Euclidean Distance Matrices and Their Applications in Rigidity Theory

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Publisher : Springer
ISBN 13 : 3319978462
Total Pages : 258 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Euclidean Distance Matrices and Their Applications in Rigidity Theory by : Abdo Y. Alfakih

Download or read book Euclidean Distance Matrices and Their Applications in Rigidity Theory written by Abdo Y. Alfakih and published by Springer. This book was released on 2018-10-13 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Handbook of Position Location

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Publisher : John Wiley & Sons
ISBN 13 : 1119434602
Total Pages : 1521 pages
Book Rating : 4.1/5 (194 download)

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Book Synopsis Handbook of Position Location by : Reza Zekavat

Download or read book Handbook of Position Location written by Reza Zekavat and published by John Wiley & Sons. This book was released on 2019-01-28 with total page 1521 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive review of position location technology — from fundamental theory to advanced practical applications Positioning systems and location technologies have become significant components of modern life, used in a multitude of areas such as law enforcement and security, road safety and navigation, personnel and object tracking, and many more. Position location systems have greatly reduced societal vulnerabilities and enhanced the quality of life for billions of people around the globe — yet limited resources are available to researchers and students in this important field. The Handbook of Position Location: Theory, Practice, and Advances fills this gap, providing a comprehensive overview of both fundamental and cutting-edge techniques and introducing practical methods of advanced localization and positioning. Now in its second edition, this handbook offers broad and in-depth coverage of essential topics including Time of Arrival (TOA) and Direction of Arrival (DOA) based positioning, Received Signal Strength (RSS) based positioning, network localization, and others. Topics such as GPS, autonomous vehicle applications, and visible light localization are examined, while major revisions to chapters such as body area network positioning and digital signal processing for GNSS receivers reflect current and emerging advances in the field. This new edition: Presents new and revised chapters on topics including localization error evaluation, Kalman filtering, positioning in inhomogeneous media, and Global Positioning (GPS) in harsh environments Offers MATLAB examples to demonstrate fundamental algorithms for positioning and provides online access to all MATLAB code Allows practicing engineers and graduate students to keep pace with contemporary research and new technologies Contains numerous application-based examples including the application of localization to drone navigation, capsule endoscopy localization, and satellite navigation and localization Reviews unique applications of position location systems, including GNSS and RFID-based localization systems The Handbook of Position Location: Theory, Practice, and Advances is valuable resource for practicing engineers and researchers seeking to keep pace with current developments in the field, graduate students in need of clear and accurate course material, and university instructors teaching the fundamentals of wireless localization.

Cooperative Localization and Navigation

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Publisher : CRC Press
ISBN 13 : 0429016670
Total Pages : 807 pages
Book Rating : 4.4/5 (29 download)

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Book Synopsis Cooperative Localization and Navigation by : Chao Gao

Download or read book Cooperative Localization and Navigation written by Chao Gao and published by CRC Press. This book was released on 2019-08-21 with total page 807 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book captures the latest results and techniques for cooperative localization and navigation drawn from a broad array of disciplines. It provides the reader with a generic and comprehensive view of modeling, strategies, and state estimation methodologies in that fields. It discusses the most recent research and novel advances in that direction, exploring the design of algorithms and architectures, benefits, and challenging aspects, as well as a potential broad array of disciplines, including wireless communication, indoor localization, robotics, emergency rescue, motion analysis, etc.

Computational Science – ICCS 2021

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Publisher : Springer Nature
ISBN 13 : 3030779610
Total Pages : 815 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Computational Science – ICCS 2021 by : Maciej Paszynski

