Lie algebras and triple systems

This thesis is dedicated to the Tits-Kantor-Koecher (TKK) construction which establishes a bijective correspondence between unital Jordan algebras and shortly graded Lie algebras with Z-grading induced by an sl_2-triple. It is based on the observation that if g is a Lie algebra with a short Z-grading and f lies in g_1, then the formula ab=[[a,f],b] defines a structure of a Jordan algebra on g_{-1}. The TKK construction has been extended to Jordan triple systems and, more recently, to the so-called Kantor triple systems. These generalizations are studied in the thesis.

Real forms of Lie algebras and Lie superalgebras

In questa tesi abbiamo studiato le forme reali di algebre e superalgebre di Lie. Il lavoro si suddivide in tre capitoli diversi, il primo è di introduzione alle algebre di Lie e serve per dare le prime basi di questa teoria e le notazioni. Nel secondo capitolo abbiamo introdotto le algebre compatte e le forme reali. Abbiamo visto come sono correlate tra di loro tramite strumenti potenti come l'involuzione di Cartan e relativa decomposizione ed i diagrammi di Vogan e abbiamo introdotto un algoritmo chiamato "push the button" utile per verificare se due diagrammi di Vogan sono equivalenti. Il terzo capitolo segue la struttura dei primi due, inizialmente abbiamo introdotto le superalgebre di Lie con relativi sistemi di radici e abbiamo proseguito studiando le relative forme reali, diagrammi di Vogan e abbiamo introdotto anche qua l'algoritmo "push the button".

Analysis and detection of partial discharges in an electric motor of a hybrid supercar.

The objective of this thesis was the development of a new detection method of partial discharge (PD) activity in the stator of an electrical hybrid supercar fed by a silicon carbide converter, for which detection with common methods make it very difficult to separate PD pulses from switching noise. This work focused on the analysis and detection of partial discharges making use of an antenna, a peak detector, and an oscilloscope capable of capturing the electromagnetic pulses emitted during PD activity. Validation of the proposed method was done by comparing the partial discharge inception voltage (PDIV) detected by this system with the one obtained from an optical method of proven accuracy, with different rise times and samples. Further development of this method, if proved successful on a full stator, can help increasing the overall reliability of the car, potentially allowing for real time detection of PD activity and predictive maintenance before failure of the insulation system in a hybrid vehicle.

Construction and detectors’ characterization of a new detection system for FAMU Experiment

From 2010, the Proton Radius has become one of the most interest value to determine. The first proof of not complete understanding of its internal structure was the measurement of the Lamb Shift using the muonic hydrogen, leading to a value 7σ lower. A new road so was open and the Proton Radius Puzzle epoch begun. FAMU Experiment is a project that tries to give an answer to this Puzzle implementing high precision experimental apparatus. The work of this thesis is based on the study, construction and first characterization of a new detection system. Thanks to the previous experiments and simulations, this apparatus is composed by 17 detectors positioned on a semicircular crown with the related electronic circuit. The detectors' characterization is based on the use of a LabView program controlling a digital potentiometer and on other two analog potentiometers, all three used to set the amplitude of each detector to a predefined value, around 1.2 V, set on the oscilloscope by which is possible to observe the signal. This is the requirement in order to have, in the final measurement, a single high peak given by the sum of all the signals coming from the detectors. Each signal has been acquired for almost half of an hour, but the entire circuit has been maintained active for more time to observe its capacity to work for longer periods. The principal results of this thesis are given by the spectra of 12 detectors and the corresponding values of Voltages, FWHM and Resolution. The outcomes of the acquisitions show also another expected behavior: the strong dependence of the detectors from the temperature, demonstrating that an its change causes fluctuations in the signal. In turn, these fluctuations will affect the spectrum, resulting in a shifting of the curve and a lower Resolution. On the other hand, a measurement performed in stable conditions will lead to accordance between the nominal and experimental measurements, as for the detectors 10, 11 and 12 of our system.

