Modelli non lineari statici e dinamici su dati microeconomici: analisi delle condizioni finanziarie delle famiglie italiane

The thesis studies the economic and financial conditions of Italian households, by using microeconomic data of the Survey on Household Income and Wealth (SHIW) over the period 1998-2006. It develops along two lines of enquiry. First it studies the determinants of households holdings of assets and liabilities and estimates their correlation degree. After a review of the literature, it estimates two non-linear multivariate models on the interactions between assets and liabilities with repeated cross-sections. Second, it analyses households financial difficulties. It defines a quantitative measure of financial distress and tests, by means of non-linear dynamic probit models, whether the probability of experiencing financial difficulties is persistent over time. Chapter 1 provides a critical review of the theoretical and empirical literature on the estimation of assets and liabilities holdings, on their interactions and on households net wealth. The review stresses the fact that a large part of the literature explain households debt holdings as a function, among others, of net wealth, an assumption that runs into possible endogeneity problems. Chapter 2 defines two non-linear multivariate models to study the interactions between assets and liabilities held by Italian households. Estimation refers to a pooling of cross-sections of SHIW. The first model is a bivariate tobit that estimates factors affecting assets and liabilities and their degree of correlation with results coherent with theoretical expectations. To tackle the presence of non normality and heteroskedasticity in the error term, generating non consistent tobit estimators, semi-parametric estimates are provided that confirm the results of the tobit model. The second model is a quadrivariate probit on three different assets (safe, risky and real) and total liabilities; the results show the expected patterns of interdependence suggested by theoretical considerations. Chapter 3 reviews the methodologies for estimating non-linear dynamic panel data models, drawing attention to the problems to be dealt with to obtain consistent estimators. Specific attention is given to the initial condition problem raised by the inclusion of the lagged dependent variable in the set of explanatory variables. The advantage of using dynamic panel data models lies in the fact that they allow to simultaneously account for true state dependence, via the lagged variable, and unobserved heterogeneity via individual effects specification. Chapter 4 applies the models reviewed in Chapter 3 to analyse financial difficulties of Italian households, by using information on net wealth as provided in the panel component of the SHIW. The aim is to test whether households persistently experience financial difficulties over time. A thorough discussion is provided of the alternative approaches proposed by the literature (subjective/qualitative indicators versus quantitative indexes) to identify households in financial distress. Households in financial difficulties are identified as those holding amounts of net wealth lower than the value corresponding to the first quartile of net wealth distribution. Estimation is conducted via four different methods: the pooled probit model, the random effects probit model with exogenous initial conditions, the Heckman model and the recently developed Wooldridge model. Results obtained from all estimators accept the null hypothesis of true state dependence and show that, according with the literature, less sophisticated models, namely the pooled and exogenous models, over-estimate such persistence.

Modeling the cosmological co-evolution of supermassive black holes and galaxies

In this Thesis, we investigate the cosmological co-evolution of supermassive black holes (BHs), Active Galactic Nuclei (AGN) and their hosting dark matter (DM) halos and galaxies, within the standard CDM scenario. We analyze both analytic, semi-analytic and hybrid techniques and use the most recent observational data available to constrain the assumptions underlying our models. First, we focus on very simple analytic models where the assembly of BHs is directly related to the merger history of DM haloes. For this purpose, we implement the two original analytic models of Wyithe & Loeb 2002 and Wyithe & Loeb 2003, compare their predictions to the AGN luminosity function and clustering data, and discuss possible modifications to the models that improve the match to the observation. Then we study more sophisticated semi-analytic models in which however the baryonic physics is neglected as well. Finally we improve the hybrid simulation of De Lucia & Blaizot 2007, adding new semi-analytical prescriptions to describe the BH mass accretion rate during each merger event and its conversion into radiation, and compare the derived BH scaling relations, fundamental plane and mass function, and the AGN luminosity function with observations. All our results support the following scenario: • The cosmological co-evolution of BHs, AGN and galaxies can be well described within the CDM model. • At redshifts z & 1, the evolution history of DM halo fully determines the overall properties of the BH and AGN populations. The AGN emission is triggered mainly by DM halo major mergers and, on average, AGN shine at their Eddington luminosity. • At redshifts z . 1, BH growth decouples from halo growth. Galaxy major mergers cannot constitute the only trigger to accretion episodes in this phase. • When a static hot halo has formed around a galaxy, a fraction of the hot gas continuously accretes onto the central BH, causing a low-energy “radio” activity at the galactic centre, which prevents significant gas cooling and thus limiting the mass of the central galaxies and quenching the star formation at late time. • The cold gas fraction accreted by BHs at high redshifts seems to be larger than at low redshifts.

