Related papers: Probabilistic Lower Bounds for the Discrepancy of …
The inverse of the star-discrepancy problem asks for point sets $P_{N,s}$ of size $N$ in the $s$-dimensional unit cube $[0,1]^s$ whose star-discrepancy $D^\ast(P_{N,s})$ satisfies $$D^\ast(P_{N,s}) \le C \sqrt{s/N},$$ where $C> 0$ is a…
We present a new method for detecting and correcting systematic errors in the distances to stars when both proper motions and line-of-sight velocities are available. The method, which is applicable for samples of 200 or more stars that have…
Geometric discrepancies are standard measures to quantify the irregularity of distributions. They are an important notion in numerical integration. One of the most important discrepancy notions is the so-called \emph{star discrepancy}.…
Latin hypercube designs (LHDs) with space-filling properties are widely used for emulating computer simulators. Over the last three decades, a wide spectrum of LHDs have been proposed with space-filling criteria like minimum correlation…
The current $>3\sigma$ tension between the Hubble constant $H_0$ measured from local distance indicators and from cosmic microwave background is one of the most highly debated issues in cosmology, as it possibly indicates new physics or…
Time delays between lensed multiple images have been known to provide an interesting probe of the Hubble constant, but such application is often limited by degeneracies with the shape of lens potentials. We propose a new statistical…
In this book chapter we survey known approaches and algorithms to compute discrepancy measures of point sets. After providing an introduction which puts the calculation of discrepancy measures in a more general context, we focus on the…
We present a cosmographic study designed to test the simplest type of accelerating cosmology: a flat universe with matter and a cosmological constant ($\Lambda$). Hubble series expansions are fit to the SCP Union2.1 supernova data set to…
Even in a universe that is homogeneous on large scales, local density fluctuations can imprint a systematic signature on the cosmological inferences we make from distant sources. One example is the effect of a local under-density on…
Resolving the tension between quantum superpositions and the uniqueness of the classical world is a major open problem. One possibility, which is extensively explored both theoretically and experimentally, is that quantum linearity breaks…
The microlensing parallax campaign with the $Spitzer$ space telescope aims to measure masses and distances of microlensing events seen towards the Galactic bulge, with a focus on planetary microlensing events. The hope is to measure how the…
We give short and simple proofs of what seem to be folklore results: * the maximum cardinality of the intersection of a lattice cube with an affine subspace; * the minimum number of affine subspaces needed to cover a lattice cube.
The precise measurement of the masses and radii of stars in eclipsing binary systems provides a window into uncertain processes in stellar evolution, especially mixing at convective boundaries. Recently, these data have been used to…
We investigate the photonsphere in the background of regular asymptotically flat compact stars. The analysis includes the general hairy compact star considering the matter fields' backreaction on the metric in various gravity theories. We…
The current discrepancy between the Hubble constant $H_0$ derived from the local distance ladder and from the cosmic microwave background is one of the most crucial issues in cosmology, as it possibly indicates unknown systematics or new…
We have developed a technique to systematically discover and study high-redshift supernovae that can be used to measure the cosmological parameters. We report here results based on the initial seven of >28 supernovae discovered to date in…
Measurements of the UV-continuum slopes provide valuable information on the physical properties of galaxies forming in the early universe, probing the dust reddening, age, metal content, and even the escape fraction. While constraints on…
Assessing the consistency of parameter constraints derived from different cosmological probes is an important way to test the validity of the underlying cosmological model. In an earlier work [Nicola et al., 2017], we computed constraints…
A long-standing issue in the theory of low mass stars is the discrepancy between predicted and observed radii and effective temperatures. In spite of the increasing availability of very precise radius determinations from eclipsing binaries…
In this paper we study the redundancy of Huffman codes. In particular, we consider sources for which the probability of one of the source symbols is known. We prove a conjecture of Ye and Yeung regarding the upper bound on the redundancy of…