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.

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.

L'influenza del sonno sull'andamento temporale della consolidazione delle abilità procedurali

Background: It is well known, since the pioneristic observation by Jenkins and Dallenbach (Am J Psychol 1924;35:605-12), that a period of sleep provides a specific advantage for the consolidation of newly acquired informations. Recent research about the possible enhancing effect of sleep on memory consolidation has focused on procedural memory (part of non-declarative memory system, according to Squire’s taxonomy), as it appears the memory sub-system for which the available data are more consistent. The acquisition of a procedural skill follows a typical time course, consisting in a substantial practice-dependent learning followed by a slow, off-line improvement. Sleep seems to play a critical role in promoting the process of slow learning, by consolidating memory traces and making them more stable and resistant to interferences. If sleep is critical for the consolidation of a procedural skill, then an alteration of the organization of sleep should result in a less effective consolidation, and therefore in a reduced memory performance. Such alteration can be experimentally induced, as in a deprivation protocol, or it can be naturally observed in some sleep disorders as, for example, in narcolepsy. In this research, a group of narcoleptic patients, and a group of matched healthy controls, were tested in two different procedural abilities, in order to better define the size and time course of sleep contribution to memory consolidation. Experimental Procedure: A Texture Discrimination Task (Karni & Sagi, Nature 1993;365:250-2) and a Finger Tapping Task (Walker et al., Neuron 2002;35:205-11) were administered to two indipendent samples of drug-naive patients with first-diagnosed narcolepsy with cataplexy (International Classification of Sleep Disorder 2nd ed., 2005), and two samples of matched healthy controls. In the Texture Discrimination task, subjects (n=22) had to learn to recognize a complex visual array on the screen of a personal computer, while in the Finger Tapping task (n=14) they had to press a numeric sequence on a standard keyboard, as quickly and accurately as possible. Three subsequent experimental sessions were scheduled for each partecipant, namely a training session, a first retrieval session the next day, and a second retrieval session one week later. To test for possible circadian effects on learning, half of the subjects performed the training session at 11 a.m. and half at 17 p.m. Performance at training session was taken as a measure of the practice-dependent learning, while performance of subsequent sessions were taken as a measure of the consolidation level achieved respectively after one and seven nights of sleep. Between training and first retrieval session, all participants spent a night in a sleep laboratory and underwent a polygraphic recording. Results and Discussion: In both experimental tasks, while healthy controls improved their performance after one night of undisturbed sleep, narcoleptic patients showed a non statistically significant learning. Despite this, at the second retrieval session either healthy controls and narcoleptics improved their skills. Narcoleptics improved relatively more than controls between first and second retrieval session in the texture discrimination ability, while their performance remained largely lower in the motor (FTT) ability. Sleep parameters showed a grater fragmentation in the sleep of the pathological group, and a different distribution of Stage 1 and 2 NREM sleep in the two groups, being thus consistent with the hypothesis of a lower consolidation power of sleep in narcoleptic patients. Moreover, REM density of the first part of the night of healthy subjects showed a significant correlation with the amount of improvement achieved at the first retrieval session in TDT task, supporting the hypothesis that REM sleep plays an important role in the consolidation of visuo-perceptual skills. Taken together, these results speak in favor of a slower, rather than lower consolidation of procedural skills in narcoleptic patients. Finally, an explanation of the results, based on the possible role of sleep in contrasting the interference provided by task repetition is proposed.

Nuovi catalizzatori per l'idrogenazione, l'idrogenolisi/ring-opening di composti aromatici policiclici