Download or read book Computational Science – ICCS 2021 written by Maciej Paszynski and published by Springer Nature. This book was released on 2021-06-10 with total page 815 pages. Available in PDF, EPUB and Kindle. Book excerpt: The six-volume set LNCS 12742, 12743, 12744, 12745, 12746, and 12747 constitutes the proceedings of the 21st International Conference on Computational Science, ICCS 2021, held in Krakow, Poland, in June 2021.* The total of 260 full papers and 57 short papers presented in this book set were carefully reviewed and selected from 635 submissions. 48 full and 14 short papers were accepted to the main track from 156 submissions; 212 full and 43 short papers were accepted to the workshops/ thematic tracks from 479 submissions. The papers were organized in topical sections named: Part I: ICCS Main Track Part II: Advances in High-Performance Computational Earth Sciences: Applications and Frameworks; Applications of Computational Methods in Artificial Intelligence and Machine Learning; Artificial Intelligence and High-Performance Computing for Advanced Simulations; Biomedical and Bioinformatics Challenges for Computer Science Part III: Classifier Learning from Difficult Data; Computational Analysis of Complex Social Systems; Computational Collective Intelligence; Computational Health Part IV: Computational Methods for Emerging Problems in (dis-)Information Analysis; Computational Methods in Smart Agriculture; Computational Optimization, Modelling and Simulation; Computational Science in IoT and Smart Systems Part V: Computer Graphics, Image Processing and Artificial Intelligence; Data-Driven Computational Sciences; Machine Learning and Data Assimilation for Dynamical Systems; MeshFree Methods and Radial Basis Functions in Computational Sciences; Multiscale Modelling and Simulation Part VI: Quantum Computing Workshop; Simulations of Flow and Transport: Modeling, Algorithms and Computation; Smart Systems: Bringing Together Computer Vision, Sensor Networks and Machine Learning; Software Engineering for Computational Science; Solving Problems with Uncertainty; Teaching Computational Science; Uncertainty Quantification for Computational Models *The conference was held virtually. Chapter “Deep Learning Driven Self-adaptive hp Finite Element Method” is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

Euclidean Distance Geometry

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Publisher : Springer
ISBN 13 : 3319607928
Total Pages : 141 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Euclidean Distance Geometry by : Leo Liberti

Download or read book Euclidean Distance Geometry written by Leo Liberti and published by Springer. This book was released on 2017-09-20 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

China Satellite Navigation Conference (CSNC) 2018 Proceedings

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Publisher : Springer
ISBN 13 : 9811300291
Total Pages : 899 pages
Book Rating : 4.8/5 (113 download)

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Book Synopsis China Satellite Navigation Conference (CSNC) 2018 Proceedings by : Jiadong Sun

Download or read book China Satellite Navigation Conference (CSNC) 2018 Proceedings written by Jiadong Sun and published by Springer. This book was released on 2018-05-03 with total page 899 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings present selected research papers from CSNC 2018, held during 23rd-25th May in Harbin, China. The theme of CSNC 2018 is Location, Time of Augmentation. These papers discuss the technologies and applications of the Global Navigation Satellite System (GNSS), and the latest progress made in the China BeiDou System (BDS) especially. They are divided into 12 topics to match the corresponding sessions in CSNC 2018, which broadly covered key topics in GNSS. Readers can learn about the BDS and keep abreast of the latest advances in GNSS techniques and applications.

Recent Advances in Computational Optimization

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Publisher : Springer
ISBN 13 : 3319598619
Total Pages : 238 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Recent Advances in Computational Optimization by : Stefka Fidanova

Download or read book Recent Advances in Computational Optimization written by Stefka Fidanova and published by Springer. This book was released on 2017-06-25 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents new optimization approaches and methods and their application in real-world and industrial problems, and demonstrates how many of the problems arising in engineering, economics and other domains can be formulated as optimization problems. Constituting a comprehensive collection of extended contributions from the 9th International Workshop on Computational Optimization (WCO) held in Gdansk, Poland, September 11–14, 2016, the book discusses important applications such as job scheduling, wildfire modeling, parameter settings for controlling different processes, capital budgeting, data mining, finding the location of sensors in a given network, identifying the conformation of molecules, algorithm correctness, decision support system, and computer memory management. Further, it shows how to develop algorithms for these based on new intelligent methods like evolutionary computations, ant colony optimization and constraint programming. The book is a valuable resource for researchers and practitioners alike.

