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.

On the renormalization flow representation of field theory and some applications

In this thesis we discuss a representation of quantum mechanics and quantum and statistical field theory based on a functional renormalization flow equation for the one-particle-irreducible average effective action, and we employ it to get information on some specific systems.

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.

The effects of aging and musical experience on the representation of tonal hierarchies

Two experiments explored the representation of the tonal hierarchy in Western music among older (aged 60 to 80) and younger (aged 15 to 22) musicians and nonmusicians. A probe tone technique was used: 4 notes from the major triad were presented, followed by 1 note chosen from the 12 notes of the chromatic scale. Whereas musicians had a better sense of the tonal hierarchy than nonmusicians, older adults were no worse than younger adults in differentiating the notes according to musical principles. However, older adults were more prone than younger adults to classify the notes by frequency proximity (pitch height) when proximity was made more salient, as were nonmusicians compared with musicians. With notes having ambiguous pitch height, pitch height effects disappeared among older adults but not nonmusicians. Older adults seem to have internalized tonal structure, but they sometimes fail to inhibit less musically relevant information.

The Representation of Motherhood in Polish Cinema

The project aimed to analyse representations of motherhood in Polish cinema as a special case of a more general system within the representation of women. It concentrated on the image of the Polish Mother created during the 19th century in Polish culture under the influence of specific political, social and religious factors. Ms. Ostrowska's initial hypothesis was that this symbolic image became one of the most stable elements in Polish cinema and as her research revealed, it was valuable for the preservation of national identity but nevertheless a fiercely constraining model for Polish femininity. In order to fully understand the nature of this persistent image it was initially necessary to related it to broader contexts and issues in representation. These included the image of the Polish Mother within general mythological structures (using the notion of myth in the Barthesian sense). Following her initial research Ms. Ostrowska felt that it was most appropriate to view the myth of the Polish Mother as a dominant ideological structure in the discourse of motherhood within Polish culture. An analysis of the myth of the Polish Mother can provide an insight into how Polish society sees itself at different periods in time and how a national identity was constructed in relation to particular ideological demands stemming from concrete historical and political situations. The analysis of the film version of this myth also revealed some aspects of the national character of Polish cinema. There the image of woman has become enshrined as the "eternal feminine", with virtues which are inevitably derived directly from Catholicism, particularly in relation to the networks of meanings around the central figure of Mary, Mother of God. In 19th century Poland these were linked with patriotic values and images of woman became part of the defence of the very idea of Poland and Polishness. After World War Two, this religious-political image system was adapted to the demands of the new communist ideology. The possibility of manipulating the ideological dimensions of the myth of the Polish Mother is due to the very nature of the image, which as a symbol of civil religion had been able to function independently of any particular state or church institution. Although in communist ideology the stress was on the patriotic aspect of the myth, its pronounced religious aspect was also transmitted, consciously or not, in the denotation process, this being of great significance in the viewer's response to the female character. This appropriation of elements derived from the national patriotic tradition into the discourse of communist ideology was a very efficient strategy to establish the illusion of continuity in national existence, which was supposed to convince society of the rightness of the new political situation. The analysis of films made in the post-war period showed the persistence of this discourse on motherhood in a range of cinematic texts regardless of the changing political situation. Ms. Ostrowska claims that the stability of this discursive formation is to a certain extent the result of the mythological aspect of the mother figure. This mythological structure also belongs to the ideology of Romanticism which in general continues to prevail in Polish cultural discourse as a meta-language of national community. The analysis of the films confirmed the hypothesis of the Polish Mother as a myth-sign whose signifier is stable whereas the signified depends on the specific historical conditions in which it is set. Therefore in the famous propaganda documentary Kobiety naszych dni (Women of Our Days, 1951) by Jan Zelnik, and in other films made after the October 1956 "thaw" it functions as an "empty sign. She concludes that it would be difficult to deny that the myth of the Polish Mother has offered Polish women a special role in national life, granting them a high moral position in the social, hierarchy. However the processes of idealisation involved have resulted in a deprivation of her subjectivity and the right to decide about her own life. This idealisation also served to strengthen traditional patriarchal structures through this set of female obligations to the mother land. In Polish ideology it is not a man who demands sacrifice from a woman but the motherland, which, deprived of the institutions of male power for nearly 150 years, had functioned as a feminine structure. That is why oppressive aspects of the myth have been obscured for so long. While Polish women were doubtless able to accept the constrictions because of their sense of national duty and any misgivings were overridden by the argument of the cause, it is important to recognise that the strength of these constructions, compounded by the ways in which they spoke of and continue to speak of a certain perfection, make them persist into contemporary Poland. Poland is however no longer embattled and the signs that made these meanings are potentially empty. This space for meaning will be and is already being contested and increasingly colonised by current western models of femininity. Ms. Ostrowska's final question is whether this will help to prevent a possible resentful victimisation of the silent and noble Polish Mother.