On the set of optimal homeomorphisms for the natural pseudo-distance associated with the Lie group S1

In this dissertation we study the natural pseudo-distance associated with the Lie group S1, a dissimilarity measure on a space of real-valued maps called filtering functions. We focus our attention on the set of the optimal homeomorphisms for the natural pseudo-distance, i.e. the homeomorphisms that represent the best correspondence between two filtering functions. We examine some differential properties that an homeomorphism has to meet in order to be optimal, and we prove the finiteness of the set of the optimal homeomorphisms if the filtering functions are Morse

Minimal surfaces, a study

Le superfici minime, sono di grande interesse in vari campi della matematica, e parecchie sono le applicazioni in architettura e in biologia, ad esempio. È possibile elencare diverse definizioni equivalenti per tali superfici, che corrispondono ad altrettanti approcci. Nella seguente tesi ne affronteremo alcuni, riguardanti: la curvatura media, l'equazione differenziale parziale di Lagrange, la proprietà di una funzione di essere armonica, i punti critici del funzionale di area, le superfici di area minima con bordo fissato e la soluzione del problema di Plateau

Inbetweenness - A reflection on Italian American cultural integration as depicted in the novel 'Ask the Dust' by John Fante

Riflessione sull'integrazione Italo Americana a Los Angeles durante il periodo della Grande Depressione basata sul romanzo di John Fante 'Ask the Dust', ed in particolare sul personaggio di Arturo Bandini

Second quantization theory for many-particles stochastic dynamics on finite transport and storage capacity network

Nella tesi viene studiato il random walk di particelle non interagenti su network con capacità di trasporto e capienza dei nodi finite. L’argomento viene affrontato introducendo per il sistema un formalismo di seconda quantizzazione. Dopo avere dimostrato l'effettiva conservazione del numero totale di particelle e che per il sistema vale una relazione di bilancio dettagliato, vengono derivate le relazioni di Onsager per il caso di un network con capacità di trasporto finita. Infine, viene ricavata l'espressione esplicita della distribuzione stazionaria di probabilità per il caso di un network con capienza finita per nodo

Studies on ToF-PET using Cherenkov radiation

La tomografia ad emissione di positroni (PET) è una tecnica di imaging di medicina nucleare, utilizzata oggi diffusamente in ambito clinico. Essa fornisce immagini e informazioni fisiologiche dei processi funzionali all’interno del corpo. La PET si basa sulla rilevazione di fotoni di annichilazione prodotti in seguito al decadimento di un radio farmaco iniettato nel paziente. I rilevatori convenzionali sono costituiti da un materiale scintillatore accoppiato ad un fotomoltiplicatore, solitamente un PMT o SiPM. Uno sviluppo della PET è la Time of Flight PET (ToF PET), attualmente già in commercio ed utilizzata con prestazioni eccellenti. Un’ulteriore modifica, che potenzialmente permetterebbe di ottenere una migliore risoluzione temporale, è la ToF PET basata sulla rilevazione di fotoni tramite radiazione Cherenkov, invece che luce di scintillazione. Questo lavoro di tesi è incentrato dunque su questa tecnica specifica. Si illustra una rassegna di pubblicazioni scientifiche degli ultimi anni riguardo ad essa con i relativi risultati ottenuti e i possibili sviluppi futuri. Infine si propone un approfondimento personale, nel quale, tramite un programma scritto in ROOT, si è realizzata una geometria di un sistema di rilevazione ToF PET. Esso prevede la rilevazione dei fotoni di annichilazione tramite un radiatore Cherenkov accoppiato ad un SiPM. In futuro questo potrà essere implementato e utilizzato per simulare il processo fisico della PET, verificando la validità e le prestazioni del sistema così sviluppato

Structure learning of graphical models for task-oriented robot grasping

In the collective imaginaries a robot is a human like machine as any androids in science fiction. However the type of robots that you will encounter most frequently are machinery that do work that is too dangerous, boring or onerous. Most of the robots in the world are of this type. They can be found in auto, medical, manufacturing and space industries. Therefore a robot is a system that contains sensors, control systems, manipulators, power supplies and software all working together to perform a task. The development and use of such a system is an active area of research and one of the main problems is the development of interaction skills with the surrounding environment, which include the ability to grasp objects. To perform this task the robot needs to sense the environment and acquire the object informations, physical attributes that may influence a grasp. Humans can solve this grasping problem easily due to their past experiences, that is why many researchers are approaching it from a machine learning perspective finding grasp of an object using information of already known objects. But humans can select the best grasp amongst a vast repertoire not only considering the physical attributes of the object to grasp but even to obtain a certain effect. This is why in our case the study in the area of robot manipulation is focused on grasping and integrating symbolic tasks with data gained through sensors. The learning model is based on Bayesian Network to encode the statistical dependencies between the data collected by the sensors and the symbolic task. This data representation has several advantages. It allows to take into account the uncertainty of the real world, allowing to deal with sensor noise, encodes notion of causality and provides an unified network for learning. Since the network is actually implemented and based on the human expert knowledge, it is very interesting to implement an automated method to learn the structure as in the future more tasks and object features can be introduced and a complex network design based only on human expert knowledge can become unreliable. Since structure learning algorithms presents some weaknesses, the goal of this thesis is to analyze real data used in the network modeled by the human expert, implement a feasible structure learning approach and compare the results with the network designed by the expert in order to possibly enhance it