Distance Geometry

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Publisher : Springer Science & Business Media
ISBN 13 : 1461451280
Total Pages : 436 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Distance Geometry by : Antonio Mucherino

Download or read book Distance Geometry written by Antonio Mucherino and published by Springer Science & Business Media. This book was released on 2012-12-22 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Handbook on Semidefinite, Conic and Polynomial Optimization

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Publisher : Springer Science & Business Media
ISBN 13 : 1461407699
Total Pages : 955 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Handbook on Semidefinite, Conic and Polynomial Optimization by : Miguel F. Anjos

Download or read book Handbook on Semidefinite, Conic and Polynomial Optimization written by Miguel F. Anjos and published by Springer Science & Business Media. This book was released on 2011-11-19 with total page 955 pages. Available in PDF, EPUB and Kindle. Book excerpt: Semidefinite and conic optimization is a major and thriving research area within the optimization community. Although semidefinite optimization has been studied (under different names) since at least the 1940s, its importance grew immensely during the 1990s after polynomial-time interior-point methods for linear optimization were extended to solve semidefinite optimization problems. Since the beginning of the 21st century, not only has research into semidefinite and conic optimization continued unabated, but also a fruitful interaction has developed with algebraic geometry through the close connections between semidefinite matrices and polynomial optimization. This has brought about important new results and led to an even higher level of research activity. This Handbook on Semidefinite, Conic and Polynomial Optimization provides the reader with a snapshot of the state-of-the-art in the growing and mutually enriching areas of semidefinite optimization, conic optimization, and polynomial optimization. It contains a compendium of the recent research activity that has taken place in these thrilling areas, and will appeal to doctoral students, young graduates, and experienced researchers alike. The Handbook’s thirty-one chapters are organized into four parts: Theory, covering significant theoretical developments as well as the interactions between conic optimization and polynomial optimization; Algorithms, documenting the directions of current algorithmic development; Software, providing an overview of the state-of-the-art; Applications, dealing with the application areas where semidefinite and conic optimization has made a significant impact in recent years.

Linear and Nonlinear Programming

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Publisher : Springer Nature
ISBN 13 : 3030854507
Total Pages : 609 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Linear and Nonlinear Programming by : David G. Luenberger

Download or read book Linear and Nonlinear Programming written by David G. Luenberger and published by Springer Nature. This book was released on 2021-10-31 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 5th edition of this classic textbook covers the central concepts of practical optimization techniques, with an emphasis on methods that are both state-of-the-art and popular. One major insight is the connection between the purely analytical character of an optimization problem and the behavior of algorithms used to solve that problem. End-of-chapter exercises are provided for all chapters. The material is organized into three separate parts. Part I offers a self-contained introduction to linear programming. The presentation in this part is fairly conventional, covering the main elements of the underlying theory of linear programming, many of the most effective numerical algorithms, and many of its important special applications. Part II, which is independent of Part I, covers the theory of unconstrained optimization, including both derivations of the appropriate optimality conditions and an introduction to basic algorithms. This part of the book explores the general properties of algorithms and defines various notions of convergence. In turn, Part III extends the concepts developed in the second part to constrained optimization problems. Except for a few isolated sections, this part is also independent of Part I. As such, Parts II and III can easily be used without reading Part I and, in fact, the book has been used in this way at many universities. New to this edition are popular topics in data science and machine learning, such as the Markov Decision Process, Farkas’ lemma, convergence speed analysis, duality theories and applications, various first-order methods, stochastic gradient method, mirror-descent method, Frank-Wolf method, ALM/ADMM method, interior trust-region method for non-convex optimization, distributionally robust optimization, online linear programming, semidefinite programming for sensor-network localization, and infeasibility detection for nonlinear optimization.

Novel Applications of the UWB Technologies

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Publisher : BoD – Books on Demand
ISBN 13 : 9533073241
Total Pages : 458 pages
Book Rating : 4.5/5 (33 download)

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Book Synopsis Novel Applications of the UWB Technologies by : Boris Lembrikov

Download or read book Novel Applications of the UWB Technologies written by Boris Lembrikov and published by BoD – Books on Demand. This book was released on 2011-08-01 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ultra wideband (UWB) communication systems are characterized by high data rates, low cost, multipath immunity, and low power transmission. In 2002, the Federal Communication Commission (FCC) legalized low power UWB emission between 3.1 GHz and 10.6 GHz for indoor communication devices stimulating rapid development of UWB technologies and applications. The proposed book Novel Applications of the UWB Technologies consists of 5 parts and 20 chapters concerning the general problems of UWB communication systems, and novel UWB applications in personal area networks (PANs), medicine, radars and localization systems. The book will be interesting for engineers and researchers occupied in the field of UWB technology.

