Related papers: Metrics for measuring distances in configuration s…

Machine Learning (ML) techniques are revolutionizing the way to perform efficient materials modeling. Nevertheless, not all the ML approaches allow for the understanding of microscopic mechanisms at play in different phenomena. To address…

Conformational transitions are ubiquitous in biomolecular systems, have significant functional roles and are subject to evolutionary pressures. Here we provide a first theoretical framework for topological transition, i.e. conformational…

The problem of recovering the configuration of points from their partial pairwise distances, referred to as the Euclidean Distance Matrix Completion (EDMC) problem, arises in a broad range of applications, including sensor network…

Quantifying similarity between data objects is an important part of modern data science. Deciding what similarity measure to use is very application dependent. In this paper, we combine insights from systems theory and machine learning, and…

We study the problem of representing all distances between $n$ points in $\mathbb R^d$, with arbitrarily small distortion, using as few bits as possible. We give asymptotically tight bounds for this problem, for Euclidean metrics, for…

Many statistical applications require the quantification of joint dependence among more than two random vectors. In this work, we generalize the notion of distance covariance to quantify joint dependence among d >= 2 random vectors. We…

This paper proposes a criterion for detecting change structures in tensor data. To accommodate tensor structure with structural mode that is not suitable to be equally treated and summarized in a distance to measure the difference between…

We continue our investigation of the configuration space of general relativity begun in I (gr-qc/9411009). Here we examine the Hamiltonian constraint when the spatial geometry is momentarily static (MS). We show that MS configurations…

Window profiles of amino acids in protein sequences are taken as a description of the amino acid environment. The relative entropy or Kullback-Leibler distance derived from profiles is used as a measure of dissimilarity for comparison of…

Descriptors are physically-inspired schemes for representing atomistic systems that play a central role in the construction of models of potential energy surfaces. Although physical intuition can be flexibly encoded into descriptor schemes,…

Given a set of sequences, the distance between pairs of them helps us to find their similarity and derive structural relationship amongst them. For genomic sequences such measures make it possible to construct the evolution tree of…

Motivated by the problem of fingerprint matching, we present geometric approximation algorithms for matching a pattern point set against a background point set, where the points have angular orientations in addition to their positions.

By a method inspired of the Stein's method, we derive an upper-bound of the Rubinstein distance between two absolutely continuous probability measures on configurations space. As an application, we show that the best way to approximate a…

Modeling signals as linear combinations of atoms from a dictionary is ubiquitous in modern signal processing. In the finite-dimensional setting, whenever atoms depend nonlinearly upon unknown parameters, the signal model is said to be…

We propose a novel method of introducing structure into existing machine learning techniques by developing structure-based similarity and distance measures. To learn structural information, low-dimensional structure of the data is captured…

Successful scientific applications of large-scale molecular dynamics often rely on automated methods for identifying the local crystalline structure of condensed phases. Many existing methods for structural identification, such as Common…

Computational molecular representations underpin virtual screening, property prediction, and materials discovery. Conventional fingerprints are efficient and deterministic but lose structural information through hash-based compression,…

This paper presents a data structure that summarizes distances between configurations across a robot configuration space, using a binary space partition whose cells contain parameters used for a locally linear approximation of the distance…

We propose a methodology for intercomparing climate models and evaluating their performance against benchmarks based on the use of the Wasserstein distance (WD). This distance provides a rigorous way to measure quantitatively the difference…

Data types that lie in metric spaces but not in vector spaces are difficult to use within the usual regression setting, either as the response and/or a predictor. We represent the information in these variables using distance matrices which…