Bayesian Analysis of Linear Inverse Problems with Applications in Economics and Finance

In my PhD thesis I propose a Bayesian nonparametric estimation method for structural econometric models where the functional parameter of interest describes the economic agent's behavior. The structural parameter is characterized as the solution of a functional equation, or by using more technical words, as the solution of an inverse problem that can be either ill-posed or well-posed. From a Bayesian point of view, the parameter of interest is a random function and the solution to the inference problem is the posterior distribution of this parameter. A regular version of the posterior distribution in functional spaces is characterized. However, the infinite dimension of the considered spaces causes a problem of non continuity of the solution and then a problem of inconsistency, from a frequentist point of view, of the posterior distribution (i.e. problem of ill-posedness). The contribution of this essay is to propose new methods to deal with this problem of ill-posedness. The first one consists in adopting a Tikhonov regularization scheme in the construction of the posterior distribution so that I end up with a new object that I call regularized posterior distribution and that I guess it is solution of the inverse problem. The second approach consists in specifying a prior distribution on the parameter of interest of the g-prior type. Then, I detect a class of models for which the prior distribution is able to correct for the ill-posedness also in infinite dimensional problems. I study asymptotic properties of these proposed solutions and I prove that, under some regularity condition satisfied by the true value of the parameter of interest, they are consistent in a "frequentist" sense. Once I have set the general theory, I apply my bayesian nonparametric methodology to different estimation problems. First, I apply this estimator to deconvolution and to hazard rate, density and regression estimation. Then, I consider the estimation of an Instrumental Regression that is useful in micro-econometrics when we have to deal with problems of endogeneity. Finally, I develop an application in finance: I get the bayesian estimator for the equilibrium asset pricing functional by using the Euler equation defined in the Lucas'(1978) tree-type models.

Sustainable inorganic Binders and Their Applications in Building Engineering: A Green Alternative to Ordinary Portland Cement

In the last decades, the building materials and construction industry has been contributing to a great extent to generate a high impact on our environment. As it has been considered one of the key areas in which to operate to significantly reduce our footprint on environment, there has been widespread belief that particular attention now has to be paid and specific measures have to be taken to limit the use of non-renewable resources.The aim of this thesis is therefore to study and evaluate sustainable alternatives to commonly used building materials, mainly based on ordinary Portland Cement, and find a supportable path to reduce CO2 emissions and promote the re-use of waste materials. More specifically, this research explores different solutions for replacing cementitious binders in distinct application fields, particularly where special and more restricting requirements are needed, such as restoration and conservation of architectural heritage. Emphasis was thus placed on aspects and implications more closely related to the concept of non-invasivity and environmental sustainability. A first part of the research was addressed to the study and development of sustainable inorganic matrices, based on lime putty, for the pre-impregnation and on-site binding of continuous carbon fiber fabrics for structural rehabilitation and heritage restoration. Moreover, with the aim to further limit the exploitation of non-renewable resources, the synthesis of chemically activated silico-aluminate materials, as metakaolin, ladle slag or fly ash, was thus successfully achieved. New sustainable binders were hence proposed as novel building materials, suitable to be used as primary component for construction and repair mortars, as bulk materials in high-temperature applications or as matrices for high-toughness fiber reinforced composites.

Fiber-reinforced ceramics for thermostructural applications, produced by polymer impregnation pyrolysis

Several CFCC (Continuous Fiber Composite Ceramics) production processes were tested, concluding that PIP (Polymer Impregnation, or Infiltration, Pyrolysis) and CBC (Chemically Bonded Ceramics) based procedures have interesting potential applications in the construction and transportation fields, thanks to low costs to get potentially useful thermomechanical performances. Among the different processes considered during the Doctorate (from the synthesis of new preceramic polymers, to the PIP production of SiC / SiC composites) the more promising results came from the PIP process with poly-siloxanes on basalt fabrics preforms. Low processing time and costs, together with fairly good thermomechanical properties were demonstrated, even after only one or two PIP steps in nitrogen flow. In alternative, pyrolysis in vacuum was also tested, a procedure still not discussed in literature, but which could originate an interesting reduction of production costs, with only a moderate detrimental effect on the mechanical properties. The resulting CFCC is a basalt / SiCO composite that can be applied for continuous operation up to 600°C, also in oxidant environment, as TG and XRD demonstrated. The failure upon loading is generally pseudo-plastic, being interlaminar delamination the most probable rupture mechanism. . The strength depends on several different factors (microstructure, polymer curing and subsequent ceramic phase evolution, fiber pull-out, fiber strength, fiber percentage) and can only be optimized empirically. In order to be open minded in selecting the best technology, also CBC (Chemically Bonded Ceramics) matrixes were considered during this Doctorate, making some preliminary investigations on fire-resistant phosphate cements. Our results on a commercial product evidenced some interesting thermomechanical capabilities, even after thermal treatments. However the experiments showed also phase change and possible cracking and deformations even on slow drying (at 130°C) and easy rehydration upon exposure to environmental humidity.

