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We develop a new spatial semidiscrete multiscale method based upon the edge multiscale methods to solve semilinear parabolic problems with heterogeneous coefficients and smooth initial data. This method allows for a cheap spatial…
We show that the existing methods for computing the f(\alpha) spectrum from a time series can be improved by using a new algorithmic scheme. The scheme relies on the basic idea that the smooth convex profile of a typical f(\alpha) spectrum…
In this work, we present an algorithmically tractable safe approximation of distributionally robust optimization (DRO) problems that contain univariate indicator functions. The latter appear in different applications, but render the model…
We present the optimal design of a spectral method widely used to initialize nonconvex optimization algorithms for solving phase retrieval and other signal recovery problems. Our work leverages recent results that provide an exact…
In this paper, we establish optimal rates of adaptive estimation of a vector in the multi-reference alignment model, a problem with important applications in fields such as signal processing, image processing, and computer vision, among…
We consider the multi-frequency inverse source problem in the presence of a non-homogeneous medium using passive measurements. Precisely, we derive stability estimates for determining the source from the knowledge of only the imaginary part…
This paper deals with the dynamic factor analysis problem for an ARMA process. To robustly estimate the number of factors, we construct a confidence region centered in a finite sample estimate of the underlying model which contains the true…
Reduced-rank regression is a dimensionality reduction method with many applications. The asymptotic theory for reduced rank estimators of parameter matrices in multivariate linear models has been studied extensively. In contrast, few…
We introduce various optimization schemes for highly accurate calculation of the eigenvalues and the eigenfunctions of the one-dimensional anharmonic oscillators. We present several methods of analytically fixing the nonlinear variational…
High-dimensional statistical inference deals with models in which the the number of parameters p is comparable to or larger than the sample size n. Since it is usually impossible to obtain consistent procedures unless $p/n\rightarrow0$, a…
The study of optimal control problems under uncertainty plays an important role in scientific numerical simulations. This class of optimization problems is strongly utilized in engineering, biology and finance. In this paper, a stochastic…
This paper studies formulations of second-order elliptic partial differential equations in nondivergence form on convex domains as equivalent variational problems. The first formulation is that of Smears \& S\"uli [SIAM J.\ Numer.\ Anal.\…
High-dimensional matrix regression has been studied in various aspects, such as statistical properties, computational efficiency and application to specific instances including multivariate regression, system identification and matrix…
We consider the problem of determining an upper bound for the value of a spectral risk measure of a loss that is a general nonlinear function of two factors whose marginal distributions are known, but whose joint distribution is unknown.…
We consider time-harmonic electromagnetic wave equations in composites of a dispersive material surrounded by a classical material. In certain frequency ranges this leads to sign-changing permittivity and/or permeability. Previously meshing…
Real-world applications such as magnetic resonance imaging with multiple coils, multi-user communication, and diffuse optical tomography often assume a linear model where several sparse signals sharing common sparse supports are acquired by…
This paper presents a fast algorithm to solve a spectral estimation problem for two-dimensional random fields. The latter is formulated as a convex optimization problem with the Itakura-Saito pseudodistance as the objective function subject…
Stochastic processes are often used to model complex scientific problems in fields ranging from biology and finance to engineering and physical science. This paper investigates rate-optimal estimation of the volatility matrix of a…
Vector autoregressive (VAR) models have become a staple in the analysis of multivariate time series and are formulated in the time domain as difference equations, with an implied covariance structure. In many contexts, it is desirable to…
The ubiquitous time-delay estimation (TDE) problem becomes nontrivial when sensors are non-co-located and communication between them is limited. Building on the recently proposed "extremum encoding" compression-estimation scheme, we address…