The defect variance of random spherical harmonics

The defect of a function $f:M\rightarrow \mathbb{R}$ is defined as the difference between the measure of the positive and negative regions. In this paper, we begin the analysis of the distribution of defect of random Gaussian spherical harmonics. By an easy argument, the defect is non-trivial only for even degree and the expected value always vanishes. Our principal result is obtaining the asymptotic shape of the defect variance, in the high frequency limit. As other geometric functionals of random eigenfunctions, the defect may be used as a tool to probe the statistical properties of spherical random fields, a topic of great interest for modern Cosmological data analysis.Comment: 19 page

A Chandra view of the clumpy reflector at the heart of the Circinus galaxy

We present a spectral and imaging analysis of the X-ray reflecting structure at the heart of the Circinus galaxy, investigating the innermost regions surrounding the central black hole. By studying an archival 200 ks Chandra ACIS-S observation, we are able to image the extended clumpy structure responsible for both cold reflection of the primary radiation and neutral iron Ka line emission. We measure an excess of the equivalent width of the iron Ka line which follows an axisymmetric geometry around the nucleus on a hundred pc scale. Spectra extracted from different regions confirm a scenario in which the dominant mechanism is the reflection of the nuclear radiation from Compton-thick gas. Significant differences in the equivalent width of the iron Ka emission line (up to a factor of 2) are found. It is argued that these differences are due to different scattering angles with respect to the line of sight rather than to different iron abundances.Comment: 6 pages, 4 figures, accepted for publication on MNRA

Introducing Mexican needlets for CMB analysis: Issues for practical applications and comparison with standard needlets

Over the last few years, needlets have a emerged as a useful tool for the analysis of Cosmic Microwave Background (CMB) data. Our aim in this paper is first to introduce in the CMB literature a different form of needlets, known as Mexican needlets, first discussed in the mathematical literature by Geller and Mayeli (2009a,b). We then proceed with an extensive study of the properties of both standard and Mexican needlets; these properties depend on some parameters which can be tuned in order to optimize the performance for a given application. Our second aim in this paper is then to give practical advice on how to adjust these parameters in order to achieve the best properties for a given problem in CMB data analysis. In particular we investigate localization properties in real and harmonic spaces and propose a recipe on how to quantify the influence of galactic and point source masks on the needlet coefficients. We also show that for certain parameter values, the Mexican needlets provide a close approximation to the Spherical Mexican Hat Wavelets (whence their name), with some advantages concerning their numerical implementation and the derivation of their statistical properties.Comment: 40 pages, 11 figures, published version, main modification: added section on more realistic galactic and point source mask

X-ray observations of the Compton-thick Seyfert 2 galaxy, NGC 5643

We present results from a ~55 ks long XMM-Newton observation of the obscured AGN, NGC 5643, performed in July 2009. A previous, shorter (about 10 ks) XMM-Newton observation in February 2003 had left two major issues open, the nature of the hard X-ray emission (Compton-thin vs Compton-thick) and of the soft X-ray excess (photoionized vs collisionally ionized matter). The new observation shows that the source is Compton-thick and that the dominant contribution to the soft X-ray emission is by photoionized matter (even if it is still unclear whether collisionally ionized matter may contribute as well). We also studied three bright X-ray sources that are in the field of NGC 5643. The ULX NGC 5643 X-1 was confirmed to be very luminous, even if more than a factor 2 fainter than in 2003. We then provided the first high quality spectrum of the cluster of galaxies Abell 3602. The last source, CXOJ143244.5-442020, is likely an unobscured AGN, possibly belonging to Abell 3602.Comment: 6 pages. Accepted for publication in A&

Exposing implicit biases and stereotypes in human and artificial intelligence: state of the art and challenges with a focus on gender

