Related papers: Computing Star Discrepancies with Numerical Black-…
Astronomers generally assume planet-forming disks are aligned with the rotation of their host star. However, recent observations have shown evidence of warping in protoplanetary disks. One can measure the statistical alignment between the…
Low-discrepancy points (also called Quasi-Monte Carlo points) are deterministically and cleverly chosen point sets in the unit cube, which provide an approximation of the uniform distribution. We explore two methods based on such…
Finding the optimal ordering of k-subsets with respect to an objective function is known to be an extremely challenging problem. In this paper we introduce a new objective for this task, rooted in the problem of star identification on…
Structured spatial navigation is a core benchmark for Large Language Models (LLMs) spatial reasoning. Existing paradigms like Visualization-of-Thought (VoT) are prone to cascading errors in complex topologies. To solve this, we propose…
The star tracker is generally affected by the atmospheric background light and the aerodynamic environment when working in near space, which results in missing stars or false stars. Moreover, high-speed maneuvering may cause star trailing,…
The L_2-discrepancy measures the irregularity of the distribution of a finite point set. In this note we prove lower bounds for the L_2 discrepancy of arbitrary N-point sets. Our main focus is on the two-dimensional case. Asymptotic upper…
$f$-divergences are a general class of divergences between probability measures which include as special cases many commonly used divergences in probability, mathematical statistics and information theory such as Kullback-Leibler…
Searching for space-time variations of the constants of Nature is a promising way to search for new physics beyond General Relativity and the standard model motivated by unification theories and models of dark matter and dark energy. We…
According to Aistleitner and Weimar, there exist two-dimensional (double) infinite matrices whose star-discrepancy $D_N^{*s}$ of the first $N$ rows and $s$ columns, interpreted as $N$ points in $[0,1]^s$, satisfies an inequality of the form…
Instance segmentation has witnessed promising advancements through deep neural network-based algorithms. However, these models often exhibit incorrect predictions with unwarranted confidence levels. Consequently, evaluating prediction…
For a probability measure $\mu$ on $[0,1]$ without discrete component, the best possible order of approximation by a finite point set in terms of the star-discrepancy is $\frac{1}{2N}$ as has been proven relatively recently. However, if…
Star clusters are often hard to find, as they may lie in a dense field of background objects or, because in the case of embedded clusters, they are surrounded by a more dispersed population of young stars. This paper discusses four…
We propose an ODE approach to solving multiple choice polynomial programming (MCPP) after assuming that the optimum point can be approximated by the expected value of so-called thermal equilibrium as usually did in simulated annealing. The…
We present the results of 16 years of monitoring stellar orbits around the massive black hole in center of the Milky Way using high resolution NIR techniques. This work refines our previous analysis mainly by greatly improving the…
We have developed a low-cost off-the-shelf component star sensor (StarSense) for use in minisatellites and CubeSats to determine the attitude of a satellite in orbit. StarSense is an imaging camera with a limiting magnitude of 6.5, which…
Context. The "mass discrepancy" in massive O stars represents a long-standing problem in stellar astrophysics with far-reaching implications for the chemical and dynamical feedback in galaxies. Aims. Our goal is to investigate this mass…
In the present paper we prove several results concerning the existence of low-discrepancy point sets with respect to an arbitrary non-uniform measure $\mu$ on the $d$-dimensional unit cube. We improve a theorem of Beck, by showing that for…
The spherical cap discrepancy is a prominent measure of uniformity for sets on the d-dimensional sphere. It is particularly important for estimating the integration error for certain classes of functions on the sphere. Building on a…
Combinatorial discrepancy is a complexity measure of a collection of sets which quantifies how well the sets in the collection can be simultaneously balanced. More precisely, we are given an n-point set $P$, and a collection $\mathcal{F} =…
We study an optimal control problem under uncertainty, where the target function is the solution of an elliptic partial differential equation with random coefficients, steered by a control function. The robust formulation of the…