Related papers: Constructing Optimal $L_{\infty}$ Star Discrepancy…
The relations between star formation and properties of molecular clouds are studied based on a sample of star forming regions in the Galactic Plane. Sources were selected by having radio recombination lines to provide identification of…
Maximum Mean Discrepancy (MMD) has been widely used in the areas of machine learning and statistics to quantify the distance between two distributions in the $p$-dimensional Euclidean space. The asymptotic property of the sample MMD has…
Ultra-Diffuse Galaxies are both extreme products of galaxy evolution and extreme environments in which to test our understanding of star formation. In this work, we contrast the spatially resolved star formation activity of a sample of 22…
Comparing alternatives in pairs is a very well known technique of ranking creation. The answer to how reliable and trustworthy ranking is depends on the inconsistency of the data from which it was created. There are many indices used for…
A great challenge in the analysis of the discrepancy function D_N is to obtain universal lower bounds on the L-infty norm of D_N in dimensions d \geq 3. It follows from the average case bound of Klaus Roth that the L-infty norm of D_N is at…
The diameter of a star is a major observable that serves to test the validity of stellar structure theories. It is also a difficult observable that is mostly obtained with indirect methods since the stars are so remote. Today only ~600…
A combinatorial rectangle may be viewed as a matrix whose entries are all +-1. The discrepancy of an m by n matrix is the maximum among the absolute values of its m row sums and n column sums. In this paper, we investigate combinatorial…
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…
A typical computational geometry problem begins: Consider a set P of n points in R^d. However, many applications today work with input that is not precisely known, for example when the data is sensed and has some known error model. What if…
We consider the joint constellation design problem for the noncoherent multiple-input multiple-output multiple-access channel (MAC). By analyzing the noncoherent maximum-likelihood detection error, we propose novel design criteria so as to…
We consider the problem of designing an optimal quantum detector to minimize the probability of a detection error when distinguishing between a collection of quantum states, represented by a set of density operators. We show that the design…
We provide probabilistic lower bounds for the star discrepancy of Latin hypercube samples. These bounds are sharp in the sense that they match the recent probabilistic upper bounds for the star discrepancy of Latin hypercube samples proved…
Star formation is a multi-scale, multi-physics problem ranging from the size scale of molecular clouds ($\sim$10s pc) down to the size scales of dense prestellar cores ($\sim$0.1 pc) that are the birth sites of stars. Several physical…
I review theoretical models of star formation and how they apply across the stellar mass spectrum. Several distinct theories are under active study for massive star formation, especially Turbulent Core Accretion, Competitive Accretion and…
We consider current state of star formation theory and requirements to observations in millimeter and submillimeter ranges which are necessary for resolution of the most actual problems of the physics of star formation. Two key features of…
We propose new optimal estimators for the Lipschitz frontier of a set of points. They are defined as kernel estimators being sufficiently regular, covering all the points and whose associated support is of smallest surface. The estimators…
The determination of chemical abundances from stellar spectra is considered a mature field of astrophysics. Digital spectra of stars are recorded and processed with standard techniques, much like samples in the biological sciences.…
The Erd\H os unit distance conjecture in the plane says that the number of pairs of points from a point set of size $n$ separated by a fixed (Euclidean) distance is $\leq C_{\epsilon} n^{1+\epsilon}$ for any $\epsilon>0$. The best known…
The $L_p$-discrepancy is a quantitative measure for the irregularity of distribution of an $N$-element point set in the $d$-dimensional unit cube, which is closely related to the worst-case error of quasi-Monte Carlo algorithms for…
Visual photometry, the estimation of stellar brightness by eye, continues to provide valuable data even in this highly-instrumented era. However, the eye-brain system functions differently from electronic sensors and its products can be…