Related papers: Computing Star Discrepancies with Numerical Black-…
Tusn\'ady's problem asks to bound the discrepancy of points and axis-parallel boxes in $\mathbb{R}^d$. Algorithmic bounds on Tusn\'ady's problem use a canonical decomposition of Matou\v{s}ek for the system of points and axis-parallel boxes,…
The Kullback-Leibler (KL) divergence is frequently used in data science. For discrete distributions on large state spaces, approximations of probability vectors may result in a few small negative entries, rendering the KL divergence…
We present a method to compute the magnification of a finite source star lensed by a triple lens system based on the image boundary (contour integration) method. We describe a new procedure to obtain continuous image boundaries from…
Developing a theory of low-mass star formation ($\sim 0.1$ to 3~M$_{\odot}$) remains one of the most elusive and important goals of theoretical astrophysics. The star-formation process is the outcome of the complex dynamics of interstellar…
We consider robust discrete minimization problems where uncertainty is defined by a convex set in the objective. We show how an integrality gap verifier for the linear programming relaxation of the non-robust version of the problem can be…
We propose a new method of constraining the redshifts of individual extragalactic sources based on celestial coordinates and their ensemble statistics. Techniques from integer linear programming are utilized to optimize simultaneously for…
Stellar models are calculated in the approximation of a uniform density distribution. Variational method was used for determination of the boundary of a stability loss, for stellar masses in the range from 2 up to $10^5$ $M_{\odot}$. The…
Orbital motions from binary stars can broaden the observed line-of-sight velocity distribution of a stellar system, artificially inflating the measured line-of-sight velocity dispersion, which can in turn lead to erroneous conclusions about…
The stellar velocity dispersion ($\sigma$) of massive elliptical galaxies is a key ingredient in breaking the mass-sheet degeneracy and obtaining precise and accurate cosmography from gravitational time delays. The relative uncertainty on…
For $m, d \in {\mathbb N}$, a jittered sampling point set $P$ having $N = m^d$ points in $[0,1)^d$ is constructed by partitioning the unit cube $[0,1)^d$ into $m^d$ axis-aligned cubes of equal size and then placing one point independently…
This paper presents detailed consideration of methodologies to calibrate differential light curves for accurate physical starspot modeling. We use the Sun and starspot models as a testbed to highlight some factors in this calibration that…
The detection of planetary transits in the light curves of active stars, featuring correlated noise in the form of stellar variability, remains a challenge. Depending on the noise characteristics, we show that the traditional technique that…
The immense amount of time series data produced by astronomical surveys has called for the use of machine learning algorithms to discover and classify several million celestial sources. In the case of variable stars, supervised learning…
Stellar elemental abundances are important for understanding the fundamental properties of a star or stellar group, such as age and evolutionary history, as well as the composition of an orbiting planet. However, as abundance measurement…
The partial coloring method is one of the most powerful and widely used method in combinatorial discrepancy problems. However, in many cases it leads to sub-optimal bounds as the partial coloring step must be iterated a logarithmic number…
The two-point correlation function of the galaxy distribution is a key cosmological observable that allows us to constrain the dynamical and geometrical state of our Universe. To measure the correlation function we need to know both the…
Robust discrete optimization is a highly active field of research where a plenitude of combinations between decision criteria, uncertainty sets and underlying nominal problems are considered. Usually, a robust problem becomes harder to…
The discrepancy function measures the deviation of the empirical distribution of a point set in $[0,1]^d$ from the uniform distribution. In this paper, we study the classical discrepancy function with respect to the BMO and exponential…
In this article we develop a max-strategy improvement algorithm for computing least fixpoints of operators on on the reals that are point-wise maxima of finitely many monotone and order-concave operators. Computing the uniquely determined…
If not properly accounted for, unresolved binary stars can induce a bias in the photometric determination of star cluster masses inferred from star counts and the luminosity function. A correction factor close to 1.15 (for a binary fraction…