Maximum principle, mean value operators and quasi boundedness in non-euclidean settings

This work deals with some classes of linear second order partial differential operators with non-negative characteristic form and underlying non- Euclidean structures. These structures are determined by families of locally Lipschitz-continuous vector fields in RN, generating metric spaces of Carnot- Carath´eodory type. The Carnot-Carath´eodory metric related to a family {Xj}j=1,...,m is the control distance obtained by minimizing the time needed to go from two points along piecewise trajectories of vector fields. We are mainly interested in the causes in which a Sobolev-type inequality holds with respect to the X-gradient, and/or the X-control distance is Doubling with respect to the Lebesgue measure in RN. This study is divided into three parts (each corresponding to a chapter), and the subject of each one is a class of operators that includes the class of the subsequent one. In the first chapter, after recalling “X-ellipticity” and related concepts introduced by Kogoj and Lanconelli in [KL00], we show a Maximum Principle for linear second order differential operators for which we only assume a Sobolev-type inequality together with a lower terms summability. Adding some crucial hypotheses on measure and on vector fields (Doubling property and Poincar´e inequality), we will be able to obtain some Liouville-type results. This chapter is based on the paper [GL03] by Guti´errez and Lanconelli. In the second chapter we treat some ultraparabolic equations on Lie groups. In this case RN is the support of a Lie group, and moreover we require that vector fields satisfy left invariance. After recalling some results of Cinti [Cin07] about this class of operators and associated potential theory, we prove a scalar convexity for mean-value operators of L-subharmonic functions, where L is our differential operator. In the third chapter we prove a necessary and sufficient condition of regularity, for boundary points, for Dirichlet problem on an open subset of RN related to sub-Laplacian. On a Carnot group we give the essential background for this type of operator, and introduce the notion of “quasi-boundedness”. Then we show the strict relationship between this notion, the fundamental solution of the given operator, and the regularity of the boundary points.

Mass transport in polymers

The study of mass transport in polymeric membranes has grown in importance due to its potential application in many processes such as separation of gases and vapors, packaging, controlled drug release. The diffusion of a low molecular weight species in a polymer is often accompanied by other phenomena like swelling, reactions, stresses, that have not been investigated in all their aspects yet. Furthermore, novel materials have been developed that include inorganic fillers, reactive functional groups or ions, that make the scenery even more complicated. The present work focused on the experimental study of systems where the diffusion is accompanied by other processes; suitable models were also developed to describe the particular circumstances in order to understand the underlying concepts and be able to design the performances of the material. The effect of solvent-induced deformation in polymeric films during sorption processes was studied since the dilation, especially in constrained membranes, can cause the development of stresses and therefore early failures of the material. The bending beam technique was used to test the effects of the dilation and the stress induced in the polymer by penetrant diffusion. A model based on the laminate theory was developed that accounts for the swelling and is able to predict the stress that raise in the material. The addition of inorganic fillers affects the transport properties of polymeric films. Mixed matrix membranes based on fluorinated, high free volume matrices show attractive performances for separation purposes but there is a need for deeper investigation of the selectivity properties towards gases and vapors. A new procedure based on the NELF model was tested on the experimental data; it allows to predict solubility of every penetrant on the basis of data for one vapor. The method has proved to be useful also for the determination of the diffusion coefficient and for an estimation of the permeability in the composite materials. Oxygen scavenging systems can overcome lack of barrier properties in common polymers that forbids their application in sensitive applications as food packaging. The final goal of obtaining a membrane almost impermeable to oxygen leads to experimental times out of reach. Hence, a simple model was developed in order to describe the transport of oxygen in a membrane with also reactive groups and analyze the experimental data collected on SBS copolymers that show attractive scavenging capacity. Furthermore, a model for predicting the oxygen barrier behavior of a film formed as a blend of OSP in a common packaging material was built, considering particles capable of reactions with oxygen embedded in a non-reactive matrix. Perfluorosulphonic acid ionomers (PFSI) are capturing attention due to a high thermal and chemical resistance coupled with very peculiar transport properties, that make them appropriate to be used in fuel cells. The possible effect of different formation procedure was studied together with the swelling due to water sorption since both water uptake and dilation can dramatically affect the fuel cells performances. The water diffusion and sorption was studied with a FTIR-ATR spectrometer that can give deeper information on the bonds between water molecules and the sulphonic hydrophilic groups and, therefore, on the microstructure of the hydrated ionomer.