Geometry of BV quantization and Mathai-Quillen formalism

Il formalismo Mathai-Quillen (MQ) è un metodo per costruire la classe di Thom di un fibrato vettoriale attraverso una forma differenziale di profilo Gaussiano. Lo scopo di questa tesi è quello di formulare una nuova rappresentazione della classe di Thom usando aspetti geometrici della quantizzazione Batalin-Vilkovisky (BV). Nella prima parte del lavoro vengono riassunti i formalismi BV e MQ entrambi nel caso finito dimensionale. Infine sfrutteremo la trasformata di Fourier “odd" considerando la forma MQ come una funzione definita su un opportuno spazio graduato

When Beauty Goes to Sleep: an analysis of the symbolism behind the sleeping beauty tale

Approaching the world of the fairy tale as an adult, one soon realizes that things are not what they once seemed during story time in bed. Something that once appeared so innocent and simple can become rather complex when digging into its origin. A kiss, for example, can mean something else entirely. I can clearly remember my sister, who is ten years older than I am, telling me that the fairy tales I was told had a mysterious hidden meaning I could not understand. I was probably 9 or 10 when she told me that the story of Sleeping Beauty, which I used to love so much in Disney’s rendering, was nothing more than the story of an adolescent girl, with all the necessary steps needed to become a woman, the bleeding of menstruation and the sexual awakening - even though she did not really put it in these terms. This shocking news troubled me for a while, so much so that I haven’t watched that movie since. But in reality it was not fear that my sister had implanted in me: it was curiosity, the feeling that I was missing something terribly important behind the words and images. But it was not until last year during my semester abroad in Germany, where I had the chance to take a very interesting English literature seminar, that I fully understood what I had been looking for all these years. Thanks to what I learned from the work of Bruno Bettelheim, Jack Zipes, Vladimir Propp, and many other authors that wrote extensively about the subject, I feel I finally have the right tools to really get to know this fairy tale. But what I also know now is that the message behind fairy tales is not to be searched for behind only one version: on the contrary, since they come from oral traditions and their form was slowly shaped by centuries of recountals and retellings, the more one digs, the more complete the understanding of the tale will be. I will therefore look for Sleeping Beauty’s hidden meaning by looking for the reason why it did stick so consistently throughout time. To achieve this goal, I have organized my analysis in three chapters: in the first chapter, I will analyze the first known literary version of the tale, the French Perceforest, and then compare it with the following Italian version, Basile’s Sun, Moon, and Talia; in the second chapter, I will focus on the most famous and by now classical literary versions of Sleeping Beauty, La Belle Au Bois Dormant, written by the Frenchman, Perrault, and the German Dornröschen, recorded by the Brothers Grimm’s; finally, in the last chapter, I will analyze Almodovar’s film Talk to Her as a modern rewriting of this tale, which after a closer look, appears closely related to the earliest version of the story, Perceforest

Comparison of radiobiological effects induced by ultra-high and standard dose rate of x-rays on a radio-resistant cell line

Radiotherapy (RT) has recently evolved with the emergence of heavy ion radiations or new fractionation schemes of photon therapy, which modify the dose rate of treatment delivery. The aim of the present study was then to evaluate the in vitro influence of a ultra-high dose rate comparing them with standard dose rate. In this regard, a radioresistant SK-MEL-28 cell line were irradiated with x-ray in order to have a total dose of 2 and 4 Gy, at two different dose rate. The ultra-high dose rate is a specific property of the dense plasma focus (DPF) device, which has pulsed operation and thus gives short and highly energetic pulses of multiple types of rays and particles, in this case, we focused our study on the influence of X-rays. While a low dose rate is obtained with conventional X-ray tube. In this study it results that a ultra-high dose rate enhances radiosensitivity of melanoma cells while reducing the adhesion, proliferation and migration ability of cells

The Wiener criterion for the Laplacian and the heat operator

La tesi presenta il criterio di regolarità di Wiener dell’ambito classico dell’operatore di Laplace ed in seguito alcune nozioni di teoria del potenziale e la dimostrazione del criterio nel caso dell’operatore del calore; in questa seconda sezione viene dedicata particolare attenzione alle formule di media e ad una diseguaglianza forte di Harnack, che risultano fondamentali nella trattazione dell’argomento centrale