Related papers: Computing magnitudes, colours, distances, and abso…
Relations are given for the correction of bias when mean absolute magnitudes are derived by the method of reduced parallaxes. The bias in the case of the derivation of the absolute magnitudes of individual objects is also considered.
We first review the current knowledge of Hipparcos systematic and random errors, in particular small-scale correlations. Then, assuming Gaussian parallax errors and using examples from the recent Hipparcos literature, we show how random…
Optimal estimation of signal amplitude, background level, and photocentre location is crucial to the combined extraction of astrometric and photometric information from focal plane images, and in particular from the one-dimensional…
We describe a modification of the usual definition of astronomical magnitudes, replacing the usual logarithm with an inverse hyperbolic sine function; we call these modified magnitudes `asinh magnitudes'. For objects detected at…
Pairwise Euclidean distance calculation is a fundamental step in many machine learning and data analysis algorithms. In real-world applications, however, these distances are frequently distorted by heteroskedastic noise$\unicode{x2014}$a…
Metric magnitude is a measure of the "size" of point clouds with many desirable geometric properties. It has been adapted to various mathematical contexts and recent work suggests that it can enhance machine learning and optimization…
Quantifying the distance between datasets is a fundamental question in mathematics and machine learning. We propose \textit{magnitude distance}, a novel distance metric defined on finite datasets using the notion of the \emph{magnitude} of…
Shuffled regression and unlinked regression represent intriguing challenges that have garnered considerable attention in many fields, including but not limited to ecological regression, multi-target tracking problems, image denoising, etc.…
We introduce a detailed analysis of the convergence of first-order methods with composite noise (sum of relative and absolute) in gradient for convex and smooth function minimization. This paper illustrates instances of practical problems…
Seismic data denoising is an important part of seismic data processing, which directly relate to the follow-up processing of seismic data. In terms of this issue, many authors proposed many methods based on rank reduction, sparse…
In this paper, we consider the problem of detecting signals in multiple, sequentially observed data streams. For each stream, the exact distribution is unknown, but characterized by a parameter that takes values in either of two disjoint…
The rapid growth of high-dimensional datasets across various scientific domains has created a pressing need for new statistical methods to compare distributions supported on their underlying structures. Assessing similarity between datasets…
The magnitude of a finite metric space has recently emerged as a novel invariant quantity, allowing to measure the effective size of a metric space. Despite encouraging first results demonstrating the descriptive abilities of the magnitude,…
Lutz-Kelker bias corrected absolute magnitude calibrations for the detached binary systems with main-sequence components are presented. The absolute magnitudes of the calibrator stars were derived at intrinsic colours of Johnson-Cousins and…
Using reliable trigonometric measurements, we find that the absolute magnitude of cataclysmic variables depends on the orbital period and de-reddened $(J-H)_{0}$ and $(H-K_{s})_{0}$ colours of {\em 2MASS} (Two Micron All Sky Survey)…
Super-resolution is a fundamental task in imaging, where the goal is to extract fine-grained structure from coarse-grained measurements. Here we are interested in a popular mathematical abstraction of this problem that has been widely…
In many real-world classification problems, the labels of training examples are randomly corrupted. Most previous theoretical work on classification with label noise assumes that the two classes are separable, that the label noise is…
In this paper, we develop convergence analysis of a modified line search method for objective functions whose value is computed with noise and whose gradient estimates are inexact and possibly random. The noise is assumed to be bounded in…
We use a Bayesian approach to derive the distance probability distribution for one object from its parallax with measurement uncertainty for two spatial distribution priors, viz. a homogeneous spherical distribution and a galactocentric…
Flux magnification is an interesting complement to shear-based lensing measurements, especially at high redshift where sources are harder to resolve. One measures either changes in the source density (magnification bias) or in the shape of…