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.

The uncertainty in standardised sound power measurements: complying with ISO 17025

In the context of “testing laboratory” one of the most important aspect to deal with is the measurement result. Whenever decisions are based on measurement results, it is important to have some indication of the quality of the results. In every area concerning with noise measurement many standards are available but without an expression of uncertainty, it is impossible to judge whether two results are in compliance or not. ISO/IEC 17025 is an international standard related with the competence of calibration and testing laboratories. It contains the requirements that testing and calibration laboratories have to meet if they wish to demonstrate that they operate to a quality system, are technically competent and are able to generate technically valid results. ISO/IEC 17025 deals specifically with the requirements for the competence of laboratories performing testing and calibration and for the reporting of the results, which may or may not contain opinions and interpretations of the results. The standard requires appropriate methods of analysis to be used for estimating uncertainty of measurement. In this point of view, for a testing laboratory performing sound power measurement according to specific ISO standards and European Directives, the measurement of uncertainties is the most important factor to deal with. Sound power level measurement, according to ISO 3744:1994 , performed with a limited number of microphones distributed over a surface enveloping a source is affected by a certain systematic error and a related standard deviation. Making a comparison of measurement carried out with different microphone arrays is difficult because results are affected by systematic errors and standard deviation that are peculiarities of the number of microphones disposed on the surface, their spatial position and the complexity of the sound field. A statistical approach could give an overview of the difference between sound power level evaluated with different microphone arrays and an evaluation of errors that afflict this kind of measurement. Despite the classical approach that tend to follow the ISO GUM this thesis present a different point of view of the problem related to the comparison of result obtained from different microphone arrays.

Internal Model Principle: extension to the switching case and applications

This thesis deals with a novel control approach based on the extension of the well-known Internal Model Principle to the case of periodic switched linear exosystems. This extension, inspired by power electronics applications, aims to provide an effective design method to robustly achieve the asymptotic tracking of periodic references with an infinite number of harmonics. In the first part of the thesis the basic components of the novel control scheme are described and preliminary results on stabilization are provided. In the second part, advanced control methods for two applications coming from the world high energy physics are presented.

Le politiche giudiziarie inglesi degli anni 2000: mutamento di paradigma e rafforzamento dell'incisività politica dei giudici

The Ph.D. dissertation analyses the reasons for which political actors (governments, legislatures and political parties) decide consciously to give away a source of power by increasing the political significance of the courts. It focuses on a single case of particular significance: the passage of the Constitutional Reform Act 2005 in the United Kingdom. This Act has deeply changed the governance and the organization of the English judicial system, has provided a much clearer separation of powers and a stronger independence of the judiciary from the executive and the legislative. What’s more, this strengthening of the judicial independence has been decided in a period in which the political role of the English judges was evidently increasing. I argue that the reform can be interpreted as a «paradigm shift» (Hall 1993), that has changed the way in which the judicial power is considered. The most diffused conceptions in the sub-system of the English judicial policies are shifted, and a new paradigm has become dominant. The new paradigm includes: (i) stronger separation of powers, (ii) collective (as well as individual) conception of the independence of the judiciary, (iii) reduction of the political accountability of the judges, (iv) formalization of the guarantees of judicial independence, (v) principle-driven (instead of pragmatic) approach to the reforms, and (vi) transformation of a non-codified constitution in a codified one. Judicialization through political decisions represent an important, but not fully explored, field of research. The literature, in particular, has focused on factors unable to explain the English case: the competitiveness of the party system (Ramseyer 1994), the political uncertainty at the time of constitutional design (Ginsburg 2003), the cultural divisions within the polity (Hirschl 2004), federal institutions and division of powers (Shapiro 2002). All these contributes link the decision to enhance the political relevance of the judges to some kind of diffusion of political power. In the contemporary England, characterized by a relative high concentration of power in the government, the reasons for such a reform should be located elsewhere. I argue that the Constitutional Reform Act 2005 can be interpreted as a result of three different kinds of reasons: (i) the social and demographical transformations of the English judiciary, which have made inefficient most of the precedent mechanism of governance, (ii) the role played by the judges in the policy process and (iii) the cognitive and normative influences originated from the European context, as a consequence of the membership of the United Kingdom to the European Union and the Council of Europe. My thesis is that only a full analysis of all these three aspects can explain the decision to reform the judicial system and the content of the Constitutional Reform Act 2005. Only the cultural influences come from the European legal complex, above all, can explain the paradigm shift previously described.

