Related papers: Symmetrized Bingham Distribution for Representing …
We construct symmetric representations of distributions over two-dimensional plane with given mean values as convex combinations of distributions with supports containing not more than three points and with the same mean values.
Dramatic increases in the size and dimensionality of many recent data sets make crucial the need for sophisticated methods that can exploit inherent structure and handle missing values. In this article we derive an expectation-maximization…
An algorithm for determining crystal structures from diffraction data is described which does not rely on the usual Fourier-space formulations of atomicity. The new algorithm implements atomicity constraints in real-space, as well as…
Polymorphism, the ability of a compound to crystallize in multiple distinct structures, plays a vital role in determining the physical, chemical, and functional properties of materials. Accurate identification and prediction of polymorphic…
Application of artificial intelligence (AI) has been ubiquitous in the growth of research in the areas of basic sciences. Frequent use of machine learning (ML) and deep learning (DL) based methodologies by researchers has resulted in…
Grain boundary plane distributions are widely used to infer the mechanisms governing grain boundary formation in polycrystalline materials. We show that such interpretations are inherently ambiguous. Using a unified eight-parameter boundary…
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…
The distribution function of particles over clusters is proposed for a system of identical intersecting spheres, the centres of which are uniformly distributed in space. Consideration is based on the concept of the rank number of clusters,…
Crystal structure design is important for the discovery of new highly functional materials because crystal structure strongly influences material properties. Crystal structures are composed of space-filling polyhedra, which affect material…
Pinwheel patterns and their higher dimensional generalisations display continuous circular or spherical symmetries in spite of being perfectly ordered. The same symmetries show up in the corresponding diffraction images. Interestingly, they…
Fourier analysis and representation of circular distributions in terms of their Fourier coefficients, is quite commonly discussed and used for model-free inference such as testing uniformity and symmetry etc. in dealing with 2-dimensional…
A mixture of shifted asymmetric Laplace distributions is introduced and used for clustering and classification. A variant of the EM algorithm is developed for parameter estimation by exploiting the relationship with the general inverse…
A functional composition of the cumulative distribution function of one probability distribution with the inverse cumulative distribution function of another is called the transmutation map. In this article, we will use the quadratic rank…
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…
In this paper we provide a general framework for estimating symmetric properties of distributions from i.i.d. samples. For a broad class of symmetric properties we identify the easy region where empirical estimation works and the difficult…
Heterogeneity of many building materials complicates numerical modelling of structural behaviour. The material randomicity can be manifested by different values of material parameters of each material specimen. To capture inherent…
Arising as a fluctuation phenomenon, the equilibrium distribution of meandering steps with mean separation $<\ell>$ on a "tilted" surface can be fruitfully analyzed using results from RMT. The set of step configurations in 2D can be mapped…
Although the specification of bivariate probability models using a collection of assumed conditional distributions is not a novel concept, it has received considerable attention in the last decade. In this study, a bivariate…
Given a parametric polynomial curve $\gamma:[a,b]\rightarrow \mathbb{R}^n$, how can we sample a random point $\mathfrak{x}\in \mathrm{im}(\gamma)$ in such a way that it is distributed uniformly with respect to the arc-length? Unfortunately,…
Spectral analysis plays a crucial role in high-dimensional statistics, where determining the asymptotic distribution of various spectral statistics remains a challenging task. Due to the difficulties of deriving the analytic form, recent…