The removal of aromatic hydrocarbons from diesel has received considerable attention after environmental regulations that require petroleum refiners to raise cetane number and to limit aromatics in diesel fuel in order to improve combustion efficiency and reduce particulate and NOx emissions. An alternative is blending with Fischer–Tropsch (FT) gas-to-liquid diesel fuel; however, this option may not be economically viable solution in case of extensive blend. Another alternative is to incorporate in the diesel pool a greater fraction of the so-called light cycle oil (LCO). Due to its high aromatics content and its low cetane number (typically between 20 and 30), the incorporation of LCO may have a negative impact on the quality of diesel. Current technologies for LCO improvement are based on hydrogenation to adjust both sulphur and cetane number but while an important fraction of the aromatics present in LCO can be saturated in a deep hydrogenation process, the cetane number may still be lower than the target values specified in diesel legislations, so further upgrading is needed. An interesting technology for improving the cetane number of diesels and maintaining meanwhile high diesel yields is achieved by combining a complete hydrogenation process with a selective ring opening (SRO) reaction of the naphthenic rings. The SRO can be defined as naphthene ring-opening to form compounds with high cetane number, but without any carbon losses. Controlling the interconversion of six- and five- membered rings via an acid-catalyzed ring-contraction step is also of great importance, since selective conversion of six-membered to five-membered naphthene rings greatly influences ring-opening rates and selectivity. High intrinsic activity may be enhanced by deposition of noble metals on acidic, high surface area supports, because it is possible to arrange close proximity of the metal and acid sites. Moreover, in large-pore supports, the diffusion resistance of liquid reactants into the pores is minimized. In addition to metal centres, the acid sites of support also plays role in aromatics hydrogenation. However, the functions of different kinds of acid sites (Brønsted vs. Lewis acidity), and their optimal concentrations and strengths, remain unclear. In the present study we investigated the upgrading of an aromatic-rich feedstock over different type of metal supported on mesoporous silica-alumina. The selective hydrogenolysis and ring opening of tetrahydronaphthalene (THN or tetralin) was carried out as representative of LCO fractions after deep hydrogenation process. In this regards the aim of this study is to evaluate both the effect of metals and that of the supports characterized by different acid distribution and strength, on conversion and selectivity. For this purpose a series of catalysts were prepared by impregnation. The catalysts were characterized and conversion tests of THN were performed in a lab-scale plant operating in the pressure range from 7.0-5.0 MPa and in the temperature range from 300 to 360°C.

Selezione e processazione di cellule Natural Killer da donatore aploidentico "KIR-ligand" incompatibile per l'immunoterapia adottiva di pazienti con Leucemia Acuta Mieloblastica ad alto rischio

The effector function of natural killer (NK) cells is regulated by activating and inhibitory receptors, termed killer immunoglobulin-like receptors (KIRs). In haploidentical T-cell depleted transplantation the donor/recipient KIR mismatch significantly impacts on NK-mediated tumor cell killing, particularly in acute myeloid leukaemia (AML). Thirty-four high risk AML patients entered a phase I-II study of adoptive NK-cell based immunotherapy and were screened for the availability of one haploidentical KIR ligand mismatched donor. Thirteen of them resulted as having one suitable donor. NK cells were enriched from steady-state leukaphereses by using a double-step immunomagnetic separation system, consisting in depletion of CD3+ T cells followed by positive selection of CD56+ NK cells. CD56+ cells were enriched from 7,70% (1,26-11,70) to 93,50% (66,41-99,20) (median recovery 53,05% (30,97-72,85), median T-depletion 3,03 log (2,15-4,52) viability >92%) and their citotoxic activity was inalterate. All patients (4 progressions, 1 partial remission and 8 complete remissions) received NK cell infusion which was preceeded by immunosuppressive chemotherapy (fludarabine and cyclophosphamide) and followed by interleukin 2 injections. The median number of reinfused NK cells was 2,74x10(e)6/kg(1,11-5,00) and contamining CD3+ T cells were always less than 1x10(e)5/kg. The procedure was well-tolerated and no significant toxicity, including GvHD, related to NK cell infusion was observed. The donor NK cells were demonstrated in 5/10 patients. Among the 8 patients in complete remission 5 patients are stable after 18, 15, 4, 2 months of follow-up. Three other patients relapsed after 2 and 7 months. The patient in partial remission obtained a complete remission, which lasted for 6 months. The 4 patients with active/progressive disease showed the persistence of disease. This clinical observation may be correlated with in vitro studies, indicating that AML cells are capable to induce NK cell apoptosis in a dose-depend manner. In summery, a two-step enrichment of CD56+ NK cells allows the collection of a suitable number of target cells to be used as adoptive immunotherapy in AML patients. Infusion of NK cells is feasible and safe and adoptively transferred NK cells can be detected after infusion.

Modellazione multibody di veicoli ferroviari: sviluppo ed implementazione di modelli innovativi per l'analisi del contatto ruota - rotaia

