Stellar Relics of the hierarchical assembly of the Galaxy

This PhD Thesis is part of a long-term wide research project, carried out by the "Osservatorio Astronomico di Bologna (INAF-OABO)", that has as primary goal the comprehension and reconstruction of formation mechanism of galaxies and their evolution history. There is now substantial evidence, both from theoretical and observational point of view, in favor of the hypothesis that the halo of our Galaxy has been at least partially, built up by the progressive accretion of small fragments, similar in nature to the present day dwarf galaxies of the Local Group. In this context, the photometric and spectroscopic study of systems which populate the halo of our Galaxy (i.e. dwarf spheroidal galaxy, tidal streams, massive globular cluster, etc) permits to discover, not only the origin and behaviour of these systems, but also the structure of our Galactic halo, combined with its formation history. In fact, the study of the population of these objects and also of their chemical compositions, age, metallicities and velocity dispersion, permit us not only an improvement in the understanding of the mechanisms that govern the Galactic formation, but also a valid indirect test for cosmological model itself. Specifically, in this Thesis we provided a complete characterization of the tidal Stream of the Sagittarius dwarf spheroidal galaxy, that is the most striking example of the process of tidal disruption and accretion of a dwarf satellite in to our Galaxy. Using Red Clump stars, extracted from the catalogue of the Sloan Digital Sky Survey (SDSS) we obtained an estimate of the distance, the depth along the line of sight and of the number density for each detected portion of the Stream (and more in general for each detected structure along our line of sight). Moreover comparing the relative number (i.e. the ratio) of Blue Horizontal Branch stars and Red Clump stars (the two features are tracers of different age/different metallicity populations) in the main body of the galaxy and in the Stream, in order to verify the presence of an age-metallicity gradient along the Stream. We also report the detection of a population of Red Clump stars probably associated with the recently discovered Bootes III stellar system. Finally, we also present the results of a survey of radial velocities over a wide region, extending from r ~ 10' out to r ~ 80' within the massive star cluster Omega Centauri. The survey was performed with FLAMES@VLT, to study the velocity dispersion profile in the outer regions of this stellar system. All the results presented in this Thesis, have already been published in refeered journals.

Differential expression analysis for sequence count data via mixtures of negative binomials

The recent advent of Next-generation sequencing technologies has revolutionized the way of analyzing the genome. This innovation allows to get deeper information at a lower cost and in less time, and provides data that are discrete measurements. One of the most important applications with these data is the differential analysis, that is investigating if one gene exhibit a different expression level in correspondence of two (or more) biological conditions (such as disease states, treatments received and so on). As for the statistical analysis, the final aim will be statistical testing and for modeling these data the Negative Binomial distribution is considered the most adequate one especially because it allows for "over dispersion". However, the estimation of the dispersion parameter is a very delicate issue because few information are usually available for estimating it. Many strategies have been proposed, but they often result in procedures based on plug-in estimates, and in this thesis we show that this discrepancy between the estimation and the testing framework can lead to uncontrolled first-type errors. We propose a mixture model that allows each gene to share information with other genes that exhibit similar variability. Afterwards, three consistent statistical tests are developed for differential expression analysis. We show that the proposed method improves the sensitivity of detecting differentially expressed genes with respect to the common procedures, since it is the best one in reaching the nominal value for the first-type error, while keeping elevate power. The method is finally illustrated on prostate cancer RNA-seq data.