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Statistically sound crystallographic symmetry classifications are obtained with information theory based methods in the presence of approximately Gaussian distributed noise. A set of three synthetic images with very strong Fedorov type…
Statistically sound crystallographic symmetry classifications are obtained with information theory based methods in the presence of approximately Gaussian distributed noise. A set of three synthetic patterns with strong Fedorov type…
A geometric form of information theory allows for reasonable, i.e. probabilistic, evidence-ranking based, and generalized noise-level dependent, classifications of the crystallographic and quasicrystallographic symmetries in noisy digital…
Crystallographic symmetry classifications from real-world images with periodicities in two dimensions (2D) are of interest to crystallographers and practitioners of computer vision studies alike. Currently, these classifications are…
The robust and automated determination of crystal symmetry is of utmost importance in material characterization and analysis. Recent studies have shown that deep learning (DL) methods can effectively reveal the correlations between X-ray or…
The recently developed information-theoretic approach to crystallographic symmetry classifications and quantifications in two dimensions (2D) from digital transmission electron and scanning probe microscope images is adapted for the…
The classifications approaches for the crystallographic symmetries of patterns that are more or less periodic in two dimensions are critically reviewed and their relative performance qualitatively evaluated. The information theory based…
A routine crystallography technique, crystal structure analysis, is rarely performed in computational condensed matter research. The lack of methods to identify and characterize crystal structures reliably in particle simulation data…
A Python program for calculating the metrics necessary to perform information-theory based symmetry classifications and quantifications of transmission electron diffraction spot patterns is introduced. It is the first of its kind, in that…
The high-level structure of a graph is a crucial ingredient for the analysis and visualization of relational data. However, discovering the salient graph patterns that form this structure is notoriously difficult for two reasons. (1)…
Symmetry is an implicit objective in structural form-finding that often reconciles efficiency and aesthetics. This paper identifies the symmetry of polyhedral diagrams in three-dimensional graphic statics (3DGS) as point groups and…
We suggest new modification (we call it a noise reduction procedure) for Steinhardt parameters which are often used for detecting crystalline structures in computer simulation of solids and soft matter systems. We have also developed a new…
Crystals are the materials which can be described by uniform periodic lattices. Traditionally, only the 1-, 2-, 3-, 4- and 6-fold rotation symmetries are allowed in crystals because other n-fold rotation symmetries are forbidden by the…
The recently developed information-theoretic approach to crystallographic symmetry classifications and quantifications in two dimensions (2D) from digital transmission electron and scanning probe microscope images is adapted for the…
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…
Determining crystal symmetry from powder X-ray diffraction is a central problem in materials characterization, yet multiple space groups can produce indistinguishable patterns, making automated classification difficult. We show that…
Computational methods that automatically extract knowledge from data are critical for enabling data-driven materials science. A reliable identification of lattice symmetry is a crucial first step for materials characterization and…
Finding an optimal match between two different crystal structures underpins many important materials science problems, including describing solid-solid phase transitions, developing models for interface and grain boundary structures. In…
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…
Momentum-space nonsymmorphic symmetries have recently attracted significant interest in both artificial and condensed-matter crystals, whereas real-space nonsymmorphic symmetries have long played an important role in the study of…