Biases in cognition are ubiquitous. Social psychologists suggested biases and stereotypes serve a multifarious set of cognitive goals, while at the same time stressing their potential harmfulness. Recently, biases and stereotypes became the purview of heated debates in the machine learning community too. Researchers and developers are becoming increasingly aware of the fact that some biases, like gender and race biases, are entrenched in the algorithms some AI applications rely upon. Here, taking into account several existing approaches that address the problem of implicit biases and stereotypes, we propose that a strategy to cope with this phenomenon is to unmask those found in AI systems by understanding their cognitive dimension, rather than simply trying to correct algorithms. To this extent, we present a discussion bridging together findings from cognitive science and insights from machine learning that can be integrated in a state-of-the-art semantic network. Remarkably, this resource can be of assistance to scholars (e.g., cognitive and computer scientists) while at the same time contributing to refine AI regulations affecting social life. We show how only through a thorough understanding of the cognitive processes leading to biases, and through an interdisciplinary effort, we can make the best of AI technology

NGC 1068: No change in the mid-IR torus structure despite X-ray variability

Context. Recent NuSTAR observations revealed a somewhat unexpected increase in the X-ray flux of the nucleus of NGC 1068. We expect the infrared emission of the dusty torus to react on the intrinsic changes of the accretion disk. Aims. We aim to investigate the origin of the X-ray variation by investigating the response of the mid-infrared environment. Methods. We obtained single-aperture and interferometric mid-infrared measurements and directly compared the measurements observed before and immediately after the X-ray variations. The average correlated and single-aperture fluxes as well as the differential phases were directly compared to detect a possible change in the structure of the nuclear emission on scales of $\sim$ 2 pc. Results. The flux densities and differential phases of the observations before and during the X-ray variation show no significant change over a period of ten years. Possible minor variations in the infrared emission are $\lesssim$ 8 %. Conclusions. Our results suggest that the mid-infrared environment of NGC 1068 has remained unchanged for a decade. The recent transient change in the X-rays did not cause a significant variation in the infrared emission. This independent study supports previous conclusions that stated that the X-ray variation detected by NuSTAR observations is due to X-ray emission piercing through a patchy section of the dusty region.Comment: 6 pages, 5 figures, 3 tables. Accepted for publication on A&

The changing X-ray time lag in MCG-6-30-15

MCG-6-30-15 is one of the most observed Narrow Line Seyfert 1 galaxies in the X-ray band. In this paper we examine the X-ray time lags in this source using a total of 600 ks in observations (440 ks exposure) taken with the XMM-Newton telescope (300 ks in 2001 and 300 ks in 2013). Both the old and new observations show the usual hard lag that increases with energy, however, the hard lag turns over to a soft lag at frequencies below ~1e-4 Hz. The highest frequencies (~1e-3 Hz) in this source show a clear soft lag, as previously presented for the first 300 ks observation, but no clear iron K lag is detected in either the old or new observation. The soft lag is more significant in the old observation than the new. The observations are consistent with a reverberation interpretation, where the soft, reflected emission is delayed with respect to the hard powerlaw component. These spectral timing results suggest that two distinct variability mechanisms are important in this source: intrinsic coronal variations (which lead to correlated variability in the reprocessed emission), and geometrical changes in the corona. Variability due to geometrical changes does not result in correlated variability in the reflection, and therefore inhibits the clear detection of an iron K lag.Comment: Resubmitted to MNRAS after minor corrections. 11 pages, 10 figure

On Nonlinear Functionals of Random Spherical Eigenfunctions

We prove Central Limit Theorems and Stein-like bounds for the asymptotic behaviour of nonlinear functionals of spherical Gaussian eigenfunctions. Our investigation combine asymptotic analysis of higher order moments for Legendre polynomials and, in addition, recent results on Malliavin calculus and Total Variation bounds for Gaussian subordinated fields. We discuss application to geometric functionals like the Defect and invariant statistics, e.g. polyspectra of isotropic spherical random fields. Both of these have relevance for applications, especially in an astrophysical environment.Comment: 24 page