The wheel - rail contact analysis plays a fundamental role in the multibody modeling of railway vehicles. A good contact model must provide an accurate description of the global contact phenomena (contact forces and torques, number and position of the contact points) and of the local contact phenomena (position and shape of the contact patch, stresses and displacements). The model has also to assure high numerical efficiency (in order to be implemented directly online within multibody models) and a good compatibility with commercial multibody software (Simpack Rail, Adams Rail). The wheel - rail contact problem has been discussed by several authors and many models can be found in the literature. The contact models can be subdivided into two different categories: the global models and the local (or differential) models. Currently, as regards the global models, the main approaches to the problem are the so - called rigid contact formulation and the semi – elastic contact description. The rigid approach considers the wheel and the rail as rigid bodies. The contact is imposed by means of constraint equations and the contact points are detected during the dynamic simulation by solving the nonlinear algebraic differential equations associated to the constrained multibody system. Indentation between the bodies is not permitted and the normal contact forces are calculated through the Lagrange multipliers. Finally the Hertz’s and the Kalker’s theories allow to evaluate the shape of the contact patch and the tangential forces respectively. Also the semi - elastic approach considers the wheel and the rail as rigid bodies. However in this case no kinematic constraints are imposed and the indentation between the bodies is permitted. The contact points are detected by means of approximated procedures (based on look - up tables and simplifying hypotheses on the problem geometry). The normal contact forces are calculated as a function of the indentation while, as in the rigid approach, the Hertz’s and the Kalker’s theories allow to evaluate the shape of the contact patch and the tangential forces. Both the described multibody approaches are computationally very efficient but their generality and accuracy turn out to be often insufficient because the physical hypotheses behind these theories are too restrictive and, in many circumstances, unverified. In order to obtain a complete description of the contact phenomena, local (or differential) contact models are needed. In other words wheel and rail have to be considered elastic bodies governed by the Navier’s equations and the contact has to be described by suitable analytical contact conditions. The contact between elastic bodies has been widely studied in literature both in the general case and in the rolling case. Many procedures based on variational inequalities, FEM techniques and convex optimization have been developed. This kind of approach assures high generality and accuracy but still needs very large computational costs and memory consumption. Due to the high computational load and memory consumption, referring to the current state of the art, the integration between multibody and differential modeling is almost absent in literature especially in the railway field. However this integration is very important because only the differential modeling allows an accurate analysis of the contact problem (in terms of contact forces and torques, position and shape of the contact patch, stresses and displacements) while the multibody modeling is the standard in the study of the railway dynamics. In this thesis some innovative wheel – rail contact models developed during the Ph. D. activity will be described. Concerning the global models, two new models belonging to the semi – elastic approach will be presented; the models satisfy the following specifics: 1) the models have to be 3D and to consider all the six relative degrees of freedom between wheel and rail 2) the models have to consider generic railway tracks and generic wheel and rail profiles 3) the models have to assure a general and accurate handling of the multiple contact without simplifying hypotheses on the problem geometry; in particular the models have to evaluate the number and the position of the contact points and, for each point, the contact forces and torques 4) the models have to be implementable directly online within the multibody models without look - up tables 5) the models have to assure computation times comparable with those of commercial multibody software (Simpack Rail, Adams Rail) and compatible with RT and HIL applications 6) the models have to be compatible with commercial multibody software (Simpack Rail, Adams Rail). The most innovative aspect of the new global contact models regards the detection of the contact points. In particular both the models aim to reduce the algebraic problem dimension by means of suitable analytical techniques. This kind of reduction allows to obtain an high numerical efficiency that makes possible the online implementation of the new procedure and the achievement of performance comparable with those of commercial multibody software. At the same time the analytical approach assures high accuracy and generality. Concerning the local (or differential) contact models, one new model satisfying the following specifics will be presented: 1) the model has to be 3D and to consider all the six relative degrees of freedom between wheel and rail 2) the model has to consider generic railway tracks and generic wheel and rail profiles 3) the model has to assure a general and accurate handling of the multiple contact without simplifying hypotheses on the problem geometry; in particular the model has to able to calculate both the global contact variables (contact forces and torques) and the local contact variables (position and shape of the contact patch, stresses and displacements) 4) the model has to be implementable directly online within the multibody models 5) the model has to assure high numerical efficiency and a reduced memory consumption in order to achieve a good integration between multibody and differential modeling (the base for the local contact models) 6) the model has to be compatible with commercial multibody software (Simpack Rail, Adams Rail). In this case the most innovative aspects of the new local contact model regard the contact modeling (by means of suitable analytical conditions) and the implementation of the numerical algorithms needed to solve the discrete problem arising from the discretization of the original continuum problem. Moreover, during the development of the local model, the achievement of a good compromise between accuracy and efficiency turned out to be very important to obtain a good integration between multibody and differential modeling. At this point the contact models has been inserted within a 3D multibody model of a railway vehicle to obtain a complete model of the wagon. The railway vehicle chosen as benchmark is the Manchester Wagon the physical and geometrical characteristics of which are easily available in the literature. The model of the whole railway vehicle (multibody model and contact model) has been implemented in the Matlab/Simulink environment. The multibody model has been implemented in SimMechanics, a Matlab toolbox specifically designed for multibody dynamics, while, as regards the contact models, the CS – functions have been used; this particular Matlab architecture allows to efficiently connect the Matlab/Simulink and the C/C++ environment. The 3D multibody model of the same vehicle (this time equipped with a standard contact model based on the semi - elastic approach) has been then implemented also in Simpack Rail, a commercial multibody software for railway vehicles widely tested and validated. Finally numerical simulations of the vehicle dynamics have been carried out on many different railway tracks with the aim of evaluating the performances of the whole model. The comparison between the results obtained by the Matlab/ Simulink model and those obtained by the Simpack Rail model has allowed an accurate and reliable validation of the new contact models. In conclusion to this brief introduction to my Ph. D. thesis, we would like to thank Trenitalia and the Regione Toscana for the support provided during all the Ph. D. activity. Moreover we would also like to thank the INTEC GmbH, the society the develops the software Simpack Rail, with which we are currently working together to develop innovative toolboxes specifically designed for the wheel rail contact analysis.

