A Geometric Buildup Algorithm for the Solution of the Distance Geometry Problem Using Least-Squares Approximation

2009 ◽  
Vol 71 (8) ◽  
pp. 1914-1933 ◽  
Author(s):  
Atilla Sit ◽  
Zhijun Wu ◽  
Yaxiang Yuan
Keyword(s):  
Least Squares ◽  
Distance Geometry ◽  
Least Squares Approximation ◽  
Geometry Problem ◽  
Distance Geometry Problem

A NOTE ON COMPUTING THE INTERSECTION OF SPHERES IN

2017 ◽  
Vol 59 (2) ◽  
pp. 271-279 ◽  
Author(s):  
D. S. MAIOLI ◽  
C. LAVOR ◽  
D. S. GONÇALVES
Keyword(s):  
Multidimensional Scaling ◽  
Distance Geometry ◽  
Qr Decomposition ◽  
Interesting Problem ◽  
Global Positioning Systems ◽  
Positioning Systems ◽  
Global Positioning ◽  
Interval Distance ◽  
Geometry Problem ◽  
Distance Geometry Problem

Finding the intersection of $n$-dimensional spheres in $\mathbb{R}^{n}$ is an interesting problem with applications in trilateration, global positioning systems, multidimensional scaling and distance geometry. In this paper, we generalize some known results on finding the intersection of spheres, based on QR decomposition. Our main result describes the intersection of any number of $n$-dimensional spheres without the assumption that the centres of the spheres are affinely independent. A possible application in the interval distance geometry problem is also briefly discussed.

A constrained interval approach to the generalized distance geometry problem

2018 ◽  
Vol 14 (2) ◽  
pp. 483-492
Author(s):  
Luiz Leduino de Salles Neto ◽  
Carlile Lavor ◽  
Weldon Lodwick
Keyword(s):  
Distance Geometry ◽  
Interval Approach ◽  
Geometry Problem ◽  
Distance Geometry Problem ◽  
Generalized Distance

diSTruct v1.0: generating biomolecular structures from distance constraints

2019 ◽  
Author(s):  
Oskar Taubert ◽  
Ines Reinartz ◽  
Henning Meyerhenke ◽  
Alexander Schug
Keyword(s):  
Graph Drawing ◽  
Distance Geometry ◽  
Life Sciences ◽  
Supplementary Information ◽  
Graph Analysis ◽  
Biological Macromolecules ◽  
Geometry Problem ◽  
Distance Data ◽  
Distance Geometry Problem ◽  
Python Package

Abstract Summary The distance geometry problem is often encountered in molecular biology and the life sciences at large, as a host of experimental methods produce ambiguous and noisy distance data. In this note, we present diSTruct; an adaptation of the generic MaxEnt-Stress graph drawing algorithm to the domain of biological macromolecules. diSTruct is fast, provides reliable structural models even from incomplete or noisy distance data and integrates access to graph analysis tools. Availability and implementation diSTruct is written in C++, Cython and Python 3. It is available from https://github.com/KIT-MBS/distruct.git or in the Python package index under the MIT license. Supplementary information Supplementary data are available at Bioinformatics online.

scholarly journals On the recognition of unit disk graphs and the Distance Geometry Problem with Ranges

2015 ◽  
Vol 197 ◽  
pp. 3-19 ◽  
Author(s):  
Guilherme Dias da Fonseca ◽  
Vinícius Gusmão Pereira de Sá ◽  
Raphael Carlos Santos Machado ◽  
Celina Miraglia Herrera de Figueiredo
Keyword(s):  
Unit Disk ◽  
Distance Geometry ◽  
Unit Disk Graphs ◽  
Geometry Problem ◽  
Distance Geometry Problem
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