相关论文: Sharp van der Corput estimates and minimal divided…

This paper is concerned with estimating the intersection point of two densities, given a sample of both of the densities. This problem arises in classification theory. The main results provide lower bounds for the probability of the…

We give a simple proof of a well-known theorem of G\'al and of the recent related results of Aistleitner, Berkes and Seip [1] regarding the size of GCD sums. In fact, our method obtains the asymptotically sharp constant in G\'al's theorem,…

We derive a new integral formula for the Stieltjes constants. The new formula permits easy computations as well as an exact approximate asymptotic formula. Both the sign oscillations and the leading order of growth are provided. The formula…

This paper proposes a fast and accurate surface normal estimation method which can be directly used on depth maps (organized point clouds). The surface normal estimation process is formulated as a closed-form expression. In order to reduce…

Fine-grained visual categorization is a classification task for distinguishing categories with high intra-class and small inter-class variance. While global approaches aim at using the whole image for performing the classification,…

We derive sharp upper and lower bounds for the pointwise concentration function of the maximum statistic of $d$ identically distributed real-valued random variables. Our first main result places no restrictions either on the common marginal…

We prove some sharp regularity results for solutions of classical first order hyperbolic initial boundary value problems. Our two main improvements on the existing litterature are weaker regularity assumptions for the boundary data and…

We develop a practical and novel method for inference on intersection bounds, namely bounds defined by either the infimum or supremum of a parametric or nonparametric function, or equivalently, the value of a linear programming problem with…

We settle the problem of finding the sharp constant in the log Sobolev inequality on the $n$-cycle for all $n\ge 4$, by showing that it is equal to half of the spectral gap. We deduce this result from an optimal cubic Sobolev inequality.

In this article, we revisit the question of fluctuations of linear statistics of beta ensembles in the single cut and non-critical regime for general potentials $V$ under mild regularity and growth assumptions. Our main objective is to…

We propose a multi-level method to increase the accuracy of machine learning algorithms for approximating observables in scientific computing, particularly those that arise in systems modeled by differential equations. The algorithm relies…

We study sharp $p$-variational inequalities for the Hardy-Littlewood maximal operator on complete graphs, answering in the affirmative a question by Feng Liu and Qingying Xue. We also use computational assistance to find sharp constants in…

The purpose of this article is twofold. First we give a very robust method for proving sharp time decay estimates for the most classical three models of dispersive Partial Differential Equations, the wave, Klein-Gordon and Schr{\"o}dinger…

For the zone of moderate deviation probabilities the local asymptotic minimax lower bound of asymptotic efficiency of estimators is established. The estimation parameter is multidimensional. The lower bound admits the interpretation as the…

Often in the analysis of first-order methods, assuming the existence of a quadratic growth bound (a generalization of strong convexity) facilitates much stronger convergence analysis. Hence the analysis is done twice, once for the general…

In this work we explore the fidelity of numerical approximations to the analytic spectra of hyperbolic partial differential equation systems with variable coefficients. We are particularly interested in the ability of discrete methods to…

We study lower bounds for the Riemann zeta function $\zeta(s)$ along vertical arithmetic progressions in the right-half of the critical strip. We show that the lower bounds obtained in the discrete case coincide, up to the constants in the…

We derive sharp bounds for the accuracy of approximate eigenvectors (Ritz vectors) obtained by the Rayleigh-Ritz process for symmetric eigenvalue problems. Using information that is available or easy to estimate, our bounds improve the…

This paper studies two spectrum estimation methods for the case that the samples are obtained at a rate lower than the Nyquist rate. The first method is the correlogram method for undersampled data. The algorithm partitions the spectrum…

In this work, we derive sharp non-asymptotic deviation bounds for weighted sums of Dirichlet random variables. These bounds are based on a novel integral representation of the density of a weighted Dirichlet sum. This representation allows…