Advances In Applied And Computational Topology
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Advances In Applied And Computational Topology
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Author : American Mathematical Society. Short Course on Computational Topology
language : en
Publisher: American Mathematical Soc.
Release Date : 2012-07-05
Advances In Applied And Computational Topology written by American Mathematical Society. Short Course on Computational Topology and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-05 with Mathematics categories.
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.
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.
Computational Geometry Topology And Physics Of Digital Images With Applications
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Author : James F. Peters
language : en
Publisher: Springer Nature
Release Date : 2019-10-03
Computational Geometry Topology And Physics Of Digital Images With Applications written by James F. Peters and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-03 with Technology & Engineering categories.
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
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Author : Herbert Edelsbrunner
language : en
Publisher:
Release Date : 2010
Computational Topology written by Herbert Edelsbrunner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Algorithms 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 alg.
Big Data Optimization Recent Developments And Challenges
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Author : Ali Emrouznejad
language : en
Publisher: Springer
Release Date : 2016-05-26
Big Data Optimization Recent Developments And Challenges written by Ali Emrouznejad and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-26 with Technology & Engineering categories.
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.
Finite Frame Theory A Complete Introduction To Overcompleteness
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Author : Kasso A. Okoudjou
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-07-13
Finite Frame Theory A Complete Introduction To Overcompleteness written by Kasso A. Okoudjou and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-13 with Approximations and expansions categories.
Frames are overcomplete sets of vectors that can be used to stably and faithfully decompose and reconstruct vectors in the underlying vector space. Frame theory stands at the intersection of many areas in mathematics such as functional and harmonic analysis, numerical analysis, matrix theory, numerical linear algebra, algebraic and differential geometry, probability, statistics, and convex geometry. At the same time its applications in engineering, medicine, computer science, and quantum computing are motivating new research problems in applied and pure mathematics. This volume is based on lectures delivered at the 2015 AMS Short Course “Finite Frame Theory: A Complete Introduction to Overcompleteness”, held January 8–9, 2015 in San Antonio, TX. Mostly written in a tutorial style, the seven chapters contained in this volume survey recent advances in the theory and applications of finite frames. In particular, it presents state-of-the-art results on foundational frame problems, and on the analysis and design of various frames, mostly motivated by specific applications. Carefully assembled, the volume quickly introduces the non-expert to the basic tools and techniques of frame theory. It then moves to develop many recent results in the area and presents some important applications. As such, the volume is designed for a diverse audience including researchers in applied and computational harmonic analysis, as well as engineers and graduate students.
Computational Topology For Biomedical Image And Data Analysis
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Author : Rodrigo Rojas Moraleda
language : en
Publisher: CRC Press
Release Date : 2019-07-12
Computational Topology For Biomedical Image And Data Analysis written by Rodrigo Rojas Moraleda and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-12 with Medical categories.
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
Self Aware Computing Systems
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Author : Samuel Kounev
language : en
Publisher: Springer
Release Date : 2017-01-23
Self Aware Computing Systems written by Samuel Kounev and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-23 with Computers categories.
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.
Sum Of Squares Theory And Applications
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Author : Pablo A. Parrilo
language : en
Publisher: American Mathematical Soc.
Release Date :
Sum Of Squares Theory And Applications written by Pablo A. Parrilo and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Education categories.
This volume is based on lectures delivered at the 2019 AMS Short Course “Sum of Squares: Theory and Applications”, held January 14–15, 2019, in Baltimore, Maryland. This book provides a concise state-of-the-art overview of the theory and applications of polynomials that are sums of squares. This is an exciting and timely topic, with rich connections to many areas of mathematics, including polynomial and semidefinite optimization, real and convex algebraic geometry, and theoretical computer science. The six chapters introduce and survey recent developments in this area; specific topics include the algebraic and geometric aspects of sums of squares and spectrahedra, lifted representations of convex sets, and the algorithmic and computational implications of viewing sums of squares as a meta algorithm. The book also showcases practical applications of the techniques across a variety of areas, including control theory, statistics, finance and machine learning.
An Excursion Through Discrete Differential Geometry
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Author : American Mathematical Society. Short Course, Discrete Differential Geometry
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-09-02
An Excursion Through Discrete Differential Geometry written by American Mathematical Society. Short Course, Discrete Differential Geometry and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-02 with Education categories.
Discrete Differential Geometry (DDG) is an emerging discipline at the boundary between mathematics and computer science. It aims to translate concepts from classical differential geometry into a language that is purely finite and discrete, and can hence be used by algorithms to reason about geometric data. In contrast to standard numerical approximation, the central philosophy of DDG is to faithfully and exactly preserve key invariants of geometric objects at the discrete level. This process of translation from smooth to discrete helps to both illuminate the fundamental meaning behind geometric ideas and provide useful algorithmic guarantees. This volume is based on lectures delivered at the 2018 AMS Short Course ``Discrete Differential Geometry,'' held January 8-9, 2018, in San Diego, California. The papers in this volume illustrate the principles of DDG via several recent topics: discrete nets, discrete differential operators, discrete mappings, discrete conformal geometry, and discrete optimal transport.