Algebraische Beschreibung von Symmetrien: das Modell der Nichtkommutativen Multi-Tori

In der Nichtkommutativen Geometrie werden Räume und Strukturen durch Algebren beschrieben. Insbesondere werden hierbei klassische Symmetrien durch Hopf-Algebren und Quantengruppen ausgedrückt bzw. verallgemeinert. Wir zeigen in dieser Arbeit, daß der bekannte Quantendoppeltorus, der die Summe aus einem kommutativen und einem nichtkommutativen 2-Torus ist, nur den Spezialfall einer allgemeineren Konstruktion darstellt, die der Summe aus einem kommutativen und mehreren nichtkommutativen n-Tori eine Hopf-Algebren-Struktur zuordnet. Diese Konstruktion führt zur Definition der Nichtkommutativen Multi-Tori. Die Duale dieser Multi-Tori ist eine Kreuzproduktalgebra, die als Quantisierung von Gruppenorbits interpretiert werden kann. Für den Fall von Wurzeln der Eins erhält man wichtige Klassen von endlich-dimensionalen Kac-Algebren, insbesondere die 8-dim. Kac-Paljutkin-Algebra. Ebenfalls für Wurzeln der Eins kann man die Nichtkommutativen Multi-Tori als Hopf-Galois-Erweiterungen des kommutativen Torus interpretieren, wobei die Rolle der typischen Faser von einer endlich-dimensionalen Hopf-Algebra gespielt wird. Der Nichtkommutative 2-Torus besitzt bekanntlich eine u(1)xu(1)-Symmetrie. Wir zeigen, daß er eine größere Quantengruppen-Symmetrie besitzt, die allerdings nicht auf die Spektralen Tripel des Nichtkommutativen Torus fortgesetzt werden kann.

The relation between geometry and matter in classical and quantum gravity and cosmology

The present thesis is divided into two main research areas: Classical Cosmology and (Loop) Quantum Gravity. The first part concerns cosmological models with one phantom and one scalar field, that provide the `super-accelerated' scenario not excluded by observations, thus exploring alternatives to the standard LambdaCDM scenario. The second part concerns the spinfoam approach to (Loop) Quantum Gravity, which is an attempt to provide a `sum-over-histories' formulation of gravitational quantum transition amplitudes. The research here presented focuses on the face amplitude of a generic spinfoam model for Quantum Gravity.

Sistemi navigazionali multi sensore per il posizionamento in presenza di brevi periodi di GPS outage

Il posizionamento terrestre negli ultimi anni è stato sempre più facilitato dallo sviluppo delle tecniche satellitari, che permettono di localizzare un punto sulla superficie terrestre con precisioni superiori a quelle richieste per la pura navigazione, tramite la comunicazione tra ricevitore e satelliti. Per la disponibilità del sistema satellitare è indispensabile l’intervisibilità ottica satellite - ricevitore, condizione che viene a mancare nel caso ad esempio di trekking sottobosco, a causa della copertura data da manto vegetale e chiome arboree che non permettono una corretta triangolazione geometrica satellitare. Rientrano nei sistemi navigazionali anche le piattaforme inerziali, sistemi che rilevano le accelerazioni impresse e l’orientamento della piattaforma stessa. Se montati su un veicolo possono fungere da ausilio alla determinazione dell’ “attitude”, cioè dell’atteggiamento del veicolo durante il suo movimento in uno spazio tridimensionale. In questo lavoro ci si propone di unire i benefici delle due tecnologie, satellitari e inerziali, grazie alla complementarietà delle loro caratteristiche sugli errori, unendone le potenzialità e verificando i benefici prodotti dal loro uso integrato. In particolare si utilizzeranno dispositivi di costo relativamente contenuto.

Procedures of quality control and data analysis of multi-site ground-based observations for the absolute flux calibration of Gaia

