[OII] Emission, Eigenvector 1 and Orientation in Radio-quiet Quasars

We present supportive evidence that the Boroson and Green eigenvector 1 is not driven by source orientation. Until recently it was generally accepted that eigenvector 1 does not depend on orientation as it strongly correlates with [OIII]5007 emission, thought to be an isotropic property. However, recent studies of radio-loud AGN have questioned the isotropy of [OIII] emission and concluded that [OII]3727 emission is isotropic. In this paper we investigate the relation between eigenvector 1 and [OII] emission in radio-quiet BQS (Bright Quasar Survey) quasars, and readdress the issue of orientation as the driver of eigenvector 1. We find significant correlations between eigenvector 1 and orientation independent [OII] emission, which implies that orientation does not drive eigenvector 1. The luminosities and equivalent widths of [OIII] and [OII] correlate with one another, and the range in luminosities and equivalent widths is similar. This suggests that the radio-quiet BQS quasars are largely free of orientation dependent dust effects and ionization dependent effects in the narrow-line region. We also conclude that neither the [OIII] emission nor the [OII]/[OIII] ratio are dependent on orientation in our radio-quiet BQS quasar sample, contrary to recent results found for radio-loud quasars.Comment: 24 pages, 12 figures, accepted for publication in Ap

Size of nodal domains of the eigenvectors of a G(n,p) graph

Consider an eigenvector of the adjacency matrix of a G(n, p) graph. A nodal domain is a connected component of the set of vertices where this eigenvector has a constant sign. It is known that with high probability, there are exactly two nodal domains for each eigenvector corresponding to a non-leading eigenvalue. We prove that with high probability, the sizes of these nodal domains are approximately equal to each other

Eigenvector Sky Subtraction

We develop a new method for estimating and removing the spectrum of the sky from deep spectroscopic observations; our method does not rely on simultaneous measurement of the sky spectrum with the object spectrum. The technique is based on the iterative subtraction of continuum estimates and Eigenvector sky models derived from Singular Value Decompositions (SVD) of sky spectra, and sky spectra residuals. Using simulated data derived from small telescope observations we demonstrate that the method is effective for faint objects on large telescopes. We discuss simple methods to combine our new technique with the simultaneous measurement of sky to obtain sky subtraction very near the Poisson limit.Comment: Accepted for publication in The Astrophysical Journal (Letters) 2000 March 7. Includes one extra figure which did not fit in a lette

Eigenvector localization in the heavy-tailed random conductance model

We generalize our former localization result about the principal Dirichlet eigenvector of the i.i.d. heavy-tailed random conductance Laplacian to the first $k$ eigenvectors. We overcome the complication that the higher eigenvectors have fluctuating signs by invoking the Bauer-Fike theorem to show that the $k$th eigenvector is close to the principal eigenvector of an auxiliary spectral problem.Comment: 14 pages. Generalizes the results of article arXiv:1608.02415 to higher order eigenvectors. For better readability, we have copied the main definition

Stable and Reliable Computation of Eigenvectors of Large Profile Matrices

Independent eigenvector computation for a given set of eigenvalues of typical engineering eigenvalue problems still is a big challenge for established subspace solution methods. The inverse vector iteration as the standard solution method often is not capable of reliably computing the eigenvectors of a cluster of bad separated eigenvalues. The following contribution presents a stable and reliable solution method for independent and selective eigenvector computation of large symmetric profile matrices. The method is an extension of the well-known and well-understood QR-method for full matrices thus having all its good numerical properties. The effects of finite arithmetic precision of computer representations of eigenvalue/eigenvector solution methods are analysed and it is shown that the numerical behavior of the new method is superior to subspace solution methods

Localization and centrality in networks

Eigenvector centrality is a common measure of the importance of nodes in a network. Here we show that under common conditions the eigenvector centrality displays a localization transition that causes most of the weight of the centrality to concentrate on a small number of nodes in the network. In this regime the measure is no longer useful for distinguishing among the remaining nodes and its efficacy as a network metric is impaired. As a remedy, we propose an alternative centrality measure based on the nonbacktracking matrix, which gives results closely similar to the standard eigenvector centrality in dense networks where the latter is well behaved, but avoids localization and gives useful results in regimes where the standard centrality fails.Comment: 5 pages, 1 figur