Application of innovative methods of source apportionment in air contamination assessment

In this work, new tools in atmospheric pollutant sampling and analysis were applied in order to go deeper in source apportionment study. The project was developed mainly by the study of atmospheric emission sources in a suburban area influenced by a municipal solid waste incinerator (MSWI), a medium-sized coastal tourist town and a motorway. Two main research lines were followed. For what concerns the first line, the potentiality of the use of PM samplers coupled with a wind select sensor was assessed. Results showed that they may be a valid support in source apportionment studies. However, meteorological and territorial conditions could strongly affect the results. Moreover, new markers were investigated, particularly focusing on the processes of biomass burning. OC revealed a good biomass combustion process indicator, as well as all determined organic compounds. Among metals, lead and aluminium are well related to the biomass combustion. Surprisingly PM was not enriched of potassium during bonfire event. The second research line consists on the application of Positive Matrix factorization (PMF), a new statistical tool in data analysis. This new technique was applied to datasets which refer to different time resolution data. PMF application to atmospheric deposition fluxes identified six main sources affecting the area. The incinerator’s relative contribution seemed to be negligible. PMF analysis was then applied to PM2.5 collected with samplers coupled with a wind select sensor. The higher number of determined environmental indicators allowed to obtain more detailed results on the sources affecting the area. Vehicular traffic revealed the source of greatest concern for the study area. Also in this case, incinerator’s relative contribution seemed to be negligible. Finally, the application of PMF analysis to hourly aerosol data demonstrated that the higher the temporal resolution of the data was, the more the source profiles were close to the real one.

Potential Analysis for Hypoelliptic Second Order PDEs with Nonnegative Characteristic Form

In this Thesis we consider a class of second order partial differential operators with non-negative characteristic form and with smooth coefficients. Main assumptions on the relevant operators are hypoellipticity and existence of a well-behaved global fundamental solution. We first make a deep analysis of the L-Green function for arbitrary open sets and of its applications to the Representation Theorems of Riesz-type for L-subharmonic and L-superharmonic functions. Then, we prove an Inverse Mean value Theorem characterizing the superlevel sets of the fundamental solution by means of L-harmonic functions. Furthermore, we establish a Lebesgue-type result showing the role of the mean-integal operator in solving the homogeneus Dirichlet problem related to L in the Perron-Wiener sense. Finally, we compare Perron-Wiener and weak variational solutions of the homogeneous Dirichlet problem, under specific hypothesis on the boundary datum.

New perspectives in statistical mechanics and high-dimensional inference

The main purpose of this thesis is to go beyond two usual assumptions that accompany theoretical analysis in spin-glasses and inference: the i.i.d. (independently and identically distributed) hypothesis on the noise elements and the finite rank regime. The first one appears since the early birth of spin-glasses. The second one instead concerns the inference viewpoint. Disordered systems and Bayesian inference have a well-established relation, evidenced by their continuous cross-fertilization. The thesis makes use of techniques coming both from the rigorous mathematical machinery of spin-glasses, such as the interpolation scheme, and from Statistical Physics, such as the replica method. The first chapter contains an introduction to the Sherrington-Kirkpatrick and spiked Wigner models. The first is a mean field spin-glass where the couplings are i.i.d. Gaussian random variables. The second instead amounts to establish the information theoretical limits in the reconstruction of a fixed low rank matrix, the “spike”, blurred by additive Gaussian noise. In chapters 2 and 3 the i.i.d. hypothesis on the noise is broken by assuming a noise with inhomogeneous variance profile. In spin-glasses this leads to multi-species models. The inferential counterpart is called spatial coupling. All the previous models are usually studied in the Bayes-optimal setting, where everything is known about the generating process of the data. In chapter 4 instead we study the spiked Wigner model where the prior on the signal to reconstruct is ignored. In chapter 5 we analyze the statistical limits of a spiked Wigner model where the noise is no longer Gaussian, but drawn from a random matrix ensemble, which makes its elements dependent. The thesis ends with chapter 6, where the challenging problem of high-rank probabilistic matrix factorization is tackled. Here we introduce a new procedure called "decimation" and we show that it is theoretically to perform matrix factorization through it.