Discrete Mathematics Days 2022

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Publisher : Ed. Universidad de Cantabria
ISBN 13 : 8419024031
Total Pages : 335 pages
Book Rating : 4.4/5 (19 download)

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Book Synopsis Discrete Mathematics Days 2022 by : Luis Felipe Tabera Alonso

Download or read book Discrete Mathematics Days 2022 written by Luis Felipe Tabera Alonso and published by Ed. Universidad de Cantabria. This book was released on 2022-07-04 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: El congreso Discrete Mathematics Days (DMD20/22) tendrá lugar del 4 al 6 de julio de 2022, en la Facultad de Ciencias de la Universidad de Cantabria (Santander, España). Este congreso internacional se centra en avances dentro del campo de la Matemática discreta, incluyendo, de manera no exhaustiva: · Algoritmos y Complejidad · Combinatoria · Teoría de Códigos · Criptografía · Geometría Discreta y Computacional · Optimización Discreta · Teoría de Grafos · Problemas de localización discreta y temas relacionados Las ediciones anteriores de este evento se celebraros en Sevilla (2018) y Barcelona (2016), estos congresos heredan la tradición de las Jornadas de Matemática Discreta y Algorítmica (JMDA), el encuentro bienal en España en Matemática Discreta (desde 1998). Durante la celebración del congreso tendrán lugar cuatro conferencias plenarias, cuarenta y dos presentaciones orales y una sesión de once pósteres. Abstract The Discrete Mathematics Days (DMD20/22) will be held on July 4-6, 2022, at Facultad de Ciencias of the Universidad de Cantabria (Santander, Spain). The main focus of this international conference is on current topics in Discrete Mathematics, including (but not limited to): Algorithms and Complexity Combinatorics Coding Theory Cryptography Discrete and Computational Geometry Discrete Optimization Graph Theory Location and Related Problems The previous editions were held in Sevilla in 2018 and in Barcelona in 2016, inheriting the tradition of the Jornadas de Matemática Discreta y Algorítmica (JMDA), the Spanish biennial meeting (since 1998) on Discrete Mathematics. The program consists on four plenary talks, 42 contributed talks and a poster session with 11 contributions.

Discrete Geometry and Optimization

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Publisher : Springer Science & Business Media
ISBN 13 : 3319002007
Total Pages : 341 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Discrete Geometry and Optimization by : Károly Bezdek

Download or read book Discrete Geometry and Optimization written by Károly Bezdek and published by Springer Science & Business Media. This book was released on 2013-07-09 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: ​Optimization has long been a source of both inspiration and applications for geometers, and conversely, discrete and convex geometry have provided the foundations for many optimization techniques, leading to a rich interplay between these subjects. The purpose of the Workshop on Discrete Geometry, the Conference on Discrete Geometry and Optimization, and the Workshop on Optimization, held in September 2011 at the Fields Institute, Toronto, was to further stimulate the interaction between geometers and optimizers. This volume reflects the interplay between these areas. The inspiring Fejes Tóth Lecture Series, delivered by Thomas Hales of the University of Pittsburgh, exemplified this approach. While these fields have recently witnessed a lot of activity and successes, many questions remain open. For example, Fields medalist Stephen Smale stated that the question of the existence of a strongly polynomial time algorithm for linear optimization is one of the most important unsolved problems at the beginning of the 21st century. The broad range of topics covered in this volume demonstrates the many recent and fruitful connections between different approaches, and features novel results and state-of-the-art surveys as well as open problems.

