Multi-variate joint PDF for non-Gaussianities: exact formulation and generic approximations

We provide an exact expression for the multi-variate joint probability distribution function of non-Gaussian fields primordially arising from local transformations of a Gaussian field. This kind of non-Gaussianity is generated in many models of inflation. We apply our expression to the non- Gaussianity estimation from Cosmic Microwave Background maps and the halo mass function where we obtain analytical expressions. We also provide analytic approximations and their range of validity. For the Cosmic Microwave Background we give a fast way to compute the PDF which is valid up to 7{\sigma} for fNL values (both true and sampled) not ruled out by current observations, which consists of expressing the PDF as a combination of bispectrum and trispectrum of the temperature maps. The resulting expression is valid for any kind of non-Gaussianity and is not limited to the local type. The above results may serve as the basis for a fully Bayesian analysis of the non-Gaussianity parameter.Comment: Matches accepted verion to JCAP; conclusions unchaged, extra references adde

CMB lensing extraction and primordial non-Gaussianity

The next generation of CMB experiments should get a better handle on cosmological parameters by mapping the weak lensing deflection field, which is separable from primary anisotropies thanks to the non-Gaussianity induced by lensing. However, the generation of perturbations in the Early Universe also produces a level of non-Gaussianity which is known to be small, but can contribute to the anisotropy trispectrum at the same level as lensing. In this work, we study whether the primordial non-Gaussianity can mask the lensing statistics. We concentrate only on the ``temperature quadratic estimator'' of lensing, which will be nearly optimal for the Planck satellite, and work in the flat-sky approximation. We find that primordial non-Gaussianity contaminates the deflection field estimator by roughly (0.1 f_NL)% at large angular scales, which represents at most a 10% contribution, not sufficient to threaten lensing extraction, but enough to be taken into account.Comment: 5 pages, 1 figur

Light-cone averages in a swiss-cheese universe

We analyze a toy swiss-cheese cosmological model to study the averaging problem. In our model, the cheese is the EdS model and the holes are constructed from a LTB solution. We study the propagation of photons in the swiss-cheese model, and find a phenomenological homogeneous model to describe observables. Following a fitting procedure based on light-cone averages, we find that the the expansion scalar is unaffected by the inhomogeneities. This is because of spherical symmetry. However, the light-cone average of the density as a function of redshift is affected by inhomogeneities. The effect arises because, as the universe evolves, a photon spends more and more time in the (large) voids than in the (thin) high-density structures. The phenomenological homogeneous model describing the light-cone average of the density is similar to the concordance model. Although the sole source in the swiss-cheese model is matter, the phenomenological homogeneous model behaves as if it has a dark-energy component. Finally, we study how the equation of state of the phenomenological model depends on the size of the inhomogeneities, and find that the equation-of-state parameters w_0 and w_a follow a power-law dependence with a scaling exponent equal to unity. That is, the equation of state depends linearly on the distance the photon travels through voids. We conclude that within our toy model, the holes must have a present size of about 250 Mpc to be able to mimic the concordance model.Comment: 20 pages, 14 figures; replaced to fit the version accepted for publication in Phys. Rev.

Analysis of tomato glycoalkaloids by liquid chromatography coupled with electrospray ionization tandem mass spectrometry.

Steroidal glycoalkaloids (SGAs) extracted from tomato leaves and berries (Lycopersicon esculentum Mill.) were separated and identified using optimized reversed-phase liquid chromatography with electrospray ionization (ESI) and ion trap mass spectrometry (ITMS). The ESI source polarity and chromatographic conditions were evaluated. The ESI spectra contain valuable information, which includes the mass of SGAs, the mass of the aglycones, and several characteristic fragment ions. Cleavage at the interglycosidic bonds proximal to the aglycones is the most prominent process in the ESI process. A protonated molecule, [M+H]+, accompanied by a mixed adduct ion, [M+H+Na]2+, was observed for a-tomatine (i.e., m/z 1034.7 and 528.9) and dehydrotomatine (i.e., m/z 1032.6 and 527.9) in positive ion mode spectra. The structures of these tomato glycoalkaloids were confirmed using tandem mass spectrometry. The identification of a new a-tomatine isomer glycoalkaloid, named filotomatine (MW 1033), which shares a common tetrasaccharide structure (i.e., lycotretraose) with a-tomatine and dehydrotomatine, and soladulcidine as an aglycone, is described for the first time. It occurs in significant amounts in the extracts of wild tomato foliage. Multistage mass spectrometry both of the protonated molecules and of the doubly charged ions was used for detailed structural elucidation of SGAs. Key fragmentations and regularities in fragmentation pathways are described and the fragmentation mechanisms involved are propose

Large-scale bias in the Universe II: redshift space bispectrum

The determination of the density parameter $\Omega_0$ from the large-scale distribution of galaxies is one of the major goals of modern cosmology. However, if galaxies are biased tracers of the underlying mass distribution, linear perturbation theory leads to a degeneracy between $\Omega_0$ and the linear bias parameter $b$, and the density parameter cannot be estimated. In Matarrese, Verde & Heavens (1997) we developed a method based on second-order perturbation theory to use the bispectrum to lift this degeneracy by measuring the bias parameter in an $\Omega_0$-independent way. The formalism was developed assuming that one has perfect information on the positions of galaxies in three dimensions. In galaxy redshift surveys, the three-dimensional information is imperfect, because of the contaminating effects of peculiar velocities, and the resulting clustering pattern in redshift space is distorted. In this paper, we combine second-order perturbation theory with a model for collapsed, virialised structures, to extend the method to redshift space, and demonstrate that the method should be successful in determining with reasonable accuracy the bias parameter from state-of-the-art surveys such as the Anglo-Australian 2 degree field survey and the Sloan digital sky survey.Comment: To appear in MNRA

Celiac disease and headache in children: A narrative state of the art

Celiac disease (CD) is one of the most important entity of the wide spectrum of gluten-related disorders (GRDs). It is well known that neurological manifestation can be present either at the onset of CD, or appear during the development of the pathology, and different can be the neurologic findings. Clinical features are very variable, ranging from typical manifestations of gastrointestinal involvement to neurologic symptom. The most frequent neurologic signs reported were headache, epileptic seizure, migraine, mental retardation, ataxia and attention deficit and hyperactive disorder. Headache either in form of migraine, or in non-specific form represents one of the main clinical presentation in CD. The aim of this work is to provide a narrative review of the pediatric literature focused on the cephalalgic features of children with CD evaluating the potential benefits of a gluten free diet (GFD). Papers were identified by searching for related literature in Medline (PubMed) and Embase using the words “Celiac Disease” and “Headache” or “Migraine” by specifying “children”/“paediatric age” for reports published since 1972 till 31th October 2018. According to our inclusion criteria, a total of 25 papers has been evaluated. Although it is still controversial if headache is prevalent in CD children a correct compliance to a GFD seems to improve the neurological symptoms even if the underlying pathogenic relationship between CD and neurologic system involvement is still not fully understood. (www.actabiomedica.it)