Development and characterization of non-oxide ceramic composites for mechanical and tribological applications

The main reasons for the attention focused on ceramics as possible structural materials are their wear resistance and the ability to operate with limited oxidation and ablation at temperatures above 2000°C. Hence, this work is devoted to the study of two classes of materials which can satisfy these requirements: silicon carbide -based ceramics (SiC) for wear applications and borides and carbides of transition metals for ultra-high temperatures applications (UHTCs). SiC-based materials: Silicon carbide is a hard ceramic, which finds applications in many industrial sectors, from heat production, to automotive engineering and metals processing. In view of new fields of uses, SiC-based ceramics were produced with addition of 10-30 vol% of MoSi2, in order to obtain electro conductive ceramics. MoSi2, indeed, is an intermetallic compound which possesses high temperature oxidation resistance, high electrical conductivity (21·10-6 Ω·cm), relatively low density (6.31 g/cm3), high melting point (2030°C) and high stiffness (440 GPa). The SiC-based ceramics were hot pressed at 1900°C with addition of Al2O3-Y2O3 or Y2O3-AlN as sintering additives. The microstructure of the composites and of the reference materials, SiC and MoSi2, were studied by means of conventional analytical techniques, such as X-ray diffraction (XRD), scanning electron microscopy (SEM) and energy dispersive spectroscopy (SEM-EDS). The composites showed a homogeneous microstructure, with good dispersion of the secondary phases and low residual porosity. The following thermo-mechanical properties of the SiC-based materials were measured: Vickers hardness (HV), Young’s modulus (E), fracture toughness (KIc) and room to high temperature flexural strength (σ). The mechanical properties of the composites were compared to those of two monolithic SiC and MoSi2 materials and resulted in a higher stiffness, fracture toughness and slightly higher flexural resistance. Tribological tests were also performed in two configurations disco-on-pin and slideron cylinder, aiming at studying the wear behaviour of SiC-MoSi2 composites with Al2O3 as counterfacing materials. The tests pointed out that the addition of MoSi2 was detrimental owing to a lower hardness in comparison with the pure SiC matrix. On the contrary, electrical measurements revealed that the addition of 30 vol% of MoSi2, rendered the composite electroconductive, lowering the electrical resistance of three orders of magnitude. Ultra High Temperature Ceramics: Carbides, borides and nitrides of transition metals (Ti, Zr, Hf, Ta, Nb, Mo) possess very high melting points and interesting engineering properties, such as high hardness (20-25 GPa), high stiffness (400-500 GPa), flexural strengths which remain unaltered from room temperature to 1500°C and excellent corrosion resistance in aggressive environment. All these properties place the UHTCs as potential candidates for the development of manoeuvrable hypersonic flight vehicles with sharp leading edges. To this scope Zr- and Hf- carbide and boride materials were produced with addition of 5-20 vol% of MoSi2. This secondary phase enabled the achievement of full dense composites at temperature lower than 2000°C and without the application of pressure. Besides the conventional microstructure analyses XRD and SEM-EDS, transmission electron microscopy (TEM) was employed to explore the microstructure on a small length scale to disclose the effective densification mechanisms. A thorough literature analysis revealed that neither detailed TEM work nor reports on densification mechanisms are available for this class of materials, which however are essential to optimize the sintering aids utilized and the processing parameters applied. Microstructural analyses, along with thermodynamics and crystallographic considerations, led to disclose of the effective role of MoSi2 during sintering of Zrand Hf- carbides and borides. Among the investigated mechanical properties (HV, E, KIc, σ from room temperature to 1500°C), the high temperature flexural strength was improved due to the protective and sealing effect of a silica-based glassy phase, especially for the borides. Nanoindentation tests were also performed on HfC-MoSi2 composites in order to extract hardness and elastic modulus of the single phases. Finally, arc jet tests on HfC- and HfB2-based composites confirmed the excellent oxidation behaviour of these materials under temperature exceeding 2000°C; no cracking or spallation occurred and the modified layer was only 80-90 μm thick.

Stability, viscous dissipation and local thermal non-equilibrium in fluid saturated porous media

In this thesis, the field of study related to the stability analysis of fluid saturated porous media is investigated. In particular the contribution of the viscous heating to the onset of convective instability in the flow through ducts is analysed. In order to evaluate the contribution of the viscous dissipation, different geometries, different models describing the balance equations and different boundary conditions are used. Moreover, the local thermal non-equilibrium model is used to study the evolution of the temperature differences between the fluid and the solid matrix in a thermal boundary layer problem. On studying the onset of instability, different techniques for eigenvalue problems has been used. Analytical solutions, asymptotic analyses and numerical solutions by means of original and commercial codes are carried out.