Calibration of the detector flight models for the HERMES and SPIRIT nanosatellite missions

The High Energy Rapid Modular Ensemble of Satellites (HERMES) is a new mission concept involving the development of a constellation of six CubeSats in low Earth orbit with new miniaturized instruments that host a hybrid Silicon Drift Detector/GAGG:Ce based system for X-ray and γ-ray detection, aiming to monitor high-energy cosmic transients, such as Gamma Ray Bursts and the electromagnetic counterparts of gravitational wave events. The HERMES constellation will also operate together with the Australian-Italian SpIRIT mission, which will house a HERMES-like detector. The HERMES pathfinder mini-constellation, consisting of six satellites plus SpIRIT, is likely to be launched in 2023. The HERMES detectors are based on the heritage of the Italian ReDSoX collaboration, with joint design and production by INFN-Trieste and Fondazione Bruno Kessler, and the involvement of several Italian research institutes and universities. An application-specific, low-noise, low-power integrated circuit (ASIC) called LYRA was conceived and designed for the HERMES readout electronics. My thesis project focuses on the ground calibrations of the first HERMES and SpIRIT flight detectors, with a performance assessment and characterization of the detectors. The first part of this work addresses measurements and experimental tests on laboratory prototypes of the HERMES detectors and their front-end electronics, while the second part is based on the design of the experimental setup for flight detector calibrations and related functional tests for data acquisition, as well as the development of the calibration software. In more detail, the calibration parameters (such as the gain of each detector channel) are determined using measurements with radioactive sources, performed at different operating temperatures between -20°C and +20°C by placing the detector in a suitable climate chamber. The final part of the thesis involves the analysis of the calibration data and a discussion of the results.

Quality controls for the Mu2e electromagnetic calorimeter and R&D studies for the muon capture rate determination

According to the SM, while Lepton Flavour Violation is allowed in the neutral sector, Charged Lepton Flavour Violation (CLFV) processes are forbidden. The Mu2e Experiment at Fermilab will search for the CLFV process of neutrinoless conversion of a muon into an electron within the field of an Al nucleus. The Mu2e detectors and its state-of-the-art superconducting magnetic system are presented, with special focus put to the electromagnetic crystal calorimeter. The calorimeter is composed by two annular disks, each one hosting pure CsI crystals read-out by custom silicon photomultipliers (SiPMs). The SiPMs are amplified by custom electronics (FEE) and are glued to copper holders in group of 2 SiPMs and 2 FEE boards thus forming a crystal Readout Unit. These Readout Units are being tested at the Quality Control (QC) Station, whose design, realization and operations are presented in this work. The QC Station allows to determine the gain, the response and the photon detection efficiency of each unit and to evaluate the dependence of these parameters from the supply voltage and temperature. The station is powered by two remotely-controlled power supplies and monitored thanks to a Slow Control system which is also illustrated in this work. In this thesis, we also demonstrated that the calorimeter can perform its own measurement of the Mu2e normalization factor, i.e. the counting of the 1.8 MeV photon line produced in nuclear muon captures. A specific calorimeter sub-system called CAPHRI, composed by four LYSO crystals with SiPM readout, has been designed and tested. We simulated the capability of this system on performing this task showing that it can get a faster and more reliable measurement of the muon capture rates with respect to the current Mu2e detector dedicated to this measurement. The characterization of energy resolution and response uniformity of the four procured LYSO crystals are llustrated.

Analysis of the Kohn Laplacian on the Heisenberg Group and on Cauchy-Riemann Manifolds

The purpose of this study is to analyse the regularity of a differential operator, the Kohn Laplacian, in two settings: the Heisenberg group and the strongly pseudoconvex CR manifolds. The Heisenberg group is defined as a space of dimension 2n+1 with a product. It can be seen in two different ways: as a Lie group and as the boundary of the Siegel UpperHalf Space. On the Heisenberg group there exists the tangential CR complex. From this we define its adjoint and the Kohn-Laplacian. Then we obtain estimates for the Kohn-Laplacian and find its solvability and hypoellipticity. For stating L^p and Holder estimates, we talk about homogeneous distributions. In the second part we start working with a manifold M of real dimension 2n+1. We say that M is a CR manifold if some properties are satisfied. More, we say that a CR manifold M is strongly pseudoconvex if the Levi form defined on M is positive defined. Since we will show that the Heisenberg group is a model for the strongly pseudo-convex CR manifolds, we look for an osculating Heisenberg structure in a neighborhood of a point in M, and we want this structure to change smoothly from a point to another. For that, we define Normal Coordinates and we study their properties. We also examinate different Normal Coordinates in the case of a real hypersurface with an induced CR structure. Finally, we define again the CR complex, its adjoint and the Laplacian operator on M. We study these new operators showing subelliptic estimates. For that, we don't need M to be pseudo-complex but we ask less, that is, the Z(q) and the Y(q) conditions. This provides local regularity theorems for Laplacian and show its hypoellipticity on M.

