相关论文: Probabilistic Lower Bounds for the Discrepancy of …
We report optical spectroscopic observations of a sample of 6 low-galactic latitude microquasar candidates selected by cross-identification of X-ray and radio point source catalogs for |b|<5 degrees. Two objects resulted to be of clear…
We use updated Hubble parameter and baryon acoustic oscillation data, as well as other lower-redshift Type Ia supernova, Mg II reverberation-measured quasar, quasar angular size, H II starburst galaxy, and Amati-correlated gamma-ray burst…
We set out to rederive the 8 Hubble parameter values obtained from estimated relative galaxy ages by Simon et al. [Physical Review D, 71, 123001 (2005)]. We find that to obtain the level of precision claimed in $H(z)$, unrealistically small…
The fitting of the observed redshifts and magnitudes of type Ia supernovae to what we would see in homogeneous cosmological models has led to constraints on cosmological parameters. However, in doing such fits it is assumed that the sampled…
We prove various estimates for the mean square lattice point discrepancy for dilates of a convex body.
The most recent Hubble constant ($H_0)$ estimates from local methods (z << 1), $H_0=73.8\pm 2.4$ km s$^{-1}$ Mpc$^{-1}$, and the one from high redshifts $H_0=67.3\pm 1.2$ km s$^{-1}$ Mpc$^{-1}$, are discrepant at $2.4 \sigma$ confidence…
We consider the discrepancy of the integer lattice with respect to the collection of all translated copies of a dilated convex body having a finite number of flat, possibly non-smooth, points in its boundary. We estimate the $L^{p}$ norm of…
An exact determination of the Hubble constant remains one of key problems in cosmology for almost a century. However, its modern values derived by various methods still disagree from each other by almost 10%; the greater values being…
A significant tension has become manifest between the current expansion rate of our Universe measured from the cosmic microwave background by the Planck satellite and from local distance probes, which has prompted for interpretations of…
We give an improved lower bound for the $L_2$-discrepancy of finite point sets in the unit square.
Discrepancy measures how uniformly distributed a point set is with respect to a given set of ranges. There are two notions of discrepancy, namely continuous discrepancy and combinatorial discrepancy. Depending on the ranges, several…
Standard maximum-likelihood estimators for binary-star and exoplanet eccentricities are biased high, in the sense that the estimated eccentricity tends to be larger than the true eccentricity. As with most non-trivial observables, a simple…
A 10\% difference in the scale for the Hubble parameter constitutes a clear problem for cosmology. Here, considering angular distribution of Type Ia supernovae (SN) within the Pantheon compilation and working within flat $\Lambda$CDM…
The star discrepancy is a quantitative measure of the uniformity of a point set in the unit cube. A central quantity of interest is the inverse of the star discrepancy, $N(\varepsilon, s)$, defined as the minimum number of points required…
The spherical cap discrepancy is a widely used measure for how uniformly a sample of points on the sphere is distributed. Being hard to compute, this discrepancy measure is typically replaced by some lower or upper estimates when designing…
We study the problem of testing the existence of a dense subhypergraph. The null hypothesis is an Erdos-Renyi uniform random hypergraph and the alternative hypothesis is a uniform random hypergraph that contains a dense subhypergraph. We…
We provide evidence that the uncertainty in detection of small and deterministic phase-shift deviations from a working point can be lower than the Heisenberg bound, for fixed finite mean number of photons. We achieve that by exploiting…
In order to clarify the tension between estimates of the Hubble Constant ($H_0$) from local ($z \ll 1$) and global ($z \gg 1$) measurements, Lima and Cunha (LC) proposed a new method to measure $H_0$ in intermediate redshifts ($z \approx…
The fractions of samples spanning a lattice at its percolation threshold are found by computer simulation of random site-percolation in two- and three-dimensional hypercubic lattices using different boundary conditions. As a byproduct we…
We derive two upper bounds for the probability of deviation of a vector-valued Lipschitz function of a collection of random variables from its expected value. The resulting upper bounds can be tighter than bounds obtained by a direct…