A moment symbolic representation of Lévy processes with applications

By using a symbolic method, known in the literature as the classical umbral calculus, a symbolic representation of Lévy processes is given and a new family of time-space harmonic polynomials with respect to such processes, which includes and generalizes the exponential complete Bell polynomials, is introduced. The usefulness of time-space harmonic polynomials with respect to Lévy processes is that it is a martingale the stochastic process obtained by replacing the indeterminate x of the polynomials with a Lévy process, whereas the Lévy process does not necessarily have this property. Therefore to find such polynomials could be particularly meaningful for applications. This new family includes Hermite polynomials, time-space harmonic with respect to Brownian motion, Poisson-Charlier polynomials with respect to Poisson processes, Laguerre and actuarial polynomials with respect to Gamma processes , Meixner polynomials of the first kind with respect to Pascal processes, Euler, Bernoulli, Krawtchuk, and pseudo-Narumi polynomials with respect to suitable random walks. The role played by cumulants is stressed and brought to the light, either in the symbolic representation of Lévy processes and their infinite divisibility property, either in the generalization, via umbral Kailath-Segall formula, of the well-known formulae giving elementary symmetric polynomials in terms of power sum symmetric polynomials. The expression of the family of time-space harmonic polynomials here introduced has some connections with the so-called moment representation of various families of multivariate polynomials. Such moment representation has been studied here for the first time in connection with the time-space harmonic property with respect to suitable symbolic multivariate Lévy processes. In particular, multivariate Hermite polynomials and their properties have been studied in connection with a symbolic version of the multivariate Brownian motion, while multivariate Bernoulli and Euler polynomials are represented as powers of multivariate polynomials which are time-space harmonic with respect to suitable multivariate Lévy processes.

The spatial representation of time

Numerosi studi mostrano che gli intervalli temporali sono rappresentati attraverso un codice spaziale che si estende da sinistra verso destra, dove gli intervalli brevi sono rappresentati a sinistra rispetto a quelli lunghi. Inoltre tale disposizione spaziale del tempo può essere influenzata dalla manipolazione dell’attenzione-spaziale. La presente tesi si inserisce nel dibattito attuale sulla relazione tra rappresentazione spaziale del tempo e attenzione-spaziale attraverso l’uso di una tecnica che modula l’attenzione-spaziale, ovvero, l’Adattamento Prismatico (AP). La prima parte è dedicata ai meccanismi sottostanti tale relazione. Abbiamo mostrato che spostando l’attenzione-spaziale con AP, verso un lato dello spazio, si ottiene una distorsione della rappresentazione di intervalli temporali, in accordo con il lato dello spostamento attenzionale. Questo avviene sia con stimoli visivi, sia con stimoli uditivi, nonostante la modalità uditiva non sia direttamente coinvolta nella procedura visuo-motoria di AP. Questo risultato ci ha suggerito che il codice spaziale utilizzato per rappresentare il tempo, è un meccanismo centrale che viene influenzato ad alti livelli della cognizione spaziale. La tesi prosegue con l’indagine delle aree corticali che mediano l’interazione spazio-tempo, attraverso metodi neuropsicologici, neurofisiologici e di neuroimmagine. In particolare abbiamo evidenziato che, le aree localizzate nell’emisfero destro, sono cruciali per l’elaborazione del tempo, mentre le aree localizzate nell’emisfero sinistro sono cruciali ai fini della procedura di AP e affinché AP abbia effetto sugli intervalli temporali. Infine, la tesi, è dedicata allo studio dei disturbi della rappresentazione spaziale del tempo. I risultati ci indicano che un deficit di attenzione-spaziale, dopo danno emisferico destro, provoca un deficit di rappresentazione spaziale del tempo, che si riflette negativamente sulla vita quotidiana dei pazienti. Particolarmente interessanti sono i risultati ottenuti mediante AP. Un trattamento con AP, efficace nel ridurre il deficit di attenzione-spaziale, riduce anche il deficit di rappresentazione spaziale del tempo, migliorando la qualità di vita dei pazienti.

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.

Sparse Signal Representation of Ultrasonic Signals for Structural Health Monitoring Applications

Assessment of the integrity of structural components is of great importance for aerospace systems, land and marine transportation, civil infrastructures and other biological and mechanical applications. Guided waves (GWs) based inspections are an attractive mean for structural health monitoring. In this thesis, the study and development of techniques for GW ultrasound signal analysis and compression in the context of non-destructive testing of structures will be presented. In guided wave inspections, it is necessary to address the problem of the dispersion compensation. A signal processing approach based on frequency warping was adopted. Such operator maps the frequencies axis through a function derived by the group velocity of the test material and it is used to remove the dependence on the travelled distance from the acquired signals. Such processing strategy was fruitfully applied for impact location and damage localization tasks in composite and aluminum panels. It has been shown that, basing on this processing tool, low power embedded system for GW structural monitoring can be implemented. Finally, a new procedure based on Compressive Sensing has been developed and applied for data reduction. Such procedure has also a beneficial effect in enhancing the accuracy of structural defects localization. This algorithm uses the convolutive model of the propagation of ultrasonic guided waves which takes advantage of a sparse signal representation in the warped frequency domain. The recovery from the compressed samples is based on an alternating minimization procedure which achieves both an accurate reconstruction of the ultrasonic signal and a precise estimation of waves time of flight. Such information is used to feed hyperbolic or elliptic localization procedures, for accurate impact or damage localization.