Robust Optimization-Directed Design

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Publisher : Springer Science & Business Media
ISBN 13 : 0387286543
Total Pages : 279 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Robust Optimization-Directed Design by : Andrew J. Kurdila

Download or read book Robust Optimization-Directed Design written by Andrew J. Kurdila and published by Springer Science & Business Media. This book was released on 2006-06-04 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Convex Optimization & Euclidean Distance Geometry

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Publisher : Meboo Publishing USA
ISBN 13 : 0976401304
Total Pages : 776 pages
Book Rating : 4.9/5 (764 download)

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Book Synopsis Convex Optimization & Euclidean Distance Geometry by : Jon Dattorro

Download or read book Convex Optimization & Euclidean Distance Geometry written by Jon Dattorro and published by Meboo Publishing USA. This book was released on 2005 with total page 776 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of Euclidean distance matrices (EDMs) fundamentally asks what can be known geometrically given onlydistance information between points in Euclidean space. Each point may represent simply locationor, abstractly, any entity expressible as a vector in finite-dimensional Euclidean space.The answer to the question posed is that very much can be known about the points;the mathematics of this combined study of geometry and optimization is rich and deep.Throughout we cite beacons of historical accomplishment.The application of EDMs has already proven invaluable in discerning biological molecular conformation.The emerging practice of localization in wireless sensor networks, the global positioning system (GPS), and distance-based pattern recognitionwill certainly simplify and benefit from this theory.We study the pervasive convex Euclidean bodies and their various representations.In particular, we make convex polyhedra, cones, and dual cones more visceral through illustration, andwe study the geometric relation of polyhedral cones to nonorthogonal bases biorthogonal expansion.We explain conversion between halfspace- and vertex-descriptions of convex cones,we provide formulae for determining dual cones,and we show how classic alternative systems of linear inequalities or linear matrix inequalities and optimality conditions can be explained by generalized inequalities in terms of convex cones and their duals.The conic analogue to linear independence, called conic independence, is introducedas a new tool in the study of classical cone theory; the logical next step in the progression:linear, affine, conic.Any convex optimization problem has geometric interpretation.This is a powerful attraction: the ability to visualize geometry of an optimization problem.We provide tools to make visualization easier.The concept of faces, extreme points, and extreme directions of convex Euclidean bodiesis explained here, crucial to understanding convex optimization.The convex cone of positive semidefinite matrices, in particular, is studied in depth.We mathematically interpret, for example,its inverse image under affine transformation, and we explainhow higher-rank subsets of its boundary united with its interior are convex.The Chapter on "Geometry of convex functions",observes analogies between convex sets and functions:The set of all vector-valued convex functions is a closed convex cone.Included among the examples in this chapter, we show how the real affinefunction relates to convex functions as the hyperplane relates to convex sets.Here, also, pertinent results formultidimensional convex functions are presented that are largely ignored in the literature;tricks and tips for determining their convexityand discerning their geometry, particularly with regard to matrix calculus which remains largely unsystematizedwhen compared with the traditional practice of ordinary calculus.Consequently, we collect some results of matrix differentiation in the appendices.The Euclidean distance matrix (EDM) is studied,its properties and relationship to both positive semidefinite and Gram matrices.We relate the EDM to the four classical axioms of the Euclidean metric;thereby, observing the existence of an infinity of axioms of the Euclidean metric beyondthe triangle inequality. We proceed byderiving the fifth Euclidean axiom and then explain why furthering this endeavoris inefficient because the ensuing criteria (while describing polyhedra)grow linearly in complexity and number.Some geometrical problems solvable via EDMs,EDM problems posed as convex optimization, and methods of solution arepresented;\eg, we generate a recognizable isotonic map of the United States usingonly comparative distance information (no distance information, only distance inequalities).We offer a new proof of the classic Schoenberg criterion, that determines whether a candidate matrix is an EDM. Our proofrelies on fundamental geometry; assuming, any EDM must correspond to a list of points contained in some polyhedron(possibly at its vertices) and vice versa.It is not widely known that the Schoenberg criterion implies nonnegativity of the EDM entries; proved here.We characterize the eigenvalues of an EDM matrix and then devisea polyhedral cone required for determining membership of a candidate matrix(in Cayley-Menger form) to the convex cone of Euclidean distance matrices (EDM cone); \ie,a candidate is an EDM if and only if its eigenspectrum belongs to a spectral cone for EDM^N.We will see spectral cones are not unique.In the chapter "EDM cone", we explain the geometric relationship betweenthe EDM cone, two positive semidefinite cones, and the elliptope.We illustrate geometric requirements, in particular, for projection of a candidate matrixon a positive semidefinite cone that establish its membership to the EDM cone. The faces of the EDM cone are described,but still open is the question whether all its faces are exposed as they are for the positive semidefinite cone.The classic Schoenberg criterion, relating EDM and positive semidefinite cones, isrevealed to be a discretized membership relation (a generalized inequality, a new Farkas''''''''-like lemma)between the EDM cone and its ordinary dual. A matrix criterion for membership to the dual EDM cone is derived thatis simpler than the Schoenberg criterion.We derive a new concise expression for the EDM cone and its dual involvingtwo subspaces and a positive semidefinite cone."Semidefinite programming" is reviewedwith particular attention to optimality conditionsof prototypical primal and dual conic programs,their interplay, and the perturbation method of rank reduction of optimal solutions(extant but not well-known).We show how to solve a ubiquitous platonic combinatorial optimization problem from linear algebra(the optimal Boolean solution x to Ax=b)via semidefinite program relaxation.A three-dimensional polyhedral analogue for the positive semidefinite cone of 3X3 symmetricmatrices is introduced; a tool for visualizing in 6 dimensions.In "EDM proximity"we explore methods of solution to a few fundamental and prevalentEuclidean distance matrix proximity problems; the problem of finding that Euclidean distance matrix closestto a given matrix in the Euclidean sense.We pay particular attention to the problem when compounded with rank minimization.We offer a new geometrical proof of a famous result discovered by Eckart \& Young in 1936 regarding Euclideanprojection of a point on a subset of the positive semidefinite cone comprising all positive semidefinite matriceshaving rank not exceeding a prescribed limit rho.We explain how this problem is transformed to a convex optimization for any rank rho.

