On the number of realizations of certain Henneberg graphs arising in protein conformation

DOI10.1016/j.dam.2013.01.020zbMath1288.05121OpenAlexW2081415437WikidataQ62562148 ScholiaQ62562148MaRDI QIDQ2448906

Jon Lee, Benoît Masson, Leo Liberti, Carlile C. Lavor, Antonio Mucherino

Publication date: 5 May 2014

Published in: Discrete Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.dam.2013.01.020

zbMATH Keywords

distance geometrygraph rigiditybranch-and-pruneprotein conformationpartial reflection

Mathematics Subject Classification ID

Applications of graph theory (05C90) Protein sequences, DNA sequences (92D20) Distance in graphs (05C12) Signed and weighted graphs (05C22)

Related Items

The Number of Realizations of a Laman Graph, The referenced vertex ordering problem: theory, applications, and solution methods, Improving the sampling process in the interval branch-and-prune algorithm for the discretizable molecular distance geometry problem, A symmetry-based splitting strategy for discretizable distance geometry problems, A least-squares approach for discretizable distance geometry problems with inexact distances, The \(K\)-discretization and \(K\)-incident graphs for discretizable distance geometry, A constrained interval approach to the generalized distance geometry problem, Recent advances on the interval distance geometry problem, Distance geometry and data science, Distance Geometry on the Sphere, A numerical-and-computational study on the impact of using quaternions in the branch-and-prune algorithm for exact discretizable distance geometry problems, Lower Bounds on the Number of Realizations of Rigid Graphs, On the maximal number of real embeddings of minimally rigid graphs in \(\mathbb{R}^2,\mathbb{R}^3\) and \(S^2\), Realizing Euclidean distance matrices by sphere intersection, Equivalent realisations of a rigid graph, Minimal NMR distance information for rigidity of protein graphs, Oriented conformal geometric algebra and the molecular distance geometry problem, Recent results on assigned and unassigned distance geometry with applications to protein molecules and nanostructures, Discretization vertex orders in distance geometry, Assigned and unassigned distance geometry: applications to biological molecules and nanostructures, On the optimality of finding DMDGP symmetries, New error measures and methods for realizing protein graphs from distance data, Geometric algebra to describe the exact discretizable molecular distance geometry problem for an arbitrary dimension, A new algorithm for the \(^K\)DMDGP subclass of distance geometry problems with exact distances, Optimal partial discretization orders for discretizable distance geometry, On the polynomiality of finding \(^K\text{DMDGP}\) re-orders, Calculating the possible conformations arising from uncertainty in the molecular distance geometry problem using constraint interval analysis, A quantum approach to the discretizable molecular distance geometry problem

Uses Software

• MD-jeep

Cites Work

• On the computation of protein backbones by using artificial backbones of hydrogens
• Discretization orders for distance geometry problems
• The discretizable molecular distance geometry problem
• Molecular modeling and simulation. An interdisciplinary guide
• Theory of semidefinite programming for sensor network localization
• Problems of distance geometry and convex properties of quadratic maps
• A geometric build-up algorithm for solving the molecular distance geometry problem with sparse distance data
• The discretizable distance geometry problem
• The interval branch-and-prune algorithm for the discretizable molecular distance geometry problem with inexact distances
• Generic global rigidity
• Universal Rigidity and Edge Sparsification for Sensor Network Localization
• Molecular distance geometry methods: from continuous to discrete
• Reconstructing a three-dimensional model with arbitrary errors
• A Branch‐and‐Prune algorithm for the Molecular Distance Geometry Problem
• On Products of Euclidean Reflections
• Infinitesimally Rigid Polyhedra. I. Statics of Frameworks
• Infinitesimally Rigid Polyhedra. II: Modified Spherical Frameworks
• Rigidity Matroids
• Conditions for Unique Graph Realizations
• On the Number of Solutions of the Discretizable Molecular Distance Geometry Problem
• Sphere and dot product representations of graphs
• MD-jeep: An Implementation of a Branch and Prune Algorithm for Distance Geometry Problems
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item