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.

Hybrid constraint programming and metaheuristic methods for large scale optimization problems

This work presents hybrid Constraint Programming (CP) and metaheuristic methods for the solution of Large Scale Optimization Problems; it aims at integrating concepts and mechanisms from the metaheuristic methods to a CP-based tree search environment in order to exploit the advantages of both approaches. The modeling and solution of large scale combinatorial optimization problem is a topic which has arisen the interest of many researcherers in the Operations Research field; combinatorial optimization problems are widely spread in everyday life and the need of solving difficult problems is more and more urgent. Metaheuristic techniques have been developed in the last decades to effectively handle the approximate solution of combinatorial optimization problems; we will examine metaheuristics in detail, focusing on the common aspects of different techniques. Each metaheuristic approach possesses its own peculiarities in designing and guiding the solution process; our work aims at recognizing components which can be extracted from metaheuristic methods and re-used in different contexts. In particular we focus on the possibility of porting metaheuristic elements to constraint programming based environments, as constraint programming is able to deal with feasibility issues of optimization problems in a very effective manner. Moreover, CP offers a general paradigm which allows to easily model any type of problem and solve it with a problem-independent framework, differently from local search and metaheuristic methods which are highly problem specific. In this work we describe the implementation of the Local Branching framework, originally developed for Mixed Integer Programming, in a CP-based environment. Constraint programming specific features are used to ease the search process, still mantaining an absolute generality of the approach. We also propose a search strategy called Sliced Neighborhood Search, SNS, that iteratively explores slices of large neighborhoods of an incumbent solution by performing CP-based tree search and encloses concepts from metaheuristic techniques. SNS can be used as a stand alone search strategy, but it can alternatively be embedded in existing strategies as intensification and diversification mechanism. In particular we show its integration within the CP-based local branching. We provide an extensive experimental evaluation of the proposed approaches on instances of the Asymmetric Traveling Salesman Problem and of the Asymmetric Traveling Salesman Problem with Time Windows. The proposed approaches achieve good results on practical size problem, thus demonstrating the benefit of integrating metaheuristic concepts in CP-based frameworks.

Characterization of fold-related fractures in the carbonate rocks of the Cingoli anticline, northern Apennines, Italy

Thrust fault-related folds in carbonate rocks are characterized by deformation accommodated by different structures, such as joints, faults, pressure solution seams, and deformation bands. Defining the development of fracture systems related to the folding process is significant both for theoretical and practical purposes. Fracture systems are useful constrains in order to understand the kinematical evolution of the fold. Furthermore, understanding the relationships between folding and fracturing provides a noteworthy contribution for reconstructing the geodynamic and the structural evolution of the studied area. Moreover, as fold-related fractures influence fluid flow through rocks, fracture systems are relevant for energy production (geothermal studies, methane and CO2 , storage and hydrocarbon exploration), environmental and social issues (pollutant distribution, aquifer characterization). The PhD project shows results of a study carried out in a multilayer carbonate anticline characterized by different mechanical properties. The aim of this study is to understand the factors which influence the fracture formation and to define their temporal sequence during the folding process. The studied are is located in the Cingoli anticline (Northern Apennines), which is characterized by a pelagic multilayer characterized by sequences with different mechanical stratigraphies. A multi-scale analysis has been made in several outcrops located in different structural positions. This project shows that the conceptual sketches proposed in literature and the strain distribution models outline well the geometrical orientation of most of the set of fractures observed in the Cingoli anticline. On the other hand, the present work suggests the relevance of the mechanical stratigraphy in particular controlling the type of fractures formed (e.g. pressure solution seams, joints or shear fractures) and their subsequent evolution. Through a multi-scale analysis, and on the basis of the temporal relationship between fracture sets and their orientation respect layering, I also suggest a conceptual model for fracture systems formation.