Non invasive assessment of right ventricle in patients with operated tetralogy of Fallot

The objective of this study was to evaluate right ventricular function in patients with right ventricular volume overload in patients with (tetralogy of Fallot, and pulmonary atresia + VSD ) underwent corrective surgery; with echocardiography measure that can be easily applied; and to study the relationship between ProBNP and the contractile function of the right ventricle, dilated right atrium, and the consequences of pulmonary insufficiency . Methods: The study included 50 patients (50% males, mean age 30.64 ± 13.30 years) with prior cardiac surgical intervention of TDF (90%) or pulmonary atresia + VSD (10%). (49 pz) have performed a cardiac MRI and clinical evaluation, (47 pz) echocardiogram, (48 pz) ECG, (34 pz) a cardiopulmonary exercise testing, (29 pz) a dosage of ProBNP. Results: The S-wave velocity (p <0.0001), the TAPSE (p <0.0001) correlated significantly with RVEF estimated by cardiac MRI. The VO2 max was 27.93 ± 12.91 ml / kg / min, 15% of patients had VE/VCO2 The peak> 35. ProBNP correlated positively and significantly with the area of the right atrium (p = 0.0001), and negative and significant with VO2 max (p = 0.04). Those who have increased pulmonary insufficiency (PVR fraction> 30%) have a significantly increased RVED volume (p = 0.01), reduced VO2 max (p = 0.04), and lower ejection fraction of LV (p = 0.02) than the group of patients with PVR ≤ 30. Conclusion: The TAPSE and S-wave velocity are fundamental and may become the technique of choice for routine assessment of RV systolic function in adult patients with TOF. The monitoring of the Pro BNP is probably a choice, given the simplicity and their information that correlate with the test cardiopulmonary. In view of the ventricular-ventricular interaction, so measures to maintain or restore the functioning of the pulmonary valve could preserve biventricular function.

Le Coliti Microscopiche nei soggetti con diarrea non ematica: uno studio prospettico

Introduzione: le Coliti Microscopiche, altrimenti note come Colite Collagena e Colite Linfocitica, sono disordini infiammatori cronici del colon che causano diarrea e colpiscono più frequentemente donne in età avanzata e soggetti in terapia farmacologica. Negli ultimi anni la loro incidenza sembra aumentata in diversi paesi occidentali ma la prevalenza in Italia è ancora incerta. Scopo: il presente studio prospettico e multicentrico è stato disegnato per valutare la prevalenza delle CM in pazienti sottoposti a colonscopia per diarrea cronica non ematica. Pazienti e metodi: dal Maggio 2010 al Settembre 2010 sono stati arruolati consecutivamente tutti i soggetti adulti afferenti in due strutture dell’area metropolitana milanese per eseguire una pancolonscopia. Nei soggetti con diarrea cronica non ematica sono state eseguite biopsie multiple nel colon ascendente, sigma e retto nonché in presenza di lesioni macroscopiche. Risultati: delle 8008 colonscopie esaminate 265 sono state eseguite per diarrea cronica; tra queste, 8 presentavano informazioni incomplete, 52 riscontri endoscopici consistenti con altri disordini intestinali (i.e. IBD, tumori, diverticoliti). 205 colonscopie sono risultate sostanzialmente negative, 175 dotate di adeguato campionamento microscopico (M:F=70:105; età mediana 61 anni). L’analisi istologica ha permesso di documentare 38 nuovi casi di CM (M:F=14:24; età mediana 67.5 anni): 27 CC (M:F=10:17; età mediana 69 anni) e 11 CL (M:F=4:7; età mediana 66 anni). In altri 25 casi sono state osservate alterazioni microscopiche prive dei sufficienti requisiti per la diagnosi di CM. Conclusioni: nel presente studio l’analisi microscopica del colon ha identificato la presenza di CM nel 21,7% dei soggetti con diarrea cronica non ematica ed indagine pancolonscopica negativa. Lo studio microscopico del colon è pertanto un passo diagnostico fondamentale per il corretto inquadramento diagnostico delle diarree croniche, specialmente dopo i 60 anni di età. Ampi studi prospettici e multicentrici dovranno chiarire ruolo e peso dei fattori di rischio associati a questi disordini.

