Homological and Hodge-theoretic aspects of matroids and polymatroids

In the first part of this thesis, we study the action of the automorphism group of a matroid on the homology space of the co-independent complex. This representation turns out to be isomorphic, up to tensoring with the sign representation, with that on the homology space associated with the lattice of flats. In the case of the cographic matroid of the complete graph, this result has application in algebraic geometry: indeed De Cataldo, Heinloth and Migliorini use this outcome to study the Hitchin fibration. In the second part, on the other hand, we use ideas from algebraic geometry to prove a purely combinatorial result. We construct a Leray model for a discrete polymatroid with arbitrary building set and we prove a generalized Goresky-MacPherson formula. The first row of the model is the Chow ring of the polymatroid; we prove Poincaré duality, Hard-Lefschetz theorem and Hodge-Riemann relations for the Chow ring.

The gender wage gap in developing and transition countries

The aim of my dissertation is to study the gender wage gap with a specific focus on developing and transition countries. In the first chapter I present the main existing theories proposed to analyse the gender wage gap and I review the empirical literature on the gender wage gap in developing and transition countries and its main findings. Then, I discuss the overall empirical issues related to the estimation of the gender wage gap and the issues specific to developing and transition countries. The second chapter is an empirical analysis of the gender wage gap in a developing countries, the Union of Comoros, using data from the multidimensional household budget survey “Enquete integrale auprès des ménages” (EIM) run in 2004. The interest of my work is to provide a benchmark analysis for further studies on the situation of women in the Comorian labour market and to contribute to the literature on gender wage gap in Africa by making available more information on the dynamics and mechanism of the gender wage gap, given the limited interest on the topic in this area of the world. The third chapter is an applied analysis of the gender wage gap in a transition country, Poland, using data from the Labour Force Survey (LSF) collected for the years 1994 and 2004. I provide a detailed examination of how gender earning differentials have changed over the period starting from 1994 to a more advanced transition phase in 2004, when market elements have become much more important in the functioning of the Polish economy than in the earlier phase. The main contribution of my dissertation is the application of the econometrical methodology that I describe in the beginning of the second chapter. First, I run a preliminary OLS and quantile regression analysis to estimate and describe the raw and conditional wage gaps along the distribution. Second, I estimate quantile regressions separately for males and females, in order to allow for different rewards to characteristics. Third, I proceed to decompose the raw wage gap estimated at the mean through the Oaxaca-Blinder (1973) procedure. In the second chapter I run a two-steps Heckman procedure by estimating a model of participation in the labour market which shows a significant selection bias for females. Forth, I apply the Machado-Mata (2005) techniques to extend the decomposition analysis at all points of the distribution. In Poland I can also implement the Juhn, Murphy and Pierce (1991) decomposition over the period 1994-2004, to account for effects to the pay gap due to changes in overall wage dispersion beyond Oaxaca’s standard decomposition.

Hepatobiliary diseases in small animals: a comparison of ultrasonography and multidetector-row computed tomography

Ultrasonography (US) is an essential imaging tool for identifying abnormalities of the liver parenchyma, biliary tract and vascular system. US has replaced radiography as the initial imaging procedure in screening for liver disease in small animals. There are few reports of the use of conventional and helical computed tomography (CT) to assess canine or feline parenchymal and neoplastic liver disease and biliary disorders. In human medicine the development of multidetector- row helical computed tomography (MDCT), with its superior spatial and temporal resolution, has resulted in improved detection and characterization of diffuse and focal liver lesions. The increased availability of MDCT in veterinary practice provides incentive to develop MDCT protocols for liver imaging in small animals. The purpose of this study is to assess the rule of MDCT in the characterization of hepatobiliary diseases in small animals; and to compare this method with conventional US. Candidates for this prospective study were 175 consecutive patients (dogs and cats) referred for evaluation of hepatobiliary disease. The patients underwent liver US and MDCT. Percutaneous needle biopsy was performed on all liver lesions or alterations encountered. As for gallbladder, histopatological evaluation was obtained from cholecystectomy specimens. Ultrasonographic findings in this study agreed well with those of previous reports. A protocol for dual-phase liver MDCT in small animals has been described. MDCT findings in parenchymal disorders of the liver, hepatic neoplasia and biliary disorders are here first described in dogs and cats and compared with the corresponding features in human medicine. The ability of MDCT in detection and characterization of hepatobiliary diseases in small animals is overall superior to conventional US. Ultrasonography and MDCT scanning, however, play complementary rules in the evaluation of these diseases. Many conditions have distinctive imaging features that may permit diagnosis. In most instances biopsy is required for definitive diagnosis.

International openness in transition countries: further evidence on foreign direct investment

The thesis focuses on the process of international openness of Transition Countries. This study provides a theoretical analysis based on reference literature, and an empirical analysis which is aimed at estimating some main effects of Foreign Direct Investment. Transition has represented a highly complex phenomenon, characterized by several aspects, whose interaction has shaped the developmental path of each country involved. Although the thesis focuses on economic issues it is outstanding to underline that Transition implies political, institutional, and even social deep changes, which must be taken into consideration in the general overview of the contex. The empirical part has been developed along two different ways: a country analysis and a firm analysis, thus allowing to widen the study and delve deeper into the use of econometric instruments. More specifically, in the first empirical stage both static (Fixed Effects) and dynamic (LSDV Corrected) methodologies have been implemented, whereas in the second stage the Cox Proportional Function has been chosen in order to handle with censored data.

Excitonic properties of transition metal oxide perovskites and workflow automatization of GW schemes

The Many-Body-Perturbation Theory approach is among the most successful theoretical frameworks for the study of excited state properties. It allows to describe the excitonic interactions, which play a fundamental role in the optical response of insulators and semiconductors. The first part of the thesis focuses on the study of the quasiparticle, optical and excitonic properties of \textit{bulk} Transition Metal Oxide (TMO) perovskites using a G$_0$W$_0$+Bethe Salpeter Equation (BSE) approach. A representative set of 14 compounds has been selected, including 3d, 4d and 5d perovskites. An approximation of the BSE scheme, based on an analytic diagonal expression for the inverse dielectric function, is used to compute the exciton binding energies and is carefully bench-marked against the standard BSE results. In 2019 an important breakthrough has been achieved with the synthesis of ultrathin SrTiO3 films down to the monolayer limit. This allows us to explore how the quasiparticle and optical properties of SrTiO3 evolve from the bulk to the two-dimensional limit. The electronic structure is computed with G0W0 approach: we prove that the inclusion of the off-diagonal self-energy terms is required to avoid non-physical band dispersions. The excitonic properties are investigated beyond the optical limit at finite momenta. Lastly a study of the under pressure optical response of the topological nodal line semimetal ZrSiS is presented, in conjunction with the experimental results from the group of Prof. Dr. Kuntscher of the Augsburg University. The second part of the thesis discusses the implementation of a workflow to automate G$_0$W$_0$ and BSE calculations with the VASP software. The workflow adopts a convergence scheme based on an explicit basis-extrapolation approach [J. Klimeš \textit{et al.}, Phys. Rev.B 90, 075125 (2014)] which allows to reduce the number of intermediate calculations required to reach convergence and to explicit estimate the error associated to the basis-set truncation.