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.

Weighted Inequalities and Lipschitz Spaces

In this thesis I have characterized the trace measures for particular potential spaces of functions defined on R^n, but "mollified" so that the potentials are de facto defined on the upper half-space of R^n. The potential functions are kind Riesz-Bessel. The characterization of trace measures for these spaces is a test condition on elementary sets of the upper half-space. To prove the test condition as sufficient condition for trace measures, I had give an extension to the case of upper half-space of the Muckenhoupt-Wheeden and Wolff inequalities. Finally I characterized the Carleson-trace measures for Besov spaces of discrete martingales. This is a simplified discrete model for harmonic extensions of Lipschitz-Besov spaces.

Frequency domain analysis of stationary time series

This thesis provides a necessary and sufficient condition for asymptotic efficiency of a nonparametric estimator of the generalised autocovariance function of a Gaussian stationary random process. The generalised autocovariance function is the inverse Fourier transform of a power transformation of the spectral density, and encompasses the traditional and inverse autocovariance functions. Its nonparametric estimator is based on the inverse discrete Fourier transform of the same power transformation of the pooled periodogram. The general result is then applied to the class of Gaussian stationary ARMA processes and its implications are discussed. We illustrate that for a class of contrast functionals and spectral densities, the minimum contrast estimator of the spectral density satisfies a Yule-Walker system of equations in the generalised autocovariance estimator. Selection of the pooling parameter, which characterizes the nonparametric estimator of the generalised autocovariance, controlling its resolution, is addressed by using a multiplicative periodogram bootstrap to estimate the finite-sample distribution of the estimator. A multivariate extension of recently introduced spectral models for univariate time series is considered, and an algorithm for the coefficients of a power transformation of matrix polynomials is derived, which allows to obtain the Wold coefficients from the matrix coefficients characterizing the generalised matrix cepstral models. This algorithm also allows the definition of the matrix variance profile, providing important quantities for vector time series analysis. A nonparametric estimator based on a transformation of the smoothed periodogram is proposed for estimation of the matrix variance profile.

Retribuzione flessibile e contrattazione collettiva

Nel presente lavoro vengono esaminate le forme impiegate dalla contrattazione collettiva per rendere aleatorio il trattamento economico dei lavoratori subordinati. Dapprima ci si occupa del limite alla “flessibilizzazione” della retribuzione dei lavoratori subordinati che viene individuato nella “retribuzione sufficiente” di cui all’art. 36 Cost., qualificata come elemento essenziale del contratto. Di seguito si sofferma l’attenzione sulla retribuzione di produttività e di redditività dei lavoratori del settore privato e sul trattamento accessorio dei dipendenti pubblici privatizzati. Nonostante a queste quote della retribuzione sia astrattamente conferita una funzione incentivante, in concreto non la svolgono: nel lavoro privato a causa della politica egualitaria del sindacato e della “modalità” di determinazione degli obiettivi, nel lavoro pubblico perché questa parte della retribuzione è stata tradizionalmente erogata “a pioggia”. Nel terzo capitolo si prendono in considerazione le liti che possono sorgere se, nel periodo di tempo che va dalla fissazione degli obiettivi a quando si deve verificare il loro conseguimento, il datore di lavoro apporti modifiche organizzative in grado di ripercuotersi sulla capacità dei prestatori di raggiungere i risultati. Al fine di risolvere tale questione, in chiusura del secondo capitolo, la clausola in tema di retribuzione flessibile è stata classificata come condizione sospensiva in quanto una parte del trattamento economico, aggiuntiva alla retribuzione “base”, viene subordinata al conseguimento di obiettivi di produttività e redditività qualificabili come eventi futuri ed incerti. Tale qualificazione è volta a consentire l’applicazione dell’art. 1359 c.c. nelle controversie sopra descritte: se i lavoratori non conseguono gli obiettivi a causa di modifiche che il datore di lavoro ha apportato all’organizzazione, si può fingere che l’evento (che non si è verificato per una condotta imputabile al datore di lavoro) si sia verificato e, di conseguenza, erogare la retribuzione di risultato ai prestatori.

Modulation of hypoxia-inducible factors as a therapeutic target for multiple myeloma

Hypoxia-inducible factor-1 alpha (HIF-1α) plays a critical role in survival and is associated with poor prognosis in solid tumors. The role of HIF-1α in multiple myeloma is not completely known. In the present study, we explored the effect of EZN2968, an locked nucleic acid antisense oligonucleotide against HIF-1α, as a molecular target in MM. A panel of MM cell lines and primary samples from MM patients were cultured in vitro in the presence of EZN2968 . Under normoxia culture condition, HIF-1α mRNA and protein expression was detectable in all MM cell lines and in CD138+ cells from newly diagnosed MM patients samples. Significant up-regulation of HIF-1α protein expression was observed after incubation with IL6 or IGF-I, confirming that HIF-1α can be further induced by biological stimuli. EZN2968 efficiently induces a selective and stable down-modulation of HIF-1α and decreased the secretion of VEGF released by MM cell. Treatment with EZN2968 gave rise to a progressive accumulation of cells in the S and subG0 phase. The analysis of p21, a cyclin-dependent kinase inhibitors controlling cell cycle check point, shows upregulation of protein levels. These results suggest that HIF-1α inhibition is sufficient for cell cycle arrest in normoxia, and for inducing an apoptotic pathways.. In the presence of bone marrow microenvironment, HIF-1α inhibition blocks MAPK kinase pathway and secretion of pro-surviaval cytokines ( IL6,VEGF,IL8) In this study we provide evidence that HIF-1α, even in the absence of hypoxia signal, is expressed in MM plasma cells and further inducible by bone marrow milieu stimuli; moreover its inhibition is sufficient to induce a permanent cell cycle arrest. Our data support the hypothesis that HIF-1α inhibition may suppress tumor growth by preventing proliferation of plasma cells through p21 activation and blocking pro-survival stimuli from bone marrow microenvironment.