Quantum Integrability in Non-Linear Sigma Models related to Gauge/String Correspondences

The Thermodynamic Bethe Ansatz analysis is carried out for the extended-CP^N class of integrable 2-dimensional Non-Linear Sigma Models related to the low energy limit of the AdS_4xCP^3 type IIA superstring theory. The principal aim of this program is to obtain further non-perturbative consistency check to the S-matrix proposed to describe the scattering processes between the fundamental excitations of the theory by analyzing the structure of the Renormalization Group flow. As a noteworthy byproduct we eventually obtain a novel class of TBA models which fits in the known classification but with several important differences. The TBA framework allows the evaluation of some exact quantities related to the conformal UV limit of the model: effective central charge, conformal dimension of the perturbing operator and field content of the underlying CFT. The knowledge of this physical quantities has led to the possibility of conjecturing a perturbed CFT realization of the integrable models in terms of coset Kac-Moody CFT. The set of numerical tools and programs developed ad hoc to solve the problem at hand is also discussed in some detail with references to the code.

Nano-fabrication of complex functional structures using non- conventional lithography

In Chapter 1 I will present a brief introduction on the state of art of nanotechnologies, nanofabrication techniques and unconventional lithography as a technique to fabricate the novel electronic device as resistive switch so-called memristor is shown. In Chapter 2 a detailed description of the main fabrication and characterization techniques employed in this work is reported. Chapter 3 parallel local oxidation lithography (pLOx) describes as a main technique to obtain accurate patterning process. All the effective parameters has been studied and the optimized condition observed to highly reproducible with excellent patterned nanostructures. The effect of negative bias, calls local reduction (LR) studied. Moreover, the use of AC bias shows faster patterning process respect to DC bias. In Chapter 4 (metal/ e-SiO2/ Si nanojunction) it is shown how the electrochemical oxide nanostructures by using pLOx can be used in the fabrication of novel devices call memristor. We demonstrate a new concept, based on conventional materials, where the lifetime problem is resolved by introducing a “regeneration” step, which restores the nano-memristor to its pristine condition by applying an appropriate voltage cycle. In Chapter 5 (Graphene/ e-SiO2/ Si), Graphene as a building block material is used as an electrode to selectively oxidize the silicon substrate by pLOx set up for the fabrication of novel resistive switch device. In Chapter 6 (surface architecture) I will show another application of pLOx in biotechnology is shown. So the surface functionalization combine with nano-patterning by pLOx used to design a new surface to accurately bind biomolecules with the possibility of studying those properties and more application in nano-bio device fabrication. So, in order to obtain biochips, electronic and optical/photonics devices Nano patterning of DNA used as scaffolds to fabricate small functional nano-components.

Developing a radiomic based machine learning model to identify patients with resected non-small-cell lung cancer at high risk of relapse

Background There is a wide variation of recurrence risk of Non-small-cell lung cancer (NSCLC) within the same Tumor Node Metastasis (TNM) stage, suggesting that other parameters are involved in determining this probability. Radiomics allows extraction of quantitative information from images that can be used for clinical purposes. The primary objective of this study is to develop a radiomic prognostic model that predicts a 3 year disease free-survival (DFS) of resected Early Stage (ES) NSCLC patients. Material and Methods 56 pre-surgery non contrast Computed Tomography (CT) scans were retrieved from the PACS of our institution and anonymized. Then they were automatically segmented with an open access deep learning pipeline and reviewed by an experienced radiologist to obtain 3D masks of the NSCLC. Images and masks underwent to resampling normalization and discretization. From the masks hundreds Radiomic Features (RF) were extracted using Py-Radiomics. Hence, RF were reduced to select the most representative features. The remaining RF were used in combination with Clinical parameters to build a DFS prediction model using Leave-one-out cross-validation (LOOCV) with Random Forest. Results and Conclusion A poor agreement between the radiologist and the automatic segmentation algorithm (DICE score of 0.37) was found. Therefore, another experienced radiologist manually segmented the lesions and only stable and reproducible RF were kept. 50 RF demonstrated a high correlation with the DFS but only one was confirmed when clinicopathological covariates were added: Busyness a Neighbouring Gray Tone Difference Matrix (HR 9.610). 16 clinical variables (which comprised TNM) were used to build the LOOCV model demonstrating a higher Area Under the Curve (AUC) when RF were included in the analysis (0.67 vs 0.60) but the difference was not statistically significant (p=0,5147).