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.

Central autonomic control in spontaneously hypertensive rats: a study on phasic phenomena during rapid-eye-movement sleep

The cardiovascular regulation undergoes wide changes in the different states of sleepwake cycle. In particular, the relationship between spontaneous fluctuations in heart period and arterial pressure clearly shows differences between the two sleep states. In non rapid-eye-movement sleep, heart rhythm is under prevalent baroreflex control, whereas in rapid-eye-movement sleep central autonomic commands prevail (Zoccoli et al., 2001). Moreover, during rapid-eye-movement sleep the cardiovascular variables show wide fluctuations around their mean value. In particular, during rapid-eyemovement sleep, the arterial pressure shows phasic hypertensive events which are superimposed upon the tonic level of arterial pressure. These phasic increases in arterial pressure are accompanied by an increase in heart rate (Sei & Morita, 1996; Silvani et al., 2005). Thus, rapid-eye-movement sleep may represent an “autonomic stress test” for the cardiovascular system, able to unmask pathological patterns of cardiovascular regulation (Verrier et al. 2005), but this hypothesis has never been tested experimentally. The aim of this study was to investigate whether rapid-eye-movement sleep may reveal derangements in central autonomic cardiovascular control in an experimental model of essential hypertension. The study was performed in Spontaneously Hypertensive Rats, which represent the most widely used model of essential hypertension, and allow full control of genetic and environmental confounding factors. In particular, we analyzed the cardiovascular, electroencephalogram, and electromyogram changes associated with phasic hypertensive events during rapid-eyemovement sleep in Spontaneously Hypertensive Rats and in their genetic Wistar Kyoto control strain. Moreover, we studied also a group of Spontaneously Hypertensive Rats made phenotypically normotensive by means of a chronic treatment with an angiotensin converting enzyme inhibitor, the Enalapril maleate, from the age of four weeks to the end of the experiment. All rats were implanted with electrodes for electroencephalographic and electromyographic recordings and with an arterial catheter for arterial pressure measurement. After six days for postoperative recovery, the rats were studied for five days, at an age of ten weeks.The study indicated that the peak of mean arterial pressure increase during the phasic hypertensive events in rapid-eye-movement sleep did not differ significantly between Spontaneously Hypertensive Rats and Wistar Kyoto rats, while on the other hand Spontaneously Hypertensive Rats showed a reduced increase in the frequency of theta rhythm and a reduced tachicardia with respect to Wistar Kyoto rats. The same pattern of changes in mean arterial pressure, heart period, and theta frequency was observed between Spontaneously Hypertensive Rats and Spontaneously Hypertensive Rats treated with Enalapril maleate. Spontaneously Hypertensive Rats do not differ from Wistar Kyoto rats only in terms of arterial hypertension, but also due to multiple unknown genetic differences. Spontaneously Hypertensive Rats were developed by selective breeding of Wistar Kyoto rats based only on the level of arterial pressure. However, in this process, multiple genes possibly unrelated to hypertension may have been selected together with the genetic determinants of hypertension (Carley et al., 2000). This study indicated that Spontaneously Hypertensive Rats differ from Wistar Kyoto rats, but not from Spontaneously Hypertensive Rats treated with Enalapril maleate, in terms of arterial pH and theta frequency. This feature may be due to genetic determinants unrelated to hypertension. In sharp contrast, the persistence of differences in the peak of heart period decrease and the peak of theta frequency increase during phasic hypertensive events between Spontaneously Hypertensive Rats and Spontaneously Hypertensive Rats treated with Enalapril maleate demonstrates that the observed reduction in central autonomic control of the cardiovascular system in Spontaneously Hypertensive Rats is not an irreversible consequence of inherited genetic determinants. Rather, the comparison between Spontaneously Hypertensive Rats and Spontaneously Hypertensive Rats treated with Enalapril maleate indicates that the observed differences in central autonomic control are the result of the hypertension per se. This work supports the view that the study of cardiovascular regulation in sleep provides fundamental insight on the pathophysiology of hypertension, and may thus contribute to the understanding of this disease, which is a major health problem in European countries (Wolf-Maier et al., 2003) with its burden of cardiac, vascular, and renal complications.

