Euclidean Distance Geometry
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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.
Convex Optimization Euclidean Distance Geometry
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Author : Jon Dattorro
language : en
Publisher: Lulu.com
Release Date : 2010-06-09
Convex Optimization Euclidean Distance Geometry written by Jon Dattorro and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-09 with Technology & Engineering categories.
Convex Analysis is the calculus of inequalities while Convex Optimization is its application. Analysis is inherently the domain of the mathematician while Optimization belongs to the engineer. In layman’s terms, the mathematical science of Optimization is the study of how to make a good choice when confronted with conflicting requirements. The qualifier Convex means: when an optimal solution is found, then it is guaranteed to be a best solution; there is no better choice. Any Convex Optimization problem has geometric interpretation. Conversely, recent advances in geometry and in graph theory hold Convex Optimization within their proofs’ core. This book is about Convex Optimization, convex geometry (with particular attention to distance geometry), and nonconvex, combinatorial, and geometrical problems that can be relaxed or transformed into convex problems. A virtual flood of new applications follows by epiphany that many problems, presumed nonconvex, can be so transformed. International Edition III
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.
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.
Geometry Of Cuts And Metrics
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Author : Michel Marie Deza
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-05-20
Geometry Of Cuts And Metrics written by Michel Marie Deza 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 1997-05-20 with Mathematics categories.
Cuts and metrics are well-known objects that arise - independently, but with many deep and fascinating connections - in diverse fields: in graph theory, combinatorial optimization, geometry of numbers, combinatorial matrix theory, statistical physics, VLSI design etc. This book presents a wealth of results, from different mathematical disciplines, in a unified comprehensive manner, and establishes new and old links, which cannot be found elsewhere. It provides a unique and invaluable source for researchers and graduate students. From the Reviews: "This book is definitely a milestone in the literature of integer programming and combinatorial optimization. It draws from the Interdisciplinarity of these fields [...]. With knowledge about the relevant terms, one can enjoy special subsections without being entirely familiar with the rest of the chapter. This makes it not only an interesting research book but even a dictionary. [...] The longer one works with it, the more beautiful it becomes." Optima 56, 1997.
Euclidean And Non Euclidean Geometry International Student Edition
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Author : Patrick J. Ryan
language : en
Publisher: Cambridge University Press
Release Date : 2009-09-04
Euclidean And Non Euclidean Geometry International Student Edition written by Patrick J. Ryan 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 2009-09-04 with Mathematics categories.
This book gives a rigorous treatment of the fundamentals of plane geometry: Euclidean, spherical, elliptical and hyperbolic.
Taxicab Geometry
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Author : Eugene F. Krause
language : en
Publisher: Courier Corporation
Release Date : 1986-01-01
Taxicab Geometry written by Eugene F. Krause and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-01-01 with Mathematics categories.
Develops a simple non-Euclidean geometry and explores some of its practical applications through graphs, research problems, and exercises. Includes selected answers.
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.
Approximation Of Euclidean Metric By Digital Distances
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Author : Jayanta Mukhopadhyay
language : en
Publisher: Springer Nature
Release Date : 2020-12-02
Approximation Of Euclidean Metric By Digital Distances written by Jayanta Mukhopadhyay and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-02 with Computers categories.
This book discusses different types of distance functions defined in an n-D integral space for their usefulness in approximating the Euclidean metric. It discusses the properties of these distance functions and presents various kinds of error analysis in approximating Euclidean metrics. It also presents a historical perspective on efforts and motivation for approximating Euclidean metrics by digital distances from the mid-sixties of the previous century. The book also contains an in-depth presentation of recent progress, and new research problems in this area.
Frontiers And Prospects Of Contemporary Applied Mathematics
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Author : Pingwen Zhang
language : en
Publisher: World Scientific
Release Date : 2006-04-17
Frontiers And Prospects Of Contemporary Applied Mathematics written by Pingwen Zhang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-17 with Mathematics categories.
This collection of articles covers the hottest topics in contemporary applied mathematics. Multiscale modeling, material computing, symplectic methods, parallel computing, mathematical biology, applied differential equations and engineering computing problems are all included. The book contains the latest results of many leading scientists and provides a window on new trends in research in the field.