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

The puzzling case of the radio-loud QSO 3C 186: a gravitational wave recoiling black hole in a young radio source?

Context. Radio-loud AGNs with powerful relativistic jets are thought to be associated with rapidly spinning black holes (BHs). BH spin-up may result from a number of processes, including accretion of matter onto the BH itself, and catastrophic events such as BH-BH mergers. Aims. We study the intriguing properties of the powerful (L_bol ~ 10^47 erg s^-1) radio-loud quasar 3C 186. This object shows peculiar features both in the images and in the spectra. Methods. We utilize near-IR Hubble Space Telescope (HST) images to study the properties of the host galaxy, and HST UV and Sloan Digital Sky Survey optical spectra to study the kinematics of the source. Chandra X-ray data are also used to better constrain the physical interpretation. Results. HST imaging shows that the active nucleus is offset by 1.3 +- 0.1 arcsec (i.e. ~11 kpc) with respect to the center of the host galaxy. Spectroscopic data show that the broad emission lines are offset by -2140 +-390 km/s with respect to the narrow lines. Velocity shifts are often seen in QSO spectra, in particular in high-ionization broad emission lines. The host galaxy of the quasar displays a distorted morphology with possible tidal features that are typical of the late stages of a galaxy merger. Conclusions. A number of scenarios can be envisaged to account for the observed features. While the presence of a peculiar outflow cannot be completely ruled out, all of the observed features are consistent with those expected if the QSO is associated with a gravitational wave (GW) recoiling BH. Future detailed studies of this object will allow us to confirm this type of scenario and will enable a better understanding of both the physics of BH-BH mergers and the phenomena associated with the emission of GW from astrophysical sources.Comment: 16 pages, 8 figures. Accepted for publication in Astronomy & Astrophysics. New appendix adde

Chiral gauge theories and anomalies in the Wilson renormalization group approach

We extend the Wilson renormalization group (RG) formulation to chiral gauge theories and show that local gauge symmetry can be implemented by a suitable choice of the RG flow boundary conditions. Since the space-time dimension is four, there is no ambiguity in handling the matrix \g_5 and left and right fermions are not coupled. As a result the ultraviolet action contains all possible globally chiral invariant interactions. Nevertheless, the correct chiral anomaly is reproduced.Comment: 16 pages, 4 figures, LaTex, uses epsfig, amssym

NuSTAR and Suzaku X-ray Spectroscopy of NGC 4151: Evidence for Reflection from the Inner Accretion Disk

We present X-ray timing and spectral analyses of simultaneous 150 ks Nuclear Spectroscopic Telescope Array (NuSTAR) and Suzaku X-ray observations of the Seyfert 1.5 galaxy NGC 4151. We disentangle the continuum emission, absorption, and reflection properties of the active galactic nucleus (AGN) by applying inner accretion disk reflection and absorption-dominated models. With a time-averaged spectral analysis, we find strong evidence for relativistic reflection from the inner accretion disk. We find that relativistic emission arises from a highly ionized inner accretion disk with a steep emissivity profile, which suggests an intense, compact illuminating source. We find a preliminary, near-maximal black hole spin a>0.9 accounting for statistical and systematic modeling errors. We find a relatively moderate reflection fraction with respect to predictions for the lamp post geometry, in which the illuminating corona is modeled as a point source. Through a time-resolved spectral analysis, we find that modest coronal and inner disk reflection flux variation drives the spectral variability during the observations. We discuss various physical scenarios for the inner disk reflection model, and we find that a compact corona is consistent with the observed features.Comment: 20 pages, 12 figures, accepted for publication in Ap

The extended empirical process test for non-Gaussianity in the CMB, with an application to non-Gaussian inflationary models

In (Hansen et al. 2002) we presented a new approach for measuring non-Gaussianity of the Cosmic Microwave Background (CMB) anisotropy pattern, based on the multivariate empirical distribution function of the spherical harmonics a_lm of a CMB map. The present paper builds upon the same ideas and proposes several improvements and extensions. More precisely, we exploit the additional information on the random phases of the a_lm to provide further tests based on the empirical distribution function. Also we take advantage of the effect of rotations in improving the power of our procedures. The suggested tests are implemented on physically motivated models of non-Gaussian fields; Monte-Carlo simulations suggest that this approach may be very promising in the analysis of non-Gaussianity generated by non-standard models of inflation. We address also some experimentally meaningful situations, such as the presence of instrumental noise and a galactic cut in the map.Comment: 15 pages, 6 figures, submitted to Phys. Rev.

