03962nam 22006975 450 991025430250332120200629215452.03-319-60792-810.1007/978-3-319-60792-4(CKB)4100000000586888(DE-He213)978-3-319-60792-4(MiAaPQ)EBC5591973(PPN)204534666(EXLCZ)99410000000058688820170921d2017 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierEuclidean Distance Geometry An Introduction /by Leo Liberti, Carlile Lavor1st ed. 2017.Cham :Springer International Publishing :Imprint: Springer,2017.1 online resource (XIII, 133 p. 60 illus., 31 illus. in color.) Springer Undergraduate Texts in Mathematics and Technology,1867-55063-319-60791-X Introduction -- 1. Motivation -- 2. The Distance Geometry Problem -- 3. Realizing Complete Graphs -- 4. Discretizability -- 5. Molecular Distance Geometry Problems -- 6.Vertex Orders -- 7. Flexibility and Rigidity -- 8. Approximate Realizations -- 9. Taking DG Further -- Appendix A. Mathematical Notions.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.Springer Undergraduate Texts in Mathematics and Technology,1867-5506Convex geometry Discrete geometryMathematical optimizationComputer science—MathematicsAlgorithmsDiscrete mathematicsConvex and Discrete Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M21014Discrete Optimizationhttps://scigraph.springernature.com/ontologies/product-market-codes/M26040Discrete Mathematics in Computer Sciencehttps://scigraph.springernature.com/ontologies/product-market-codes/I17028Algorithmshttps://scigraph.springernature.com/ontologies/product-market-codes/M14018Discrete Mathematicshttps://scigraph.springernature.com/ontologies/product-market-codes/M29000Convex geometry .Discrete geometry.Mathematical optimization.Computer science—Mathematics.Algorithms.Discrete mathematics.Convex and Discrete Geometry.Discrete Optimization.Discrete Mathematics in Computer Science.Algorithms.Discrete Mathematics.514.3Liberti Leoauthttp://id.loc.gov/vocabulary/relators/aut767458Lavor Carlileauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910254302503321Euclidean Distance Geometry1985612UNINA