Essays in Health Economics

In the first chapter we develop a theoretical model investigating food consumption and body weight with a novel assumption regarding human caloric expenditure (i.e. metabolism), in order to investigate why individuals can be rationally trapped in an excessive weight equilibrium and why they struggle to lose weight even when offered incentives for weight-loss. This assumption allows the theoretical model to have multiple equilibria and to provide an explanation for why losing weight is so difficult even in the presence of incentives, without relying on rational addiction, time-inconsistency preferences or bounded rationality. In addition to this result we are able to characterize under which circumstances a temporary incentive can create a persistent weight loss. In the second chapter we investigate the possible contributions that social norms and peer effects had on the spread of obesity. In recent literature peer effects and social norms have been characterized as important pathways for the biological and behavioral spread of body weight, along with decreased food prices and physical activity. We add to this literature by proposing a novel concept of social norm related to what we define as social distortion in weight perception. The theoretical model shows that, in equilibrium, the effect of an increase in peers' weight on i's weight is unrelated to health concerns while it is mainly associated with social concerns. Using regional data from England we prove that such social component is significant in influencing individual weight. In the last chapter we investigate the relationship between body weight and employment probability. Using a semi-parametric regression we show that men and women employment probability do not follow a linear relationship with body mass index (BMI) but rather an inverted U-shaped one, peaking at a BMI way over the clinical threshold for overweight.

Gravitational Lensing as a Tool on Galactic and Cosmological Scales

This work considers the reconstruction of strong gravitational lenses from their observed effects on the light distribution of background sources. After reviewing the formalism of gravitational lensing and the most common and relevant lens models, new analytical results on the elliptical power law lens are presented, including new expressions for the deflection, potential, shear and magnification, which naturally lead to a fast numerical scheme for practical calculation. The main part of the thesis investigates lens reconstruction with extended sources by means of the forward reconstruction method, in which the lenses and sources are given by parametric models. The numerical realities of the problem make it necessary to find targeted optimisations for the forward method, in order to make it feasible for general applications to modern, high resolution images. The result of these optimisations is presented in the \textsc{Lensed} algorithm. Subsequently, a number of tests for general forward reconstruction methods are created to decouple the influence of sourced from lens reconstructions, in order to objectively demonstrate the constraining power of the reconstruction. The final chapters on lens reconstruction contain two sample applications of the forward method. One is the analysis of images from a strong lensing survey. Such surveys today contain $\sim 100$ strong lenses, and much larger sample sizes are expected in the future, making it necessary to quickly and reliably analyse catalogues of lenses with a fixed model. The second application deals with the opposite situation of a single observation that is to be confronted with different lens models, where the forward method allows for natural model-building. This is demonstrated using an example reconstruction of the ``Cosmic Horseshoe''. An appendix presents an independent work on the use of weak gravitational lensing to investigate theories of modified gravity which exhibit screening in the non-linear regime of structure formation.

Semi-synthetic bile acids as novel drug candidate in liver diseases: physico-chemical characterization and HPLC-ES-MS/MS methods for their quali-quantitative analysis in different experimental animal models

