Related papers: The Density Fingerprint of a Periodic Point Set

Measuring similarities/dissimilarities between atomic structures is important for the exploration of potential energy landscapes. However, the cell vectors together with the coordinates of the atoms, which are generally used to describe…

Periodic point sets model all solid crystalline materials (crystals) whose atoms can be considered zero-sized points with or without atomic types. This paper addresses the fundamental problem of checking whether claimed crystals are novel,…

Recently, reported a comments on the our paper [JAP21-AR-03574R].. For clarification, we applied the fingerprint theory to examine the similarity between the distinct structures. The fingerprint function is a crystal structure descriptor,…

Periodic material or crystal property prediction using machine learning has grown popular in recent years as it provides a computationally efficient replacement for classical simulation methods. A crucial first step for any of these…

In this study, we present a novel molecular fingerprint generation method based on multiparameter persistent homology. This approach reveals the latent structures and relationships within molecular geometry, and detects topological features…

We introduce a new fingerprint that allows distinguishing between liquid-like and solid-like atomic environments. This fingerprint is based on an approximate expression for the entropy projected on individual atoms. When combined with a…

Identifying similar materials, i.e., those sharing a certain property or feature, requires interoperable data of high quality. It also requires means to measure similarity. We demonstrate how a spectral fingerprint as a descriptor, combined…

Periodic point sets model all solid crystalline materials whose structures are determined in a rigid form and should be studied up to rigid motion or isometry preserving inter-point distances. In 2021 H.Edelsbrunner et al. introduced an…

The fundamental model of any periodic crystal is a periodic set of points at all atomic centres. Since crystal structures are determined in a rigid form, their strongest equivalence is rigid motion (composition of translations and…

This paper presents a new approach for the visualization and analysis of the spatial variability of features of interest represented by critical points in ensemble data. Our framework, called Persistence Atlas, enables the visualization of…

The fundamental model of a periodic structure is a periodic point set up to rigid motion or isometry. Our recent paper in SoCG 2021 defined isometry invariants (density functions), which are complete in general position and continuous under…

Accurate description of crystal structures is a prerequisite for predicting the physicochemical properties of materials. However, conventional X-ray diffraction (XRD) characterization often encounters intrinsic bottlenecks when applied to…

Crystal material representation is the foundation of crystal material research. Existing works consider crystal molecules as graph data with different representation methods and leverage the advantages of techniques in graph learning. A…

Fingerprints are the most widely deployed form of biometric identification. No two individuals share the same fingerprint because they have unique biometric identifiers. This paper presents an efficient fingerprint verification algorithm…

Many real objects are modeled as discrete sets of points, such as corners or other salient features. For our main applications in chemistry, points represent atomic centers in a molecule or a solid material. We study the problem of…

This paper develops a new continuous approach to a similarity between periodic lattices of ideal crystals. Quantifying a similarity between crystal structures is needed to substantially speed up the Crystal Structure Prediction, because the…

Crystal Structure Prediction (CSP) aims to discover solid crystalline materials by optimizing periodic arrangements of atoms, ions or molecules. CSP takes weeks of supercomputer time because of slow energy minimizations for millions of…

This paper rigorously solves the challenging problem of recognizing periodic patterns under rigid motion in Euclidean geometry. The 3-dimensional case is practically important for justifying the novelty of solid crystalline materials…

Molecular fingerprints, i.e. feature vectors describing atomistic neighborhood configurations, is an important abstraction and a key ingredient for data-driven modeling of potential energy surface and interatomic force. In this paper, we…

Significant progress in many classes of materials could be made with the availability of experimentally-derived large datasets composed of atomic identities and three-dimensional coordinates. Methods for visualizing the local atomic…