Studio della stabilità con la forma normale di Birkhoff. Applicazioni alla meccanica celeste.

In questa tesi si discute la teoria della forma normale di Birkhoff per lo studio della stabilità dei moti vicino ad un punto di equilibro linearmente stabile in sistemi hamiltoniani quasi-integrabili. Si presentano le principali stime teoriche sulla maggiorazione del resto delle serie di Birkhoff e il loro uso per lo studio della stabilità. In conclusione si espone un'applicazione al modello di Hénon-Heiles e al problema della stabilità dei moti degli asteroidi troiani di Giove

Tagli massimi di ordine k e bipartizioni di insiemi: algoritmi approssimati ed esatti

In questa tesi vengono analizzati due articoli riguardanti i tagli massimi di ordine k e bipartizioni. Il problema principale di questa tipologia di problemi è che non sono stati trovati algoritmi risolutivi che trovino una soluzione in un tempo polinomiale. Per ovviare a questo limite si utilizzano algoritmi eseguibili in tempi polinomiali di due tipologie differenti: algoritmi esatti e approssimati. I primi non sono esattamente algoritmi polinomiali perché il loro tempo di calcolo viene definito da due parametri che sono: la dimensione dell'insieme di partenza "n" e il numero di sottoinsiemi da tagliare "t". Il risultato è un algoritmo polinomiale in "n" ed esponenziale in "t". I secondi sono algoritmi polinomiali che non trovano a priori la soluzione ottima, cercano però di usare delle approssimazioni che possano avere un fattore di approssimazione migliore possibile. Nel caso presentato il fattore sarà pari a 1/2

Homological stability for the moduli space of Riemann surfaces with boundary

Moduli spaces frequently arise as solutions to classification problems. Showing that a collection of objects can be given the structure of a geometric space facilitates the research of a possible parametrization on the resulting space. The goal of the present work is to prove homological stability results for the moduli space of Riemann surfaces, exclusively looking at the case of Riemann surfaces with non-empty boundary and fixed positive length at the boundary components. The reason why we restrict to such a condition can be found in the famous and often quoted article "Stability of the Homology of the Mapping Class Groups of Orientable Surfaces" published in the Annals of Mathematics by John Harer in 1985. The stability results he addresses refer to the homology of an algebraic invariant for manifolds, the so-called mapping class group. As a matter of fact, it turns out that, given a connected, compact and oriented surfaces $S$ with non-empty boundary, the moduli space of Riemann surfaces $\operatorname{M}(S)$ is a model for the classifying space of the mapping class group $\operatorname{MCG}(S)$. Therefore, under this condition, the homology of the mapping class groups of $S$ equals the homology of $\operatorname{M}(S)$. The relevance of the Harer's stability theorem lies in its application in the Mumford's conjecture, formulated in 1983 by David Mumford and solved by Ib Madsen and Michael Weiss in 2007. According to the Mumford conjecture, the rational cohomology ring of the moduli space of Riemann surfaces is a polynomial algebra on the so-called Mumford-Morita-Miller classes, in a range of degrees increasing with the genus of the surface. Despite the numerous improvements of Harer's result, due to professor Nikolai V. Ivanov in 1989, Harer itself in 1993, O. Randal-Williams in 2009, and many more over a range of 35 years, variations of the paper are subjects of nowadays active research: the last attempt to improve the statement was achieved by Søren K. Boldsen in 2010 in the paper "Improved homological stability for the mapping class group with integral or twisted coefficient"; professor Nathalie Wahl reorganized all the literature concerning the stability of the mapping class groups in her paper “Homological stability for mapping class group of surfaces”, published in the third volume of the "Handbook of the moduli" in 2013

Development of teaching-learning sequences on quantum physics for the Italian secondary school

In the past 15 years, quantum mechanics has been included in most secondary school standards, including the Italian ones, but still in a rather marginal way. The conceptual complexity of quantum mechanics is often a hurdle for students as well as for teachers; as a consequence, most teachers and textbooks opt for narrative/historical approaches which, however, are not sufficient to grasp the deepest conceptual aspects of quantum physics, nor to deal with its technological applications. Teaching quantum physics in secondary school is therefore a challenge that calls for a close collaboration between physics teachers and physics education researchers. The goal of this work is to develop and test research-based teaching-learning sequences (TLS) based on the study of relevant literature in physics education research and on a survey to be conducted with secondary school teachers. More specifically, the thesis work will include the following phases. A review of the literature on the teaching and learning of quantum mechanics, with particular reference to the proposals developed in the Italian context. A survey with a sample of secondary school physics teachers aimed at understanding the needs and difficulties of teaching quantum mechanics. On the basis of the literature and of the results of the survey, development of a teaching-learning sequence (TLS) on quantum mechanics for the fifth year of the Italian “liceo scientifico”. Testing and evaluation of the TLS in a real classroom context

Incremental clustering of continuous perceptions

This thesis aims to develop a framework for the incremental clustering of the perceptions ofan agent. The agent moves in a simulated environment and collects data about its position and its surroundings, in particular the egocentric images seen by its on-board camera. In this context, clustering is useful to group together the perceptions of a same object, in particular to recognize objects which have already been seen by the agent. This task is performed with the aid of a neural network, pre-trained to recognize if two perceptions are associated to a same object. In this thesis we analyze the tuning and training performed for the neural network, the clustering algorithm and its performance

Studio e progettazione di un intervento di rinnovo tecnologico di sottostazione elettrica (SSE) ferroviaria di conversione

L'elaborato fornisce lo studio di una ignota sottostazione elettrica ferroviaria di conversione per la trazione elettrica alla tensione di 3 kVcc, sottoposta ad un intervento di rinnovo tecnologico con finalità di risolvere i problemi emersi durante il suo esercizio attraverso un'analisi e una progettazione secondo le normative vigenti