Development of human visual system analysis for the implementation of a new instrument for flicker measurement

Flicker is a power quality phenomenon that applies to cycle instability of light intensity resulting from supply voltage fluctuation, which, in turn can be caused by disturbances introduced during power generation, transmission or distribution. The standard EN 61000-4-15 which has been recently adopted also by the IEEE as IEEE Standard 1453 relies on the analysis of the supply voltage which is processed according to a suitable model of the lamp – human eye – brain chain. As for the lamp, an incandescent 60 W, 230 V, 50 Hz source is assumed. As far as the human eye – brain model is concerned, it is represented by the so-called flicker curve. Such a curve was determined several years ago by statistically analyzing the results of tests where people were subjected to flicker with different combinations of magnitude and frequency. The limitations of this standard approach to flicker evaluation are essentially two. First, the provided index of annoyance Pst can be related to an actual tiredness of the human visual system only if such an incandescent lamp is used. Moreover, the implemented response to flicker is “subjective” given that it relies on the people answers about their feelings. In the last 15 years, many scientific contributions have tackled these issues by investigating the possibility to develop a novel model of the eye-brain response to flicker and overcome the strict dependence of the standard on the kind of the light source. In this light of fact, this thesis is aimed at presenting an important contribution for a new Flickermeter. An improved visual system model using a physiological parameter that is the mean value of the pupil diameter, has been presented, thus allowing to get a more “objective” representation of the response to flicker. The system used to both generate flicker and measure the pupil diameter has been illustrated along with all the results of several experiments performed on the volunteers. The intent has been to demonstrate that the measurement of that geometrical parameter can give reliable information about the feeling of the human visual system to light flicker.

Effect of estrogen suppression on lung function in pulmonary Lymphangioleiomyomatosis

Background: Lymphangioleiomyomatosis (LAM), a rare progressive disease, is characterized by the proliferation of abnormal smooth muscle cells (LAM cells) in the lung, which leads to cystic parenchymal destruction and progressive respiratory failure. Estrogen receptors are present in LAM cells. LAM affects almost exclusively women of childbearing age. These findings, along with reports of disease progression during pregnancy or treatment with exogenous estrogens, have led to the assumption that hormonal factors play an important role in the pathogenesis of LAM. So, various therapies aim at preventing estrogen receptors (ER) by lowering circulating estrogen levels, by trying to block ER activity, or by attempting to lower ER expression in LAM. Prior experience have yielded conflicting results. Objective: The goal of this study was to evaluate, retrospectively, the effect of estrogen suppression in 21 patients with LAM. Design: We evaluated hormonal assays, pulmonary function tests and gas-exchange at baseline and after 12, 24 and 36 months after initiating hormonal manipulation. Results: The mean yearly rates of decline in FEV1 and DLCO are lower than those observed in prior studies and just DLCO decline was statistically significant. We also found an improvement of mean value of FVC and PaO2. Conclusions: Estrogen suppression appears to prevent decline in lung function in LAM.

Sviluppo di metodologie per la Stima in Tempo Reale delle Grandezze Indicate in Motori a Combustione Interna

Modern Internal Combustion Engines are becoming increasingly complex in terms of their control systems and strategies. The growth of the algorithms’ complexity results in a rise of the number of on-board quantities for control purposes. In order to improve combustion efficiency and, simultaneously, limit the amount of pollutant emissions, the on-board evaluation of two quantities in particular has become essential; namely indicated torque produced by the engine and the angular position where 50% of fuel mass injected over an engine cycle is burned (MFB50). The above mentioned quantities can be evaluated through the measurement of in-cylinder pressure. Nonetheless, at the time being, the installation of in-cylinder pressure sensors on vehicles is extremely uncommon mainly because of measurement reliability and costs. This work illustrates a methodological approach for the estimation of indicated torque and MFB50 that is based on the engine speed fluctuation measurement. This methodology is compatible with the typical on-board application restraints. Moreover, it requires no additional costs since speed can be measured using the system already mounted on the vehicle, which is made of a magnetic pick-up faced to a toothed wheel. The estimation algorithm consists of two main parts: first, the evaluation of indicated torque fluctuation based on speed measurement and secondly, the evaluation of the mean value of the indicated torque (over an engine cycle) and MFB50 by using the relationship with the indicated torque harmonic and other engine quantities. The procedure has been successfully applied to an L4 turbocharged Diesel engine mounted on-board a vehicle.

