Related papers: An optimal trace estimate for microlocal square fu…
With the aim of assessing internal wave-driven mixing in the ocean, we develop a new technique for direct numerical simulations of stratified turbulence. Since the spatial scale of oceanic internal gravity waves is typically much larger…
This article addresses the microlocalization of eigenfunctions for the semiclassical Schr\"odinger operator $-h^2\Delta+V$ on closed Riemann surfaces with real bounded potentials. Our primary aim is to establish quantitative bounds on the…
In this work, a time-fractional nonlocal diffusion equation is considered. Based on the $L2$-$1_{\sigma}$ scheme on a graded mesh in time and the standard finite element method (FEM) in space, the fully-discrete $L2$-$1_{\sigma}$ finite…
This paper studies optimal estimation of large-dimensional nonlinear factor models. The key challenge is that the observed variables are possibly nonlinear functions of some latent variables where the functional forms are left unspecified.…
Many recent problems in signal processing and machine learning such as compressed sensing, image restoration, matrix/tensor recovery, and non-negative matrix factorization can be cast as constrained optimization. Projected gradient descent…
We consider the inverse source problem of thermo- and photoacoustic tomography, with data registered on an open surface partially surrounding the source of acoustic waves. Under the assumption of constant speed of sound we develop an…
De-embedding antennas from the channel using Spherical Wave Functions (SWF) is a useful method to reduce the numerical effort in the simulation of wearable antennas. In this paper an analytical solution to the De-embedding problem is…
In this work, we consider the numerical solution of an initial boundary value problem for the distributed order time fractional diffusion equation. The model arises in the mathematical modeling of ultra-slow diffusion processes observed in…
The problem of optimal linear estimation of functionals depending on the unknown values of a random field $\zeta(t,x)$, which is mean-square continuous periodically correlated with respect to time argument $t\in\mathbb R$ and isotropic on…
We develop a scalable algorithmic framework for sparse convex quantile regression (SCQR), addressing key computational challenges in the literature. Enhancing the classical CQR model, we introduce L2-norm regularization and an…
It is proposed a class of statistical estimators $\hat H =(\hat H_1, \ldots, \hat H_d)$ for the Hurst parameters $H=(H_1, \ldots, H_d)$ of fractional Brownian field via multi-dimensional wavelet analysis and least squares, which are…
The molecular motion in heterogeneous media displays anomalous diffusion by the mean-squared displacement $\langle X^2(t) \rangle = 2 D t^\alpha$. Motivated by experiments reporting populations of the anomalous diffusion parameters $\alpha$…
The purpose of this paper is to improve the known estimates for Mockenhaupt's square function in $\mathbb R^3$ and for Sogge's local smoothing in $\mathbb R^{2+1}$ spacetime. For this we use the trilinear approach of S. Lee and A. Vargas…
This paper deals with tactics for fast computation in least squares regression in high dimensions. These tactics include: (a) the majorization-minimization (MM) principle, (b) smoothing by Moreau envelopes, and (c) the proximal distance…
We build the electromagnetic trace anomaly effective term for a generalized linear sigma model with two chiral nonets, one with a quark-antiquark structure, the other one with a four quark content. In the leading order of this framework, we…
We consider the problem of estimating an unknown signal $x_0$ from noisy linear observations $y = Ax_0 + z\in R^m$. In many practical instances, $x_0$ has a certain structure that can be captured by a structure inducing convex function…
Classical Laguerre spectral approximations are highly effective on the half-line when the target function is smooth in the usual polynomial scale. However, their accuracy deteriorates for nonsmooth functions. Such behavior appears naturally…
We report a linear-scaling random Green's function (rGF) method for large-scale electronic structure calculation. In this method, the rGF is defined on a set of random states to stochastically express the density matrix, and rGF is…
Passive scalar dynamics in wall-bounded turbulence is studied via Direct Numerical Simulations of plane channel flow, for a friction Reynolds number $Re_* = 160$ and a Schmidt number $Sc=1$. Peculiar to the present research is that the…
The modified Gerchberg-Saxton algorithm (MGSA) is one of the standard methods for phase retrieval. In this work we apply the MGSA in the paraxial domain. For three given physical parameters - i.e. wavelength, propagation distance and pixel…