L'associazione Tipifarnib-Bortezomib nel trattamento delle leucemie acute mieloidi: risultati di uno studio multicentrico di fase I/II e validazione di un profilo genico predittivo di risposta

Background. Outcome of elderly acute myeloid leukemia (AML) patients is dismal. Targeted-therapies might improve current results by overcoming drug-resistance and reducing toxicity. Aim. We conduced a phase II study aiming to assess efficacy and toxicity of Tipifarnib (Zarnestra®) and Bortezomib (Velcade®) association in AML patients >18 years, unfit for conventional therapy, or >60 years, in relapse. Furthermore, we aimed to evaluated the predictive value of the RASGRP1/APTX ratio, which was previously found to be associated to treatment sensitivity in patients receiving Zarnestra alone. Methods. Velcade (1.0 mg/m2) was administered as weekly infusion for 3 weeks (days 1, 8, 15). Zarnestra was administered at dose of 300-600 mg BID for 21 consecutive days. Real-time quantitative-PCR (q-PCR) was used for RASGRP1/APTX quantification. Results. 50 patients were enrolled. Median age was 71 years (56-89). 3 patients achieved complete remission (CR) and 1 partial response (PR). 2 patients obtained an hematological improvement (HI), and 3 died during marrow aplasia. 10 had progressive disease (PD) and the remaining showed stable disease (SD). RASGRP1/APTX was evaluated before treatment initiation on bone marrow (BM) and/or peripheral blood (PB). The median RASGRP/APTX value on BM was higher in responder (R) patients than in non responders (NR) ones, respectively (p=0.006). Interestingly, no marrow responses were recorded in patients with BM RASGRP1/APTX ratio <12, while the response rate was 50% in patients with ratio >12. Toxicity was overall mild, the most common being febrile neutropenia. Conclusion. We conclude that the clinical efficacy of the combination Zarnestra-Velcade was similar to what reported for Zarnestra alone. However we could confirm that the RASGPR1/APTX level is an effective predictor of response. Though higher RASGRP1/APTX is relatively rare (~10% of cases), Zarnestra (±Velcade) may represent an important option in a subset of high risk/frail AML patients.

Finite element models of coseismic deformation due to the 2009 L'Aquila (Italy) and 2008 Wenchuan(China) earthquakes

The topic of my Ph.D. thesis is the finite element modeling of coseismic deformation imaged by DInSAR and GPS data. I developed a method to calculate synthetic Green functions with finite element models (FEMs) and then use linear inversion methods to determine the slip distribution on the fault plane. The method is applied to the 2009 L’Aquila Earthquake (Italy) and to the 2008 Wenchuan earthquake (China). I focus on the influence of rheological features of the earth's crust by implementing seismic tomographic data and the influence of topography by implementing Digital Elevation Models (DEM) layers on the FEMs. Results for the L’Aquila earthquake highlight the non-negligible influence of the medium structure: homogeneous and heterogeneous models show discrepancies up to 20% in the fault slip distribution values. Furthermore, in the heterogeneous models a new area of slip appears above the hypocenter. Regarding the 2008 Wenchuan earthquake, the very steep topographic relief of Longmen Shan Range is implemented in my FE model. A large number of DEM layers corresponding to East China is used to achieve the complete coverage of the FE model. My objective was to explore the influence of the topography on the retrieved coseismic slip distribution. The inversion results reveals significant differences between the flat and topographic model. Thus, the flat models frequently adopted are inappropriate to represent the earth surface topographic features and especially in the case of the 2008 Wenchuan earthquake.