Ruolo del test da sforzo cardiopolmonare nei pazienti affetti da cardiomiopatia ipertrofica in età pediatrica

Background Decreased exercise capacity, and reduction in peak oxygen uptake are present in most patients affected by hypertrophic cardiomyopathy (HCM) . In addition an abnormal blood pressure response during a maximal exercise test was seen to be associated with high risk for sudden cardiac death in adult patients affected by HCM. Therefore exercise test (CPET) has become an important part of the evaluation of the HCM patients, but data on its role in patients with HCM in the pediatric age are quite limited. Methods and results Between 2004 and 2010, using CPET and echocardiography, we studied 68 children (mean age 13.9 ± 2 years) with HCM. The exercise test was completed by all the patients without adverse complications. The mean value of achieved VO2 max was 31.4 ± 8.3 mL/Kg/min which corresponded to 77.5 ± 16.9 % of predicted range. 51 patients (75%) reached a subnormal value of VO2max. On univariate analysis the achieved VO2 as percentage of predicted and the peak exercise systolic blood pressure (BP) Z score were inversely associated with max left ventricle (LV) wall thickness, with E/Ea ratio, and directly related with Ea and Sa wave velocities No association was found with the LV outflow tract gradient. During a mean follow up of 2.16 ± 1.7 years 9 patients reached the defined clinical end point of death, transplantation, implanted cardioverter defibrillator (ICD) shock, ICD implantation for secondary prevention or myectomy. Patients with peak VO2 < 52% or with peak systolic BP Z score < -5.8 had lower event free survival at follow up. Conclusions Exercise capacity is decreased in patients with HCM in pediatric age and global ventricular function seems being the most important determinant of exercise capacity in these patients. CPET seems to play an important role in prognostic stratification of children affected by HCM.

Inferences on earthquake kinematic properties from data inversion: two different approaches

During my PhD, starting from the original formulations proposed by Bertrand et al., 2000 and Emolo & Zollo 2005, I developed inversion methods and applied then at different earthquakes. In particular large efforts have been devoted to the study of the model resolution and to the estimation of the model parameter errors. To study the source kinematic characteristics of the Christchurch earthquake we performed a joint inversion of strong-motion, GPS and InSAR data using a non-linear inversion method. Considering the complexity highlighted by superficial deformation data, we adopted a fault model consisting of two partially overlapping segments, with dimensions 15x11 and 7x7 km2, having different faulting styles. This two-fault model allows to better reconstruct the complex shape of the superficial deformation data. The total seismic moment resulting from the joint inversion is 3.0x1025 dyne.cm (Mw = 6.2) with an average rupture velocity of 2.0 km/s. Errors associated with the kinematic model have been estimated of around 20-30 %. The 2009 Aquila sequence was characterized by an intense aftershocks sequence that lasted several months. In this study we applied an inversion method that assumes as data the apparent Source Time Functions (aSTFs), to a Mw 4.0 aftershock of the Aquila sequence. The estimation of aSTFs was obtained using the deconvolution method proposed by Vallée et al., 2004. The inversion results show a heterogeneous slip distribution, characterized by two main slip patches located NW of the hypocenter, and a variable rupture velocity distribution (mean value of 2.5 km/s), showing a rupture front acceleration in between the two high slip zones. Errors of about 20% characterize the final estimated parameters.

