The thesis surveys some recent results obtained in the field of nonlinear partial differential equations and calculus of variations about eigenvalues of nonlinear operators.

In the classical theory, the fractional diffusion is ruled by two different types of fractional Laplacians. Formerly known since 60s, the spectral fractional Laplacian had an important development in the recent mathematical study with the initial contributes of L. Caffarelli, L. Silvestre and X. Cabré, X.Tan. The integral version of the fractional Laplacian, recently discussed by M. Fukushima, Y. Oshima, M Takeda, and Song, Vondracek, is considered in a semilinear elliptic problem in presence of a general logistic function and an indefinite weight. In particular we look for a multiplicity result for the associated Dirichlet problem. In the second part, starting from the classical works of T.Hillen and G. Othmer and taking the Generalized velocity jump processes presented in a recent work of J.T.King, we obtain the fractional diffusion as limit of this last processes using the technique used in another recent work of Mellet, without the classical Hilbert or Cattaneo approximation's methods.

We present a mathematical model describing the dynamics occurring between two interacting populations, one of amoebae and one of virulent bacteria; it is meant to describe laboratory experiments with these two species in a mathematical framework and help understanding the role of the different mechanisms involved. In particular we aim to focus on how bacterial virulence may affect the dynamics of the system. The model is a modified reaction-diffusion-chemotaxis predator-prey one with a mechanism of redistribution of ingested biomass between amoeboid cells. The spatially homogeneous case is analyzed in detail; conditions for pattern formation are established; numerical simulations for the complete model are performed.

The thesis deals with the study of a natural extension of classical finite-dimensional time-optimal control problem to the space of positive Borel measures. This approach has two main motivations: to model real-life situations in which the knowledge of the initial state is only probabilistic, and to model the statistical distribution of a huge number of agents for applications in multi-agent systems. We deal with a deterministic dynamics and treat the problem first in a mass-preserving setting: we give a definition of generalized target, its properties, admissible trajectories and generalized minimum time function, we prove a Dynamic Programming Principle, attainability results, regularity results and an Hamilton-Jacobi-Bellman equation solved in a suitable viscosity sense by the generalized minimum time function, and finally we study the definition of an object intended to reflect the classical Lie bracket but in a measure-theoretic setting. We also treat a case with mass loss thought for modelling the situation in which we are interested in the study of an averaged cost functional and a strongly invariant target set. Also more general cost functionals are analysed which takes into account microscopical and macroscopical effects, and we prove sufficient conditions ensuring their lower semicontinuity and a dynamic programming principle in a general formulation.

The interplay between human behavior and the spreading of an epidemics represents a challenge in modeling the dynamics of infectious diseases. The technological revolution that we are experiencing nowadays gives access to new sources of digital data, capable of capturing behavioral patterns and social dynamics of our society and opening, in fact, the path to new opportunities for mathematical modelers. Provided by such tools, we discuss two different aspects of the dynamics of infectious diseases associated with human behavior. In the first part of the thesis, we focus on the mechanism driving the awareness of individuals during public health emergencies and describe epidemiological models especially tailored to better understand the underline features of the risk perception. The proposed framework is able to disentangle and characterize the contribution of media drivers and social contagion mechanisms in the building of awareness of individuals about infectious diseases. In the second part of the thesis, we present a data driven computational model aiming to assess the potential risk of experiencing measles re-emergence in Turkey. This study takes into consideration the recent massive migration of Syrian refugees in Turkey, which changed the social structure and focuses on the possible outbreak of an infectious disease, such as measles, as a consequence of the great concentration of Syrian refugees not adequately immunized against it. The model proposed is informed with mobility patterns inferred from mobile phone data and accounts for the different hypothetical policies adopted to integrate the refugees with the Turkish population.

