Distance Geometry: Theory, Methods, and Applications

Front Cover
Antonio Mucherino, Carlile Lavor, Leo Liberti, Nelson Maculan
Springer Science & Business Media, Dec 22, 2012 - Mathematics - 420 pages

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.

 

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Contents

Distance
16
Mucherino
26
The Discretizable Molecular Distance Geometq
70
Is the Distance Geometry Problem in
3
Problems
14
Rigidity Theory
15
Solving Spatial Constraints with Generalized Distance
16
A Topological Interpretation of the Walk Distances
44
An Eigenvector Synchronization Algorithm
29
Global Optimization for Atomic Cluster Distance
1874
Solving Molecular Distance Geometq Problems Using
1893
A Simple Fast
1956
Crippen
1981
Mucherino et al 16
Antonio Mucherino
An Overview on Protein Structure Determination

Distance Geometq Methods for Protein Structure
8
Mucherino et al 16
16

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