Environmental influence on the phenotype: Morphological variation in human dentition

This work is about the role that environment plays in the production of evolutionary significant variations. It starts with an historical introduction about the concept of variation and the role of environment in its production. Then, I show how a lack of attention to these topics may lead to serious mistakes in data interpretation. A statistical re-analysis of published data on the effects of malnutrition on dental eruption, shows that what has been interpreted as an increase in the mean value, is actually linked to increase of variability. In Chapter 3 I present the topic of development as a link between variability and environmental influence, giving a review of the possible mechanisms by which development influences evolutionary dynamics. Chapter 4 is the core chapter of the thesis; I investigated the role of environment in the development of dental morphology. I used dental hypoplasia as a marker of stress, characterizing two groups. Comparing the morphology of upper molars in the two groups, three major results came out: (i) there is a significant effect of environmental stressors on the overall morphology of upper molars; (ii) the developmental response increases morphological variability of the stressed population; (iii) increase of variability is directional: stressed individuals have increased cusps dimensions and number. I also hypothesized the molecular mechanisms that could be responsible of the observed effects. In Chapter 5, I present future perspectives for developing this research. The direction of dental development response is the same direction of the trend in mammalian dental evolution. Since malnutrition triggers the developmental response, and this particular kind of stressor must have been very common in our class evolutionary history, I propose the possibility that environmental stress actively influenced mammals evolution. Moreover, I discuss the possibility of reconsidering the role of natural selection in the evolution of dental morphology.

Circadian rhythms, sleep and autonomic function in progressive supranuclear palsy: characteristic features and reciprocal interactions

Background: Progressive supranuclear palsy (PSP) is a rare neurodegenerative condition. The aims of this study were to evaluate the association between sleep, the circadian system and autonomic function in a cohort of PSP patients. Methods: Patients with PSP diagnosed according to consensus criteria were recruited prospectively and retrospectively and performed the following tests: body core temperature (BcT), sleep-wake cycle, systolic and diastolic blood pressure (SBP, DBP) continuous monitoring for 48 h under controlled environmental conditions; cardiovascular reflex tests (CRTs). The analysis of circadian rhythmicity was performed with the single cosinor method. For state-dependent analysis, the mean value of variables in each sleep stage was calculated as well as the difference to the value in wake. Results: PSP patients presented a reduced total duration of night sleep, with frequent and prolonged awakenings. During daytime, patients had very short naps, suggesting a state of profound sleep deprivation across the 24-h. REM sleep behaviour disorder was found in 15%, restless legs syndrome in 46%, periodic limb movements in 52% and obstructive sleep apnea in 54%. BcT presented the expected fall during night-time, however, compared to controls, mean values during day and night were higher. However BcT state-dependent modulation was maintained. Increased BcT could be attributed to an inability to properly reduce sympathetic activity favoured by the sleep deprivation. At CRTs, PSP presented mild cardiovascular adrenergic impairment and preserved cardiovagal function. 14% had non-neurogenic orthostatic hypotension. Only 2 PSP presented the expected BP dipping pattern, possibly as a consequence of sleep disruption. State-dependent analysis showed a partial loss of the state-dependent modulation for SBP. Discussion: This study showed that PSP presented abnormalities of sleep, circadian rhythms and cardiovascular autonomic function that are likely to be closely linked one to another.

Analyzing the dependence structure of microarray data: a copula–based approach

The main aim of this Ph.D. dissertation is the study of clustering dependent data by means of copula functions with particular emphasis on microarray data. Copula functions are a popular multivariate modeling tool in each field where the multivariate dependence is of great interest and their use in clustering has not been still investigated. The first part of this work contains the review of the literature of clustering methods, copula functions and microarray experiments. The attention focuses on the K–means (Hartigan, 1975; Hartigan and Wong, 1979), the hierarchical (Everitt, 1974) and the model–based (Fraley and Raftery, 1998, 1999, 2000, 2007) clustering techniques because their performance is compared. Then, the probabilistic interpretation of the Sklar’s theorem (Sklar’s, 1959), the estimation methods for copulas like the Inference for Margins (Joe and Xu, 1996) and the Archimedean and Elliptical copula families are presented. In the end, applications of clustering methods and copulas to the genetic and microarray experiments are highlighted. The second part contains the original contribution proposed. A simulation study is performed in order to evaluate the performance of the K–means and the hierarchical bottom–up clustering methods in identifying clusters according to the dependence structure of the data generating process. Different simulations are performed by varying different conditions (e.g., the kind of margins (distinct, overlapping and nested) and the value of the dependence parameter ) and the results are evaluated by means of different measures of performance. In light of the simulation results and of the limits of the two investigated clustering methods, a new clustering algorithm based on copula functions (‘CoClust’ in brief) is proposed. The basic idea, the iterative procedure of the CoClust and the description of the written R functions with their output are given. The CoClust algorithm is tested on simulated data (by varying the number of clusters, the copula models, the dependence parameter value and the degree of overlap of margins) and is compared with the performance of model–based clustering by using different measures of performance, like the percentage of well–identified number of clusters and the not rejection percentage of H0 on . It is shown that the CoClust algorithm allows to overcome all observed limits of the other investigated clustering techniques and is able to identify clusters according to the dependence structure of the data independently of the degree of overlap of margins and the strength of the dependence. The CoClust uses a criterion based on the maximized log–likelihood function of the copula and can virtually account for any possible dependence relationship between observations. Many peculiar characteristics are shown for the CoClust, e.g. its capability of identifying the true number of clusters and the fact that it does not require a starting classification. Finally, the CoClust algorithm is applied to the real microarray data of Hedenfalk et al. (2001) both to the gene expressions observed in three different cancer samples and to the columns (tumor samples) of the whole data matrix.

