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.

Tecniche di progettazione tollerante alle variazioni per circuiti digitali in tecnologie nanometriche

The digital electronic market development is founded on the continuous reduction of the transistors size, to reduce area, power, cost and increase the computational performance of integrated circuits. This trend, known as technology scaling, is approaching the nanometer size. The lithographic process in the manufacturing stage is increasing its uncertainty with the scaling down of the transistors size, resulting in a larger parameter variation in future technology generations. Furthermore, the exponential relationship between the leakage current and the threshold voltage, is limiting the threshold and supply voltages scaling, increasing the power density and creating local thermal issues, such as hot spots, thermal runaway and thermal cycles. In addiction, the introduction of new materials and the smaller devices dimension are reducing transistors robustness, that combined with high temperature and frequently thermal cycles, are speeding up wear out processes. Those effects are no longer addressable only at the process level. Consequently the deep sub-micron devices will require solutions which will imply several design levels, as system and logic, and new approaches called Design For Manufacturability (DFM) and Design For Reliability. The purpose of the above approaches is to bring in the early design stages the awareness of the device reliability and manufacturability, in order to introduce logic and system able to cope with the yield and reliability loss. The ITRS roadmap suggests the following research steps to integrate the design for manufacturability and reliability in the standard CAD automated design flow: i) The implementation of new analysis algorithms able to predict the system thermal behavior with the impact to the power and speed performances. ii) High level wear out models able to predict the mean time to failure of the system (MTTF). iii) Statistical performance analysis able to predict the impact of the process variation, both random and systematic. The new analysis tools have to be developed beside new logic and system strategies to cope with the future challenges, as for instance: i) Thermal management strategy that increase the reliability and life time of the devices acting to some tunable parameter,such as supply voltage or body bias. ii) Error detection logic able to interact with compensation techniques as Adaptive Supply Voltage ASV, Adaptive Body Bias ABB and error recovering, in order to increase yield and reliability. iii) architectures that are fundamentally resistant to variability, including locally asynchronous designs, redundancy, and error correcting signal encodings (ECC). The literature already features works addressing the prediction of the MTTF, papers focusing on thermal management in the general purpose chip, and publications on statistical performance analysis. In my Phd research activity, I investigated the need for thermal management in future embedded low-power Network On Chip (NoC) devices.I developed a thermal analysis library, that has been integrated in a NoC cycle accurate simulator and in a FPGA based NoC simulator. The results have shown that an accurate layout distribution can avoid the onset of hot-spot in a NoC chip. Furthermore the application of thermal management can reduce temperature and number of thermal cycles, increasing the systemreliability. Therefore the thesis advocates the need to integrate a thermal analysis in the first design stages for embedded NoC design. Later on, I focused my research in the development of statistical process variation analysis tool that is able to address both random and systematic variations. The tool was used to analyze the impact of self-timed asynchronous logic stages in an embedded microprocessor. As results we confirmed the capability of self-timed logic to increase the manufacturability and reliability. Furthermore we used the tool to investigate the suitability of low-swing techniques in the NoC system communication under process variations. In this case We discovered the superior robustness to systematic process variation of low-swing links, which shows a good response to compensation technique as ASV and ABB. Hence low-swing is a good alternative to the standard CMOS communication for power, speed, reliability and manufacturability. In summary my work proves the advantage of integrating a statistical process variation analysis tool in the first stages of the design flow.

Organic fertilization of peach trees: implication on nitrogen availability, root growth and carbon distribution within plant

