Related papers: Star discrepancy for new stratified random samplin…
We consider the problem of allocating samples to a finite set of discrete distributions in order to learn them uniformly well in terms of four common distance measures: $\ell_2^2$, $\ell_1$, $f$-divergence, and separation distance. To…
Models of neutron stars are considered in the case of a uniform density distribution. An algebraic equation, valid for any equation of state, is obtained. This equation allows one to find the approximate mass of a star of a given density…
We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a…
We present a large ${\sim 30" \times 30"}$ spectroscopic survey of the Galactic Center using the SINFONI IFU at the VLT. Combining observations of the last two decades we compile spectra of over $2800$ stars. Using the Bracket-$\gamma$…
We introduce a new method to measure the dispersion of mmax values of star clusters and show that the observed sample of mmax is inconsistent with random sampling from an universal stellar initial mass function (IMF) at a 99.9% confidence…
The Standard Simplex Conjecture of Isaksson and Mossel asks for the partition $\{A_{i}\}_{i=1}^{k}$ of $\mathbb{R}^{n}$ into $k\leq n+1$ pieces of equal Gaussian measure of optimal noise stability. That is, for $\rho>0$, we maximize $$…
There is a growing number of tasks that work directly on point clouds. As the size of the point cloud grows, so do the computational demands of these tasks. A possible solution is to sample the point cloud first. Classic sampling…
Recently, Schneider and Schneider defined a new class of partitions called sequentially congruent partitions, in which each part is congruent to the next part modulo its index, and they proved two partition bijections involving these…
The star-discrepancy is a quantitative measure for the irregularity of distribution of a point set in the unit cube that is intimately linked to the integration error of quasi-Monte Carlo algorithms. These popular integration rules are…
Context. Dusty debris discs around main sequence stars are observed to vary widely in terms of their vertical thickness. Their vertical structure may be affected by damping in inelastic collisions. Although kinetic models have often been…
We consider composite-composite testing problems for the expectation in the Gaussian sequence model where the null hypothesis corresponds to a convex subset $\mathcal{C}$ of $\mathbb{R}^d$. We adopt a minimax point of view and our primary…
A popular approach for testing if two univariate random variables are statistically independent consists of partitioning the sample space into bins, and evaluating a test statistic on the binned data. The partition size matters, and the…
We present numerical investigations into the formation of massive stars from centrally condensed turbulent cores. The results of five hydrodynamical simulations are described, following the collapse of the core, fragmentation and the…
A growing fraction of Simple Stellar Population (SSP) models, in an aim to create more realistic simulations capable of including stochastic variation in their outputs, begin their simulations with a distribution of discrete stars following…
Determining star cluster distances is essential to analyse their properties and distribution in the Galaxy. In particular it is desirable to have a reliable, purely photometric distance estimation method for large samples of newly…
We fit model spectral energy distributions to each pixel in 67 nearby (<z>=0.0057) galaxies using broadband photometry from the Sloan Digital Sky Survey and GALEX. For each galaxy, we compare the stellar mass derived by summing the mass of…
Simulations have indicated that most of the escaped Lyman continuum photons escape through a minority of solid angles with near complete transparency, with the remaining majority of the solid angles largely opaque, resulting in a very broad…
We introduce polystar bodies: compact starshaped sets whose gauge or radial functions are expressible by polynomials, enabling tractable computations, such as that of intersection bodies. We prove that polystar bodies are uniformly dense in…
In classification problems, sampling bias between training data and testing data is critical to the ranking performance of classification scores. Such bias can be both unintentionally introduced by data collection and intentionally…
Understanding the formation and evolution of young star clusters requires quantitative statistical measures of their structure. We investigate the structures of observed and modelled star-forming clusters. By considering the different…