Advances In Applied And Computational Topology

Author : American Mathematical Society. Short Course on Computational Topology
Publisher : American Mathematical Soc.
Page : 250 pages
File Size : 43,9 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.

Author : Herbert Edelsbrunner,John L. Harer
Publisher : American Mathematical Society
Page : 241 pages
File Size : 48,6 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.

Author : James F. Peters
Publisher : Springer Nature
Page : 440 pages
File Size : 48,6 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.

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.

Author : Ali Emrouznejad
Publisher : Springer
Page : 487 pages
File Size : 47,9 Mb
Release : 2016-05-26
Category : Technology & Engineering
ISBN : 9783319302652

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Big Data Optimization: Recent Developments and Challenges by Ali Emrouznejad Pdf

The main objective of this book is to provide the necessary background to work with big data by introducing some novel optimization algorithms and codes capable of working in the big data setting as well as introducing some applications in big data optimization for both academics and practitioners interested, and to benefit society, industry, academia, and government. Presenting applications in a variety of industries, this book will be useful for the researchers aiming to analyses large scale data. Several optimization algorithms for big data including convergent parallel algorithms, limited memory bundle algorithm, diagonal bundle method, convergent parallel algorithms, network analytics, and many more have been explored in this book.

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.

Author : Herbert Edelsbrunner
Publisher : Unknown
Page : 241 pages
File Size : 47,7 Mb
Release : 2010
Category : Algorithms
ISBN : 147041208X

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Computational Topology by Herbert Edelsbrunner 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 alg.

Author : Samuel Kounev,Jeffrey O. Kephart,Aleksandar Milenkoski,Xiaoyun Zhu
Publisher : Springer
Page : 722 pages
File Size : 55,8 Mb
Release : 2017-01-23
Category : Computers
ISBN : 9783319474748

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Self-Aware Computing Systems by Samuel Kounev,Jeffrey O. Kephart,Aleksandar Milenkoski,Xiaoyun Zhu Pdf

This book provides formal and informal definitions and taxonomies for self-aware computing systems, and explains how self-aware computing relates to many existing subfields of computer science, especially software engineering. It describes architectures and algorithms for self-aware systems as well as the benefits and pitfalls of self-awareness, and reviews much of the latest relevant research across a wide array of disciplines, including open research challenges. The chapters of this book are organized into five parts: Introduction, System Architectures, Methods and Algorithms, Applications and Case Studies, and Outlook. Part I offers an introduction that defines self-aware computing systems from multiple perspectives, and establishes a formal definition, a taxonomy and a set of reference scenarios that help to unify the remaining chapters. Next, Part II explores architectures for self-aware computing systems, such as generic concepts and notations that allow a wide range of self-aware system architectures to be described and compared with both isolated and interacting systems. It also reviews the current state of reference architectures, architectural frameworks, and languages for self-aware systems. Part III focuses on methods and algorithms for self-aware computing systems by addressing issues pertaining to system design, like modeling, synthesis and verification. It also examines topics such as adaptation, benchmarks and metrics. Part IV then presents applications and case studies in various domains including cloud computing, data centers, cyber-physical systems, and the degree to which self-aware computing approaches have been adopted within those domains. Lastly, Part V surveys open challenges and future research directions for self-aware computing systems. It can be used as a handbook for professionals and researchers working in areas related to self-aware computing, and can also serve as an advanced textbook for lecturers and postgraduate students studying subjects like advanced software engineering, autonomic computing, self-adaptive systems, and data-center resource management. Each chapter is largely self-contained, and offers plenty of references for anyone wishing to pursue the topic more deeply.