In the last years, sustainable horticulture has been increasing; however, to be successful this practice needs an efficient soil fertility management to maintain a high productivity and fruit quality standards. For this purpose composted organic materials from agri-food industry and municipal solid waste has been used as a source to replace chemical fertilizers and increase soil organic matter. To better understand the influence of compost application on soil fertility and plant growth, we carried out a study comparing organic and mineral nitrogen (N) fertilization in micro propagated plants, potted trees and commercial peach orchard with these aims: 1. evaluation of tree development, CO2 fixation and carbon partition to the different organs of two-years-old potted peach trees. 2. Determination of soil N concentration and nitrate-N effect on plant growth and root oxidative stress of micro propagated plant after increasing rates of N applications. 3. Assessment of soil chemical and biological fertility, tree growth and yield and fruit quality in a commercial orchard. The addition of compost at high rate was effective in increasing CO2 fixation, promoting root growth, shoot and fruit biomass. Furthermore, organic fertilizers influenced C partitioning, favoring C accumulation in roots, wood and fruits. The higher CO2 fixation was the result of a larger tree leaf area, rather than an increase in leaf photosynthetic efficiency, showing a stimulation of plant growth by application of compost. High concentrations of compost increased total soil N concentration, but were not effective in increasing nitrate-N soil concentration; in contrast mineral-N applications increased linearly soil nitrate-N, even at the lowest rate tested. Soil nitrate-N concentration influenced positively plant growth at low rate (60- 80 mg kg-1), whereas at high concentrations showed negative effects. In this trial, the decrease of root growth, as a response to excessive nitrate-N soil concentration, was not anticipated by root oxidative stress. Continuous annual applications of compost for 10 years enhanced soil organic matter content and total soil N concentration. Additionally, high rate of compost application (10 t ha-1 year-1) enhanced microbial biomass. On the other hand, different fertilizers management did not modify tree yield, but influenced fruit size and precocity index. The present data support the idea that organic fertilizers can be used successfully as a substitute of mineral fertilizers in fruit tree nutrient management, since they promote an increase of soil chemical and biological fertility, prevent excessive nitrate-N soil concentration, promote plant growth and potentially C sequestration into the soil.

Recupero della funzione renale in pazienti con acute kidney injury (AKI) sottoposti a terapia sostitutiva renale

L’insufficienza renale acuta(AKI) grave che richiede terapia sostitutiva, è una complicanza frequente nelle unità di terapia intensiva(UTI) e rappresenta un fattore di rischio indipendente di mortalità. Scopo dello studio é stato valutare prospetticamente, in pazienti “critici” sottoposti a terapie sostitutive renali continue(CRRT) per IRA post cardiochirurgia, la prevalenza ed il significato prognostico del recupero della funzione renale(RFR). Pazienti e Metodi:Pazienti(pz) con AKI dopo intervento di cardiochirurgia elettivo o in emergenza con disfunzione di due o più organi trattati con CRRT. Risultati:Dal 1996 al 2011, 266 pz (M 195,F 71, età 65.5±11.3aa) sono stati trattati con CRRT. Tipo di intervento: CABG(27.6%), dissecazione aortica(33%), sostituzione valvolare(21.1%), CABG+sostituzione valvolare(12.6%), altro(5.7%). Parametri all’inizio del trattamento: BUN 86.1±39.4, creatininemia(Cr) 3.96±1.86mg/dL, PAM 72.4±13.6mmHg, APACHE II score 30.7±6.1, SOFAscore 13.7±3. RIFLE: Risk (11%), Injury (31.4%), Failure (57.6%). AKI oligurica (72.2%), ventilazione meccanica (93.2%), inotropi (84.5%). La sopravvivenza a 30 gg ed alla dimissione è stata del 54.2% e del 37.1%. La sopravvivenza per stratificazione APACHE II: <24=85.1 e 66%, 25-29=63.5 e 48.1%, 30-34=51.8 e 31.8%, >34=31.6 e 17.7%. RFR ha consentito l’interruzione della CRRT nel 87.8% (86/98) dei survivors (Cr 1.4±0.6mg/dL) e nel 14.5% (24/166) dei nonsurvivors (Cr 2.2±0.9mg/dL) con un recupero totale del 41.4%. RFR è stato osservato nel 59.5% (44/74) dei pz non oligurici e nel 34.4% dei pz oligurici (66/192). La distribuzione dei pz sulla base dei tempi di RFR è stata:<8=38.2%, 8-14=20.9%, 15-21=11.8%, 22-28=10.9%, >28=18.2%. All’analisi multivariata, l’oliguria, l’età e il CV-SOFA a 7gg dall’inizio della CRRT si sono dimostrati fattori prognostici sfavorevoli su RFR(>21gg). RFR si associa ad una sopravvivenza elevata(78.2%). Conclusioni:RFR significativamente piu frequente nei pz non oligurici si associa ad una sopravvivenza alla dimissione piu elevata. La distribuzione dei pz in rapporto ad APACHE II e SOFAscore dimostra che la sopravvivenza e RFR sono strettamente legati alla gravità della patologia.

