Euclidean Distance Matrices And Their Applications In Rigidity Theory
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Euclidean Distance Matrices And Their Applications In Rigidity Theory
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Author : Abdo Y. Alfakih
language : en
Publisher:
Release Date : 2018
Euclidean Distance Matrices And Their Applications In Rigidity Theory written by Abdo Y. Alfakih and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with MATHEMATICS categories.
This book offers a comprehensive and accessible exposition of Euclidean Distance Matrices (EDMs) and rigidity theory of bar-and-joint frameworks. It is based on the one-to-one correspondence between EDMs and projected Gram matrices. Accordingly the machinery of semidefinite programming is a common thread that runs throughout the book. As a result, two parallel approaches to rigidity theory are presented. The first is traditional and more intuitive approach that is based on a vector representation of point configuration. The second is based on a Gram matrix representation of point configuration. Euclidean Distance Matrices and Their Applications in Rigidity Theory begins by establishing the necessary background needed for the rest of the book. The focus of Chapter 1 is on pertinent results from matrix theory, graph theory and convexity theory, while Chapter 2 is devoted to positive semidefinite (PSD) matrices due to the key role these matrices play in our approach. Chapters 3 to 7 provide detailed studies of EDMs, and in particular their various characterizations, classes, eigenvalues and geometry. Chapter 8 serves as a transitional chapter between EDMs and rigidity theory. Chapters 9 and 10 cover local and universal rigidities of bar-and-joint frameworks. This book is self-contained and should be accessible to a wide audience including students and researchers in statistics, operations research, computational biochemistry, engineering, computer science and mathematics.
Euclidean Distance Matrices And Their Applications In Rigidity Theory
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Author : Abdo Y. Alfakih
language : en
Publisher: Springer
Release Date : 2018-10-13
Euclidean Distance Matrices And Their Applications In Rigidity Theory written by Abdo Y. Alfakih and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-13 with Mathematics categories.
This book offers a comprehensive and accessible exposition of Euclidean Distance Matrices (EDMs) and rigidity theory of bar-and-joint frameworks. It is based on the one-to-one correspondence between EDMs and projected Gram matrices. Accordingly the machinery of semidefinite programming is a common thread that runs throughout the book. As a result, two parallel approaches to rigidity theory are presented. The first is traditional and more intuitive approach that is based on a vector representation of point configuration. The second is based on a Gram matrix representation of point configuration. Euclidean Distance Matrices and Their Applications in Rigidity Theory begins by establishing the necessary background needed for the rest of the book. The focus of Chapter 1 is on pertinent results from matrix theory, graph theory and convexity theory, while Chapter 2 is devoted to positive semidefinite (PSD) matrices due to the key role these matrices play in our approach. Chapters 3 to 7 provide detailed studies of EDMs, and in particular their various characterizations, classes, eigenvalues and geometry. Chapter 8 serves as a transitional chapter between EDMs and rigidity theory. Chapters 9 and 10 cover local and universal rigidities of bar-and-joint frameworks. This book is self-contained and should be accessible to a wide audience including students and researchers in statistics, operations research, computational biochemistry, engineering, computer science and mathematics.
Rigidity Theory And Applications
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Author : M.F. Thorpe
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-11
Rigidity Theory And Applications written by M.F. Thorpe 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 2006-04-11 with Computers categories.
Although rigidity has been studied since the time of Lagrange (1788) and Maxwell (1864), it is only in the last twenty-five years that it has begun to find applications in the basic sciences. The modern era starts with Laman (1970), who made the subject rigorous in two dimensions, followed by the development of computer algorithms that can test over a million sites in seconds and find the rigid regions, and the associated pivots, leading to many applications. This workshop was organized to bring together leading researchers studying the underlying theory, and to explore the various areas of science where applications of these ideas are being implemented.
Distance Geometry
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Author : Antonio Mucherino
language : en
Publisher: Springer
Release Date : 2015-01-28
Distance Geometry written by Antonio Mucherino and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-28 with Mathematics categories.
This volume is a collection of research surveys on the Distance Geometry Problem (DGP) and its applications. It will be divided into three parts: Theory, Methods and Applications. Each part will contain at least one survey and several research papers. The first part, Theory, will deal with theoretical aspects of the DGP, including a new class of problems and the study of its complexities as well as the relation between DGP and other related topics, such as: distance matrix theory, Euclidean distance matrix completion problem, multispherical structure of distance matrices, distance geometry and geometric algebra, algebraic distance geometry theory, visualization of K-dimensional structures in the plane, graph rigidity, and theory of discretizable DGP: symmetry and complexity. The second part, Methods, will discuss mathematical and computational properties of methods developed to the problems considered in the first chapter including continuous methods (based on Gaussian and hyperbolic smoothing, difference of convex functions, semidefinite programming, branch-and-bound), discrete methods (based on branch-and-prune, geometric build-up, graph rigidity), and also heuristics methods (based on simulated annealing, genetic algorithms, tabu search, variable neighborhood search). Applications will comprise the third part and will consider applications of DGP to NMR structure calculation, rational drug design, molecular dynamics simulations, graph drawing and sensor network localization. This volume will be the first edited book on distance geometry and applications. The editors are in correspondence with the major contributors to the field of distance geometry, including important research centers in molecular biology such as Institut Pasteur in Paris.
Euclidean Distance Geometry
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Author : Leo Liberti
language : en
Publisher: Springer
Release Date : 2017-09-20
Euclidean Distance Geometry written by Leo Liberti and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-20 with Mathematics categories.