The thesis deals with various problems arising in deterministic control, jumping processes and control for locomotion in fluids. It is divided in three parts. The first part is focused on some optimal control problems on network and stratified domains with junctions, where each edge/hyper-plane has its own controlled dynamics and cost. We consider some possible approximations for such a problems given by the use of a switching rule of delayed-relay type and study the passage to the limit when the parameter of the approximation goes to zero. First, we take into account some problems on network: a twofold junction problem, a threefold junction one and an extension of the last one. For each of these problems we characterize the limit functions as viscosity solution and maximal subsolution of a suitable Hamilton-Jacobi problem. Secondly, we consider a bi-dimensional multi-domain problem and as done for the problems on network we characterize the limit function as viscosity solution of a suitable Hamilton-Jacobi problem. The second part studies a decentralized routing problem over a network, using the paradigm of mean-field games with large number of players. Building on a state-space extension technique, we turn the problem into an optimal control one for each single player. The main contribution is an explicit expression of the optimal decentralized control which guarantees the convergence both to local and to global equilibrium points. Furthermore, we study the stability of the system also in the presence of a delay which we model using an hysteresis operator. As a result of the hysteresis, we prove existence of multiple equilibrium points and analyze convergence conditions. In the last part of the thesis we investigate different strategies to overcome the so-called scallop paradox concerning periodic locomotion in fluid. We show how to obtain a net motion exploiting the fluid's type change during a periodic deformation. We consider two different models: in the first one that change is linked to the magnitude of the opening and closing velocity of the scallop's valves. Instead, in the second one it is related to the sign of the above velocity. In both cases we prove that the mechanical system is controllable, i.e. the scallop is able to move both forward and backward using cyclical deformations.

Basata sul reperimento di un’ampia mole di testi giornalistici (come cronache, interviste, elzeviri e articoli di “Terza”) dedicati alle pratiche coreiche e pubblicati in Italia nel corso del ventennio fascista, la tesi ricostruisce i lineamenti di quello che, seppure ancora embrionale e certo non specialistico, si può comunque ritenere una sorta di “pensiero italiano” sulla danza del Primo Novecento. A partire dalla ricognizione sistematica di numerose testate quotidiane e periodiche e, pertanto, dalla costruzione di un nutrito corpus di fonti primarie, si è proceduto all’analisi dei testi reperiti attraverso un approccio metodologico che, fondamentalmente storiografico, accoglie tuttavia alcuni rudimenti interpretativi elaborati in ambito semiotico (con particolare riferimento alle teorizzazioni di Jurij Lotman e Umberto Eco), il tutto al fine di cogliere, pur nell’estrema varietà formale e contenutistica offerta dal materiale documentario, alcune dinamiche culturali di fondo attraverso le quali disegnare, da un lato, il panorama delle tipologie di danza effettivamente praticate sulle scene italiane del Ventennio,e, dall’altro, quello dell’insieme di pensieri, opinioni e gusti orbitanti attorno ad esse Ne è scaturita una trattazione fondamentalmente tripartita in cui, dopo la messa in campo delle questioni metodologiche, si passa dapprima attraverso l’indagine dei tre principali generi di danza che, nella stampa del periodo fascista, si ritenevano caratteristici della scena coreica internazionale – qui definiti nei termini di “ballo teatrale”, “ballo russo” e “danze libere” – e, successivamente, si presenta un approfondimento su tre singolari figure di intellettuali che, ognuno con un’attitudine estremamente personale, hanno dedicato alla danza un’attenzione speciale: Anton Giulio Bragaglia, Paolo Fabbri e Marco Ramperti. Un’ampia antologia critica completa il lavoro ripercorrendone gli snodi principali. / The dissertation investigates the relationship between dance and press during the fascist period in order to reconstruct the narrative on dance dominating in Italy in the first half of the Twentieth Century and aims to think about the birth of dance criticism in Italy. Unlike what happens in the rest of Europe and in America, in fact, throughout the first half of the twentieth century, Italian press can’t boast the presence of an authentic dance criticism. Grounded on these assumptions, my inquiry focuses on a particular and controversial phase of Italian history such as the Fascist period, aiming, on the one hand , to reconstruct the discourses on dance elaborated by Italian journalism in the early twentieth century, and trying, on the other hand, to wonder about the cultural dynamic underlying the lack of a authentic dance criticism in Italy during the Fascism . Starting from the recognition of some formal and conceptual elements characterising the discourses on dance published on daily newspapers and periodicals, I propose a methodological approach that intertwines an historiographical perspective with concepts derived from semiotics of culture. By this I analyze the discourses mentioned above by posing the following questions: how can dance become one of the topics of journalistic discourse? What's the image of the dancing body developed in Italian journalism during the fascist period? What kind of cultural dynamics can generate the development of a critical discourse on dance? And, on the contrary, in which case is the emergence of a dance criticism inhibited? A special attention is dedicated to three intellectuals who wrote about dance during the fascist period adopting a particularly interesting insight: Anton Giulio Bragaglia, Paolo Fabbri and Marco Ramperti.

