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In this paper we discuss various connections between geometric discrepancy measures, such as discrepancy with respect to convex sets (and convex sets with smooth boundary in particular), and applications to numerical analysis and…

The modeling of large deformation fracture mechanics has been a challenging problem regarding the accuracy of numerical methods and their ability to deal with considerable changes in deformations of meshes where having the presence of…

Scattered neutron spectroscopy is a diagnostic technique commonly used to measure areal density in ICF experiments. Deleterious areal density asymmetries modify the shape of the scattered neutron spectrum. In this work a novel analysis is…

The detection of new or enlarged white-matter lesions in multiple sclerosis is a vital task in the monitoring of patients undergoing disease-modifying treatment for multiple sclerosis. However, the definition of 'new or enlarged' is not…

This paper presents a new approach on stretch processing for a fine range estimation using MPM (Matrix Pencil Method). The conventional method utilizes FFT (Fast Fourier Transform) with limited range resolution with its fixed number of…

Estimating errors is a crucial part of any scientific analysis. Whenever a parameter is estimated (model-based or not), an error estimate is necessary. Any parameter estimate that is given without an error estimate is meaningless.…

For the first time we introduce an error estimator for the numerical approximation of the equations describing the dynamics of sea ice. The idea of the estimator is to identify different error contributions coming from spatial and temporal…

Calculus and geometry are ubiquitous in the theoretical modelling of scientific phenomena, but have historically been very challenging to apply directly to real data as statistics. Diffusion geometry is a new theory that reformulates…

This article performs a unified convergence analysis of a variety of numerical methods for a model of the miscible displacement of one incompressible fluid by another through a porous medium. The unified analysis is enabled through the…

Spectral kernel methods are techniques for transforming data into a coordinate system that efficiently reveals the geometric structure - in particular, the "connectivity" - of the data. These methods depend on certain tuning parameters. We…

The main goal of this paper is to provide a brief survey of recent results which connect together results from different areas of research. It is well known that numerical integration of functions with mixed smoothness is closely related to…

Dispersive approaches provide model independent description of meson-meson scattering. We first review here the use of dispersion relations to obtain a model independent unitarization of Chiral Perturbation Theory amplitudes, that establish…

We propose a novel regression adjustment method designed for estimating distributional treatment effect parameters in randomized experiments. Randomized experiments have been extensively used to estimate treatment effects in various…

The presence of measurement error is a widespread issue which, when ignored, can render the results of an analysis unreliable. Numerous corrections for the effects of measurement error have been proposed and studied, often under the…

The Gradient Scheme framework provides a unified analysis setting for many different families of numerical methods for diffusion equations. We show in this paper that the Gradient Scheme framework can be adapted to elasticity equations, and…

Some spectral data analysis methods that are useful for the two-dimensional imaging diagnostics data are introduced. It is shown that the frequency spectrum, the local dispersion relation, the flow shear, and the nonlinear energy transfer…

We design the conforming virtual element method for the numerical approximation of the two dimensional elastodynamics problem. We prove stability and convergence of the semi-discrete approximation and derive optimal error estimates under…

Despite the widespread use of Scanning Transmission Electron Microscopy (STEM) for observing the structure of materials at the atomic scale, a detailed understanding of some relevant electron beam damage mechanisms is limited. Recent…

Moved by the need for rigorous and reliable numerical tools for the analysis of peridynamic materials, the authors propose a model able to capture the dispersive features of nonlocal soliton-like solutions obtained by a peridynamic…

The standard method for the propagation of errors, based on a Taylor series expansion, is approximate and frequently inadequate for realistic problems. A simple and generic technique is described in which the likelihood is constructed…