The Gaia space mission is a major project for the European astronomical community. As challenging as it is, the processing and analysis of the huge data-flow incoming from Gaia is the subject of thorough study and preparatory work by the DPAC (Data Processing and Analysis Consortium), in charge of all aspects of the Gaia data reduction. This PhD Thesis was carried out in the framework of the DPAC, within the team based in Bologna. The task of the Bologna team is to define the calibration model and to build a grid of spectro-photometric standard stars (SPSS) suitable for the absolute flux calibration of the Gaia G-band photometry and the BP/RP spectrophotometry. Such a flux calibration can be performed by repeatedly observing each SPSS during the life-time of the Gaia mission and by comparing the observed Gaia spectra to the spectra obtained by our ground-based observations. Due to both the different observing sites involved and the huge amount of frames expected (≃100000), it is essential to maintain the maximum homogeneity in data quality, acquisition and treatment, and a particular care has to be used to test the capabilities of each telescope/instrument combination (through the “instrument familiarization plan”), to devise methods to keep under control, and eventually to correct for, the typical instrumental effects that can affect the high precision required for the Gaia SPSS grid (a few % with respect to Vega). I contributed to the ground-based survey of Gaia SPSS in many respects: with the observations, the instrument familiarization plan, the data reduction and analysis activities (both photometry and spectroscopy), and to the maintenance of the data archives. However, the field I was personally responsible for was photometry and in particular relative photometry for the production of short-term light curves. In this context I defined and tested a semi-automated pipeline which allows for the pre-reduction of imaging SPSS data and the production of aperture photometry catalogues ready to be used for further analysis. A series of semi-automated quality control criteria are included in the pipeline at various levels, from pre-reduction, to aperture photometry, to light curves production and analysis.

A panchromatic view of the evolution of supermassive black holes

This PhD Thesis is devoted to the accurate analysis of the physical properties of Active Galactic Nuclei (AGN) and the AGN/host-galaxy interplay. Due to the broad-band AGN emission (from radio to hard X-rays), a multi-wavelength approach is mandatory. Our research is carried out over the COSMOS field, within the context of the XMM-Newton wide-field survey. To date, the COSMOS field is a unique area for comprehensive multi-wavelength studies, allowing us to define a large and homogeneous sample of QSOs with a well-sampled spectral coverage and to keep selection effects under control. Moreover, the broad-band information contained in the COSMOS database is well-suited for a detailed analysis of AGN SEDs, bolometric luminosities and bolometric corrections. In order to investigate the nature of both obscured (Type-2) and unobscured (Type-1) AGN, the observational approach is complemented with a theoretical modelling of the AGN/galaxy co-evolution. The X-ray to optical properties of an X-ray selected Type-1 AGN sample are discussed in the first part. The relationship between X-ray and optical/UV luminosities, parametrized by the spectral index αox, provides a first indication about the nature of the central engine powering the AGN. Since a Type-1 AGN outshines the surrounding environment, it is extremely difficult to constrain the properties of its host-galaxy. Conversely, in Type-2 AGN the host-galaxy light is the dominant component of the optical/near-IR SEDs, severely affecting the recovery of the intrinsic AGN emission. Hence a multi-component SED-fitting code is developed to disentangle the emission of the stellar populationof the galaxy from that associated with mass accretion. Bolometric corrections, luminosities, stellar masses and star-formation rates, correlated with the morphology of Type-2 AGN hosts, are presented in the second part, while the final part concerns a physically-motivated model for the evolution of spheroidal galaxies with a central SMBH. The model is able to reproduce two important stages of galaxy evolution, namely the obscured cold-phase and the subsequent quiescent hot-phase.

Hsp90 characterization and inhibition: a multi-methodological study

Many physiological and pathological processes are mediated by the activity of proteins assembled in homo and/or hetero-oligomers. The correct recognition and association of these proteins into a functional complex is a key step determining the fate of the whole pathway. This has led to an increasing interest in selecting molecules able to modulate/inhibit these protein-protein interactions. In particular, our research was focused on Heat Shock Protein 90 (Hsp90), responsible for the activation and maturation and disposition of many client proteins [1], [2] [3]. Circular Dichroism (CD) spectroscopy, Surface Plasmon Resonance (SPR) and Affinity Capillary Electrophoresis (ACE) were used to characterize the Hsp90 target and, furthermore, its inhibition process via C-terminal domain driven by the small molecule Coumermycin A1. Circular Dichroism was used as powerful technique to characterize Hsp90 and its co-chaperone Hop in solution for secondary structure content, stability to different pHs, temperatures and solvents. Furthermore, CD was used to characterize ATP but, unfortunately, we were not able to monitor an interaction between ATP and Hsp90. The utility of SPR technology, on the other hand, arises from the possibility of immobilizing the protein on a chip through its N-terminal domain to later study the interaction with small molecules able to disrupt the Hsp90 dimerization on the C-terminal domain. The protein was attached on SPR chip using the “amine coupling” chemistry so that the C-terminal domain was free to interact with Coumermycin A1. The goal of the experiment was achieved by testing a range of concentrations of the small molecule Coumermycin A1. Despite to the large difference in the molecular weight of the protein (90KDa) and the drug (1110.08 Da), we were able to calculate the affinity constant of the interaction that was found to be 11.2 µm. In order to confirm the binding constant calculated for the Hsp90 on the chip, we decided to use Capillary Electrophoresis to test the Coumermycin binding to Hsp90. First, this technique was conveniently used to characterize the Hsp90 sample in terms of composition and purity. The experimental conditions were settled on two different systems, the bared fused silica and the PVA-coated capillary. We were able to characterize the Hsp90 sample in both systems. Furthermore, we employed an application of capillary electrophoresis, the Affinity Capillary Electrophoresis (ACE), to measure and confirm the binding constant calculated for Coumermycin on Optical Biosensor. We found a KD = 19.45 µM. This result compares favorably with the KD previously obtained on biosensor. This is a promising result for the use of our novel approach to screen new potential inhibitors of Hsp90 C-terminal domain.

