Related papers: Shifted Matrix-Sign Reflectors for Prescribed-Inde…
The refined inertia of a square real matrix $A$ is the ordered $4$-tuple $(n_+, n_-, n_z, 2n_p)$, where $n_+$ (resp., $n_-$) is the number of eigenvalues of $A$ with positive (resp., negative) real part, $n_z$ is the number of zero…
Isospectral reduction is an important tool for network/matrix analysis as it reduces the dimension of a matrix/network while preserving its eigenvalues and eigenvectors. The main contribution of this manuscript is a proposed algorithmic…
Immersed reflection gratings improve spectral resolving power by enabling diffraction within a high refractive index medium. This principle has been widely adopted to make grating spectrometers more compact. Conventional immersed gratings…
Neural implicit methods have achieved high-quality 3D object surfaces under slight specular highlights. However, high specular reflections (HSR) often appear in front of target objects when we capture them through glasses. The complex…
This article is dedicated to the following class of problems. Start with an $N\times N$ Hermitian matrix randomly picked from a matrix ensemble - the reference matrix. Applying a rank-$t$ perturbation to it, with $t$ taking the values $1\le…
Forward scatter radar (FSR) has emerged as an effective imaging modality for target detection, utilizing forward scattering (FS) signals to reconstruct two-dimensional shadow profile images of objects. However, real-world FS signals are…
In this paper, we address the line spectral estimation problem with multiple measurement corrupted vectors. Such scenarios appear in many practical applications such as radar, optics, and seismic imaging in which the signal of interest can…
Inverse scattering is the process of estimating the spatial distribution of the scattering potential of an object by measuring the scattered wavefields around it. In this paper, we consider reflection tomography of high contrast objects…
Random sampling of large Markov matrices with a tunable spectral gap, a nonuniform stationary distribution, and a nondegenerate limiting empirical spectral distribution (ESD) is useful. Fix $c>0$ and $p>0$. Let $A_n$ be the adjacency matrix…
Self-injection locking is a dynamic phenomenon which provides passive stabilization of a lasers emission frequency via resonant optical feedback. The stabilization coefficient depends on the level of resonant feedback and quality factor of…
Electromagnetic Inverse Scattering Problems (EISP) seek to reconstruct relative permittivity from scattered fields and are fundamental to applications like medical imaging. This inverse process is inherently ill-posed and highly nonlinear,…
Recently, the use of intelligent reflecting surface (IRS) has gained considerable attention in wireless communications. By intelligently adjusting the passive reflection angle, IRS is able to assist the base station (BS) to extend the…
This letter attempts to design a surveillance scheme by adopting an active reconfigurable intelligent surface (RIS). Different from the conventional passive RIS, the active RIS could not only adjust the phase shift but also amplify the…
Modern imaging and sensing in complex environments, ranging from biomedical diagnostics to wireless communication, relies on accurately measuring and then controlling the wave propagation. Conventional approaches demand large arrays of…
The eigenmirror problem asks: ``When does the reflection of a surface in a curved mirror appear undistorted to an observer?'' We call such a surface an {\em eigensurface} and the corresponding mirror an {\em eigenmirror}. The data for an…
Speckle is the spatial fluctuation of irradiance seen when coherent light is reflected from a rough surface. It is due to light reflected from the surface's many nooks and crannies accumulating vastly-discrepant time delays, spanning much…
Conventional mirrors obey Snell's reflection law: a plane wave is reflected as a plane wave, at the same angle. To engineer spatial distributions of fields reflected from a mirror, one can either shape the reflector (for example, creating a…
Let $X,X_1,\dots, X_n$ be i.i.d. Gaussian random variables in a separable Hilbert space ${\mathbb H}$ with zero mean and covariance operator $\Sigma={\mathbb E}(X\otimes X),$ and let $\hat \Sigma:=n^{-1}\sum_{j=1}^n (X_j\otimes X_j)$ be the…
This study delves into the radiation pattern synthesis of reconfigurable intelligent surfaces (RIS) / reflection metasurfaces. Through superimposing multiple single-reflection profiles, which comprise the amplitude and/or phase settings of…
The limiting distribution of eigenvalues of N x N random matrices has many applications. One of the most studied ensembles are real symmetric matrices with independent entries iidrv; the limiting rescaled spectral measure (LRSM)…