Related papers: Statistical Distribution of Crystallographic Group…
It is now possible to measure detailed spectral indices for stellar populations in spiral disks. We propose to interpret these data using evolutionary synthesis models computed from the Star Formation Histories obtained from chemical…
Prediction of stable crystal structures at given pressure-temperature conditions, based only on the knowledge of the chemical composition, is a central problem of condensed matter physics. This extremely challenging problem is often termed…
Coagulation-fragmentation processes describe the stochastic association and dissociation of particles in clusters. Cluster dynamics with cluster-cluster interactions for a finite number of particles has recently attracted attention…
Exact expressions for probability densities of conjugate pair separation in euclidean isometries are obtained, for the cosmic crystallography.These are the theoretical counterparts of the mean histograms arising from computer simulation of…
Data mining is a recognized predictive tool in a variety of areas ranging from bioinformatics and drug design to crystal structure prediction. In the present study, an electronic structure implementation has been combined with structural…
This work presents a simple scheme for finding new crystalline compounds by adapting structure types from neighbor atoms compounds. The approach is demonstrated for the selenide and sulfide families of binary compounds. It predicts ten new…
A crystallographic cell is a representation of a lattice, but each lattice can be represented just as well by any of an infinite number of such unit cells. Searching for matches to an experimentally determined crystallographic unit cell in…
Composed ensembles of random unitary matrices are defined via products of matrices, each pertaining to a given canonical circular ensemble of Dyson. We investigate statistical properties of spectra of some composed ensembles and demonstrate…
Generative models have achieved impressive results in many domains including image and text generation. In the natural sciences, generative models have led to rapid progress in automated drug discovery. Many of the current methods focus on…
In this thesis we consider crystal groups in dimension $n$ and their natural unitary representation on $L^2(\mathbb{R}^n)$. We show that this representation is unitarily equivalent to a direct integral of factor representations, and use…
Counts in cells are used to analyse the higher order properties of the statistics of the EDSGC survey. The probability distribution is obtained from an equal area projection source catalog with infinite oversampling over the range…
Crystalline structure prediction is an essential prerequisite for designing materials with targeted properties. Yet, it is still an open challenge in materials design and drug discovery. Despite recent advances in computational materials…
A theory of structure is formulated for systems of many structureless classical particles with stable local interactions in Euclidean space. Such systems are shown to have their structure in thermodynamic equilibrium determined exactly by a…
Data clustering is the process of identifying natural groupings or clusters within multidimensional data based on some similarity measure. Clustering is a fundamental process in many different disciplines. Hence, researchers from different…
Materials property predictions have improved from advances in machine learning algorithms, delivering materials discoveries and novel insights through data-driven models of structure-property relationships. Nearly all available models rely…
Describing the deviation of a real structure from a hypothetical higher-symmetry ideal can be a powerful tool to understand and interpret phase transitions. Here we introduce a simple yet effective metric that quantifies the degree of unit…
Machine learning algorithms based on artificial neural networks have proven very useful for a variety of classification problems. Here we apply them to a well-known problem in crystallography, namely the classification of X-ray diffraction…
Three methods for detecting and characterizing structure in point data, such as that generated by redshift surveys, are described: classification using self-organizing maps, segmentation using Bayesian blocks, and density estimation using…
The quaternion Bingham distribution has been used to model preferred crystallographic orientation, or crystallographic texture, in polycrystalline materials in the materials science and geological communities. A primary difficulty in…
We explain how following the representation of 3D crystallographic space groups in geometric algebra it is further possible to similarly represent the 162 socalled subperiodic groups of crystallography in geometric algebra. We construct a…