Unbiased clustering estimation in the presence of missing observations

In order to be efficient, spectroscopic galaxy redshift surveys do not obtain redshifts for all galaxies in the population targeted. The missing galaxies are often clustered, commonly leading to a lower proportion of successful observations in dense regions. One example is the close-pair issue for SDSS spectroscopic galaxy surveys, which have a deficit of pairs of observed galaxies with angular separation closer than the hardware limit on placing neighbouring fibers. Spatially clustered missing observations will exist in the next generations of surveys. Various schemes have previously been suggested to mitigate these effects, but none works for all situations. We argue that the solution is to link the missing galaxies to those observed with statistically equivalent clustering properties, and that the best way to do this is to rerun the targeting algorithm, varying the angular position of the observations. Provided that every pair has a non-zero probability of being observed in one realisation of the algorithm, then a pair-upweighting scheme linking targets to successful observations, can correct these issues. We present such a scheme, and demonstrate its validity using realisations of an idealised simple survey strategy.Comment: 14 pages, 8 figures, published in MNRA

Improving the modelling of redshift-space distortions: I. A bivariate Gaussian description for the galaxy pairwise velocity distributions

As a step towards a more accurate modelling of redshift-space distortions in galaxy surveys, we develop a general description of the probability distribution function of galaxy pairwise velocities within the framework of the so-called streaming model. For a given galaxy separation $\vec{r}$, such function can be described as a superposition of virtually infinite local distributions. We characterize these in terms of their moments and then consider the specific case in which they are Gaussian functions, each with its own mean $\mu$ and dispersion $\sigma$. Based on physical considerations, we make the further crucial assumption that these two parameters are in turn distributed according to a bivariate Gaussian, with its own mean and covariance matrix. Tests using numerical simulations explicitly show that with this compact description one can correctly model redshift-space distorsions on all scales, fully capturing the overall linear and nonlinear dynamics of the galaxy flow at different separations. In particular, we naturally obtain Gaussian/exponential, skewed/unskewed distribution functions, depending on separation as observed in simulations and data. Also, the recently proposed single-Gaussian description of redshift-space distortions is included in this model as a limiting case, when the bivariate Gaussian is collapsed to a two-dimensional Dirac delta function. We also show how this description naturally allows for the Taylor expansion of $1+\xi_S(\vec{s})$ around $1+\xi_R(r)$, which leads to the Kaiser linear formula when truncated to second order, expliciting its connection with the moments of the velocity distribution functions. More work is needed, but these results indicate a very promising path to make definitive progress in our program to improve RSD estimators.Comment: 11 pages, 3 figures, 2 table

Improving the modelling of redshift-space distortions - II. A pairwise velocity model covering large and small scales

We develop a model for the redshift-space correlation function, valid for both dark matter particles and halos on scales $>5\,h^{-1}$Mpc. In its simplest formulation, the model requires the knowledge of the first three moments of the line-of-sight pairwise velocity distribution plus two well-defined dimensionless parameters. The model is obtained by extending the Gaussian-Gaussianity prescription for the velocity distribution, developed in a previous paper, to a more general concept allowing for local skewness, which is required to match simulations. We compare the model with the well known Gaussian streaming model and the more recent Edgeworth streaming model. Using N-body simulations as a reference, we show that our model gives a precise description of the redshift-space clustering over a wider range of scales. We do not discuss the theoretical prescription for the evaluation of the velocity moments, leaving this topic to further investigation.Comment: 18 pages, 10 figures, published in MNRA

Advanced Techniques for the synthesis of wideband array antennas

Antenna arrays are the most effective solution for radiating systems that need high directivity and low sidelobe level, such as radio astronomy, remote sensing, and radar applications. Typically, antenna arrays are only designed for narrowband applications, thus several radiating systems are to be employed, one per each operating bandwidth. Recently, with the aim of reducing the number of antenna system onboard a vehicle, such as aircrafts, satellites or terrestrial vehicles, a great interest has been focused on techniques for designing wideband antenna arrays. Therefore most of the dissertation deals with novel techniques for the synthesis of both narrowband and wideband planar antenna array, aiming to provide a pretty good wide-angle scanning while imposing several constraints to meet imposed by the designer. In addition, an advanced technique for the synthesis of a wideband miniaturized single-element antenna placed in realistic environments has been developed. Furthermore an hybrid technique for the analysis of conformal arrays of antennas as well several synthesis procedures have been developed. Mutual coupling has been also taken into account

Diffusion equations and inverse problems regularization.

The present thesis can be split into two dfferent parts: The first part mainly deals with the porous and fast diffusion equations. Chapter 2 presents these equations in the Euclidean setting highlighting the technical issues that arise when trying to extend results in a Riemannian setting. Chapter 3 is devoted to the construction of exhaustion and cut-o_ functions with controlled gradient and Laplacian, on manifolds with Ricci curvature bounded from below by a (possibly unbounded) nonpositive function of the distance from a fixed reference point, and without any assumptions on the topology or the injectivity radius. The cut-offs are then applied to the study of the fast and porous media diffusion, of Lq-properties of the gradient and of the selfadjointness of Schrödinger-type operators. The second part is concerned with inverse problems regularization applied to image deblurring. In Chapter 5 new variants of the Tikhonov filter method, called fractional and weighted Tikhonov, are presented alongside their saturation properties and converse results on their convergence rates. New iterated fractional Tikhonov regularization methods are then introduced. In Chapter 6 the modified linearized Bregman algorithm is investigated. It is showed that the standard approach based on the block circulant circulant block preconditioner may provide low quality restored images and different preconditioning strategies are then proposed, which improve the quality of the restoration

Semi-analytic galaxy formation in coupled dark energy cosmologies

Among the possible alternatives to the standard cosmological model ($\Lambda$CDM), coupled Dark Energy models postulate that Dark Energy (DE), seen as a dynamical scalar field, may interact with Dark Matter (DM), giving rise to a "fifth-force", felt by DM particles only. In this paper, we study the impact of these cosmologies on the statistical properties of galaxy populations by combining high-resolution numerical simulations with semi-analytic models (SAM) of galaxy formation and evolution. New features have been implemented in the reference SAM in order to have it run self-consistently and calibrated on these cosmological simulations. They include an appropriate modification of the mass temperature relation and of the baryon fraction in DM haloes, due to the different virial scalings and to the gravitational bias, respectively. Our results show that the predictions of our coupled-DE SAM do not differ significantly from theoretical predictions obtained with standard SAMs applied to a reference $\Lambda$CDM simulation, implying that the statistical properties of galaxies provide only a weak probe for these alternative cosmological models. On the other hand, we show that both galaxy bias and the galaxy pairwise velocity distribution are sensitive to coupled DE models: this implies that these probes might be successfully applied to disentangle among quintessence, $f(R)$-Gravity and coupled DE models.Comment: 8 pages, 1 Table, 5 Figures, MNRAS submitte