Related papers: Linearization Routines for the Parameter Space Con…
We present a formalism for the scattering of an arbitrary linear or acyclic branched structure build by joining mutually non-interacting arbitrary functional sub-units. The formalism consists of three equations expressing the structural…
Based on the partition of parameter space, two algorithms for computing the rational univariate representation of zero-dimensional ideals with parameters are presented in the paper. Unlike the rational univariate representation of…
In many Direct and Inverse Scattering problems one has to use a parameter-fitting procedure, because analytical inversion procedures are often not available. In this paper a variety of such methods is presented with a discussion of…
Crystal structure prediction (CSP), which aims to predict the three-dimensional atomic arrangement of a crystal from its composition, is central to materials discovery and mechanistic understanding. However, given the composition in a unit…
Currently, identification of crystallization pathways in polymers is being carried out using molecular simulation-based data on a preset cut-off point on a single order parameter (OP) to define nucleated or crystallized regions. Aside from…
Sparse principal component analysis (sparse PCA) is a widely used technique for dimensionality reduction in multivariate analysis, addressing two key limitations of standard PCA. First, sparse PCA can be implemented in high-dimensional low…
To study how geometrical shape affect the light scattering properties for an ensemble of randomly orientated particles, the single scattering matrices including complete polarization information are calculated statistically for a group of…
We present two backscattering polarimetric scanning setups based on point-illumination schemes, that are designed to probe the optical properties of subsurface media. We describe their advantages and limitations, characterize their…
Stein's unbiased risk estimator (SURE) has been shown to be an effective metric for determining optimal parameters for many applications. The topic of this article is focused on the use of SURE for determining parameters for blind…
Ultrafast scattering using X-rays or electrons is an emerging method to obtain structure dynamics at the atomic length and time scales. However, directly resolving in real-space atomic motions is inherently limited by the finite detector…
Principal component analysis (PCA) is an important tool in exploring data. The conventional approach to PCA leads to a solution which favours the structures with large variances. This is sensitive to outliers and could obfuscate interesting…
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…
Diffraction tomography aims to recover an object's scattering potential from measured wave fields. In the classical setting, the object is illuminated by plane waves from many directions, and the Fourier diffraction theorem provides a…
A new phasing algorithm has been used to determine the phases of diffuse elastic X-ray scattering from a non-periodic array of gold balls of 50 nm diameter. Two-dimensional real-space images, showing the charge-density distribution of the…
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…
The structure-property hypothesis says that the properties of all materials are determined by an underlying crystal structure. The main obstacle was the ambiguity of conventional crystal representations based on incomplete or discontinuous…
A multilayered particle is illuminated by plane acoustic or electromagnetic waves of one or several frequencies. We consider the inverse scattering problem for the identification of the layers and of the refraction coefficients of the…
This work is devoted to the study of the symmetries of (quasi)periodic architectured materials. For this purpose, the weaker symmetry criterion of indistinguishability is used. It relies on a statistical description of the mesostructure and…
Parametric model checking (PMC) computes algebraic formulae that express key non-functional properties of a system (reliability, performance, etc.) as rational functions of the system and environment parameters. In software engineering, PMC…
This paper explores optimal methods for obtaining one-dimensional (1D) powder pattern intensities from two-dimensional (2D) planar detectors with good estimates of their standard deviations. We describe methods to estimate uncertainties…