Practical Algebraic Renormalization

A practical approach is presented which allows the use of a non-invariant regularization scheme for the computation of quantum corrections in perturbative quantum field theory. The theoretical control of algebraic renormalization over non-invariant counterterms is translated into a practical computational method. We provide a detailed introduction into the handling of the Slavnov-Taylor and Ward-Takahashi identities in the Standard Model both in the conventional and the background gauge. Explicit examples for their practical derivation are presented. After a brief introduction into the Quantum Action Principle the conventional algebraic method which allows for the restoration of the functional identities is discussed. The main point of our approach is the optimization of this procedure which results in an enormous reduction of the calculational effort. The counterterms which have to be computed are universal in the sense that they are independent of the regularization scheme. The method is explicitly illustrated for two processes of phenomenological interest: QCD corrections to the decay of the Higgs boson into two photons and two-loop electroweak corrections to the process $B \to X_s \gamma$.Comment: version to be published in Annals of Physic

Splines and Wavelets on Geophysically Relevant Manifolds

Analysis on the unit sphere $\mathbb{S}^{2}$ found many applications in seismology, weather prediction, astrophysics, signal analysis, crystallography, computer vision, computerized tomography, neuroscience, and statistics. In the last two decades, the importance of these and other applications triggered the development of various tools such as splines and wavelet bases suitable for the unit spheres $\mathbb{S}^{2}$, $\>\>\mathbb{S}^{3}$ and the rotation group $SO(3)$. Present paper is a summary of some of results of the author and his collaborators on generalized (average) variational splines and localized frames (wavelets) on compact Riemannian manifolds. The results are illustrated by applications to Radon-type transforms on $\mathbb{S}^{d}$ and $SO(3)$.Comment: The final publication is available at http://www.springerlink.co

Effects of Goji berries supplementation on the productive performance of rabbit

Abstract Recognized by the traditional medicine and recent scientific research studies, Lycium barbarum berries (Goji berries) have beneficial effects on human and animal health. The aim of our study was to evaluate the effects of Goji berries on the productive performance of rabbits. One month before insemination, 60 New Zealand White does were randomly assigned to one of the following 3 dietary treatments: commercial standard diet (C); C supplemented with 1% Goji berries (LG); and C supplemented with 3% Goji berries (HG). After weaning up to 91 days of age, 15 randomly selected rabbits/group were fed the same diet as the mothers (C, LG, and HG). Non-pregnant and lactating does of C group showed the highest feed intake (P < 0.01), although no significant differences in body weight (BW) were observed between groups. Nutritional treatment did not affect the offspring's feed intake. However, the rabbits fed with Goji supplementation showed not only higher mean BW both during growth (P < 0.001) and at slaughter (P < 0.01), but also better feed conversion ratio (FCR; P < 0.01) than the control group. Rabbits of LG group showed the best performances in the pre-weaning period which was probably related to the highest milk production of the LG does (P < 0.001). Indeed, LG group showed lower pre-weaning mortality (P < 0.05), higher litter size (P < 0.05), and higher litter weight (P < 0.05) at day 18 as well as higher litter size at weaning (P = 0.05) compared to C group. In conclusion, the present study demonstrates that a low percentage of dietary supplementation with Goji berry improves both reproductive and productive traits of rabbits. Although further studies are needed, our study paves the way for the use of Goji berries in the rabbit nutrition

Glycosidases during chick embryo lung development and their colocalization with proteoglycans and growth factors

During development, the epithelial component of the lung goes through a complex orderly process of branching, following strict patterns of space and time. Proteoglycans, glycosaminoglycans and growth factors are fundamental components of the extracellular matrix and perform a key role in differentiative processes. The embryonic chick lung shows a specific glycosaminoglycan composition at different levels of branching and at different embryonic stages. Proteoglycan and glycosaminoglycan accumulation is the result of secretion, absorption and degradation processes. In this pathway, enzymes, such as glycosidases, growth factors and cytokines are involved. We examined the behaviour of glycosidases, such as ß-hexosaminidases (ß-N-acetyl-D-glucosaminidase, ß- N-acetyl-D-galactosaminidase), ß-glucuronidase and ß-galactosidase, during the development of the lung bud. Our data show that the activity of the enzymes is closely linked to the processes of epithelial proliferation, bronchial tubule lengthening and infiltration of the surrounding mesenchyme. The glycosaminoglycans colocalize with transforming growth factor ß2 and inter- leukin-1 in the basement membrane and in the mesenchymal areas where the epithelium grows, and are complementary to the presence of the glycosidases. In conclusion, the activity of these glycosidases is spatially and temporally programmed and favors the release of the factors and the events which they influence

Use of agro-industrial by-products for fattening lambs: pasta factory residues. Influence on meat production and meat quality

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