I sottotipi H1N1, H1N2 e H3N2 di influenza A virus sono largamente diffusi nella popolazione suina di tutto il mondo. Nel presente lavoro è stato sviluppato un protocollo di sequenziamento di c.d. nuova generazione, su piattaforma Ion Torrent PGM, idoneo per l’analisi di tutti i virus influenzali suini (SIV). Per valutare l’evoluzione molecolare dei SIV italiani, sono stati sequenziati ed analizzati mediante analisi genomica e filogenetica un totale di sessantadue ceppi di SIV appartenenti ai sottotipi H1N1, H1N2 e H3N2, isolati in Italia dal 1998 al 2014. Sono stati evidenziati in sei campioni due fenomeni di riassortimento: tutti i SIV H1N2 esaminati presentavano una neuraminidasi di derivazione umana, diversa da quella dei SIV H1N2 circolanti in Europa, inoltre l’emoagglutinina (HA) di due isolati H1N2 era originata dal riassortimento con un SIV H1N1 avian-like. L’analisi molecolare dell’HA ha permesso di rivelare un’inserzione di due amminoacidi in quattro SIV H1N1 pandemici e una delezione di due aminoacidi in quattro SIV H1N2, entrambe a livello del sito di legame con il recettore cellulare. E’ stata inoltre evidenziata un’elevata omologia di un SIV H1N1 con ceppi europei isolati negli anni ’80, suggerendo la possibile origine vaccinale di questo virus. E’ stato possibile, in aggiunta, applicare il nuovo protocollo sviluppato per sequenziare un virus influenzale aviare altamente patogeno trasmesso all’uomo, direttamente da campione biologico. La diversità genetica nei SIV esaminati in questo studio conferma l’importanza di un continuo monitoraggio della costellazione genomica dei virus influenzali nella popolazione suina. / Three major swine influenza virus (SIV) subtypes (H1N1, H1N2, and H3N2) are currently identified in pigs worldwide. In this study, a protocol able to sequence all SIV subtypes using the Ion Torrent next generation sequencing technology was developed. Moreover, to investigate the genetic characteristics and the molecular evolution of Italian SIV circulating strains, we conducted genomic and phylogenetic analysis for each segment of sixty-two SIVs isolated in Italy between 1998 and 2014 comprising H1N1, H1N2 and H3N2 strains. Two independent reassortment events in six SIV strains were detected. H1N2 SIVs showed the introduction of a human-like neuraminidase, different from the homologous of circulating H1N2 detected in Europe from swine. Two of these reassortant H1N2 strains contained an avian-like hemagglutinin (HA). Analysis of HA revealed a two-amino acid insertion in four H1N1 pandemic strains and a two-amino acid deletion in four H1N2 strains, both at the HA receptor binding site. High nucleotide identity between an H1N1 of this study and European field strains isolated in the 80s was revealed, suggesting a probable vaccine origin for this strain. Translational benefit of the newly developed protocol was immediately achieved by sequencing a H7N7 high pathogenic avian influenza virus, which caused disease in humans. The genetic diversity of SIVs demonstrated in our investigation confirms the importance of continuous monitoring of SIV genomic constellation.

