相关论文: Probabilistic Lower Bounds for the Discrepancy of …

We develop a new family of linear programs, that yield upper bounds on the rate of binary linear codes of a given distance. Our bounds apply {\em only to linear codes.} Delsarte's LP is the weakest member of this family and our LP yields…

Given a set C in R^d, let p(C) be the probability that a random d-dimensional unimodular lattice, chosen according to Haar measure on SL(d,Z)\SL(d,R), is disjoint from C\{0}. For special convex sets C we prove bounds on p(C) which are sharp…

We establish a novel criterion for comparing the performance of two densities, $g_1$ and $g_2$, within the context of corrupted data. Utilizing this criterion, we propose an algorithm to construct a density estimator within a star-shaped…

We formulate uncertainty relations for arbitrary $N$ observables. Two uncertainty inequalities are presented in terms of the sum of variances and standard deviations, respectively. The lower bounds of the corresponding sum uncertainty…

We compare the absolute visual magnitude of the majority of bright O stars in the sky as predicted from their spectral type with the absolute magnitude calculated from their apparent magnitude and the Hipparcos parallax. We find that many…

Adopting the low-redshift observational datasets, including the Pantheon sample of Type Ia supernovae, baryon acoustic oscillation measurements, and the tomographic Alcock-Paczynski method, we determine the Hubble constant to be…

Different measurements of the Hubble constant ($H_{0}$) are not consistent and a tension between the CMB based methods and cosmic distance ladder based methods has been observed. Measurements from various distance based methods are also…

We present a new analysis of the dust obscuration in starburst galaxies at low and high redshift. This study is motivated by our unique sample of the most extreme UV-selected starburst galaxies in the nearby universe (z<0.3), found to be…

The $L_{\infty}$ star discrepancy is a very well-studied measure used to quantify the uniformity of a point set distribution. Constructing optimal point sets for this measure is seen as a very hard problem in the discrepancy community.…

Recent determination of the Hubble constant via Cepheid-calibrated supernovae by \citet{riess_2.4_2016} (R16) find $\sim 3\sigma$ tension with inferences based on cosmic microwave background temperature and polarization measurements from…

Correlations between planetary and stellar properties, particularly age, can provide insight on planetary formation and evolution processes. However, the underlying source of such trends can be unclear, and measurement uncertainties and…

We give the proof of a tight lower bound on the probability that a binomial random variable exceeds its expected value. The inequality plays an important role in a variety of contexts, including the analysis of relative deviation bounds in…

Despite the tremendous advance of observational cosmology, the value of the Hubble constant ($H_0$) is still controversial (the so called ``Hubble tension'') because of the inconsistency between local/late-time measurements and those…

Coherent lower previsions are general probabilistic models allowing incompletely specified probability distributions. However, for complete description of a coherent lower prevision -- even on finite underlying sample spaces -- an infinite…

We show that the d-cube is determined by the spectrum of its distance matrix.

We initiate the study of quadratic discrepancy for finite point sets on the Heisenberg group $\mathbb H^n$ with respect to upper Ahlfors regular probability measures. For a natural family of test sets given by left translations and…

Many star bodies have convex subsets with approximately the same Gaussian measure (of the complement). Inspired by this phenomenon, and in connection with the randomized Dvoretzky theorem for Lorentz spaces, we derive bounds on the…

This article derives lower bounds on the supremal (strict) p-negative type of finite metric spaces using purely elementary techniques. The bounds depend only on the cardinality and the (scaled) diameter of the underlying finite metric…

We compare galaxy number counts in HST/ACS fields containing moderate-redshift (0.2<z<1.0) strong gravitational lenses with those in two control samples: (1) the first square degree of the COSMOS survey, comprising 259 ACS fields and (2) 20…

In this note, pointwise best-possible (lower and upper) bounds on the set of copulas with a given value of the Gini's gamma coefficient are established. It is shown that, unlike the best-possible bounds on the set of copulas with a given…