Il contributo del telerilevamento multi ed iperspettrale per la caratterizzazione del territorio e la sostenibilità ambientale

L’evoluzione dei sensori multispettrali e la prospettiva di sviluppo dei sensori iperspettrali nel campo del telerilevamento ottico offrono nuovi strumenti per l’indagine del territorio e rinnovano la necessità di ridefinire potenzialità, limiti e accuratezza delle metodologie tradizionali. Nel caso delle immagini iperspettrali, in particolare, l’elevatissima risoluzione spettrale apre nuove possibilità di sviluppo di modelli fisicamente basati per correlare grandezze radiometriche con indicatori fisico-chimici caratteristici delle superfici osservate, a prezzo però di maggiori oneri nella gestione del dato. Il presente lavoro mira appunto ad esaminare, per alcune applicazioni di carattere ambientale e attraverso casi di studio specifici, le criticità del problema del rilevamento da remoto nel suo complesso: dai problemi di correzione radiometrica delle immagini, all'acquisizione di dati di calibrazione sul campo, infine all'estrazione delle informazioni di interesse dal dato telerilevato. A tal fine sono stati sperimentati diversi modelli di trasferimento radiativo ed è stata sviluppata un’interfaccia per la gestione del modello 6SV. Per quest’ultimo sono state inoltre sviluppate routine specifiche per il supporto dei sensori Hyperion e World View 2. La ricerca svolta intende quindi offrire un contributo alla definizione di procedure operative ripetibili, per alcune applicazioni intimamente connesse all’indagine conoscitiva ed al monitoraggio dei processi in atto sul territorio. Nello specifico, si è scelto il caso di studio dell’oasi del Fayyum, in Egitto, per valutare il contenuto informativo delle immagini satellitari sotto tre diversi profili, soltanto in apparenza distinti: la classificazione della litologia superficiale, la valutazione dello stato di qualità delle acque ed il monitoraggio delle opere di bonifica. Trattandosi di un’oasi, le aree coltivate del Fayyum sono circondate dai suoli aridi del deserto libico. La mancanza di copertura vegetale rappresenta una condizione privilegiata per l’osservazione della litologia superficiale da remoto, auspicabile anche per la scarsa accessibilità di alcune aree. Il fabbisogno idrico dell’oasi è garantito dall’apporto di acque del fiume Nilo attraverso una rete di irrigazione che ha, come recettore finale, il lago Qarun, situato nella porzione più depressa dell’oasi. Questo lago, privo di emissari, soffre enormi problemi di salinizzazione, visto il clima iper-arido in cui si trova, e di inquinamento da fertilizzanti agricoli. Il problema della sostenibilità ambientale dello sfruttamento agricolo intensivo dell’oasi è un problema di deterioramento della qualità dell’acqua e della qualità dei suoli. È un problema che richiede una adeguata conoscenza del contesto geologico in cui questi terreni sono inseriti ed una capacità di monitoraggio degli interventi di bonifica ed estensione delle coltivazioni in atto; entrambe conoscenze necessarie alla definizione di un piano di sviluppo economico sostenibile. Con l’intento di contribuire ad una valutazione delle effettive potenzialità del telerilevamento come strumento di informazione territoriale, sono state sperimentate tecniche di classificazione di immagini multispettrali ASTER ed iperspettrali Hyperion di archivio per discriminare la litologia superficiale sulle aree adiacenti al lago Qarun nell’oasi del Fayyum. Le stesse immagini Hyperion di archivio più altre appositamente acquisite sono state utilizzate, assieme ad immagini multispettrali ALI, per la valutazione qualitativa e quantitativa di parametri di qualità delle acque, attraverso l’applicazione di modelli empirici di correlazione. Infine, per valutare l’ipotesi che il deterioramento della qualità delle acque possa essere correlato ai processi di bonifica ed estensione delle coltivazioni in atto negli ultimi decenni, le immagini dell’archivio Landsat sono state utilizzate per analisi di change detection. Per quanto riguarda il problema della validazione dei risultati, si è fatto uso di alcuni dati di verità a terra acquisiti nel corso di un survey preliminare effettuato nell’Ottobre 2010. I campioni di roccia prelevati e le misure di conducibilità elettrica delle acque del lago, benché in numero estremamente limitato per la brevità della missione e le ovvie difficoltà logistiche, consentono alcune valutazioni preliminari sui prodotti ottenuti dalle elaborazioni. Sui campioni di roccia e sabbie sciolte, in particolare, sono state effettuate misure di riflettività in laboratorio ed analisi mineralogiche dettagliate. Per la valutazione della qualità delle acque, più precisamente delle concentrazioni di clorofilla, la metodologia utilizzata per il caso di studio egiziano è stata applicata anche sul tratto costiero adriatico antistante le foci dei fiumi Tronto e Salinello. In questo sito sono state effettuate misure in situ di conducibilità elettrica ed il prelievo di campioni di acqua per la determinazione in laboratorio delle concentrazioni di clorofilla. I risultati ottenuti hanno evidenziato le potenzialità offerte dall’informazione spettrale contenuta nelle immagini satellitari e consentono l’individuazione di alcune pratiche operative. D’altro canto hanno anche messo in luce le carenze dei modelli attualmente esistenti, nonché le criticità legate alla correzione atmosferica delle grandezze radiometriche rilevate.

