Related papers: Minimal dispersion on the cube and the torus

We elaborate on the intimate connection between the largest volume of an empty axis-parallel box in a set of $n$ points from $[0,1]^d$ and cover-free families from the extremal set theory. This connection was discovered in a recent paper of…

Spark plays a great role in studying uniqueness of sparse solutions of the underdetermined linear equations. In this article, we derive a new lower bound of spark. As an application, we obtain a new criterion for the uniqueness of sparse…

The letter presents a method for the reduction in the mutual coherence of an overcomplete Gaussian or Bernoulli random matrix, which is fairly small due to the lower bound given here on the probability of the event that the aforesaid mutual…

A fundamental tool in network information theory is the covering lemma, which lower bounds the probability that there exists a pair of random variables, among a give number of independently generated candidates, falling within a given set.…

This article presents some interesting and novel results concerning the average modulus of random polynomials on the unit circle and the unit disc, with coefficients distributed as standard normal variates. The paper also introduces new…

Upper bounds are given for the weight distribution of binary weakly self-dual codes. To get these new bounds, we introduce a novel method of utilizing unitary operations on Hilbert spaces. This method is motivated by recent progress on…

We briefly review known results on upper bounds for the minimal domination number $\gamma_n$ of a hypercube of dimension $n$, then present a new method for constructing dominating sets. Write $n =2^{\hat{n}}-1 +{\check{n}}$ with $0\leq…

This paper provides an overview of results and concepts in minimax robust hypothesis testing for two and multiple hypotheses. It starts with an introduction to the subject, highlighting its connection to other areas of robust statistics and…

We study the size (or volume) of balls in the metric space of permutations, $S_n$, under the infinity metric. We focus on the regime of balls with radius $r = \rho \cdot (n\!-\!1)$, $\rho \in [0,1]$, i.e., a radius that is a constant…

We consider the problem of parameter estimation in a Bayesian setting and propose a general lower-bound that includes part of the family of $f$-Divergences. The results are then applied to specific settings of interest and compared to other…

Pseudoline arrangements are fundamental objects in discrete and computational geometry, and different works have tackled the problem of improving the known bounds on the number of simple arrangements of $n$ pseudolines over the past…

We correct claims about lower bounds on mutual information (MI) between real-valued random variables made in A. Kraskov {\it et al.}, Phys. Rev. E {\bf 69}, 066138 (2004). We show that non-trivial lower bounds on MI in terms of linear…

We present a new proof rule for verifying lower bounds on quantities of probabilistic programs. Our proof rule is not confined to almost-surely terminating programs -- as is the case for existing rules -- and can be used to establish…

Let $p_1,\ldots,p_n$ be a set of points in the unit square and let $T_1,\ldots,T_n$ be a set of $\delta$-tubes such that $T_j$ passes through $p_j$. We prove a lower bound for the number of incidences between the points and tubes under a…

In this paper we establish lower bounds on information divergence from a distribution to certain important classes of distributions as Gaussian, exponential, Gamma, Poisson, geometric, and binomial. These lower bounds are tight and for…

Dispersion is a fundamental concept in statistics, yet standard approaches - especially via stochastic orders - face limitations in the discrete setting. In particular, the classical dispersive order, well-established for continuous…

We provide a lower bound for the convergence radius of the Mayer series of the Lennard-Jones gas which strongly improves on the classical bound obtained by Penrose and Ruelle 1963. To obtain this result we use an alternative estimate…

In this paper, we investigate the distribution of the maximum of partial sums of certain cubic exponential sums, commonly known as "Birch sums". Our main theorem gives upper and lower bounds (of nearly the same order of magnitude) for the…

The least upper bounds of the powers extracted and scattered by bi-anisotropic particles are investigated analytically. A rigorous derivation for particles having invertible polarizability tensors is presented, and the particles with…

The probabilistic learning on manifolds (PLoM) introduced in 2016 has solved difficult supervised problems for the ``small data'' limit where the number N of points in the training set is small. Many extensions have since been proposed,…