相关论文: Distance-sparsity transference for vertices of cor…

Recovery of the sparsity pattern (or support) of an unknown sparse vector from a small number of noisy linear measurements is an important problem in compressed sensing. In this paper, the high-dimensional setting is considered. It is shown…

In this note we study packing or covering integer programs with at most k constraints, which are also known as k-dimensional knapsack problems. For any integer k > 0 and real epsilon > 0, we observe there is a polynomial-sized LP for the…

We improve the best known upper bounds on the density of corner-free sets over quasirandom groups from inverse poly-logarithmic to quasi-polynomial. We make similarly substantial improvements to the best known lower bounds on the…

This paper addresses the task of estimating a covariance matrix under a patternless sparsity assumption. In contrast to existing approaches based on thresholding or shrinkage penalties, we propose a likelihood-based method that regularizes…

This paper studies the convergence properties the well-known message-passing algorithm for convex optimisation. Under the assumption of pairwise separability and scaled diagonal dominance, asymptotic convergence is established and a simple…

We apply the replica analysis established by Gardner to the multi-constraint continuous knapsack problem,which is one of the linear programming problems and a most fundamental problem in the field of operations research (OR). For a large…

We develop theoretical results that establish a connection across various regression methods such as the non-negative least squares, bounded variable least squares, simplex constrained least squares, and lasso. In particular, we show in…

We investigate how quantum coherence can be distributed among the several off-diagonal elements of an arbitrary density matrix. An easily computable quantity that captures this variability notion is proposed and it is argued that it…

This article investigates the interplay of rounding objective coefficients in binary programs and almost symmetries. Empirically, reducing the number of significant bits through rounding often leads to instances that are easier to solve.…

We derive fidelity benchmarks for the quantum storage and teleportation of squeezed states of continuous variable systems, for input ensembles where the degree of squeezing $s$ is fixed, no information about its orientation in phase space…

The support recovery problem consists of determining a sparse subset of a set of variables that is relevant in generating a set of observations, and arises in a diverse range of settings such as compressive sensing, and subset selection in…

We discuss applications of some concepts of Compressed Sensing in the recent work on invertibility of random matrices due to Rudelson and the author. We sketch an argument leading to the optimal bound N^{-1/2} on the median of the smallest…

We consider the problem of approximating a function in a general nonlinear subset of $L^2$, when only a weighted Monte Carlo estimate of the $L^2$-norm can be computed. Of particular interest in this setting is the concept of sample…

We study the proximity of the optimal value of the m-dimensional knapsack problem to the optimal value of that problem with the additional restriction that only one type of items is allowed to include in the solution. We derive exact and…

We derive a new estimate of the size of finite sets of points in metric spaces with few distances. The following applications are considered: (1) we improve the Ray-Chaudhuri--Wilson bound of the size of uniform intersecting families of…

We obtain optimal lower and upper bounds for the (additive) integrality gaps of integer knapsack problems. In a randomised setting, we show that the integrality gap of a "typical" knapsack problem is drastically smaller than the integrality…

A recent work of Abbasi et al. [FOCS 2023] introduced the notion of $\varepsilon$-scatter dimension of a metric space and showed a general framework for efficient parameterized approximation schemes (so-called EPASes) for a wide range of…

We show that any subset of the squares of positive relative upper density contains non-trivial solutions to a translation-invariant linear equation in five or more variables, with explicit quantitative bounds. As a consequence, we establish…

Instance sparsification is well-known in the world of exact computation since it is very closely linked to the Exponential Time Hypothesis. In this paper, we extend the concept of sparsification in order to capture subexponential time…

We present an extension of known semidefinite and linear programming upper bounds for spherical codes. We apply the main result for the distance distribution of a spherical code and show that this method can work effectively In particular,…