Euclidean Distance Geometry and Applications

By Leo Liberti, Carlile Lavor, Nelson Maculan, Antonio Mucherino. SIAM Review, 2012

561 citations recorded by the source corpus.

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 set of distances and the output is a set of points in Euclidean space realizing those given distances. We survey the theory of Euclidean distance geometry and its most important applications, with special emphasis on molecular conformation problems.

Subfields: Applied Mathematics, Computer Graphics and Computer-Aided Design, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/4720fd86dc3fddca2ee5a2552d9b5eb586e669dd

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Minkai Xu
2. Jian Tang
3. Yang Song
4. Yoshua Bengio
5. Stefano Ermon
6. Emilio Carrizosa
7. Lantao Yu

In Computer Graphics and Computer-Aided Design

1. Minkai Xu
2. Jian Tang
3. Yang Song
4. Yoshua Bengio
5. Stefano Ermon
6. Leo Liberti
7. Shitong Luo

In Numerical Analysis

1. Minkai Xu
2. Jian Tang
3. Yang Song
4. Vanesa Guerrero
5. Yoshua Bengio
6. Stefano Ermon
7. Dolores Romero Morales
8. Leo Liberti

Citations in the corpus

• Learning Gradient Fields for Molecular Conformation Generation (2021, methodology): “In general, these approaches (Simm & Hernandez-Lobato, 2020; Xu et al., 2021) are divided into two stages, which first predict the molecular distance geometry, i.e., interatomic distances, and then convert the distances to 3D coordinates via post-processing algorithms (Liberti et al., 2014).”
• Prototype-Incorporated Emotional Neural Network (2018, background): “The Euclidean distance metric is defined in [56]”
• Visualizing data as objects by DC (difference of convex) optimization (2017, background): “Ours can also be seen as a problem in Distance Geometry optimization, as carefully reviewed in [39].”
• GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation (2022, methodology): “, 2021a) proposed to predict the interatomic distance matrix by VAE and Flow respectively, and then solve the geometry through the Distance Geometry (DG) technique (Liberti et al., 2014), which searches reasonable coordinates that matches with the predicted”
• Distance geometry and data science (2019, background): “rk that the input of the DGP can also be represented by a partial n ndistance matrix Dwhere only the entries d uv corresponding to fu;vg2Eare specied. Many more notions about the DGP can be found in [118, 115]. 3.2 Number of solutions A DGP instance may have no solutions if the given distances do no”
• Learning Neural Generative Dynamics for Molecular Conformation Generation (2021, background): “, the distances between atoms)—which are rotationally and translationally invariant—and then generate the molecular conformation based on the distance geometry through a post-processing algorithm (Liberti et al., 2014).”