Multilevel Analysis in Household Survey: An Application to Health Condition Data

The aim of this thesis is to apply multilevel regression model in context of household surveys. Hierarchical structure in this type of data is characterized by many small groups. In last years comparative and multilevel analysis in the field of perceived health have grown in size. The purpose of this thesis is to develop a multilevel analysis with three level of hierarchy for Physical Component Summary outcome to: evaluate magnitude of within and between variance at each level (individual, household and municipality); explore which covariates affect on perceived physical health at each level; compare model-based and design-based approach in order to establish informativeness of sampling design; estimate a quantile regression for hierarchical data. The target population are the Italian residents aged 18 years and older. Our study shows a high degree of homogeneity within level 1 units belonging from the same group, with an intraclass correlation of 27% in a level-2 null model. Almost all variance is explained by level 1 covariates. In fact, in our model the explanatory variables having more impact on the outcome are disability, unable to work, age and chronic diseases (18 pathologies). An additional analysis are performed by using novel procedure of analysis :"Linear Quantile Mixed Model", named "Multilevel Linear Quantile Regression", estimate. This give us the possibility to describe more generally the conditional distribution of the response through the estimation of its quantiles, while accounting for the dependence among the observations. This has represented a great advantage of our models with respect to classic multilevel regression. The median regression with random effects reveals to be more efficient than the mean regression in representation of the outcome central tendency. A more detailed analysis of the conditional distribution of the response on other quantiles highlighted a differential effect of some covariate along the distribution.

The KIT gene in familial mastocytosis

Familial cutaneous mastocytosis is an exceptional condition of unknown etiology. In this study we report the largest series of patients with familial cutaneous mastocytosis without other manifestations (18 affected subjects from seven unrelated families), and we investigate the role of germ-line KIT mutations in the pathogenesis of the disease. The mean age at onset was 5.4 years (range from birth to 22 years), and the clinical behavior was variable over a mean follow up period of 15.1 years (range 2-36): improvement in seven, stability in eight and worsening in the remaining three patients. The pattern of inheritance was compatible with an autosomal dominant trait with incomplete penetrance; a female preponderance (14 females vs 4 males, ratio 3.5:1) was noted; among the six women who have been pregnant at least once, three experienced important clinical changes during pregnancy. No germ-line mutation was found in the exons 10, 11, and 17 of the KIT proto-oncogene, which are the most commonly mutated exons in sporadic mastocytosis. However, in the majority of affected subjects we found the Met541Leu polymorphic variant of the KIT gene, which seems to confer a growth advantage to mast cells in vitro. This observation further suggests that the Met541Leu may be a predisposing factor of cutaneous mastocytosis, although it seems to be neither necessary nor sufficient for the development of the disease.

Role of αvβ3 – Integrin and TLR2 in the innate response to Herpes Simplex Virus infection and Delivery of retargeted oncolytic Herpes Simplex via carrier cells

In the first part of my thesis I studied the mechanism of initiation of the innate response to HSV-1. Innate immune response is the first line of defense set up by the cell to counteract pathogens infection and it is elicited by the activation of a number of membrane or intracellular receptors and sensors, collectively indicated as PRRs, Patter Recognition Receptors. We reported that the HSV pathogen-associated molecular patterns (PAMP) that activate Toll-like receptor 2 (TLR2) and lead to the initiation of innate response are the virion glycoproteins gH/gL and gB, which constitute the conserved fusion core apparatus across the Herpesvirus. Specifically gH/gL is sufficient to initiate a signaling cascade which leads to NF-κB activation. Then, by gain and loss-of-function approaches, we found that αvβ3-integrin is a sensor of and plays a crucial role in the innate defense against HSV-1. We showed that αvβ3-integrin signals through a pathway that concurs with TLR2, affects activation/induction of interferons type 1, NF-κB, and a polarized set of cytokines and receptors. Thus, we demonstrated that gH/gL is sufficient to induce IFN1 and NF-κB via this pathway. From these data, we proposed that αvβ3-integrin is considered a class of non-TLR pattern recognition receptors. In the second part of my thesis I studied the capacity of human mesenchymal stromal cells isolated by fetal membranes (FM-hMSCs) to be used as carrier cells for the delivery of retargeted R-LM249 virus. The use of systemically administrated carrier cells to deliver oncolytic viruses to tumoral targets is a promising strategy in oncolytic virotherapy. We observed that FM-hMSCs can be infected by R-LM249 and we optimized the infection condition; then we demonstrate that stromal cells sustain the replication of retargeted R-LM249 and spread it to target tumoral cells. From these preliminary data FM-hMSCs resulted suitable to be used as carrier cells