Related papers: Quasar Main Sequence: a line or a plane?
Principal component analysis (PCA) is a dimensionality reduction method in data analysis that involves diagonalizing the covariance matrix of the dataset. Recently, quantum algorithms have been formulated for PCA based on diagonalizing a…
There is evidence from radio-loud quasars to suggest that the distribution of the H$\beta$ broad emission line (BEL) gas is arranged in a predominantly planar orientation, and this result may well also apply to radio-quiet quasars. This…
In this work we introduce a new residual for normal linear models that are suitable for situations in which we are dealing with heteroskedasticity of unknown form, they are referred to by principal component analysis (PCA) residuals. These…
In the course of the last century, Principal Component Analysis (PCA) have become one of the pillars of modern scientific methods. Although PCA is normally addressed as a statistical tool aiming at finding orthogonal directions on which the…
We perform a systematic search for sub-parsec binary supermassive black holes (BHs) in normal broad line quasars at z<0.8, using multi-epoch SDSS spectroscopy of the broad Hbeta line. Our working model is that: only one of the two BHs in…
We measure the width of the MgII $\lambda2799$ line in quasar spectra from the SDSS, 2QZ and 2SLAQ surveys and, by invoking an unnormalised virial mass estimator, relate the scatter in line width to the scatter in mass in the underlying…
Principal Component Analysis (PCA) is a cornerstone of dimensionality reduction, yet its classical formulation relies critically on second-order moments and is therefore fragile in the presence of heavy-tailed data and impulsive noise.…
Several observational analyses suggest that matter is spatially structured at $\approx 130h^{-1}Mpc$ at low redshifts. This peak in the power spectrum provides a standard ruler in comoving space which can be used to compare the local…
Principal Component Analysis (PCA) is an efficient tool to optimize the multiparameter tests of general relativity (GR) where one tests for simultaneous deviations in multiple post-Newtonian (PN) phasing coefficients by introducing…
In this paper we review the basic Poissonian formulation of quasar variability, using it as a mathematical tool to extract relevant parameters such as the energy, rate and lifetimes of the flares through the analysis of observed light…
This paper introduces a Projected Principal Component Analysis (Projected-PCA), which employs principal component analysis to the projected (smoothed) data matrix onto a given linear space spanned by covariates. When it applies to…
A small fraction of quasars have long been known to show bulk velocity offsets in the broad Balmer lines with respect to the systemic redshift of the host galaxy. Models to explain these offsets usually invoke broad-line region gas…
We study attention mechanisms through the lens of a canonical unsupervised problem: principal component analysis (PCA). We show that, when trained on Gaussian data, both softmax and linear attention layers learn parameters that align with…
Linear principal component analysis (PCA) learns (semi-)orthogonal transformations by orienting the axes to maximize variance. Consequently, it can only identify orthogonal axes whose variances are clearly distinct, but it cannot identify…
The thesis concerns the analysis of the Active Galactic Nuclei. These are galaxies with an active core. The most luminous type of Active Galactic Nuclei is Quasar. It contains the supermassive black hole at the center. One of the least…
Principal Component Analysis (PCA) minimizes the reconstruction error given a class of linear models of fixed component dimensionality. Probabilistic PCA adds a probabilistic structure by learning the probability distribution of the PCA…
Dual and lensed quasars are valuable astrophysical targets in many aspects. Dual quasars, considered as the precursors of supermassive black hole binaries, can provide crucial insights into how black hole mergers drive the growth of…
Quasars are effective tracers of the large-scale distribution of galaxies at high redshift thanks to their high luminosity and dedicated surveys. Previous studies have shown that quasars exhibit a bias similar to that of rich groups,…
Principal component analysis (PCA) is widely used for dimensionality reduction, with well-documented merits in various applications involving high-dimensional data, including computer vision, preference measurement, and bioinformatics. In…
We performed the check of supposition about the possibility of manifestation of the previously observed phenomenon of central symmetry of the celestial sphere through existence of the opposite quasars. We discovered the existence of some…