On the geometry of the spin-statistics connection in quantum mechanics

The Spin-Statistics theorem states that the statistics of a system of identical particles is determined by their spin: Particles of integer spin are Bosons (i.e. obey Bose-Einstein statistics), whereas particles of half-integer spin are Fermions (i.e. obey Fermi-Dirac statistics). Since the original proof by Fierz and Pauli, it has been known that the connection between Spin and Statistics follows from the general principles of relativistic Quantum Field Theory. In spite of this, there are different approaches to Spin-Statistics and it is not clear whether the theorem holds under assumptions that are different, and even less restrictive, than the usual ones (e.g. Lorentz-covariance). Additionally, in Quantum Mechanics there is a deep relation between indistinguishabilty and the geometry of the configuration space. This is clearly illustrated by Gibbs' paradox. Therefore, for many years efforts have been made in order to find a geometric proof of the connection between Spin and Statistics. Recently, various proposals have been put forward, in which an attempt is made to derive the Spin-Statistics connection from assumptions different from the ones used in the relativistic, quantum field theoretic proofs. Among these, there is the one due to Berry and Robbins (BR), based on the postulation of a certain single-valuedness condition, that has caused a renewed interest in the problem. In the present thesis, we consider the problem of indistinguishability in Quantum Mechanics from a geometric-algebraic point of view. An approach is developed to study configuration spaces Q having a finite fundamental group, that allows us to describe different geometric structures of Q in terms of spaces of functions on the universal cover of Q. In particular, it is shown that the space of complex continuous functions over the universal cover of Q admits a decomposition into C(Q)-submodules, labelled by the irreducible representations of the fundamental group of Q, that can be interpreted as the spaces of sections of certain flat vector bundles over Q. With this technique, various results pertaining to the problem of quantum indistinguishability are reproduced in a clear and systematic way. Our method is also used in order to give a global formulation of the BR construction. As a result of this analysis, it is found that the single-valuedness condition of BR is inconsistent. Additionally, a proposal aiming at establishing the Fermi-Bose alternative, within our approach, is made.

A LES study of a modified Ahmed body geometry

A numerical study using Large Eddy Simulation Coherent Structure Model (LES-CSM), of the flow around a simplified Ahmed body, has been done in this work of thesis. The models used are two salient geometries from the experimental investigation performed in [1], and consist, in particular, in two notch-back body geometries. Six simulation are carried out in total, changing Reynolds number and back-light angle of the model’s rear part. The Reynolds numbers used, based on the height of the models and the free stream velocity, are Re = 10000, Re = 30000 and Re = 50000. The back-light angles of the slanted surface with respect to the horizontal roof surface, that characterizes the vehicle, are taken as B = 31.8◦ and B = 42◦ respectively. The experimental results in [1] have shown that, depending on the parameter B, asymmetric and symmetric averaged flow over the back-light and in the wake for a symmetric geometry can be observed. The aims of the present work of master thesis are principally two. The first aim is to investigate and confirm the influence of the parameter B on the presence of the asymmetry of the averaged flow, and confirm the features described in the experimental results. The second important aspect is to investigate and observe the influence of the second variable, the Reynolds number, in the developing of the asymmetric flow itself. The results have shown the presence of the mentioned asymmetry as well as an influence of the Reynolds number on it.

