Download or read book Distance Geometry and Molecular Conformation written by G. M. Crippen and published by John Wiley & Sons. This book was released on 1988 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Reviews in Computational Chemistry Volume 5 written by Kenny B. Lipkowitz and published by John Wiley & Sons. This book was released on 2009-09-22 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: Führende Experten auf dem Gebiet der Computer-Chemie präsentieren in dem fünften Band der erfolgreichen Reihe 'Reviews in Computational Chemistry' die neuesten Entwicklungen. Um den interessierten Chemiker auf dem aktuellen Stand zu halten, ist der Reihe im Anhang eine Liste mit der Software zum Thema beigefügt
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 133 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.
Download or read book Distance Geometry and Molecular Conformation written by G. M. Crippen and published by . This book was released on 1988 with total page 566 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book An Introduction to Distance Geometry applied to Molecular Geometry written by Carlile Lavor and published by Springer. This book was released on 2017-07-12 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a pedagogical presentation aimed at advanced undergraduate students, beginning graduate students and professionals who are looking for an introductory text to the field of Distance Geometry, and some of its applications. This versions profits from feedback acquired at undergraduate/graduate courses in seminars and a number of workshops.
Download or read book Distance Geometry and Conformational Calculations written by G. M. Crippen and published by Research Studies Press Limited. This book was released on 1981 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Systems Patterns and Data Engineering with Geometric Calculi written by Sebastià Xambó-Descamps and published by Springer Nature. This book was released on 2021-07-16 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: The intention of this collection agrees with the purposes of the homonymous mini-symposium (MS) at ICIAM-2019, which were to overview the essentials of geometric calculus (GC) formalism, to report on state-of-the-art applications showcasing its advantages and to explore the bearing of GC in novel approaches to deep learning. The first three contributions, which correspond to lectures at the MS, offer perspectives on recent advances in the application GC in the areas of robotics, molecular geometry, and medical imaging. The next three, especially invited, hone the expressiveness of GC in orientation measurements under different metrics, the treatment of contact elements, and the investigation of efficient computational methodologies. The last two, which also correspond to lectures at the MS, deal with two aspects of deep learning: a presentation of a concrete quaternionic convolutional neural network layer for image classification that features contrast invariance and a general overview of automatic learning aimed at steering the development of neural networks whose units process elements of a suitable algebra, such as a geometric algebra. The book fits, broadly speaking, within the realm of mathematical engineering, and consequently, it is intended for a wide spectrum of research profiles. In particular, it should bring inspiration and guidance to those looking for materials and problems that bridge GC with applications of great current interest, including the auspicious field of GC-based deep neural networks.
Download or read book Reviews in Computational Chemistry Volume 2 written by Kenny B. Lipkowitz and published by John Wiley & Sons. This book was released on 2009-09-22 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second volume of the series 'Reviews in Computational Chemistry' explores new applications, new methodologies, and new perspectives. The topics covered include conformational analysis, protein folding, force field parameterizations, hydrogen bonding, charge distributions, electrostatic potentials, electronic spectroscopy, molecular property correlations, and the computational chemistry literature. Methodologies described include conformational search strategies, distance geometry, molecular mechanics, molecular dynamics, ab initio and semiempirical molecular orbital calculations, and quantitative structure-activity relationships (QSAR) using topological and electronic descriptors. A compendium of molecular modeling software will help users select the computational tools they need. Each chapter in 'Reviews in Computational Chemistry' serves as a brief tutorial for organic, physical, pharmaceutical, and biological chemists new to the field. Practitioners will be interested in the recent advances.
Download or read book Statistics in Molecular Biology and Genetics written by Françoise Seillier-Moiseiwitsch and published by IMS. This book was released on 1999 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Reviews in Computational Chemistry Volume 3 written by Kenny B. Lipkowitz and published by John Wiley & Sons. This book was released on 2009-09-22 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Reviews in Computational Chemistry' ist ein unverzichtbares Nachschlagewerk - ein Mu? uberall dort in der Chemie, wo Molekulmodellierung als selbstverstandlicher Ansatz zur Problemlosung genutzt wird. Die Reihe verfolgt die zahlreichen Entwicklungen in der Computerchemie. Sie bringt Beitrage, mit denen der Leser Probleme erkennen und losen kann. Gleichzeitig kann er damit Schlusselarbeiten rasch ausfindig machen. Ziel des dritten Bandes ist die Problemlosung von Computermethoden und der Nachweis von Schlusselarbeiten. Das Werk zahlt die wichtigsten Konzepte auf und erlautert sie eingehend: - Mathematische Grundlagen - Grundlegende Strukturen der Vereinfachung - Methoden der Modellierung Das Buch ist somit gleicherma?en eine Hilfe fur den Praktiker und ein Kurs fur Neulinge auf dem Gebiet
Download or read book Protein Conformation written by Derek J. Chadwick and published by John Wiley & Sons. This book was released on 2008-04-30 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: How the amino acid sequence of a protein determines its three-dimensional structure is a major problem in biology and chemistry. Leading experts in the fields of NMR spectroscopy, X-ray crystallography, protein engineering and molecular modeling offer provocative insights into current views on the protein folding problem and various aspects for future progress.
Download or read book Bioinformatics and Biomedical Engineering written by Ignacio Rojas and published by Springer. This book was released on 2019-04-30 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two-volume set LNBI 11465 and LNBI 11466 constitutes the proceedings of the 7th International Work-Conference on Bioinformatics and Biomedical Engineering, IWBBIO 2019, held in Granada, Spain, in May 2019. The total of 97 papers presented in the proceedings, was carefully reviewed and selected from 301 submissions. The papers are organized in topical sections as follows: Part I: High-throughput genomics: bioinformatics tools and medical applications; omics data acquisition, processing, and analysis; bioinformatics approaches for analyzing cancer sequencing data; next generation sequencing and sequence analysis; structural bioinformatics and function; telemedicine for smart homes and remote monitoring; clustering and analysis of biological sequences with optimization algorithms; and computational approaches for drug repurposing and personalized medicine. Part II: Bioinformatics for healthcare and diseases; computational genomics/proteomics; computational systems for modelling biological processes; biomedical engineering; biomedical image analysis; and biomedicine and e-health.
Download or read book Mathematical Challenges from Theoretical Computational Chemistry written by National Research Council and published by National Academies Press. This book was released on 1995-03-29 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational methods are rapidly becoming major tools of theoretical, pharmaceutical, materials, and biological chemists. Accordingly, the mathematical models and numerical analysis that underlie these methods have an increasingly important and direct role to play in the progress of many areas of chemistry. This book explores the research interface between computational chemistry and the mathematical sciences. In language that is aimed at non-specialists, it documents some prominent examples of past successful cross-fertilizations between the fields and explores the mathematical research opportunities in a broad cross-section of chemical research frontiers. It also discusses cultural differences between the two fields and makes recommendations for overcoming those differences and generally promoting this interdisciplinary work.
Download or read book Encyclopedia of Optimization written by Christodoulos A. Floudas and published by Springer Science & Business Media. This book was released on 2008-09-04 with total page 4646 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".
Download or read book Molecular Design and Modeling written by John Joseph Langone and published by Gulf Professional Publishing. This book was released on 1991 with total page 864 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computer-based design and modeling, computational approaches, and instrumental methods for elucidating molecular mechanisms of protein folding and ligand-acceptor interactions are included in Volumes 202 and 203, as are genetic and chemical methods for the production of functional molecules including antibodies and antigens, enzymes, receptors, nucleic acids and polysaccharides, and drugs.