The physico-chemical characterization, structure-pharmacokinetic and metabolism studies of new semi synthetic analogues of natural bile acids (BAs) drug candidates have been performed. Recent studies discovered a role of BAs as agonists of FXR and TGR5 receptor, thus opening new therapeutic target for the treatment of liver diseases or metabolic disorders. Up to twenty new semisynthetic analogues have been synthesized and studied in order to find promising novel drugs candidates. In order to define the BAs structure-activity relationship, their main physico-chemical properties (solubility, detergency, lipophilicity and affinity with serum albumin) have been measured with validated analytical methodologies. Their metabolism and biodistribution has been studied in “bile fistula rat”, model where each BA is acutely administered through duodenal and femoral infusion and bile collected at different time interval allowing to define the relationship between structure and intestinal absorption and hepatic uptake ,metabolism and systemic spill-over. One of the studied analogues, 6α-ethyl-3α7α-dihydroxy-5β-cholanic acid, analogue of CDCA (INT 747, Obeticholic Acid (OCA)), recently under approval for the treatment of cholestatic liver diseases, requires additional studies to ensure its safety and lack of toxicity when administered to patients with a strong liver impairment. For this purpose, CCl4 inhalation to rat causing hepatic decompensation (cirrhosis) animal model has been developed and used to define the difference of OCA biodistribution in respect to control animals trying to define whether peripheral tissues might be also exposed as a result of toxic plasma levels of OCA, evaluating also the endogenous BAs biodistribution. An accurate and sensitive HPLC-ES-MS/MS method is developed to identify and quantify all BAs in biological matrices (bile, plasma, urine, liver, kidney, intestinal content and tissue) for which a sample pretreatment have been optimized.

Measurement of top quark pairs production cross-section in the semi-leptonic channel with the ATLAS experiment

This thesis is about three major aspects of the identification of top quarks. First comes the understanding of their production mechanism, their decay channels and how to translate theoretical formulae into programs that can simulate such physical processes using Monte Carlo techniques. In particular, the author has been involved in the introduction of the POWHEG generator in the framework of the ATLAS experiment. POWHEG is now fully used as the benchmark program for the simulation of ttbar pairs production and decay, along with MC@NLO and AcerMC: this will be shown in chapter one. The second chapter illustrates the ATLAS detectors and its sub-units, such as calorimeters and muon chambers. It is very important to evaluate their efficiency in order to fully understand what happens during the passage of radiation through the detector and to use this knowledge in the calculation of final quantities such as the ttbar production cross section. The last part of this thesis concerns the evaluation of this quantity deploying the so-called "golden channel" of ttbar decays, yielding one energetic charged lepton, four particle jets and a relevant quantity of missing transverse energy due to the neutrino. The most important systematic errors arising from the various part of the calculation are studied in detail. Jet energy scale, trigger efficiency, Monte Carlo models, reconstruction algorithms and luminosity measurement are examples of what can contribute to the uncertainty about the cross-section.

Numerical models of trench migration for lateral heterogeneous subducting plates

The aim of this Thesis is to investigate the effect of heterogeneities within the subducting plate on the dynamics of subduction. In particular, I study the motion of the trench for oceanic and continental subduction, first, separately, and, then, together in the same system to understand how they interact. The understanding of these features is fundamental to reconstruct the evolution of complex subduction zones, such as the Central Mediterranean. For this purpose, I developed 2D and 3D numerical models of oceanic and continental subduction where the rheological, geometrical and compositional properties of the plates are varied. In these models, the trench and the overriding plate move self-consistently as a function of the dynamics of the system. The effect of continental subduction on trench migration is largely investigated. Results from a parametric study showed that despite different rheological properties of the plates, all models with a uniform continental crust share the same kinematic behaviour: the trench starts to advance once the continent arrives at the subduction zone. Hence, the advancing mode in continental collision scenarios is at least partly driven by an intrinsic feature of the system. Moreover, the presence of a weak lower crust within the continental plate can lead to the occurrence of delamination. Indeed, by changing the viscosity of the lower crust, both delamination and slab detachment can occur. Delamination is favoured by a low viscosity value of the lower crust, because this makes the mechanical decoupling easier between crust and lithospheric mantle. These features are observed both in 2D and 3D models, but the numerical results of the 3D models also showed that the rheology of the continental crust has a very strong effect on the dynamics of the whole system, since it influences not only the continental part of plate but also the oceanic sides.

Lesion detection and classification in breast cancer: evaluation of approaches based on morphological features, tracer kinetic modelling and semi-quantitative parameters in MR functional imaging (DCE-MRI)