4g Mobile and Wireless Communications Technologies

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Publisher : CRC Press
ISBN 13 : 1000792005
Total Pages : 361 pages
Book Rating : 4.0/5 (7 download)

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Book Synopsis 4g Mobile and Wireless Communications Technologies by : Sofoklis Kyriazakos

Download or read book 4g Mobile and Wireless Communications Technologies written by Sofoklis Kyriazakos and published by CRC Press. This book was released on 2022-09-01 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mobile and wireless communications are moving towards a new era that will be characterized by the seamless collaboration of heterogeneous systems, the need for high speed communications while on the move and for advanced services with quality guarantees. Recent market research studies show that most of the traffic in the future wireless networks will be produced by mobile multimedia services which are expected to proliferate by the year 2010. On the other hand mobile and wireless communications technology is becoming more and more important in developing countries where people demand fast deployment and low cost for broadband wireless internet services.The objective of this volume is to gather research and development on topics shaping the fourth generation (4G) in mobile and wireless communications and reveal the key trends and enabling technologies for 4G. We envisage 4G wireless communication systems as IP based solution providing integrated services (voice, data, multimedia) regardless of time and end-users? location. 4G technologies will manifest the benefits of the wireless and wired technologies convergence, through enabling a wide range of innovative (both indoor and outdoor) applications. 4G applications will feature premium quality, high security and an affordable cost. The vision, though fantastic, is associated with a host of technical and technological challenges.A great deal of the latter are discussed in the articles of this volume, which aims at providing insights on the research issues and solutions that are directly associated with leading edge 4G technologies and services.Taking into account recent developments in the world of wireless communications we have given emphasis to cover all these technologies and aspects that are considered as cornerstones for achieving the goals set for 4G and that will further boost research and development of next-generation mobile communications.

Research in Computational Molecular Biology

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Publisher : Springer
ISBN 13 : 3642296270
Total Pages : 388 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Research in Computational Molecular Biology by : Benny Chor

Download or read book Research in Computational Molecular Biology written by Benny Chor and published by Springer. This book was released on 2012-04-13 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 16th Annual International Conference on Research in Computational Molecular Biology, RECOMB 2012, held in Barcelona, Spain, in April 2012. The 31 revised full papers presented together with 5 keynote lectures were carefully reviewed and selected from 200 submissions. The papers feature current research in all areas of computational molecular biology, including: molecular sequence analysis; recognition of genes and regulatory elements; molecular evolution; protein structure; structural genomics; analysis of gene expression; biological networks; sequencing and genotyping technologies; drug design; probabilistic and combinatorial algorithms; systems biology; computational proteomics; structural and functional genomics; information systems for computational biology and imaging.