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Matrix Riccati differential equations arise in many different areas and are particular important within the field of control theory. In this paper we consider numerical integration for large-scale systems of stiff matrix Riccati…
We propose a multiscale approach for a nonlinear Helmholtz problem with possible oscillations in the Kerr coefficient, the refractive index, and the diffusion coefficient. The method does not rely on structural assumptions on the…
A theoretical framework is presented that permits investigations of the relation between inelastic backscattering from microparticles and bulk samples of Raman-active materials. It is based on the Lorentz reciprocity theorem and no…
Using the Cryogenic, High-Accuracy Refraction Measuring System (CHARMS) at NASA's Goddard Space Flight Center, we have measured the absolute refractive index of five specimens taken from a very large boule of Corning 7980 fused silica from…
Machine learning continues to grow in popularity in academia, in industry, and is increasingly used in other fields. However, most of the common metrics used to evaluate even simple binary classification models have shortcomings that are…
High-resolution magnetic resonance imaging (MRI) is essential in clinical diagnosis. However, its long acquisition time remains a critical issue. Parallel imaging (PI) is a common approach to reduce acquisition time by periodically skipping…
Molecular dipoles near interfaces emit highly directional radiation due to near-field interactions, making surface-bound fluorophores sensitive probes of local physicochemical changes. We introduce smart coverslips, stably coated with…
In this work, we report the application of Raman microspectroscopy for analysis of the refractive index of a range of tissue phantoms. Using both a custom-developed setup with visible laser source and a commercial micro-spectrometer with…
Motivated by non-destructive testing of optical fiber, we consider the problem of determining the index of refraction of a two-dimensional medium from magnitude of the total field resulting from known incident plane waves at a fixed…
Simulating complex astrophysical reacting flows is computationally expensive -- reactions are stiff and typically require implicit integration methods. The reaction update is often the most expensive part of a simulation, which motivates…
The scientific community has witnessed tremendous expansion of research on layered (i.e. two-dimensional, 2D) materials, with increasing recent focus on applications to photonics. Layered materials are particularly exciting for manipulating…
Reflectometry is a technique that uses the light reflected by a sample to determine properties of the sample. Interferometric reflectometry uses interference between two beams, one of which is incident on ---and reflected back by--- a…
The paper illustrates an application of the Resampling approach [2] for the estimation of the aircraft circulation plan reliability. Resampling is an intensive computer statistical method, which can be used effectively in the case of small…
The dispersive part of the refractive index of vanadium is determined by measuring the angular displacement of the first order diffraction peak of a V/Fe superlattice. The measurements were made using elliptically polarized synchrotron…
Robust principal component analysis (RPCA) is a widely used tool for dimension reduction. In this work, we propose a novel non-convex algorithm, coined Iterated Robust CUR (IRCUR), for solving RPCA problems, which dramatically improves the…
Here we re-examine one of the most basic quantities in optics: the refractive index. Considering propagation in a plane, we first develop a general formalism for calculating the direction dependent refractive index in a general…
The equations for the effective medium refractive index and for the confinement factor in the waveguide design for quantum cascade lasers are derived.Compared to equations used in prior literature, by applying rigorous perturbation theory…
Dense encoders and LLM-based rerankers struggle with long documents: single-vector representations dilute fine-grained relevance, while cross-encoders are often too expensive for practical reranking. We present an efficient long-document…
We implement an efficient method of computation of two dimensional Fourier-type integrals based on approximation of the integrand by Gaussian radial basis functions, which constitute a standard tool in approximation theory. As a result, we…
When light hits a multilayer planar stack, it is reflected, refracted, and absorbed in a way that can be derived from the Fresnel equations. The analysis is treated in many textbooks, and implemented in many software programs, but certain…