Deep geometry of subduction below the Andean belt of Colombia as revealed by seismic tomography

In this study new tomographic models of Colombia were calculated. I used the seismicity recorded by the Colombian seismic network during the period 2006-2009. In this time period, the improvement of the seismic network yields more stable hypocentral results with respect to older data set and allows to compute new 3D Vp and Vp/Vs models. The final dataset consists of 10813 P- and 8614 S-arrival times associated to 1405 earthquakes. Tests with synthetic data and resolution analysis indicate that velocity models are well constrained in central, western and southwestern Colombia to a depth of 160 km; the resolution is poor in the northern Colombia and close to Venezuela due to a lack of seismic stations and seismicity. The tomographic models and the relocated seismicity indicate the existence of E-SE subducting Nazca lithosphere beneath central and southern Colombia. The North-South changes in Wadati-Benioff zone, Vp & Vp/Vs pattern and volcanism, show that the downgoing plate is segmented by slab tears E-W directed, suggesting the presence of three sectors. Earthquakes in the northernmost sector represent most of the Colombian seimicity and concentrated on 100-170 km depth interval, beneath the Eastern Cordillera. Here a massive dehydration is inferred, resulting from a delay in the eclogitization of a thickened oceanic crust in a flat-subduction geometry. In this sector a cluster of intermediate-depth seismicity (Bucaramanga Nest) is present beneath the elbow of the Eastern Cordillera, interpreted as the result of massive and highly localized dehydration phenomenon caused by a hyper-hydrous oceanic crust. The central and southern sectors, although different in Vp pattern show, conversely, a continuous, steep and more homogeneous Wadati-Benioff zone with overlying volcanic areas. Here a "normalthickened" oceanic crust is inferred, allowing for a gradual and continuous metamorphic reactions to take place with depth, enabling the fluid migration towards the mantle wedge.

Kinematics of the Sicily and Calabria Subduction System from Elastic Block Modeling of GPS Data

We use data from about 700 GPS stations in the EuroMediterranen region to investigate the present-day behavior of the the Calabrian subduction zone within the Mediterranean-scale plates kinematics and to perform local scale studies about the strain accumulation on active structures. We focus attenction on the Messina Straits and Crati Valley faults where GPS data show extentional velocity gradients of ∼3 mm/yr and ∼2 mm/yr, respectively. We use dislocation model and a non-linear constrained optimization algorithm to invert for fault geometric parameters and slip-rates and evaluate the associated uncertainties adopting a bootstrap approach. Our analysis suggest the presence of two partially locked normal faults. To investigate the impact of elastic strain contributes from other nearby active faults onto the observed velocity gradient we use a block modeling approach. Our models show that the inferred slip-rates on the two analyzed structures are strongly impacted by the assumed locking width of the Calabrian subduction thrust. In order to frame the observed local deformation features within the present- day central Mediterranean kinematics we realyze a statistical analysis testing the indipendent motion (w.r.t. the African and Eurasias plates) of the Adriatic, Cal- abrian and Sicilian blocks. Our preferred model confirms a microplate like behaviour for all the investigated blocks. Within these kinematic boundary conditions we fur- ther investigate the Calabrian Slab interface geometry using a combined approach of block modeling and χ2ν statistic. Almost no information is obtained using only the horizontal GPS velocities that prove to be a not sufficient dataset for a multi-parametric inversion approach. Trying to stronger constrain the slab geometry we estimate the predicted vertical velocities performing suites of forward models of elastic dislocations varying the fault locking depth. Comparison with the observed field suggest a maximum resolved locking depth of 25 km.

Convertitori di potenza multi-sorgente per applicazioni di energy harvesting

L’obiettivo di questa tesi è stato lo svilippo di un convertitore di potenza per applicazioni di energy harvesting in grado di convogliare l’energia estratta da diversi tipi di trasduttori di grandezze ambientali in un unico dispositivo di storage, ad es. un condensatore, utilizzabile per alimentare circuiti a basso consumo. L’idea di base è stata quella di ottimizzare il trasferimento di energia, attraverso una rete logica in grado di gestire le priorità di conversione dalle diverse tipologie di sorgenti e grazie ad una implementazione di un algoritmo di Maximum Power Point Tracking. In base alle specifiche di progetto, in una prima fase è stata sviluppata la rete a livello funzionale, poi sono stati scelti i componenti più opportuni ed infine si è verificato il funzionamento attraverso simulazioni circuitali.