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The {\it assumption of additive absorptivity} by different components in compound particles is a widely used method applied in the literature to the analysis of the chemical and structural properties of astronomical (circumstellar,…
Persistence diagrams (PDs) are used as signatures of point cloud data. Two clouds of points can be compared using the bottleneck distance d_B between their PDs. A potential drawback of this pipeline is that point clouds sampled from…
Coherence properties and wavelength of light sources are indispensable for optical coherence microscopy/tomography as they greatly influence the signal to noise ratio, axial resolution, and penetration depth of the system. In the present…
Optical spectrometers have propelled scientific and technological advancements in a wide range of fields. While sophisticated systems with excellent performance metrics are serving well in controlled laboratory environments, many…
Plastically deforming crystals exhibit scale-free fluctuations that are similar to those observed in driven disordered elastic systems close to depinning, but the nature of the yielding critical point is still debated. Here, we study the…
We describes a new approach for performing quantitative structure-factor analysis and density measurements of liquids using x-ray diffraction with a pink-spectrum x-ray source. The methodology corrects for the pink beam effect by performing…
The size of the smallest detectable sample feature in an x-ray imaging system is usually restricted by the spatial resolution of the system. This limitation can now be overcome using the diffusive dark-field signal, which is generated by…
Orientation mapping is a widely used technique for revealing the microstructure of a polycrystalline sample. The crystalline orientation at each point in the sample is determined by analysis of the diffraction pattern, a process known as…
Widely used pipelines for analyzing high-dimensional data utilize two-dimensional visualizations. These are created, for instance, via t-distributed stochastic neighbor embedding (t-SNE). A crucial element of the t-SNE embedding procedure…
Plastic deformation of heterogeneous solid structures is often characterized by random intermittent local plastic events. On the mesoscale this feature can be represented by a spatially fluctuating local yield threshold. Here we study the…
The calculation of the transfer matrix for a large non-periodic multilayered system may become unstable in the presence of absorption. We discuss the origin of this instability and we explore two methods to overcome it: the use of a total…
This paper focuses on the construction and analysis of explicit numerical methods of high dimensional stochastic nonlinear Schrodinger equations (SNLSEs). We first prove that the classical explicit numerical methods are unstable and suffer…
Ridge regression is an indispensable tool in big data analysis. Yet its inherent bias poses a significant and longstanding challenge, compromising both statistical efficiency and scalability across various applications. To tackle this…
Scatterometry is a tested method for measuring periodic semiconductor structures. Since the sizes of modern semiconductor structures have reached the nanoscale regime, the challenge is to determine the shape of periodic nanostructures with…
The present paper provides a general formula for the dimension of spline space over T-meshes using smoothing cofactor-conformality method. And we introduce a new notion, Diagonalizable T-mesh, over which the dimension formula is only…
Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…
Strain-engineering of materials encompasses significant elastic deformation and leads to breaking of the lattice symmetry and as a consequence to the emergence of optical anisotropy. However, the capability to image and map local strain…
This paper concerns a posteriori error analysis for the streamline diffusion (SD) finite element method for the one and one-half dimensional relativistic Vlasov-Maxwell system. The SD scheme yields a weak formulation, that corresponds to an…
This paper studies sequential methods for recovery of sparse signals in high dimensions. When compared to fixed sample size procedures, in the sparse setting, sequential methods can result in a large reduction in the number of samples…
Microscopy research often requires recovering particle-size distributions in three dimensions from only a few (10 - 200) profile measurements in the section. This problem is especially relevant for petrographic and mineralogical studies,…