This textbook, the first of its kind, presents the fundamentals of distance geometry: theory, useful methodologies for obtaining solutions, and real world applications. Concise proofs are given and step-by-step algorithms for solving fundamental problems efficiently and precisely are presented in Mathematica®, enabling the reader to experiment with concepts and methods as they are introduced. Descriptive graphics, examples, and problems, accompany the real gems of the text, namely the applications in visualization of graphs, localization of sensor networks, protein conformation from distance data, clock synchronization protocols, robotics, and control of unmanned underwater vehicles, to name several. Aimed at intermediate undergraduates, beginning graduate students, researchers, and practitioners, the reader with a basic knowledge of linear algebra will gain an understanding of the basic theories of distance geometry and why they work in real life.
Handbook Of Wireless Sensor Networks Issues And Challenges In Current Scenario S
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Author : Pradeep Kumar Singh
language : en
Publisher: Springer Nature
Release Date : 2020-02-08
Handbook Of Wireless Sensor Networks Issues And Challenges In Current Scenario S written by Pradeep Kumar Singh and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-08 with Technology & Engineering categories.
This book explores various challenging problems and applications areas of wireless sensor networks (WSNs), and identifies the current issues and future research challenges. Discussing the latest developments and advances, it covers all aspects of in WSNs, from architecture to protocols design, and from algorithm development to synchronization issues. As such the book is an essential reference resource for undergraduate and postgraduate students as well as scholars and academics working in the field.
Handbook Of Geometric Constraint Systems Principles
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Author : Meera Sitharam
language : en
Publisher: CRC Press
Release Date : 2018-07-20
Handbook Of Geometric Constraint Systems Principles written by Meera Sitharam and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-20 with Mathematics categories.
The Handbook of Geometric Constraint Systems Principles is an entry point to the currently used principal mathematical and computational tools and techniques of the geometric constraint system (GCS). It functions as a single source containing the core principles and results, accessible to both beginners and experts. The handbook provides a guide for students learning basic concepts, as well as experts looking to pinpoint specific results or approaches in the broad landscape. As such, the editors created this handbook to serve as a useful tool for navigating the varied concepts, approaches and results found in GCS research. Key Features: A comprehensive reference handbook authored by top researchers Includes fundamentals and techniques from multiple perspectives that span several research communities Provides recent results and a graded program of open problems and conjectures Can be used for senior undergraduate or graduate topics course introduction to the area Detailed list of figures and tables About the Editors: Meera Sitharam is currently an Associate Professor at the University of Florida’s Department of Computer & Information Science and Engineering. She received her Ph.D. at the University of Wisconsin, Madison. Audrey St. John is an Associate Professor of Computer Science at Mount Holyoke College, who received her Ph. D. from UMass Amherst. Jessica Sidman is a Professor of Mathematics on the John S. Kennedy Foundation at Mount Holyoke College. She received her Ph.D. from the University of Michigan.
Sensors Theory Algorithms And Applications
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Author : Vladimir L. Boginski
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-24
Sensors Theory Algorithms And Applications written by Vladimir L. Boginski 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 2011-11-24 with Mathematics categories.
The objective of this book is to advance the current knowledge of sensor research particularly highlighting recent advances, current work, and future needs. The goal is to share current technologies and steer future efforts in directions that will benefit the majority of researchers and practitioners working in this broad field of study.
Distance Geometry
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Author : Antonio Mucherino
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-22
Distance Geometry written by Antonio Mucherino 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 2012-12-22 with Mathematics categories.
This volume is a collection of research surveys on the Distance Geometry Problem (DGP) and its applications. It will be divided into three parts: Theory, Methods and Applications. Each part will contain at least one survey and several research papers. The first part, Theory, will deal with theoretical aspects of the DGP, including a new class of problems and the study of its complexities as well as the relation between DGP and other related topics, such as: distance matrix theory, Euclidean distance matrix completion problem, multispherical structure of distance matrices, distance geometry and geometric algebra, algebraic distance geometry theory, visualization of K-dimensional structures in the plane, graph rigidity, and theory of discretizable DGP: symmetry and complexity. The second part, Methods, will discuss mathematical and computational properties of methods developed to the problems considered in the first chapter including continuous methods (based on Gaussian and hyperbolic smoothing, difference of convex functions, semidefinite programming, branch-and-bound), discrete methods (based on branch-and-prune, geometric build-up, graph rigidity), and also heuristics methods (based on simulated annealing, genetic algorithms, tabu search, variable neighborhood search). Applications will comprise the third part and will consider applications of DGP to NMR structure calculation, rational drug design, molecular dynamics simulations, graph drawing and sensor network localization. This volume will be the first edited book on distance geometry and applications. The editors are in correspondence with the major contributors to the field of distance geometry, including important research centers in molecular biology such as Institut Pasteur in Paris.
Robust Optimization Directed Design
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Author : Andrew J. Kurdila
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-04
Robust Optimization Directed Design written by Andrew J. Kurdila 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 2006-06-04 with Mathematics categories.
Robust design—that is, managing design uncertainties such as model uncertainty or parametric uncertainty—is the often unpleasant issue crucial in much multidisciplinary optimal design work. Recently, there has been enormous practical interest in strategies for applying optimization tools to the development of robust solutions and designs in several areas, including aerodynamics, the integration of sensing (e.g., laser radars, vision-based systems, and millimeter-wave radars) and control, cooperative control with poorly modeled uncertainty, cascading failures in military and civilian applications, multi-mode seekers/sensor fusion, and data association problems and tracking systems. The contributions to this book explore these different strategies. The expression "optimization-directed” in this book’s title is meant to suggest that the focus is not agonizing over whether optimization strategies identify a true global optimum, but rather whether these strategies make significant design improvements.