The diagnosis, grading and classification of tumours has benefited considerably from the development of DCE-MRI which is now essential to the adequate clinical management of many tumour types due to its capability in detecting active angiogenesis. Several strategies have been proposed for DCE-MRI evaluation. Visual inspection of contrast agent concentration curves vs time is a very simple yet operator dependent procedure, therefore more objective approaches have been developed in order to facilitate comparison between studies. In so called model free approaches, descriptive or heuristic information extracted from time series raw data have been used for tissue classification. The main issue concerning these schemes is that they have not a direct interpretation in terms of physiological properties of the tissues. On the other hand, model based investigations typically involve compartmental tracer kinetic modelling and pixel-by-pixel estimation of kinetic parameters via non-linear regression applied on region of interests opportunely selected by the physician. This approach has the advantage to provide parameters directly related to the pathophysiological properties of the tissue such as vessel permeability, local regional blood flow, extraction fraction, concentration gradient between plasma and extravascular-extracellular space. Anyway, nonlinear modelling is computational demanding and the accuracy of the estimates can be affected by the signal-to-noise ratio and by the initial solutions. The principal aim of this thesis is investigate the use of semi-quantitative and quantitative parameters for segmentation and classification of breast lesion. The objectives can be subdivided as follow: describe the principal techniques to evaluate time intensity curve in DCE-MRI with focus on kinetic model proposed in literature; to evaluate the influence in parametrization choice for a classic bi-compartmental kinetic models; to evaluate the performance of a method for simultaneous tracer kinetic modelling and pixel classification; to evaluate performance of machine learning techniques training for segmentation and classification of breast lesion.

Models and Simulations of Diamond-like Carbon for large-area high voltage power diodes

Silicon-based discrete high-power devices need to be designed with optimal performance up to several thousand volts and amperes to reach power ratings ranging from few kWs to beyond the 1 GW mark. To this purpose, a key element is the improvement of the junction termination (JT) since it allows to drastically reduce surface electric field peaks which may lead to an earlier device failure. This thesis will be mostly focused on the negative bevel termination which from several years constitutes a standard processing step in bipolar production lines. A simple methodology to realize its counterpart, a planar JT with variation of the lateral doping concentration (VLD) will be also described. On the JT a thin layer of a semi insulating material is usually deposited, which acts as passivation layer reducing the interface defects and contributing to increase the device reliability. A thorough understanding of how the passivation layer properties affect the breakdown voltage and the leakage current of a fast-recovery diode is fundamental to preserve the ideal termination effect and provide a stable blocking capability. More recently, amorphous carbon, also called diamond-like carbon (DLC), has been used as a robust surface passivation material. By using a commercial TCAD tool, a detailed physical explanation of DLC electrostatic and transport properties has been provided. The proposed approach is able to predict the breakdown voltage and the leakage current of a negative beveled power diode passivated with DLC as confirmed by the successfully validation against the available experiments. In addition, the VLD JT proposed to overcome the limitation of the negative bevel architecture has been simulated showing a breakdown voltage very close to the ideal one with a much smaller area consumption. Finally, the effect of a low junction depth on the formation of current filaments has been analyzed by performing reverse-recovery simulations.

Variational and learning models for image and time series inverse problems

Inverse problems are at the core of many challenging applications. Variational and learning models provide estimated solutions of inverse problems as the outcome of specific reconstruction maps. In the variational approach, the result of the reconstruction map is the solution of a regularized minimization problem encoding information on the acquisition process and prior knowledge on the solution. In the learning approach, the reconstruction map is a parametric function whose parameters are identified by solving a minimization problem depending on a large set of data. In this thesis, we go beyond this apparent dichotomy between variational and learning models and we show they can be harmoniously merged in unified hybrid frameworks preserving their main advantages. We develop several highly efficient methods based on both these model-driven and data-driven strategies, for which we provide a detailed convergence analysis. The arising algorithms are applied to solve inverse problems involving images and time series. For each task, we show the proposed schemes improve the performances of many other existing methods in terms of both computational burden and quality of the solution. In the first part, we focus on gradient-based regularized variational models which are shown to be effective for segmentation purposes and thermal and medical image enhancement. We consider gradient sparsity-promoting regularized models for which we develop different strategies to estimate the regularization strength. Furthermore, we introduce a novel gradient-based Plug-and-Play convergent scheme considering a deep learning based denoiser trained on the gradient domain. In the second part, we address the tasks of natural image deblurring, image and video super resolution microscopy and positioning time series prediction, through deep learning based methods. We boost the performances of supervised, such as trained convolutional and recurrent networks, and unsupervised deep learning strategies, such as Deep Image Prior, by penalizing the losses with handcrafted regularization terms.

