Related papers: A tight lower bound on the minimal dispersion
We prove that if for the curved $n$-body problem the masses are given, the minimum distance between the point masses of a specific type of relative equilibrium solution to that problem has a universal lower bound that is not equal to zero.…
In this short note we give a new upper bound for the size of a set family with a single Hamming distance. Our proof is an application of the linear algebra bound method.
For a point set of $n$ elements in the $d$-dimensional unit cube and a class of test sets we are interested in the largest volume of a test set which does not contain any point. For all natural numbers $n$, $d$ and under the assumption of a…
This article is an exposition of recent results on self-similar sets, asserting that if the dimension is smaller than the trivial upper bound then there are almost overlaps between cylinders. We give a heuristic derivation of the theorem…
Residuation theory concerns the study of partially ordered algebraic structures, most often monoids, equipped with a weak inverse for the monoidal operator. One of its area of application has been constraint programming, whose key…
We prove a simple, explicit lower bound on the radius of a zero-free disk for Gibbs point processes defined by finite-range, repulsive multi-body interactions. Our lower bound improves on those previously known, and we demonstrate that it…
We study the dispersion of point sets in the unit square; i.e. the size of the largest axes-parallel box amidst such point sets. It is known that $\liminf_{N\to\infty} N\mathrm{disp}(N,2)\in \left[\frac54,2\right],$ where…
We prove lower bounds for the smallest singular value of rectangular, multivariate Vandermonde matrices with nodes on the complex unit circle. The nodes are ``off the grid'', groups of nodes cluster, and the studied minimal singular value…
We consider diffraction at random point scatterers on general discrete point sets in $\R^\nu$, restricted to a finite volume. We allow for random amplitudes and random dislocations of the scatterers. We investigate the speed of convergence…
In this paper we introduce an enhanced notion of extremal systems for sets in locally convex topological vector spaces and obtain efficient conditions for set extremality in the convex case. Then we apply this machinery to deriving new…
We derive lower bounds on the maximal rates for multiple packings in high-dimensional Euclidean spaces. Multiple packing is a natural generalization of the sphere packing problem. For any $ N>0 $ and $ L\in\mathbb{Z}_{\ge2} $, a multiple…
The ball-constrained weighted maximin dispersion problem $(\rm P_{ball})$ is to find a point in an $n$-dimensional Euclidean ball such that the minimum of the weighted Euclidean distance from given $m$ points is maximized. We propose a new…
We look for minimizers of the buckling load problem with perimeter constraint in any dimension. In dimension 2, we show that the minimizing plates are convex; in higher dimension, by passing through a weaker formulation of the problem, we…
Learning the minimum/maximum mean among a finite set of distributions is a fundamental sub-task in planning, game tree search and reinforcement learning. We formalize this learning task as the problem of sequentially testing how the minimum…
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…
The conventional definition of extremality of a finite collection of sets is extended by replacing a fixed point (extremal point) in the intersection of the sets by a collection of sequences of points in the individual sets with the…
We present a new lower bound on the Bowen-Radin maximal density of radius-R ball packings in the m-dimensional hyperbolic space, improving on the basic covering bound by factor \Omega(m(R+\ln m)) as m tends to infinity. This is done by…
Minimizing divergence measures under a constraint is an important problem. We derive a sufficient condition that binary divergence measures provide lower bounds for symmetric divergence measures under a given triangular discrimination or…
This paper proves the minimum size of a supersequence over a set of eight elements is 52. This disproves a conjecture that the lower bound of the supersequence is the partial sum of the geometric Connell sequence. By studying the internal…
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.…