Author : Ryuei Nishii,Shin-ichiro Ei,Miyuki Koiso,Hiroyuki Ochiai,Kanzo Okada,Shingo Saito,Tomoyuki Shirai
Publisher : Springer
Page : 497 pages
File Size : 55,9 Mb
Release : 2014-07-14
Category : Technology & Engineering
ISBN : 9784431550600

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A Mathematical Approach to Research Problems of Science and Technology by Ryuei Nishii,Shin-ichiro Ei,Miyuki Koiso,Hiroyuki Ochiai,Kanzo Okada,Shingo Saito,Tomoyuki Shirai Pdf

This book deals with one of the most novel advances in mathematical modeling for applied scientific technology, including computer graphics, public-key encryption, data visualization, statistical data analysis, symbolic calculation, encryption, error correcting codes, and risk management. It also shows that mathematics can be used to solve problems from nature, e.g., slime mold algorithms. One of the unique features of this book is that it shows readers how to use pure and applied mathematics, especially those mathematical theory/techniques developed in the twentieth century, and developing now, to solve applied problems in several fields of industry. Each chapter includes clues on how to use "mathematics" to solve concrete problems faced in industry as well as practical applications. The target audience is not limited to researchers working in applied mathematics and includes those in engineering, material sciences, economics, and life sciences.

Author : Rodrigo Rojas Moraleda,Nektarios A. Valous,Wei Xiong,Niels Halama
Publisher : CRC Press
Page : 116 pages
File Size : 51,9 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

Author : Herbert Edelsbrunner
Publisher : Cambridge University Press
Page : 206 pages
File Size : 50,6 Mb
Release : 2001-05-28
Category : Computers
ISBN : 0521793092

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Geometry and Topology for Mesh Generation by Herbert Edelsbrunner Pdf

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.

Author : S.-Y. Hahn
Publisher : Elsevier
Page : 766 pages
File Size : 52,9 Mb
Release : 2013-10-22
Category : Technology & Engineering
ISBN : 9781483290560

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Advanced Computational and Design Techniques in Applied Electromagnetic Systems by S.-Y. Hahn Pdf

This symposium was concerned with advanced computational and design techniques in applied electromagnetic systems including devices and materials. The scope of the proceedings cover a wide variety of topics in applied electromagnetic fields: optimal design techniques and applications, inverse problems, advanced numerical techniques, mechanism and dynamics of new actuators, physics and applications of magnetic levitation, electromagnetic propulsion and superconductivity, modeling and applications of magnetic fluid, plasma and arc discharge, high-frequency field computations, electronic device simulations and magnetic materials.

Author : Macario Vives, Sergio
Publisher : Publicacions de la Universitat Jaume I
Page : 184 pages
File Size : 51,6 Mb
Release : 2012-10-22
Category : Mathematics
ISBN : 9788480218801

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Applied topology: recent progress for computer science, fuzzy mathematics and economics. by Macario Vives, Sergio Pdf

En las últimas décadas, la Topología se ha revelado como una poderosa herramienta para acometer diferentes problemas relacionados con un amplio espectro de ciencias aplicadas más allá de las matemáticas, como Economía, Inteligencia Artificial, Ciencias de la Computación o Sistemas Dinámicos. El presente volumen recoge las ponencias del Workshop in Applied Topology WiAT¿12, celebrado en junio de 2012 en la Universitat Jaume I, en el que participaron diferentes grupos de investigación del área de la Topología General y sus Aplicaciones.

Author : Michael Robinson
Publisher : Springer Science & Business Media
Page : 245 pages
File Size : 43,8 Mb
Release : 2014-01-07
Category : Technology & Engineering
ISBN : 9783642361043

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Topological Signal Processing by Michael Robinson Pdf

Signal processing is the discipline of extracting information from collections of measurements. To be effective, the measurements must be organized and then filtered, detected, or transformed to expose the desired information. Distortions caused by uncertainty, noise, and clutter degrade the performance of practical signal processing systems. In aggressively uncertain situations, the full truth about an underlying signal cannot be known. This book develops the theory and practice of signal processing systems for these situations that extract useful, qualitative information using the mathematics of topology -- the study of spaces under continuous transformations. Since the collection of continuous transformations is large and varied, tools which are topologically-motivated are automatically insensitive to substantial distortion. The target audience comprises practitioners as well as researchers, but the book may also be beneficial for graduate students.

Author : Kathryn Hess,Frédéric Chazal,Umberto Lupo
Publisher : Frontiers Media SA
Page : 229 pages
File Size : 55,7 Mb
Release : 2022-11-07
Category : Science
ISBN : 9782832504123

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Topology in Real-World Machine Learning and Data Analysis by Kathryn Hess,Frédéric Chazal,Umberto Lupo Pdf