X-ray and lensing mass estimates in galaxy clusters

In this Thesis we have presented our work on the analysis of galaxy clusters through their X-ray emission and the gravitational lensing effect that they induce. Our research work was mainly finalised to verify and possibly explain the observed mismatch between the galaxy cluster mass distributions estimated through two of the most promising techniques, i.e. the X-ray and the gravitational lensing analyses. Moreover, it is an established evidence that combined, multi-wavelength analyses are extremely effective in addressing and explaining the open issues in astronomy: however, in order to follow this approach, it is crucial to test the reliability and the limitations of the individual analysis techniques. In this Thesis we also assessed the impact of some factors that could affect both the X-ray and the strong lensing analyses.

An optimal estimator for the correlation of CMB anisotropies with Large Scale Structures and its application to WMAP-7year and NVSS

In the thesis we present the implementation of the quadratic maximum likelihood (QML) method, ideal to estimate the angular power spectrum of the cross-correlation between cosmic microwave background (CMB) and large scale structure (LSS) maps as well as their individual auto-spectra. Such a tool is an optimal method (unbiased and with minimum variance) in pixel space and goes beyond all the previous harmonic analysis present in the literature. We describe the implementation of the QML method in the {\it BolISW} code and demonstrate its accuracy on simulated maps throughout a Monte Carlo. We apply this optimal estimator to WMAP 7-year and NRAO VLA Sky Survey (NVSS) data and explore the robustness of the angular power spectrum estimates obtained by the QML method. Taking into account the shot noise and one of the systematics (declination correction) in NVSS, we can safely use most of the information contained in this survey. On the contrary we neglect the noise in temperature since WMAP is already cosmic variance dominated on the large scales. Because of a discrepancy in the galaxy auto spectrum between the estimates and the theoretical model, we use two different galaxy distributions: the first one with a constant bias $b$ and the second one with a redshift dependent bias $b(z)$. Finally, we make use of the angular power spectrum estimates obtained by the QML method to derive constraints on the dark energy critical density in a flat $\Lambda$CDM model by different likelihood prescriptions. When using just the cross-correlation between WMAP7 and NVSS maps with 1.8° resolution, we show that $\Omega_\Lambda$ is about the 70\% of the total energy density, disfavouring an Einstein-de Sitter Universe at more than 2 $\sigma$ CL (confidence level).

Educational mismathc in Italian an European labour markets (starting from the UK)

The present doctoral thesis is structured as a collection of three essays. The first essay, “SOC(HE)-Italy: a classification for graduate occupations” presents the conceptual basis, the construction, the validation and the application to the Italian labour force of the occupational classification termed SOC(HE)-Italy. I have developed this classification under the supervision of Kate Purcell during my period as a visiting research student at the Warwick Institute for Emplyment Research. This classification links the constituent tasks and duties of a particular job to the relevant knowledge and skills imparted via Higher Education (HE). It is based onto the SOC(HE)2010, an occupational classification first proposed by Kate Purcell in 2013, but differently constructed. In the second essay “Assessing the incidence and wage effects of overeducation among Italian graduates using a new measure for educational requirements” I utilize this classification to build a valid and reliable measure for job requirements. The lack of an unbiased measure for this dimension constitutes one of the major constraints to achieve a generally accepted measurement of overeducation. Estimations of overeducation incidence and wage effects are run onto AlmaLaurea data from the survey on graduates career paths. I have written this essay and obtained these estimates benefiting of the help and guidance of Giovanni Guidetti and Giulio Pedrini. The third and last essay titled “Overeducation in the Italian labour market: clarifying the concepts and addressing the measurement error problem” addresses a number of theoretical issues concerning the concepts of educational mismatch and overeducation. Using Istat data from RCFL survey I run estimates of the ORU model for the whole Italian labour force. In my knowledge, this is the first time ever such model is estimated on such population. In addition, I adopt the new measure of overeducation based onto the SOC(HE)-Italy classification.

Spectral estimates and preconditioning for saddle point systems arising from optimization problems

In this thesis, we consider the problem of solving large and sparse linear systems of saddle point type stemming from optimization problems. The focus of the thesis is on iterative methods, and new preconditioning srategies are proposed, along with novel spectral estimtates for the matrices involved.