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For three dimensional complete Riemannian manifolds with scalar curvature no less than one, we obtain the sharp upper bound of complete stable minimal surfaces' diameter.
We investigate the discrepancy principle for choosing smoothing parameters for kernel density estimation. The method is based on the distance between the empirical and estimated distribution functions. We prove some new positive and…
This article deals with the numerical approximation of effective coefficients in stochastic homogenization of discrete linear elliptic equations. The originality of this work is the use of a well-known abstract spectral representation…
We present an analytically explicit study of optimal discrete quantization on spherical geometries equipped with the geodesic metric, focusing on highly symmetric configurations on the unit sphere $\mathbb S^2$. Three discrete uniform…
A precision matrix is the inverse of a covariance matrix. In this paper, we study the problem of estimating the precision matrix with a known graphical structure under high-dimensional settings. We propose a simple estimator of the…
A multi-domain spectral method for computing very high precision 3-D stellar models is presented. The boundary of each domain is chosen in order to coincide with a physical discontinuity (e.g. the star's surface). In addition, a…
The problem deals with an exact calculation of the intersection area of a circle arbitrary placed on a grid of square shaped elements with gaps between them (finite fill factor). Usually an approximation is used for the calculation of the…
In this work, we prove rigorous convergence properties for a semi-discrete, moment-based approximation of a model kinetic equation in one dimension. This approximation is equivalent to a standard spectral method in the velocity variable of…
A multifactor parameterization is described to permit the efficient calculation of collision efficiency (E) between electrically charged aerosol particles and neutral cloud droplets in numerical cloud and climate models. The four parameter…
The problem of the optimal approximation of circular arcs by parametric polynomial curves is considered. The optimality relates to the curvature error. Parametric polynomial curves of low degree are used and a geometric continuity is…
We investigate general aspects of molecular line formation under conditions which are typical of prestellar cores. Focusing on simple linear molecules, we study formation of their rotational lines by radiative transfer simulations. We…
Approximation using Fourier features is a popular technique for scaling kernel methods to large-scale problems, with myriad applications in machine learning and statistics. This method replaces the integral representation of a…
Almost sure bounds are established on the uniform error of smoothing spline estimators in nonparametric regression with random designs. Some results of Einmahl and Mason (2005) are used to derive uniform error bounds for the approximation…
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…
Optical quasar spectra can be used to trace variations of the fine-structure constant alpha. Controversial results that have been published in last years suggest that in addition to to wavelength calibration problems systematic errors might…
Straight lines are common features in human made environments, which makes them a frequently explored feature for control applications. Many control schemes, like Visual Servoing, require the 3D parameters of the features to be estimated.…
The famous Gelfand formula $\rho(A)= \limsup_{n\to\infty}\|A^{n}\|^{1/n}$ for the spectral radius of a matrix is of great importance in various mathematical constructions. Unfortunately, the range of applicability of this formula is…
While direct statements for kernel based interpolation on regions $\Omega \subset \mathbb{R}^d$ are well researched, far less is known about corresponding inverse statements. The available inverse statements for kernel based interpolation…
For acoustic waves in lined ducts, at given frequencies, the dispersion relation leads to a transcendental equation for the wavenumber that has to be solved by numerical methods. Based on Eckart explicit expression initially derived for…
We study stability of the sharp spectral gap bounds for metric-measure spaces satisfying a curvature bound. Our main result, new even in the smooth setting, is a sharp quantitative estimate showing that if the spectral gap of an RCD$(N-1,…