Euclidean distance geometry and applications
Euclidean distance geometry is the study of Euclidean geometry based on the concept of
distance. This is useful in several applications where the input data consist of an incomplete …
distance. This is useful in several applications where the input data consist of an incomplete …
Recent advances on the interval distance geometry problem
We discuss a discretization-based solution approach for a classic problem in global
optimization, namely the distance geometry problem (DGP). We focus our attention on a …
optimization, namely the distance geometry problem (DGP). We focus our attention on a …
Distance geometry and data science
L Liberti - Top, 2020 - Springer
Data are often represented as graphs. Many common tasks in data science are based on
distances between entities. While some data science methodologies natively take graphs as …
distances between entities. While some data science methodologies natively take graphs as …
[HTML][HTML] Discretization vertex orders in distance geometry
When a weighted graph is an instance of the Distance Geometry Problem (DGP), certain
types of vertex orders (called discretization orders) allow the use of a very efficient, precise …
types of vertex orders (called discretization orders) allow the use of a very efficient, precise …
An algorithm to enumerate all possible protein conformations verifying a set of distance constraints
Background The determination of protein structures satisfying distance constraints is an
important problem in structural biology. Whereas the most common method currently …
important problem in structural biology. Whereas the most common method currently …
The number of realizations of a Laman graph
J Capco, M Gallet, G Grasegger, C Koutschan… - SIAM Journal on Applied …, 2018 - SIAM
Laman graphs model planar frameworks that are rigid for a general choice of distances
between the vertices. There are finitely many ways, up to isometries, to realize a Laman …
between the vertices. There are finitely many ways, up to isometries, to realize a Laman …
[HTML][HTML] Minimal NMR distance information for rigidity of protein graphs
Abstract Nuclear Magnetic Resonance (NMR) experiments provide distances between
nearby atoms of a protein molecule. The corresponding structure determination problem is …
nearby atoms of a protein molecule. The corresponding structure determination problem is …
Assigned and unassigned distance geometry: applications to biological molecules and nanostructures
Considering geometry based on the concept of distance, the results found by Menger and
Blumenthal originated a body of knowledge called distance geometry. This survey covers …
Blumenthal originated a body of knowledge called distance geometry. This survey covers …
Calculating the possible conformations arising from uncertainty in the molecular distance geometry problem using constraint interval analysis
TM Costa, H Bouwmeester, WA Lodwick, C Lavor - Information Sciences, 2017 - Elsevier
The calculation of the 3D structure of a protein molecule is important because it is
associated to its biological function. Nuclear Magnetic Resonance (NMR) experiments can …
associated to its biological function. Nuclear Magnetic Resonance (NMR) experiments can …