Media
Page : 416 pages
File Size : 45,5 Mb
Release : 2008-01-08
Category : Mathematics
ISBN : 3540730516

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Combinatorial Algebraic Topology by Dimitry Kozlov Pdf

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.

Elementary Applied Topology

Robert W. Ghrist
Elementary Applied Topology Book PDF

Author : Robert W. Ghrist
Publisher : Createspace Independent Publishing Platform
Page : 0 pages
File Size : 51,9 Mb
Release : 2014
Category : Mathematics
ISBN : 1502880857

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Elementary Applied Topology by Robert W. Ghrist Pdf

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.

Computational Topology in Image Context

Massimo Ferri,Patrizio Frosini,Claudia Landi,Andrea Cerri,Barbara Di Fabio
Computational Topology in Image Context Book PDF

Author : Massimo Ferri,Patrizio Frosini,Claudia Landi,Andrea Cerri,Barbara Di Fabio
Publisher : Springer
Page : 157 pages
File Size : 41,9 Mb
Release : 2012-06-13
Category : Computers
ISBN : 9783642302381

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Computational Topology in Image Context by Massimo Ferri,Patrizio Frosini,Claudia Landi,Andrea Cerri,Barbara Di Fabio Pdf

This book constitutes the proceedings of the 4th International Workshop on Computational Topology in Image Context, CTIC 2012, held in Bertinoro, Italy, in May 2012. The 16 papers presented in this volume were carefully reviewed and selected for inclusion in this book. They focus on the topology and computation in image context. The workshop is devoted to computational methods using topology for the analysis and comparison of images. The involved research fields comprise computational topology and geometry, discrete topology and geometry, geometrical modeling, algebraic topology for image applications, and any other field involving a geometric-topological approach to image processing.

Geometry and Topology for Mesh Generation

Herbert Edelsbrunner
Geometry and Topology for Mesh Generation Book PDF

Author : Herbert Edelsbrunner
Publisher : Cambridge University Press
Page : 206 pages
File Size : 53,6 Mb
Release : 2001-05-28
Category : Mathematics
ISBN : 0521793092

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Geometry and Topology for Mesh Generation by Herbert Edelsbrunner Pdf

This graduate text combines geometry, topology, algorithms, and engineering and emphasizes topics that are both elementary and useful.

Computational Homology

Tomasz Kaczynski,Konstantin Mischaikow,Marian Mrozek
Computational Homology Book PDF

Author : Tomasz Kaczynski,Konstantin Mischaikow,Marian Mrozek
Publisher : Springer Science & Business Media
Page : 488 pages
File Size : 49,5 Mb
Release : 2006-04-18
Category : Mathematics
ISBN : 9780387215976

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Computational Homology by Tomasz Kaczynski,Konstantin Mischaikow,Marian Mrozek Pdf

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.