Research In Computational Topology 2

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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 : 43,7 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.

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 : 51,5 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 : 49,9 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.

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 : 47,7 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.

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 : 47,9 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.

Open Problems in Topology II

Elliott Pearl
Open Problems in Topology II Book PDF

Author : Elliott Pearl
Publisher : Elsevier Science Limited
Page : 763 pages
File Size : 44,7 Mb
Release : 2007
Category : Mathematics
ISBN : 0444522085

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Open Problems in Topology II by Elliott 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

Topology for Computing

Afra J. Zomorodian
Topology for Computing Book PDF

Author : Afra J. Zomorodian
Publisher : Cambridge University Press
Page : 264 pages
File Size : 45,7 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 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 : 42,5 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 : 105 pages
File Size : 46,9 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.

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 : 44,9 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

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 : 45,5 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.

Computational Topology in Image Context

Alexandra Bac,Jean-Luc Mari
Computational Topology in Image Context Book PDF

Author : Alexandra Bac,Jean-Luc Mari
Publisher : Springer
Page : 303 pages
File Size : 44,5 Mb
Release : 2016-06-01
Category : Computers
ISBN : 9783319394411

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Computational Topology in Image Context by Alexandra Bac,Jean-Luc Mari Pdf

This book constitutes the proceedings of the 6th International Workshop on Computational Topology in Image Context, CTIC 2016, held in Marseille, France, in June 2016. The 24 papers presented in this volume were carefully reviewed and selected from 35 submissions. Additionally, this volume contains 2 invited papers. CTIC covers a wide range of topics such as: topological invariants and their computation, homology, cohomology, linking number, fundamental groups; algorithm optimization in discrete geometry, transfer of mathematical tools, parallel computation in multi-dimensional volume context, hierarchical approaches; experimental evaluation of algorithms and heuristics; combinatorial or multi-resolution models; discrete or computational topology; geometric modeling guided by topological constraints; computational topological dynamics; and use of topological information in discrete geometry applications.

Advances in Applied and Computational Topology

American Mathematical Society. Short Course on Computational Topology
Advances in Applied and Computational Topology Book PDF

Author : American Mathematical Society. Short Course on Computational Topology
Publisher : American Mathematical Soc.
Page : 250 pages
File Size : 55,6 Mb
Release : 2012-07-05
Category : Mathematics
ISBN : 9780821853276

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Advances in Applied and Computational Topology by American Mathematical Society. Short Course on Computational Topology Pdf

What is the shape of data? How do we describe flows? Can we count by integrating? How do we plan with uncertainty? What is the most compact representation? These questions, while unrelated, become similar when recast into a computational setting. Our input is a set of finite, discrete, noisy samples that describes an abstract space. Our goal is to compute qualitative features of the unknown space. It turns out that topology is sufficiently tolerant to provide us with robust tools. This volume is based on lectures delivered at the 2011 AMS Short Course on Computational Topology, held January 4-5, 2011 in New Orleans, Louisiana. The aim of the volume is to provide a broad introduction to recent techniques from applied and computational topology. Afra Zomorodian focuses on topological data analysis via efficient construction of combinatorial structures and recent theories of persistence. Marian Mrozek analyzes asymptotic behavior of dynamical systems via efficient computation of cubical homology. Justin Curry, Robert Ghrist, and Michael Robinson present Euler Calculus, an integral calculus based on the Euler characteristic, and apply it to sensor and network data aggregation. Michael Erdmann explores the relationship of topology, planning, and probability with the strategy complex. Jeff Erickson surveys algorithms and hardness results for topological optimization problems.

Mathematics in Cyber Research

Paul L. Goethals,Natalie M. Scala,Daniel T. Bennett
Mathematics in Cyber Research Book PDF

Author : Paul L. Goethals,Natalie M. Scala,Daniel T. Bennett
Publisher : CRC Press
Page : 512 pages
File Size : 51,6 Mb
Release : 2022-02-07
Category : Business & Economics
ISBN : 9781000542714

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Mathematics in Cyber Research by Paul L. Goethals,Natalie M. Scala,Daniel T. Bennett Pdf

In the last decade, both scholars and practitioners have sought novel ways to address the problem of cybersecurity. Innovative outcomes have included applications such as blockchain as well as creative methods for cyber forensics, software development, and intrusion prevention. Accompanying these technological advancements, discussion on cyber matters at national and international levels has focused primarily on the topics of law, policy, and strategy. The objective of these efforts is typically to promote security by establishing agreements among stakeholders on regulatory activities. Varying levels of investment in cyberspace, however, comes with varying levels of risk; in some ways, this can translate directly to the degree of emphasis for pushing substantial change. At the very foundation or root of cyberspace systems and processes are tenets and rules governed by principles in mathematics. Topics such as encrypting or decrypting file transmissions, modeling networks, performing data analysis, quantifying uncertainty, measuring risk, and weighing decisions or adversarial courses of action represent a very small subset of activities highlighted by mathematics. To facilitate education and a greater awareness of the role of mathematics in cyber systems and processes, a description of research in this area is needed. Mathematics in Cyber Research aims to familiarize educators and young researchers with the breadth of mathematics in cyber-related research. Each chapter introduces a mathematical sub-field, describes relevant work in this field associated with the cyber domain, provides methods and tools, as well as details cyber research examples or case studies. Features One of the only books to bring together such a diverse and comprehensive range of topics within mathematics and apply them to cyber research. Suitable for college undergraduate students or educators that are either interested in learning about cyber-related mathematics or intend to perform research within the cyber domain. The book may also appeal to practitioners within the commercial or government industry sectors. Most national and international venues for collaboration and discussion on cyber matters have focused primarily on the topics of law, policy, strategy, and technology. This book is among the first to address the underpinning mathematics.

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 : 166 pages
File Size : 49,7 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.