Analysis and developments of uncertainty processors for real time flood forecasting

The hydrologic risk (and the hydro-geologic one, closely related to it) is, and has always been, a very relevant issue, due to the severe consequences that may be provoked by a flooding or by waters in general in terms of human and economic losses. Floods are natural phenomena, often catastrophic, and cannot be avoided, but their damages can be reduced if they are predicted sufficiently in advance. For this reason, the flood forecasting plays an essential role in the hydro-geological and hydrological risk prevention. Thanks to the development of sophisticated meteorological, hydrologic and hydraulic models, in recent decades the flood forecasting has made a significant progress, nonetheless, models are imperfect, which means that we are still left with a residual uncertainty on what will actually happen. In this thesis, this type of uncertainty is what will be discussed and analyzed. In operational problems, it is possible to affirm that the ultimate aim of forecasting systems is not to reproduce the river behavior, but this is only a means through which reducing the uncertainty associated to what will happen as a consequence of a precipitation event. In other words, the main objective is to assess whether or not preventive interventions should be adopted and which operational strategy may represent the best option. The main problem for a decision maker is to interpret model results and translate them into an effective intervention strategy. To make this possible, it is necessary to clearly define what is meant by uncertainty, since in the literature confusion is often made on this issue. Therefore, the first objective of this thesis is to clarify this concept, starting with a key question: should be the choice of the intervention strategy to adopt based on the evaluation of the model prediction based on its ability to represent the reality or on the evaluation of what actually will happen on the basis of the information given by the model forecast? Once the previous idea is made unambiguous, the other main concern of this work is to develope a tool that can provide an effective decision support, making possible doing objective and realistic risk evaluations. In particular, such tool should be able to provide an uncertainty assessment as accurate as possible. This means primarily three things: it must be able to correctly combine all the available deterministic forecasts, it must assess the probability distribution of the predicted quantity and it must quantify the flooding probability. Furthermore, given that the time to implement prevention strategies is often limited, the flooding probability will have to be linked to the time of occurrence. For this reason, it is necessary to quantify the flooding probability within a horizon time related to that required to implement the intervention strategy and it is also necessary to assess the probability of the flooding time.

Il principio di precauzione in diritto penale

Oggetto della ricerca è la rilevanza nell’ambito del diritto penale del principio di precauzione. Quest’ultimo deve la sua diffusione e popolarità al fatto di presentarsi come criterio guida al problema del rischio e dell’incertezza. L’esigenza di adottare scelte normative in condizioni di incertezza scientifica è infatti oggi ineludibile. Si cercherà in primo luogo di circoscrivere l’oggetto dell’indagine analizzando il rilievo che il principio di precauzione ha a livello legislativo e giurisprudenziale. Quindi si analizzeranno le problematiche che il ricorso allo stesso suscita con riferimento alla struttura classica del reato e legate al contesto di incertezza nel quale viene invocato. Tali problematiche si riferiscono alla possibilità o meno di dare rilevanza al modello del reato di pericolo, alla ricostruzione del nesso causale e all’influenza che il principio di precauzione può determinare nell’accertamento dell’elemento soggettivo delle colpa. Si concluderà l’analisi analizzando le diverse posizioni assunte dalla dottrina italiana circa l’opportunità o meno dell’intervento penale in contesti di incertezza scientifica, individuando, in caso di risposta affermativa, le modalità di intervento.

Bayesian space-time data fusion for real-time forecasting and map uncertainty

Environmental computer models are deterministic models devoted to predict several environmental phenomena such as air pollution or meteorological events. Numerical model output is given in terms of averages over grid cells, usually at high spatial and temporal resolution. However, these outputs are often biased with unknown calibration and not equipped with any information about the associated uncertainty. Conversely, data collected at monitoring stations is more accurate since they essentially provide the true levels. Due the leading role played by numerical models, it now important to compare model output with observations. Statistical methods developed to combine numerical model output and station data are usually referred to as data fusion. In this work, we first combine ozone monitoring data with ozone predictions from the Eta-CMAQ air quality model in order to forecast real-time current 8-hour average ozone level defined as the average of the previous four hours, current hour, and predictions for the next three hours. We propose a Bayesian downscaler model based on first differences with a flexible coefficient structure and an efficient computational strategy to fit model parameters. Model validation for the eastern United States shows consequential improvement of our fully inferential approach compared with the current real-time forecasting system. Furthermore, we consider the introduction of temperature data from a weather forecast model into the downscaler, showing improved real-time ozone predictions. Finally, we introduce a hierarchical model to obtain spatially varying uncertainty associated with numerical model output. We show how we can learn about such uncertainty through suitable stochastic data fusion modeling using some external validation data. We illustrate our Bayesian model by providing the uncertainty map associated with a temperature output over the northeastern United States.

Networks, Uncertainty, Applications and a Crusade for Optimality

In this thesis we address a collection of Network Design problems which are strongly motivated by applications from Telecommunications, Logistics and Bioinformatics. In most cases we justify the need of taking into account uncertainty in some of the problem parameters, and different Robust optimization models are used to hedge against it. Mixed integer linear programming formulations along with sophisticated algorithmic frameworks are designed, implemented and rigorously assessed for the majority of the studied problems. The obtained results yield the following observations: (i) relevant real problems can be effectively represented as (discrete) optimization problems within the framework of network design; (ii) uncertainty can be appropriately incorporated into the decision process if a suitable robust optimization model is considered; (iii) optimal, or nearly optimal, solutions can be obtained for large instances if a tailored algorithm, that exploits the structure of the problem, is designed; (iv) a systematic and rigorous experimental analysis allows to understand both, the characteristics of the obtained (robust) solutions and the behavior of the proposed algorithm.