3D bioprinted organ models for drug screening

In recent years, 3D bioprinting has emerged as an innovative and versatile technology able to produce in vitro models that resemble the native spatial organization of organ tissues, by employing or more bioinks composed of various types of cells suspended in hydrogels. Natural and semi-synthetic hydrogels are extensively used for 3D bioprinting models since they can mimic the natural composition of the tissues, they are biocompatible and bioactive with customizable mechanical properties, allowing to support cell growth. The possibility to tailor hydrogels mechanical properties by modifying the chemical structures to obtain photo-crosslinkable materials, while maintaining their biocompatibility and biomimicry, make their use versatile and suitable to simulate a broad spectrum of physiological features. In this PhD Thesis, 3D bioprinted in vitro models with tailored mechanical properties and physiologically-like features were fabricated. AlgMa-based bioinks were employed to produce a living platform with gradient stiffness, with the aim to create an easy to handle and accessible biological tool to evaluate mechanobiology. In addition, GelMa, collagen and IPN of GelMa and collagen were used as bioinks to fabricate a proof-of-concept of 3D intestinal barrier, which include multiple cell components and multi-layered structure. A useful rheological guide to drive users to the selection of the suitable bioinks for 3D bioprinting and to correlate the model’s mechanical stability after crosslinking is proposed. In conclusion, a platform capable to reproduce models with physiological gradient stiffness was developed and the fabrication of 3D bioprinted intestinal models displaying a good hierarchical structure and cells composition was fully reported and successfully achieved. The good biological results obtained demonstrated that 3D bioprinting can be used for the fabrications of 3D models and that the mechanical properties of the external environment plays a key role on the cell pathways, viability and morphology.

Models for reliability estimation of HVDC cable systems

The work carried out in this thesis aims at: - studying – in both simulative and experimental methods – the effect of electrical transients (i.e., Voltage Polarity Reversals VPRs, Temporary OverVoltages TOVs, and Superimposed Switching Impulses SSIs) on the aging phenomena in HVDC extruded cable insulations. Dielectric spectroscopy, conductivity measurements, Fourier Transform Infra-Red FTIR spectroscopy, and space charge measurements show variation in the insulating properties of the aged Cross-Linked Polyethylene XLPE specimens compared to non-aged ones. Scission in XLPE bonds and formation of aging chemical bonds is also noticed in aged insulations due to possible oxidation reactions. The aged materials show more ability to accumulate space charges compared to non-aged ones. An increase in both DC electrical conductivity and imaginary permittivity has been also noticed. - The development of life-based geometric design of HVDC cables in a detailed parametric analysis of all parameters that affect the design. Furthermore, the effect of both electrical and thermal transients on the design is also investigated. - The intrinsic thermal instability in HVDC cables and the effect of insulation characteristics on the thermal stability using a temperature and field iterative loop (using numerical methods – Finite Difference Method FDM). The dielectric loss coefficient is also calculated for DC cables and found to be less than that in AC cables. This emphasizes that the intrinsic thermal instability is critical in HVDC cables. - Fitting electrical conductivity models to the experimental measurements using both models found in the literature and modified models to find the best fit by considering the synergistic effect between field and temperature coefficients of electrical conductivity.

Spectral asymptotic properties of semi-regular non-commutative harmonic oscillators

The study carried out in this thesis is devoted to spectral analysis of systems of PDEs related also with quantum physics models. Namely, the research deals with classes of systems that contain certain quantum optics models such as Jaynes-Cummings, Rabi and their generalizations that describe light-matter interaction. First we investigate the spectral Weyl asymptotics for a class of semiregular systems, extending to the vector-valued case results of Helffer and Robert, and more recently of Doll, Gannot and Wunsch. Actually, the asymptotics by Doll, Gannot and Wunsch is more precise (that is why we call it refined) than the classical result by Helffer and Robert, but deals with a less general class of systems, since the authors make an hypothesis on the measure of the subset of the unit sphere on which the tangential derivatives of the X-Ray transform of the semiprincipal symbol vanish to infinity order. Abstract Next, we give a meromorphic continuation of the spectral zeta function for semiregular differential systems with polynomial coefficients, generalizing the results by Ichinose and Wakayama and Parmeggiani. Finally, we state and prove a quasi-clustering result for a class of systems including the aforementioned quantum optics models and we conclude the thesis by showing a Weyl law result for the Rabi model and its generalizations.