Populism as a battlefield Populist actors and their representation on social and legacy media during the european parliament elections 2019 in Finland, Italy and the Netherlands

The objective of the present research is to describe and explain populist actors and populism as a concept and their representation on social and legacy media during the 2019 EU elections in Finland, Italy and The Netherlands. This research tackles the topic of European populism in the context of political communication and its relation to both the legacy and digital media within the hybrid media system. Departing from the consideration that populism and populist rhetoric are challenging concepts to define, I suggest that they should be addressed and analyzed through the usage of a combination of methods and theoretical perspectives, namely Communication Studies, Corpus Linguistics, Political theory, Rhetoric and Corpus-Assisted Discourse Studies. This thesis considers data of different provenance. On the one hand, for the Legacy media part, newspapers articles were collected in the three countries under study from the 1st until the 31st of May 2019. Each country’s legacy system is represented by three different quality papers and the articles were collected according to a selection of keywords (European Union Elections and Populism in each of the three languages). On the other hand, the Digital media data takes into consideration Twitter tweets collected during the same timeframe based on particular country-specific hashtags and tweets by identified populist actors. In order to meet the objective of this study, three research questions are posed and the analysis leading to the results are exhaustively presented and further discussed. The results of this research provide valuable and novel insights on how populism as a theme and a concept is being portrayed in the context of the European elections both in legacy and digital media and political communication in general.

Victorian letter writing and its representation in literature and painting: the case study of love letters

One of the main features of nineteenth-century fiction is the quasi-total disappearance of the epistolary novel that had had its heydays in the previous century. For this reason, some scholars have declared the “death” of the letter in literature after the transitional romantic period. However, Victorian novels overflow with letters that are embedded, quoted in part or described and commented on by narrators or characters. Even when its content is not revealed to the reader, the letter becomes a signifier loaded with meanings, also and particularly so, when it is burnt, torn, hidden, found or buried. The Postal Reform of 1839-40 caused the number of letters sent every year in Britain to grow from 75 to 410 million in only 14 years, and the mediatic campaign that supported it drew the attention of the population to the material aspects concerning this means of communication. Newspapers became more affordable too and they promoted a taste for sensationalism that often involved the “spectacularization” of private correspondence. Starting from an excursus on the history of the letter aimed at identifying the key aspects of the genre, this work deals with some real love correspondences from people belonging to different classes in the period from 1840 to the 1870s, to then analyse their fictional and pictorial counterparts. The general picture that emerges from this analysis is that of a Victorian society where letters were able to break down the boundaries between high and low forms of cultural expressions and where, more than ever, letters were present in people’s everyday lives as well as in the art and literature they enjoyed.

About stabilization of non-minimum phase systems by output feedback

This thesis work has been motivated by an internal benchmark dealing with the output regulation problem of a nonlinear non-minimum phase system in the case of full-state feedback. The system under consideration structurally suffers from finite escape time, and this condition makes the output regulation problem very hard even for very simple steady-state evolution or exosystem dynamics, such as a simple integrator. This situation leads to studying the approaches developed for controlling Non-minimum phase systems and how they affect feedback performances. Despite a lot of frequency domain results, only a few works have been proposed for describing the performance limitations in a state space system representation. In particular, in our opinion, the most relevant research thread exploits the so-called Inner-Outer Decomposition. Such decomposition allows splitting the Non-minimum phase system under consideration into a cascade of two subsystems: a minimum phase system (the outer) that contains all poles of the original system and an all-pass Non-minimum phase system (the inner) that contains all the unavoidable pathologies of the unstable zero dynamics. Such a cascade decomposition was inspiring to start working on functional observers for linear and nonlinear systems. In particular, the idea of a functional observer is to exploit only the measured signals from the system to asymptotically reconstruct a certain function of the system states, without necessarily reconstructing the whole state vector. The feature of asymptotically reconstructing a certain state functional plays an important role in the design of a feedback controller able to stabilize the Non-minimum phase system.

SPHERA, a new Italian convection-permitting regional reanalysis: improving heavy-rainfall representation and describing hail-prone environments

Extreme weather events related to deep convection are high-impact critical phenomena whose reliable numerical simulation is still challenging. High-resolution (convection-permitting) modeling setups allow to switch off physical parameterizations accountable for substantial errors in convection representation. A new convection-permitting reanalysis over Italy (SPHERA) has been produced at ARPAE to enhance the representation and understanding of extreme weather situations. SPHERA is obtained through a dynamical downscaling of the global reanalysis ERA5 using the non-hydrostatic model COSMO at 2.2 km grid spacing over 1995-2020. This thesis aims to verify the expectations placed on SPHERA by analyzing two weather phenomena that are particularly challenging to simulate: heavy rainfall and hail. A quantitative statistical analysis over Italy during 2003-2017 for daily and hourly precipitation is presented to compare the performance of SPHERA with its driver ERA5 considering the national network of rain gauges as reference. Furthermore, two extreme precipitation events are deeply investigated. SPHERA shows a quantitative added skill over ERA5 for moderate to severe and rapid accumulations in terms of adherence to the observations, higher detailing of the spatial fields, and more precise temporal matching. These results prompted the use of SPHERA for the investigation of hailstorms, for which the combination of multiple information is crucial to reduce the substantial uncertainties permeating their understanding. A proxy for hail is developed by combining hail-favoring environmental numerical predictors with observations of ESWD hail reports and satellite overshooting top detections. The procedure is applied to the extended summer season (April-October) of 2016-2018 over the whole SPHERA spatial domain. The results indicate maximum hail likelihood over pre-Alpine regions and the northern Adriatic sea around 15 UTC in June-July, in agreement with recent European hail climatologies. The method demonstrates enhanced performance in case of severe hail occurrences and the ability to separate between ambient signatures depending on hail severity.