Spatial Disparity and Dynamic Trajectory of Convergence in China: Construction and Application of a Composite Index of Regional Development

China is a large country characterized by remarkable growth and distinct regional diversity. Spatial disparity has always been a hot issue since China has been struggling to follow a balanced growth path but still confronting with unprecedented pressures and challenges. To better understand the inequality level benchmarking spatial distributions of Chinese provinces and municipalities and estimate dynamic trajectory of sustainable development in China, I constructed the Composite Index of Regional Development (CIRD) with five sub pillars/dimensions involving Macroeconomic Index (MEI), Science and Innovation Index (SCI), Environmental Sustainability Index (ESI), Human Capital Index (HCI) and Public Facilities Index (PFI), endeavoring to cover various fields of regional socioeconomic development. Ranking reports on the five sub dimensions and aggregated CIRD were provided in order to better measure the developmental degrees of 31 or 30 Chinese provinces and municipalities over 13 years from 1998 to 2010 as the time interval of three “Five-year Plans”. Further empirical applications of this CIRD focused on clustering and convergence estimation, attempting to fill up the gap in quantifying the developmental levels of regional comprehensive socioeconomics and estimating the dynamic convergence trajectory of regional sustainable development in a long run. Four clusters were benchmarked geographically-oriented in the map on the basis of cluster analysis, and club-convergence was observed in the Chinese provinces and municipalities based on stochastic kernel density estimation.

Synthesis of constrained peptidomimetics for therapeutic, diagnostic and theranostic applications

This thesis work deals, principally, with the development of different chemical protocols ranging from environmental sustainability peptide synthesis to asymmetric synthesis of modified tryptophans to a series of straightforward procedures for constraining peptide backbones without the need for a pre-formed scaffold. Much efforts have been dedicated to the structural analysis in a biomimetic environment, fundamental for predicting the in vivo conformation of compounds, as well as for giving a rationale to the experimentally determined bioactivity. The conformational analyses in solution has been done mostly by NMR (2D gCosy, Roesy, VT, titration experiments, molecular dynamics, etc.), FT-IR and ECD spectroscopy. As a practical application, 3D rigid scaffolds have been employed for the synthesis of biological active compounds based on peptidomimetic and retro-mimetic structures. These mimics have been investigated for their potential as antiflammatory agents and actually the results obtained are very promising. Moreover, the synthesis of Amo ring permitted the development of an alternative high effective synthetic pathway for obtaining Linezolid antibiotic. The final section is, instead, dedicated to the construction of a new biosensor based on zeolite L SAMs functionalized with the integrin ligand c[RGDfK], that has showed high efficiency for the selective detection of tumor cells. Such kind of sensor could, in fact, enable the convenient, non-invasive detection and diagnosis of cancer in early stages, from a few drops of a patient's blood or other biological fluids. In conclusion, the researches described herein demonstrate that the peptidomimetic approach to 3D definite structures, allows unambiguous investigation of the structure-activity relationships, giving an access to a wide range bioactive compounds of pharmaceutical interest to use not only as potential drugs but also for diagnostic and theranostic applications.

Advanced polymeric materials for applications in technical equipment for snow sports

The thesis is divided in three chapters, each one covering one topic. Initially, the thermo-mechanical and impact properties of materials used for back protectors have been analysed. Dynamical mechanical analysis (DMTA) has shown that materials used for soft-shell protectors present frequency-sensitive properties. Furthermore, through impact tests, the shock absorbing characteristics of the materials have been investigated proving the differences between soft and hard-shell protectors; moreover it has been demonstrated that the materials used for soft-shell protectors maintain their protective properties after multi-impacts. The second chapter covers the effect of the visco-elastic properties of the thermoplastic polymers on the flexural and rebound behaviours of ski boots. DMTA analysis on the materials and flexural and rebound testing on the boots have been performed. A comparison of the results highlighted a correlation between the visco-elastic properties and the flexural and rebound behaviour of ski boots. The same experimental methods have been used to investigate the influence of the design on the flexural and rebound behaviours. Finally in the third chapter the thermoplastic materials employed for the construction of ski boots soles have been characterized in terms of chemical composition, hardness, crystallinity, surface roughness and coefficient of friction (COF). The results showed a relation between material hardness and grip, in particular softer materials provide more grip with respect to harder materials. On the contrary, the surface roughness has a negative effect on friction because of the decrease in contact area. The measure of grip on inclined wet surfaces showed again a relation between hardness and grip. The performance ranking of the different materials has been the same for the COF and for the slip angle tests, indicating that COF can be used as a parameter for the choice of the optimal material to be used for the soles of ski boots.

Analysis and design of high performance multiphase electric drives for vehicle and aircraft applications

The first part of this thesis has focused on the construction of a twelve-phase asynchronous machine for More Electric Aircraft (MEA) applications. In fact, the aerospace world has found in electrification the way to improve the efficiency, reliability and maintainability of an aircraft. This idea leads to the aircraft a new management and distribution of electrical services. In this way is possible to remove or to reduce the hydraulic, mechanical and pneumatic systems inside the aircraft. The second part of this dissertation is dedicated on the enhancement of the control range of matrix converters (MCs) operating with non-unity input power factor and, at the same time, on the reduction of the switching power losses. The analysis leads to the determination in closed form of a modulation strategy that features a control range, in terms of output voltage and input power factor, that is greater than that of the traditional strategies under the same operating conditions, and a reduction in the switching power losses.