Related papers: $\texttt{Spglib}$: a software library for crystal …
The latticework structure known as the cosmic web provides a valuable insight into the assembly history of large-scale structures. Despite the variety of methods to identify the cosmic web structures, they mostly rely on the assumption that…
Semidefinite programming (SDP) is a powerful framework from convex optimization that has striking potential for data science applications. This paper develops a provably correct randomized algorithm for solving large, weakly constrained SDP…
As is well known, crystals have discrete space translational symmetry. It was recently noticed that one-dimensional crystals possibly have discrete Poincar\'{e} symmetry, which contains discrete Lorentz and discrete time translational…
Crystal structure prediction (CSP) is now increasingly used in the discovery of novel materials with applications in diverse industries. However, despite decades of developments, the problem is far from being solved. With the progress of…
Discovering new materials is a challenging task in materials science crucial to the progress of human society. Conventional approaches based on experiments and simulations are labor-intensive or costly with success heavily depending on…
The paper describes an extension of the Liga algorithm for structure solution from atomic pair distribution function (PDF), to handle periodic crystal structures with multiple elements in the unit cell. The procedure is performed in 2…
Commonly-used clustering algorithms usually find ellipsoidal, spherical or other regular-structured clusters, but are more challenged when the underlying groups lack formal structure or definition. Syncytial clustering is the name that we…
Crystal structures are defined by the periodic arrangement of atoms in 3D space, inherently making them equivariant to SO(3) group. A fundamental requirement for crystal property prediction is that the model's output should remain invariant…
This article presents an automated method to quantify and detect symmetry elements in 2D patterns by means of image processing. Escher's woodcuts, a widely recognized didactic tool for crystallographic education of students, were used to…
Semidefinite programs (SDP) are one of the most versatile frameworks in numerical optimization, serving as generalizations of many conic programs and as relaxations of NP-hard combinatorial problems. Their main drawback is their…
Structural search and feature extraction are a central subject in modern materials design, the efficiency of which is currently limited, but can be potentially boosted by machine learning (ML). Here, we develop an ML-based…
Symmetries play an critical role in finding analytic solutions to nonlinear differential equations. A symmetry is a mapping of the solutions of the differential equation into the solutions and have been studied extensively for over a…
polyDB is a database for discrete geometric objects. The database is accessible via web and an interface from the software package polymake. It contains various datasets from the area of lattice polytopes, combinatorial polytopes, matroids…
This paper introduces the 2019 version of \us{}, a novel Constraint Programming framework for floating point verification problems expressed with the SMT language of SMTLIB. SMT solvers decompose their task by delegating to specific…
Clustering is an unsupervised technique of Data Mining. It means grouping similar objects together and separating the dissimilar ones. Each object in the data set is assigned a class label in the clustering process using a distance measure.…
Current catalogues of open clusters are rather heterogeneous and incomplete lists of clusters than true catalogues. Before there has been no attempts of automatic search for open clusters in huge photometric catalogues using homogeneous…
This document describes our freely distributed Maple library {\sc spectra}, for Semidefinite Programming solved Exactly with Computational Tools of Real Algebra. It solves linear matrix inequalities with symbolic computation in exact…
The flawless functioning of a protein is essentially linked to its own three-dimensional structure. Therefore, the prediction of a protein structure from its amino acid sequence is a fundamental problem in many fields that draws researchers…
For a given linear program (LP) a permutation of its variables that sends feasible points to feasible points and preserves the objective function value of each of its feasible points is a symmetry of the LP. The set of all symmetries of an…
We put forward a technique to unveil to which symmetry group a nonlinear crystal belongs, making use of nonlinear optics with structured light. We consider as example the process of spontaneous parametric down-conversion. The crystal, which…