Distance Geometry: Theory, Methods, and Applications

  title={Distance Geometry: Theory, Methods, and Applications},
  author={A. Mucherino and C. Lavor and Leo Liberti and N. Maculan},
  booktitle={Distance Geometry},
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… Expand
Clifford Algebra and the Discretizable Molecular Distance Geometry Problem
Nuclear Magnetic Resonance experiments can provide distances between pairs of atoms of a protein that are close enough and the problem is how to determine the 3D protein structure based on thisExpand
Álgebra geométrica conforme em geometria de distâncias com incertezas
The Discretizable Molecular Distance Geometry Problem (DMDGP) consists of determining the 3D structure of a protein using information of inter atomic distances obtained in experiments of NuclearExpand
Oriented Conformal Geometric Algebra and the Molecular Distance Geometry Problem
The problem of 3D protein structure determination using distance information from nuclear magnetic resonance (NMR) experiments is a classical problem in distance geometry. NMR data and the chemistryExpand
New Error Measures and Methods for Realizing Protein Graphs from Distance Data
This paper focuses on the application to the conformation of proteins in space, which is a basic step in determining protein function: given interval estimations of some of the inter-atomic distances, find their shape. Expand
An application-based characterization of dynamical distance geometry problems
This work proposes an application-based characterization of dynDGP instances, where the main criteria are the presence or absence of a skeletal structure, and the rigidity of such a skeletalructure. Expand
Recent advances on the interval distance geometry problem
The result is an improved method for estimating 3D structures of small proteins based only on the knowledge of some distance restraints between pairs of atoms. Expand
Distance Geometry in Structural Biology: New Perspectives
This chapter focuses on methods for structure determination based on distance information obtained by nuclear magnetic resonance (NMR) experiments, and gives a brief overview of a new promising approach to the molecular distance geometry problem (MDGP). Expand
Energy-based pruning devices for the BP algorithm applied to Distance Geometry
Computer experiments show that the newly added pruning devices are able to improve the performance of the BP algorithm, as well as the quality (in terms of energy) of the conformations in the solution set. Expand
Calculating the possible conformations arising from uncertainty in the molecular distance geometry problem using constraint interval analysis
This paper proposes a new methodology to compute possible conformations on the presence of uncertainties arising from NMR distance measurements using a constraint interval analysis approach. Expand
A new algorithm for the KDMDGP subclass of Distance Geometry Problems
A new algorithm is presented, which exploits DMDGP symmetries more effectively than its predecessors, and the speedup, with respect to the classic BP algorithm, is considerable for sparse DMD GP instances related to protein conformation. Expand