Distance Geometry [electronic resource] : Theory, Methods, and Applications / edited by Antonio Mucherino, Carlile Lavor, Leo Liberti, Nelson Maculan.

Preface -- 1. Universal Rigidity of Bar Frameworks in General Position (A. Alfakih) -- 2. Mixed Volume and Distance Geometry Techniques for Counting Euclidean Embeddings of Rigid Graphs (I. Emiris, E. Tsigaridas, A. Varvitsiotis) -- 3. (The discretizable molecular distance Geometry Problem Seems Easier on Proteins (L. Liberti, C. Lavor, A. Mucherino) -- 4. Spheres Unions and Intersections and Some of Their Applications in Molecular Modeling (M. Petitjean) -- 5. Is the Distance Geometry Problem in NP? (N. Beeker, S. Gaubert, C. Glusa, L. Liberti) -- 6. Solving Spatial Constraints with Generalized Distance Geometry (L. Yang) -- 7. A Topological Interpretation of the Walk Distances (P. Chebotarev, M. Deza) -- 8. Distance Geometry Methods for Protein Structure Determination (Z. Voller, Z. Wu) -- 9. Solving the discretizable molecular distance geometry problem by multiple realization trees (P. Nucci, L. Nogueira, C. Lavor) -- 10.-ASAP - An Eigenvector Synchronization Algorithm for the Graph Realization Problem (M. Cucuringu) -- 11. Global Optimization for Atomic Cluster Distance Geometry Problems (M. Locatelli, F. Schoen) -- 12. Solving molecular distance geometry problems using a continuous optimization approach (R. Lima, J.M. Martinez) -- 13. DC Programming Approaches for Distance Geometry Problems (H. Thi, T. Dinh) -- 14. Stochastic Proximity Embedding (D. Agrafiotis, D. Bandyopadhyay, E. Yang) -- 15. Distance Geometry for Realistic Molecular Conformations -- 16. Distance Geometry in Structural Biology (T. Malliavin, A. Mucherino, M. Nilges) -- 17. Using a Distributed SDP Approach to Solve Simulated Protein Molecular Conformation Problems (X. Fang, K-C. Toh) -- 18. An Overview on Protein Structure Determintion by NMR - Historical and Future Perspectives of the Use of Distance Geometry Methods.-Index.

Distance Geometry: Theory, Methods, and Applications is the first collection of research surveys dedicated to distance geometry and its applications. The first part of the book discusses theoretical aspects of the Distance Geometry Problem (DGP), where the relation between DGP and other related subjects are also presented. Covered topics include distance matrix theory, Euclidean distance matrix completion, multispherical structure of distance matrices, geometric algebra, algebraic distance geometry theory, visualization of K-dimensional structures in the plane, graph rigidity, and theory of discretizable DGP. The second part of this volume presents mathematical and computational properties of methods developed to the problems discussed in the first portion, 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 comprise the third part of the book, which is mainly devoted to the application of DGP to NMR structure calculation. This is an important and strongly multidisciplinary application in biology and biomedicine.