Related papers: A sharp square function estimate for the moment cu…
We present an algorithm to compute best least-squares approximations of discrete real-valued functions by first-degree splines (broken lines) with free knots. We demonstrate that the algorithm delivers after a finite number of steps a…
We consider the square function (known as Stein's square function) estimate associated with the Bochner-Riesz means. The previously known range of sharp estimate is improved. Our results are based on vector valued extensions of…
Surface roughness is an important quantity to many engineering and precision manufacturing disciplines. In this paper we investigate the problem of estimating the root-mean-square roughness of a sample by passive linear optical methods. By…
Quantitative formulations of Fefferman's counterexample for the ball multiplier are naturally linked to square function estimates for conical and directional multipliers. In this article we develop a novel framework for these square…
A T-curve of degree $d$ is given by a regular unimodular triangulation of $d \cdot \Delta_2$ together with a sign distribution on its lattice points. By Viro's Patchworking Theorem, this determines the ambient isotopy type (a.k.a. real…
We identify a new way to divide the $\delta$-neighborhood of surfaces $\mathcal{M}\subset\mathbb{R}^3$ into a finitely-overlapping collection of rectangular boxes $S$. We obtain a sharp $(l^2,L^p)$ decoupling estimate using this…
There has been substantial recent work on methods for estimating the slope function in linear regression for functional data analysis. However, as in the case of more conventional finite-dimensional regression, much of the practical…
Functions with discontinuities appear in many applications such as image reconstruction, signal processing, optimal control problems, interface problems, engineering applications and so on. Accurate approximation and interpolation of these…
Sharp estimates for mean curvature flow of graphs are shown and examples are given to illustrate why these are sharp. The estimates improves earlier (non-sharp) estimates of Klaus Ecker and Gerhard Huisken.
We introduce an estimation method for the scaled skewness coefficient of the sample mean of short and long memory linear processes. This method can be extended to estimate higher moments such as curtosis coefficient of the sample mean. Also…
We derive integral and sup-estimates for the curvature of stably marginally outer trapped surfaces in a sliced space-time. The estimates bound the shear of a marginally outer trapped surface in terms of the intrinsic and extrinsic curvature…
The main purpose of the paper is to study sharp estimates of approximation of periodic functions in the H\"older spaces $H_p^{r,\alpha}$ for all $0<p\le\infty$ and $0<\alpha\le r$. By using modifications of the classical moduli of…
An algorithm to efficiently compute the moments of volumetric images is disclosed. The approach demonstrates a reduction in processing time by reducing the computational complexity significantly. Specifically, the algorithm reduces…
In this paper we describe active set type algorithms for minimization of a smooth function under general order constraints, an important case being functions on the set of bimonotone r-by-s matrices. These algorithms can be used, for…
ConicCurv is a new derivative-free algorithm to estimate the curvature of a plane curve from a sample of data points. It is based on a known tangent estimator method grounded on classic results of Projective Geometry and B\'ezier rational…
Quasi-Monte Carlo (qMC) methods are a powerful alternative to classical Monte-Carlo (MC) integration. Under certain conditions, they can approximate the desired integral at a faster rate than the usual Central Limit Theorem, resulting in…
We use decoupling theory to prove a sharp (up to $N^\epsilon$ losses) estimate for Vinogradov's mean value theorem in two dimensions
We prove a sharp decoupling for a certain two dimensional surface in R^9. As an application, we obtain the full range of expected estimates for the cubic Parsell-Vinogradov system in two dimensions.
In this paper we characterize sharp time-data tradeoffs for optimization problems used for solving linear inverse problems. We focus on the minimization of a least-squares objective subject to a constraint defined as the sub-level set of a…
Analysis of signals with oscillatory modes with crossover instantaneous frequencies is a challenging problem in time series analysis. One way to handle this problem is lifting the 2-dimensional time-frequency representation to a…