Related papers: Scalar Compandor Design Based on Optimal Compresso…
We investigate the interplay of band structure topology and localization properties of Wannier functions. To this end, we extend a recently proposed compressed sensing based paradigm for the search for maximally localized Wannier functions…
We prove lower bounds on the error incurred when approximating any oscillating function using piecewise polynomial spaces. The estimates are explicit in the polynomial degree and have optimal dependence on the meshwidth and frequency when…
In most compressive sensing problems l1 norm is used during the signal reconstruction process. In this article the use of entropy functional is proposed to approximate the l1 norm. A modified version of the entropy functional is continuous,…
In this paper, we study a class of approximation problems, appearing in data approximation and signal processing. The approximations are constructed as combinations of polynomial splines (piecewise polynomials), whose parameters are subject…
Exhausters and coexhausters are notions of constructive nonsmooth analysis which are used to study extremal properties of functions. An upper exhauster (coexhauster) is used to get an approximation of a considered function in the…
A method is proposed for constructing a spline curve of the Bezier type, which is continuous along with its first derivative by a piecewise polynomial function. Conditions for its existence and uniqueness are given. The constructed curve…
First-order Marcum $Q$-function is observed in various problem formulations. However, it is not an easy-to-handle function. For this reason, in this paper, we first present a semi-linear approximation of the Marcum $Q$-function. Our…
This paper proposes a new deterministic sampling strategy for constructing polynomial chaos approximations for expensive physics simulation models. The proposed approach, effectively subsampled quadratures involves sparsely subsampling an…
A new differential-recurrence relation for the B-spline functions of the same degree is proved. From this relation, a recursive method of computing the coefficients of B-spline functions of degree $m$ in the Bernstein-B\'{e}zier form is…
Non-Gaussian statistics are a challenge for data assimilation. Linear methods oversimplify the problem, yet fully nonlinear methods are often too expensive to use in practice. The best solution usually lies between these extremes.…
This paper investigates the mean square error optimal estimation of scale invariant Wigner spectrum for the class of Gaussian locally self-similar processes, by the multitaper method. In this method, the spectrum is estimated as a weighted…
The maximum absolute correlation between regressors, which is called mutual coherence, plays an essential role in sparse estimation. A regressor matrix whose columns are highly correlated may result from optimal input design, since there is…
The problem of reconstructing functions from their asymptotic expansions in powers of a small variable is addressed by deriving a novel type of approximants. The derivation is based on the self-similar approximation theory, which presents…
Multivariate piecewise polynomial functions (or splines) on polyhedral complexes have been extensively studied over the past decades and find applications in diverse areas of applied mathematics including numerical analysis, approximation…
We present a systematic method for computing explicit approximations to martingale representations for a large class of Brownian functionals. The approximations are obtained by obtained by computing a directional derivative of the weak…
The practice of collider physics typically involves the marginalization of multi-dimensional collider data to uni-dimensional observables relevant for some physics task. In any cases, such as classification or anomaly detection, the…
Submodular functions are an important class of functions in combinatorial optimization which satisfy the natural properties of decreasing marginal costs. The study of these functions has led to strong structural properties with applications…
Sub-sampling is a common and often effective method to deal with the computational challenges of large datasets. However, for most statistical models, there is no well-motivated approach for drawing a non-uniform subsample. We show that the…
In this paper we analyze a greedy procedure to approximate a linear functional defined in a Reproducing Kernel Hilbert Space by nodal values. This procedure computes a quadrature rule which can be applied to general functionals, including…
This work explores an extension of machine learning-optimized piecewise polynomial approximation by incorporating energy optimization as an additional objective. Traditional closed-form solutions enable continuity and approximation targets…