Improved ground motion intensity measures for reliability-based demand analysis of structures

In Performance-Based Earthquake Engineering (PBEE), evaluating the seismic performance (or seismic risk) of a structure at a designed site has gained major attention, especially in the past decade. One of the objectives in PBEE is to quantify the seismic reliability of a structure (due to the future random earthquakes) at a site. For that purpose, Probabilistic Seismic Demand Analysis (PSDA) is utilized as a tool to estimate the Mean Annual Frequency (MAF) of exceeding a specified value of a structural Engineering Demand Parameter (EDP). This dissertation focuses mainly on applying an average of a certain number of spectral acceleration ordinates in a certain interval of periods, Sa,avg (T1,…,Tn), as scalar ground motion Intensity Measure (IM) when assessing the seismic performance of inelastic structures. Since the interval of periods where computing Sa,avg is related to the more or less influence of higher vibration modes on the inelastic response, it is appropriate to speak about improved IMs. The results using these improved IMs are compared with a conventional elastic-based scalar IMs (e.g., pseudo spectral acceleration, Sa ( T(¹)), or peak ground acceleration, PGA) and the advanced inelastic-based scalar IM (i.e., inelastic spectral displacement, Sdi). The advantages of applying improved IMs are: (i ) "computability" of the seismic hazard according to traditional Probabilistic Seismic Hazard Analysis (PSHA), because ground motion prediction models are already available for Sa (Ti), and hence it is possibile to employ existing models to assess hazard in terms of Sa,avg, and (ii ) "efficiency" or smaller variability of structural response, which was minimized to assess the optimal range to compute Sa,avg. More work is needed to assess also "sufficiency" and "scaling robustness" desirable properties, which are disregarded in this dissertation. However, for ordinary records (i.e., with no pulse like effects), using the improved IMs is found to be more accurate than using the elastic- and inelastic-based IMs. For structural demands that are dominated by the first mode of vibration, using Sa,avg can be negligible relative to the conventionally-used Sa (T(¹)) and the advanced Sdi. For structural demands with sign.cant higher-mode contribution, an improved scalar IM that incorporates higher modes needs to be utilized. In order to fully understand the influence of the IM on the seismis risk, a simplified closed-form expression for the probability of exceeding a limit state capacity was chosen as a reliability measure under seismic excitations and implemented for Reinforced Concrete (RC) frame structures. This closed-form expression is partuclarly useful for seismic assessment and design of structures, taking into account the uncertainty in the generic variables, structural "demand" and "capacity" as well as the uncertainty in seismic excitations. The assumed framework employs nonlinear Incremental Dynamic Analysis (IDA) procedures in order to estimate variability in the response of the structure (demand) to seismic excitations, conditioned to IM. The estimation of the seismic risk using the simplified closed-form expression is affected by IM, because the final seismic risk is not constant, but with the same order of magnitude. Possible reasons concern the non-linear model assumed, or the insufficiency of the selected IM. Since it is impossibile to state what is the "real" probability of exceeding a limit state looking the total risk, the only way is represented by the optimization of the desirable properties of an IM.