Related papers: On the Relation of Schatten Norms and the Thompson…
We study the Tate resolutions and the maximal Cohen-Macaulay approximations of Cohen-Macaulay modules over Gorenstein rings. One consequence is an extension of a well-known result about linkage of complete intersections.
This paper enfolds a medius analysis for the Stokes equations and compares different finite element methods (FEMs). A first result is a best approximation result for a P1 non-conforming FEM. The main comparison result is that the error of…
Examining the extent to which measurements of rotation matrices are close to each other is challenging due measurement noise. To overcome this, data is typically smoothed and Riemannian and Euclidean metrics are applied. However, if…
We investigate the distance-redshift relation in a realistic inhomogeneous universe where the mass distribution is described by the mass function of Sheth and Tormen. It is found that the derived distance deviates systematically from the…
We explore the relationship between approximate symmetries of a gapped Hamiltonian and the structure of its ground space. We start by showing that approximate symmetry operators---unitary operators whose commutators with the Hamiltonian…
This paper reveals a conceptually new connection from information theory to approximation theory via quantum algorithms for entropy estimation. Specifically, we provide an information-theoretic lower bound $\Omega(\sqrt{n})$ on the…
We consider a robust variant of the classical $k$-median problem, introduced by Anthony et al. \cite{AnthonyGGN10}. In the \emph{Robust $k$-Median problem}, we are given an $n$-vertex metric space $(V,d)$ and $m$ client sets $\set{S_i…
We consider the Tur\'an-type problem of bounding the size of a set $M \subseteq \mathbb{F}_2^n$ that does not contain a linear copy of a given fixed set $N \subseteq \mathbb{F}_2^k$, where $n$ is large compared to $k$. An Erd\H{o}s-Stone…
Murthy and Sethi (Sankhya Ser B \textbf{27}, 201--210 (1965)) gave a sharp upper bound on the variance of a real random variable in terms of the range of values of that variable. We generalise this bound to the complex case and, more…
Covariance matrix plays a central role in multivariate statistical analysis. Significant advances have been made recently on developing both theory and methodology for estimating large covariance matrices. However, a minimax theory has yet…
We study the problem of mean estimation for high-dimensional distributions, assuming access to a statistical query oracle for the distribution. For a normed space $X = (\mathbb{R}^d, \|\cdot\|_X)$ and a distribution supported on vectors $x…
We give upper and lower bounds for Diophantine exponents measuring how well a point in the plane can be approximated by points in the orbit of a lattice $\Gamma<\mathrm{SL}_2(\mathbb{R})$ acting linearly on $\mathbb{R}^2$. Our method gives…
In this work we study the problem of single-shot discrimination of von Neumann measurements, which we associate with measure-and-prepare channels. There are two possible approaches to this problem. The first one is simple and does not…
Rank-constrained matrix problems appear frequently across science and engineering. The convergence analysis of iterative algorithms developed for these problems often hinges on local error bounds, which correlate the distance to the…
Many statistical applications, such as the Principal Component Analysis, matrix completion, tensor regression and many others, rely on accurate estimation of leading eigenvectors of a matrix. The Davis-Kahan theorem is known to be…
Stein's method for Gaussian process approximation can be used to bound the differences between the expectations of smooth functionals $h$ of a c\`adl\`ag random process $X$ of interest and the expectations of the same functionals of a well…
Maximum consensus estimation plays a critically important role in robust fitting problems in computer vision. Currently, the most prevalent algorithms for consensus maximization draw from the class of randomized hypothesize-and-verify…
In this paper, we investigate the generalized low rank approximation to the symmetric positive semidefinite matrix in the Frobenius norm: $$\underset{ rank(X)\leq k}{\min} \sum^m_{i=1}\left \Vert A_i - B_i XB_i^T \right \Vert^2_F,$$ where…
Many machine learning models involve solving optimization problems. Thus, it is important to deal with a large-scale optimization problem in big data applications. Recently, subsampled Newton methods have emerged to attract much attention…
We study the problem of distinguishing between two symmetric probability distributions over $n$ bits by observing $k$ bits of a sample, subject to the constraint that all $k-1$-wise marginal distributions of the two distributions are…