Starch distribution in pear tree organs in relation to training systems, rootstocks and fruit quality

Starch is the main form in which plants store carbohydrates reserves, both in terms of amounts and distribution among different plant species. Carbohydrates are direct products of photosynthetic activity, and it is well know that yield efficiency and production are directly correlated to the amount of carbohydrates synthesized and how these are distributed among vegetative and reproductive organs. Nowadays, in pear trees, due to the modernization of orchards, through the introduction of new rootstocks and the development of new training systems, the understanding and the development of new approaches regarding the distribution and storage of carbohydrates, are required. The objective of this research work was to study the behavior of carbohydrate reserves, mainly starch, in different pear tree organs and tissues: i.e., fruits, leaves, woody organs, roots and flower buds, at different physiological stages during the season. Starch in fruit is accumulated at early stages, and reached a maximum concentration during the middle phase of fruit development; after that, its degradation begins with a rise in soluble carbohydrates. Moreover, relationships between fruit starch degradation and different fruit traits, soluble sugars and organic acids were established. In woody organs and roots, an interconversion between starch and soluble carbohydrates was observed during the dormancy period that confirms its main function in supporting the growth and development of new tissues during the following spring. Factors as training systems, rootstocks, types of bearing wood, and their position on the canopy, influenced the concentrations of starch and soluble carbohydrates at different sampling dates. Also, environmental conditions and cultural practices must be considered to better explain these results. Thus, a deeper understanding of the dynamics of carbohydrates reserves within the plant could provide relevant information to improve several management practices to increase crop yield efficiency.

On the Luminous and Dark Matter Distribution in Early-Type Galaxies

The way mass is distributed in galaxies plays a major role in shaping their evolution across cosmic time. The galaxy's total mass is usually determined by tracing the motion of stars in its potential, which can be probed observationally by measuring stellar spectra at different distances from the galactic centre, whose kinematics is used to constrain dynamical models. A class of such models, commonly used to accurately determine the distribution of luminous and dark matter in galaxies, is that of equilibrium models. In this Thesis, a novel approach to the design of equilibrium dynamical models, in which the distribution function is an analytic function of the action integrals, is presented. Axisymmetric and rotating models are used to explain observations of a sample of nearby early-type galaxies in the Calar Alto Legacy Integral Field Area survey. Photometric and spectroscopic data for round and flattened galaxies are well fitted by the models, which are then used to get the galaxies' total mass distribution and orbital anisotropy. The time evolution of massive early-type galaxies is also investigated with numerical models. Their structural properties (mass, size, velocity dispersion) are observed to evolve, on average, with redshift. In particular, they appear to be significantly more compact at higher redshift, at fixed stellar mass, so it is interesting to investigate what drives such evolution. This Thesis focuses on the role played by dark-matter haloes: their mass-size and mass-velocity dispersion correlations evolve similarly to the analogous correlations of ellipticals; at fixed halo mass, the haloes are more compact at higher redshift, similarly to massive galaxies; a simple model, in which all the galaxy's size and velocity-dispersion evolution is due to the cosmological evolution of the underlying halo population, reproduces the observed size and velocity-dispersion of massive compact early-type galaxies up to redshift of about 2.

Analysis of slip distribution of large earthquakes oriented to tsunamigenesis characterisation

The present thesis focuses on the on-fault slip distribution of large earthquakes in the framework of tsunami hazard assessment and tsunami warning improvement. It is widely known that ruptures on seismic faults are strongly heterogeneous. In the case of tsunamigenic earthquakes, the slip heterogeneity strongly influences the spatial distribution of the largest tsunami effects along the nearest coastlines. Unfortunately, after an earthquake occurs, the so-called finite-fault models (FFM) describing the coseismic on-fault slip pattern becomes available over time scales that are incompatible with early tsunami warning purposes, especially in the near field. Our work aims to characterize the slip heterogeneity in a fast, but still suitable way. Using finite-fault models to build a starting dataset of seismic events, the characteristics of the fault planes are studied with respect to the magnitude. The patterns of the slip distribution on the rupture plane, analysed with a cluster identification algorithm, reveal a preferential single-asperity representation that can be approximated by a two-dimensional Gaussian slip distribution (2D GD). The goodness of the 2D GD model is compared to other distributions used in literature and its ability to represent the slip heterogeneity in the form of the main asperity is proven. The magnitude dependence of the 2D GD parameters is investigated and turns out to be of primary importance from an early warning perspective. The Gaussian model is applied to the 16 September 2015 Illapel, Chile, earthquake and used to compute early tsunami predictions that are satisfactorily compared with the available observations. The fast computation of the 2D GD and its suitability in representing the slip complexity of the seismic source make it a useful tool for the tsunami early warning assessments, especially for what concerns the near field.