Coral reefs are the most biodiverse ecosystems of the ocean and they provide notable ecosystem services. Nowadays, they are facing a number of local anthropogenic threats and environmental change is threatening their survivorship on a global scale. Large-scale monitoring is necessary to understand environmental changes and to perform useful conservation measurements. Governmental agencies are often underfunded and are not able of sustain the necessary spatial and temporal large-scale monitoring. To overcome the economic constrains, in some cases scientists can engage volunteers in environmental monitoring. Citizen Science enables the collection and analysis of scientific data at larger spatial and temporal scales than otherwise possible, addressing issues that are otherwise logistically or financially unfeasible. “STE: Scuba Tourism for the Environment” was a volunteer-based Red Sea coral reef biodiversity monitoring program. SCUBA divers and snorkelers were involved in the collection of data for 72 taxa, by completing survey questionnaires after their dives. In my thesis, I evaluated the reliability of the data collected by volunteers, comparing their questionnaires with those completed by professional scientists. Validation trials showed a sufficient level of reliability, indicating that non-specialists performed similarly to conservation volunteer divers on accurate transects. Using the data collected by volunteers, I developed a biodiversity index that revealed spatial trends across surveyed areas. The project results provided important feedbacks to the local authorities on the current health status of Red Sea coral reefs and on the effectiveness of the environmental management. I also analysed the spatial and temporal distribution of each surveyed taxa, identifying abundance trends related with anthropogenic impacts. Finally, I evaluated the effectiveness of the project to increase the environmental education of volunteers and showed that the participation in STEproject significantly increased both the knowledge on coral reef biology and ecology and the awareness of human behavioural impacts on the environment.

La tesi indaga l’esperienza del teatro comunitario, una delle espressioni artistiche più originali e pressoché sconosciute nel panorama teatrale novecentesco, che ha avuto in Argentina un punto di riferimento fondamentale. Questo fenomeno, che oggi conta cinquanta compagnie dal nord al sud del paese latinoamericano, e qualcuna in Europa, affonda le sue radici nella Buenos Aires della post-dittatura, in una società che continua a risentire degli esiti del terrore di Stato. Il teatro comunitario nasce dalla necessità di un gruppo di persone di un determinato quartiere di riunirsi in comunità e comunicare attraverso il teatro, con l'obiettivo di costruire un significato sociale e politico. La prima questione messa a fuoco riguarda la definizione della categoria di studio: quali sono i criteri che consentono di identificare, all’interno della molteplicità di pratiche teatrali collettive, qualcosa di sicuramente riconducibile a questo fenomeno. Nel corso dell’indagine si è rivelata fondamentale la comprensione dei conflitti dell’esperienza reale e l’individuazione dei caratteri comuni, al fine di procedere a un esercizio di generalizzazione. La ricerca ha imposto la necessità di comprendere i meccanismi mnemonici e identitari che hanno determinato e, a loro volta, sono stati riattivati dalla nascita di questa esperienza. L’analisi, supportata da studi filosofici e antropologici, è volta a comprendere come sia cambiata la percezione della corporeità in un contesto di sparizione dei corpi, dove il lavoro sulla memoria riguarda in particolare i corpi assenti (desaparecidos). L’originalità del tema ha imposto la riflessione su un approccio metodologico in grado di esercitare una adeguata funzione euristica, e di fungere da modello per studi futuri. Sono stati pertanto scavalcati i confini degli studi teatrologici, con particolare attenzione alle svolte culturali e storiche che hanno preceduto e affiancato l’evoluzione del fenomeno. / The thesis investigates the community theater experience as one of the most original and least known artistic expressions of the 20th century theater scene, which had a fundamental reference point in Argentina. To date this phenomenon, which counts fifty companies all over Latin America and some in Europe, has its roots in post-dictatorship Buenos Aires, in a society that continues to be affected by State Terror. Community theatre came to light from the need of a group of neighbors to gather in community and communicate through theatre to build social and political meaning. The first issue is the definition of study category: what criteria allow to identify, within the multiplicity of collective theatre practices, something to clearly trace back to this phenomenon. During the investigation, essentials were the understanding of real experience conflicts and the identification of common traits in order to carry out generalization. Research has imposed the need to understand identitarian and mnemonic mechanisms that in turn determined and have been reactivated by the birth of this experience. The analysis, supported by studies in philosophy and anthropology, is intended to understand how the perception of corporeality changes in the context of the disappearance of the body, in particular where the work on memory concerns the absent bodies (desaparecidos). The uniqueness of the topic has imposed the research of a methodological approach suitable to exert an adequate heuristic function, and act as a model for future studies. Therefore, Theatrological studies boundaries were crossed, paying special attention to the cultural and historical turns that preceded and accompanied the phenomenon's evolution.