Fermion masses, leptogenesis and gravitational waves in SO(10)

Grand Unification Theories (GUTs) predict the unification of three of the fundamental forces and are a possible extension of the Standard Model, some of them predict neutrino mass and baryon asymmetry. We consider a minimal non-supersymmetric $SO(10)$ GUT model that can reproduce the observed fermionic masses and mixing parameters of the Standard Model. We calculate the scales of spontaneous symmetry breaking from the GUT to the Standard Model gauge group using two-loop renormalisation group equations. This procedure determines the proton decay rate and the scale of $U(1)_{B-L}$ breaking, which generates cosmic strings, and the right-handed neutrino mass scales. Consequently, the regions of parameter space where thermal leptogenesis is viable are identified and correlated with the fermion masses and mixing, the neutrinoless double beta decay rate, the proton decay rate, and the gravitational wave signal resulting from the network of cosmic strings. We demonstrate that this framework, which can explain the Standard Model fermion masses and mixing and the observed baryon asymmetry, will be highly constrained by the next generation of gravitational wave detectors and neutrino oscillation experiments which will also constrain the proton lifetime

Ict security: Defence strategies against targeted attacks

L’avanzare delle tecnologie ICT e l’abbattimento dei costi di produzione hanno portato ad un aumento notevole della criminalità informatica. Tuttavia il cambiamento non è stato solamente quantitativo, infatti si può assistere ad un paradigm-shift degli attacchi informatici da completamente opportunistici, ovvero senza un target specifico, ad attacchi mirati aventi come obiettivo una particolare persona, impresa o nazione. Lo scopo della mia tesi è quello di analizzare modelli e tassonomie sia di attacco che di difesa, per poi valutare una effettiva strategia di difesa contro gli attacchi mirati. Il lavoro è stato svolto in un contesto aziendale come parte di un tirocinio. Come incipit, ho effettuato un attacco mirato contro l’azienda in questione per valutare la validità dei sistemi di difesa. L’attacco ha avuto successo, dimostrando l’inefficacia di moderni sistemi di difesa. Analizzando i motivi del fallimento nel rilevare l’attacco, sono giunto a formulare una strategia di difesa contro attacchi mirati sotto forma di servizio piuttosto che di prodotto. La mia proposta è un framework concettuale, chiamato WASTE (Warning Automatic System for Targeted Events) il cui scopo è fornire warnings ad un team di analisti a partire da eventi non sospetti, ed un business process che ho nominato HAZARD (Hacking Approach for Zealot Attack Response and Detection), che modella il servizio completo di difesa contro i targeted attack. Infine ho applicato il processo all’interno dell’azienda per mitigare minacce ed attacchi informatici.

Machine learning "as a service" for high energy physics (MLaaS4HEP): evolution of a framework for ML-based physics analyses

The scientific success of the LHC experiments at CERN highly depends on the availability of computing resources which efficiently store, process, and analyse the amount of data collected every year. This is ensured by the Worldwide LHC Computing Grid infrastructure that connect computing centres distributed all over the world with high performance network. LHC has an ambitious experimental program for the coming years, which includes large investments and improvements both for the hardware of the detectors and for the software and computing systems, in order to deal with the huge increase in the event rate expected from the High Luminosity LHC (HL-LHC) phase and consequently with the huge amount of data that will be produced. Since few years the role of Artificial Intelligence has become relevant in the High Energy Physics (HEP) world. Machine Learning (ML) and Deep Learning algorithms have been successfully used in many areas of HEP, like online and offline reconstruction programs, detector simulation, object reconstruction, identification, Monte Carlo generation, and surely they will be crucial in the HL-LHC phase. This thesis aims at contributing to a CMS R&D project, regarding a ML "as a Service" solution for HEP needs (MLaaS4HEP). It consists in a data-service able to perform an entire ML pipeline (in terms of reading data, processing data, training ML models, serving predictions) in a completely model-agnostic fashion, directly using ROOT files of arbitrary size from local or distributed data sources. This framework has been updated adding new features in the data preprocessing phase, allowing more flexibility to the user. Since the MLaaS4HEP framework is experiment agnostic, the ATLAS Higgs Boson ML challenge has been chosen as physics use case, with the aim to test MLaaS4HEP and the contribution done with this work.