Interpreting Judgements using Knowledge Representation Methods and Computational Models of Argument

The goal of the present research is to define a Semantic Web framework for precedent modelling, by using knowledge extracted from text, metadata, and rules, while maintaining a strong text-to-knowledge morphism between legal text and legal concepts, in order to fill the gap between legal document and its semantics. The framework is composed of four different models that make use of standard languages from the Semantic Web stack of technologies: a document metadata structure, modelling the main parts of a judgement, and creating a bridge between a text and its semantic annotations of legal concepts; a legal core ontology, modelling abstract legal concepts and institutions contained in a rule of law; a legal domain ontology, modelling the main legal concepts in a specific domain concerned by case-law; an argumentation system, modelling the structure of argumentation. The input to the framework includes metadata associated with judicial concepts, and an ontology library representing the structure of case-law. The research relies on the previous efforts of the community in the field of legal knowledge representation and rule interchange for applications in the legal domain, in order to apply the theory to a set of real legal documents, stressing the OWL axioms definitions as much as possible in order to enable them to provide a semantically powerful representation of the legal document and a solid ground for an argumentation system using a defeasible subset of predicate logics. It appears that some new features of OWL2 unlock useful reasoning features for legal knowledge, especially if combined with defeasible rules and argumentation schemes. The main task is thus to formalize legal concepts and argumentation patterns contained in a judgement, with the following requirement: to check, validate and reuse the discourse of a judge - and the argumentation he produces - as expressed by the judicial text.

Il trattamento delle fratture e lussazioni vertebrali nei piccoli animali

Treatment of spinal fracture and luxation in small animals Traumatic spinal injuries usually result from a mechanic trauma. Spinal facture and luxations generally occur in the junction between and more mobile parts of the spinal column: close to the skull, thorax and pelvis. Fractures may occur alone or in combination with luxation as fracture/luxation. When the fractures are not stable the best solution is the surgical fixation. Internal and external fixation are the surgical methods for the treatment of vertebral fractures and luxations. The authors report the treatment of 12 cases of thoracic and lumbar vertebral fractures and luxations in small animals using the screws/pins and Polymethylmethacrylate technique. The analysis of results is a contribute I the valutation of surgical technique and complications in the post-surgical period.

Se il lavoro è l’unica risposta. Studio comparato sulle pratiche di accompagnamento al lavoro di fasce svantaggiate nelle città di Bologna e Valencia

Scopo del presente lavoro di ricerca è quello di comparare due contesti metropolitani, valenciano e bolognese, sulle pratiche di accompagnamento al lavoro rivolte a fasce svantaggiate, in particolare persone con problemi di dipendenza da sostanze psicotrope. L’indagine propone un confronto su alcune tematiche trasversali (tipologia di azioni messe in campo, organizzazione territoriale e governance, profilo degli utenti, inserimento sociale, coinvolgimento del mondo produttivo) e pone in evidenza gli elementi che ci consentono di individuare e segnalare sia delle buone pratiche trasferibili sia delle linee progettuali, partendo dunque dal presupposto che capacitare una persona significa innanzitutto offrirle congrue opportunità di scelta, nel senso seniano e come spiegato dalla stessa Nussbaum, ma soprattutto accompagnarla e sostenerla nel percorso di inserimento lavorativo e, in parallelo, sociale. Il bisogno raccolto è quello di un sostegno, motivazionale e orientativo, che segua un approccio socio educativo capace di fornire, alla persona, una risposta integrata, di unicità, capace dunque di agire sull’autonomia, sull’autostima, sull’elaborazione delle proprie esperienze di vita e lavorative, nonché su elementi anche di contesto quali la casa, le reti amicali e familiari, spesso compromesse. L’elemento distintivo che consente di agire in questa direzione è il lavoro di collaborazione tra i diversi servizi e la co-progettazione del percorso con l’utente stesso. Il tema degli inserimenti lavorativi è un argomento molto complesso che chiama in causa diversi aspetti: i mutamenti sociali e le trasformazioni del lavoro; l’emergere di nuove fasce deboli e il rischio di aggravamento delle condizioni di esclusione per le fasce deboli “tradizionali”; l’importanza del lavoro per la costruzione di percorsi identitari e di riconoscimento; l’impatto delle politiche attive sulle fasce svantaggiate e i concetti di capitazione e attivazione; il ruolo del capitale sociale e l’emergere di nuovi welfare; la rete degli attori coinvolti dal processo di inserimento e il tema della governace territoriale.