Related papers: Minimal dispersion on the cube and the torus
Determining the maximal density $m_1(\mathbb{R}^2)$ of planar sets without unit distances is a fundamental problem in combinatorial geometry. This paper investigates lower bounds for this quantity. We introduce a novel approach to…
Recently, there has been an increasing interest in designing distributed convex optimization algorithms under the setting where the data matrix is partitioned on features. Algorithms under this setting sometimes have many advantages over…
The method is described and tested for analysis of statistical parameters of reduced neutron widths distributions accounting for possibility of coexistence of superposition of some functions with non-zero mean values of neutron amplitude…
In this paper, we study the lower- and upper-bounded covering (LUC) problem, where we are given a set $P$ of $n$ points, a collection $\mathcal{B}$ of balls, and parameters $L$ and $U$. The goal is to find a minimum-sized subset…
Let $X_1, \ldots, X_n$ be independent random points drawn from an absolutely continuous probability measure with density $f$ in $\mathbb{R}^d$. Under mild conditions on $f$, we derive a Poisson limit theorem for the number of large…
Maximum entropy models are increasingly being used to describe the collective activity of neural populations with measured mean neural activities and pairwise correlations, but the full space of probability distributions consistent with…
A set-system $S\subseteq \{0,1\}^n$ is cube-ideal if its convex hull can be described by capacity and generalized set covering inequalities. In this paper, we use combinatorics, convex geometry, and polyhedral theory to give exponential…
This paper extends the standard chaining technique to prove excess risk upper bounds for empirical risk minimization with random design settings even if the magnitude of the noise and the estimates is unbounded. The bound applies to many…
We investigate the problem of jointly testing a pair of composite hypotheses and, depending on the test result, estimating a random parameter under distributional uncertainties. Specifically, it is assumed that the distribution of the data…
For the optimal success probability under minimum-error discrimination between $r\geq2$ arbitrary quantum states prepared with any a priori probabilities, we find new general analytical lower and upper bounds and specify the relations…
We prove lower bounds for the worst case error of quadrature formulas that use given sample points $\X_n = \{ x_1, \dots , x_n \}$. We are mainly interested in optimal point sets $\X_n$, but also prove lower bounds that hold with high…
We develop quadrature rules for the isogeometric analysis of wave propagation and structural vibrations that minimize the discrete dispersion error of the approximation. The rules are optimal in the sense that they only require two…
We extend known methods to establish upper bounds on the least character non-residues contingent on different zero-free regions within the critical strip, in particular on bounded rectangles within the critical strip along the $\sigma=1$…
Lower bounds involving $f$-divergences between the underlying probability measures are proved for the minimax risk in estimation problems. Our proofs just use simple convexity facts. Special cases and straightforward corollaries of our…
We obtain new upper bounds on the minimal density of lattice coverings of Euclidean space by dilates of a convex body K. We also obtain bounds on the probability (with respect to the natural Haar-Siegel measure on the space of lattices)…
Using ideas from the geometry of compression, we improve on the current upper and lower bounds of the Heilbronn triangle problem. In particular, let $\Delta(s)$ denote the minimal area of the triangle induced by $s$ points on a unit disk.…
The question of what can be computed, and how efficiently, are at the core of computer science. Not surprisingly, in distributed systems and networking research, an equally fundamental question is what can be computed in a…
We find the laws for the spreading of the spatial widths (parallel and transverse to the direction of average motion) of the relativistic position probability density for a massive, spinless particle. We find that when the momentum width of…
We present novel bounds for estimating discrete probability distributions under the $\ell_\infty$ norm. These are nearly optimal in various precise senses, including a kind of instance-optimality. Our data-dependent convergence guarantees…
Although there is an extensive literature on the upper bound for cumulative standard normal distribution, there are relatively not sharp for all values of the interested argument x. The aim of this paper is to establish a sharp upper bound…