Sviluppo di un'applicazione bioinformatica per la gestione dei dati di antibiotico sensibilità di isolati clinici

Il problema dell'antibiotico-resistenza è un problema di sanità pubblica per affrontare il quale è necessario un sistema di sorveglianza basato sulla raccolta e l'analisi dei dati epidemiologici di laboratorio. Il progetto di dottorato è consistito nello sviluppo di una applicazione web per la gestione di tali dati di antibiotico sensibilità di isolati clinici utilizzabile a livello di ospedale. Si è creata una piattaforma web associata a un database relazionale per avere un’applicazione dinamica che potesse essere aggiornata facilmente inserendo nuovi dati senza dover manualmente modificare le pagine HTML che compongono l’applicazione stessa. E’ stato utilizzato il database open-source MySQL in quanto presenta numerosi vantaggi: estremamente stabile, elevate prestazioni, supportato da una grande comunità online ed inoltre gratuito. Il contenuto dinamico dell’applicazione web deve essere generato da un linguaggio di programmazione tipo “scripting” che automatizzi operazioni di inserimento, modifica, cancellazione, visualizzazione di larghe quantità di dati. E’ stato scelto il PHP, linguaggio open-source sviluppato appositamente per la realizzazione di pagine web dinamiche, perfettamente utilizzabile con il database MySQL. E’ stata definita l’architettura del database creando le tabelle contenenti i dati e le relazioni tra di esse: le anagrafiche, i dati relativi ai campioni, microrganismi isolati e agli antibiogrammi con le categorie interpretative relative al dato antibiotico. Definite tabelle e relazioni del database è stato scritto il codice associato alle funzioni principali: inserimento manuale di antibiogrammi, importazione di antibiogrammi multipli provenienti da file esportati da strumenti automatizzati, modifica/eliminazione degli antibiogrammi precedenti inseriti nel sistema, analisi dei dati presenti nel database con tendenze e andamenti relativi alla prevalenza di specie microbiche e alla chemioresistenza degli stessi, corredate da grafici. Lo sviluppo ha incluso continui test delle funzioni via via implementate usando reali dati clinici e sono stati introdotti appositi controlli e l’introduzione di una semplice e pulita veste grafica.

Sviluppo di un approccio congiunto fuzzy-Bayesiano per l'analisi e la modellizzazione degli ecosistemi: applicazione ad ecosistemi marini costieri.

Nell’attuale contesto di aumento degli impatti antropici e di “Global Climate Change” emerge la necessità di comprenderne i possibili effetti di questi sugli ecosistemi inquadrati come fruitori di servizi e funzioni imprescindibili sui quali si basano intere tessiture economiche e sociali. Lo studio previsionale degli ecosistemi si scontra con l’elevata complessità di questi ultimi in luogo di una altrettanto elevata scarsità di osservazioni integrate. L’approccio modellistico appare il più adatto all’analisi delle dinamiche complesse degli ecosistemi ed alla contestualizzazione complessa di risultati sperimentali ed osservazioni empiriche. L’approccio riduzionista-deterministico solitamente utilizzato nell’implementazione di modelli non si è però sin qui dimostrato in grado di raggiungere i livelli di complessità più elevati all’interno della struttura eco sistemica. La componente che meglio descrive la complessità ecosistemica è quella biotica in virtù dell’elevata dipendenza dalle altre componenti e dalle loro interazioni. In questo lavoro di tesi viene proposto un approccio modellistico stocastico basato sull’utilizzo di un compilatore naive Bayes operante in ambiente fuzzy. L’utilizzo congiunto di logica fuzzy e approccio naive Bayes è utile al processa mento del livello di complessità e conseguentemente incertezza insito negli ecosistemi. I modelli generativi ottenuti, chiamati Fuzzy Bayesian Ecological Model(FBEM) appaiono in grado di modellizare gli stati eco sistemici in funzione dell’ elevato numero di interazioni che entrano in gioco nella determinazione degli stati degli ecosistemi. Modelli FBEM sono stati utilizzati per comprendere il rischio ambientale per habitat intertidale di spiagge sabbiose in caso di eventi di flooding costiero previsti nell’arco di tempo 2010-2100. L’applicazione è stata effettuata all’interno del progetto EU “Theseus” per il quale i modelli FBEM sono stati utilizzati anche per una simulazione a lungo termine e per il calcolo dei tipping point specifici dell’habitat secondo eventi di flooding di diversa intensità.