Lipschitz regularity for weak solutions of parabolic p-Laplacian type equations in certain subriemannian structures

The main aim of the thesis is to prove the local Lipschitz regularity of the weak solutions to a class of parabolic PDEs modeled on the parabolic p-Laplacian. This result is well known in the Euclidean case and recently has been extended in the Heisenberg group, while higher regularity results are not known in subriemannian parabolic setting. In this thesis we will consider vector fields more general than those in the Heisenberg setting, introducing some technical difficulties. To obtain our main result we will use a Moser-like iteration. Due to the non linearity of the equation, we replace the usual parabolic cylinders with new ones, whose dimension also depends on the L^p norm of the solution. In addition, we deeply simplify the iterative procedure, using the standard Sobolev inequality, instead of the parabolic one.

Gpu-based many-core architecture emulation: A double level approach

The efficient emulation of a many-core architecture is a challenging task, each core could be emulated through a dedicated thread and such threads would be interleaved on an either single-core or a multi-core processor. The high number of context switches will results in an unacceptable performance. To support this kind of application, the GPU computational power is exploited in order to schedule the emulation threads on the GPU cores. This presents a non trivial divergence issue, since GPU computational power is offered through SIMD processing elements, that are forced to synchronously execute the same instruction on different memory portions. Thus, a new emulation technique is introduced in order to overcome this limitation: instead of providing a routine for each ISA opcode, the emulator mimics the behavior of the Micro Architecture level, here instructions are date that a unique routine takes as input. Our new technique has been implemented and compared with the classic emulation approach, in order to investigate the chance of a hybrid solution.

The Scrum approach to software development

Agile methodologies have become the standard approach to software development. The most popular and used one is Scrum. Scrum is a very simple and flexible framework that respond to unpredictability in a really effective way. However, his implementation must be correct, and since Scrum tells you what to do but not how to do it, this is not trivial. In this thesis I will describe the Scrum Framework, how to implement it and a tool that can help to do this. The thesis is divided into three parts. The first part is called Scrum. Here I will introduce the framework itself, its key concepts and its components. In Scrum there are three components: roles, meetings and artifacts. Each of these is meant to accomplish a series of specific tasks. After describing the “what to do”, in the second part, Best Practices, I will focus on the “how to do it”. For example, how to decide which items should be included in the next sprint, how to estimate tasks, and how should the team workspace be. Finally, in the third part called Tools, I will introduce Visual Studio Online, a cloud service from Microsoft that offers Git and TFVC repositories and the opportunity to manage projects with Scrum. == Versione italiana: I metodi Agile sono diventati l’approccio standard per lo sviluppo di software. Il più famoso ed utilizzato è Scrum. Scrum è un framework molto semplice e flessibile che risponde ai cambiamenti in una maniera molto efficace. La sua implementazione deve però essere corretta, e visto che Scrum ci dice cosa fare ma non come farlo, questo non risulta essere immediato. In questa tesi descriverò Scrum, come implementarlo ed uno strumento che ci può aiutare a farlo. La tesi è divisa in tre parti. La prima parte è chiamata Scrum. Qui introdurrò il framework, i suoi concetti base e le sue componenti. In Scrum ci sono tre componenti: i ruoli, i meeting e gli artifact. Ognuno di questi è studiato per svolgere una serie di compiti specifici. Dopo aver descritto il “cosa fare”, nella seconda parte, Best Practices, mi concentrerò sul “come farlo”. Ad esempio, come decidere quali oggetti includere nella prossima sprint, come stimare ogni task e come dovrebbe essere il luogo di lavoro del team. Infine, nella terza parte chiamata Tools, introdurrò Visual Studio Online, un servizio cloud della Microsoft che offre repository Git e TFVC e l’opportunità di gestire un progetto con Scrum.

Variational Quantum Splines: Moving Beyond Linearity for Quantum Activation Functions

Activation functions within neural networks play a crucial role in Deep Learning since they allow to learn complex and non-trivial patterns in the data. However, the ability to approximate non-linear functions is a significant limitation when implementing neural networks in a quantum computer to solve typical machine learning tasks. The main burden lies in the unitarity constraint of quantum operators, which forbids non-linearity and poses a considerable obstacle to developing such non-linear functions in a quantum setting. Nevertheless, several attempts have been made to tackle the realization of the quantum activation function in the literature. Recently, the idea of the QSplines has been proposed to approximate a non-linear activation function by implementing the quantum version of the spline functions. Yet, QSplines suffers from various drawbacks. Firstly, the final function estimation requires a post-processing step; thus, the value of the activation function is not available directly as a quantum state. Secondly, QSplines need many error-corrected qubits and a very long quantum circuits to be executed. These constraints do not allow the adoption of the QSplines on near-term quantum devices and limit their generalization capabilities. This thesis aims to overcome these limitations by leveraging hybrid quantum-classical computation. In particular, a few different methods for Variational Quantum Splines are proposed and implemented, to pave the way for the development of complete quantum activation functions and unlock the full potential of quantum neural networks in the field of quantum machine learning.

Motor Unit Spike Trains Recontruction from sEMG Signals for Gesture Classification on a Low-Power Processing Platform

Hand gesture recognition based on surface electromyography (sEMG) signals is a promising approach for the development of intuitive human-machine interfaces (HMIs) in domains such as robotics and prosthetics. The sEMG signal arises from the muscles' electrical activity, and can thus be used to recognize hand gestures. The decoding from sEMG signals to actual control signals is non-trivial; typically, control systems map sEMG patterns into a set of gestures using machine learning, failing to incorporate any physiological insight. This master thesis aims at developing a bio-inspired hand gesture recognition system based on neuromuscular spike extraction rather than on simple pattern recognition. The system relies on a decomposition algorithm based on independent component analysis (ICA) that decomposes the sEMG signal into its constituent motor unit spike trains, which are then forwarded to a machine learning classifier. Since ICA does not guarantee a consistent motor unit ordering across different sessions, 3 approaches are proposed: 2 ordering criteria based on firing rate and negative entropy, and a re-calibration approach that allows the decomposition model to retain information about previous sessions. Using a multilayer perceptron (MLP), the latter approach results in an accuracy up to 99.4% in a 1-subject, 1-degree of freedom scenario. Afterwards, the decomposition and classification pipeline for inference is parallelized and profiled on the PULP platform, achieving a latency < 50 ms and an energy consumption < 1 mJ. Both the classification models tested (a support vector machine and a lightweight MLP) yielded an accuracy > 92% in a 1-subject, 5-classes (4 gestures and rest) scenario. These results prove that the proposed system is suitable for real-time execution on embedded platforms and also capable of matching the accuracy of state-of-the-art approaches, while also giving some physiological insight on the neuromuscular spikes underlying the sEMG.

Gravitational waves as dark sirens: an astrophysical and cosmological analysis

Despite the success of the ΛCDM model in describing the Universe, a possible tension between early- and late-Universe cosmological measurements is calling for new independent cosmological probes. Amongst the most promising ones, gravitational waves (GWs) can provide a self-calibrated measurement of the luminosity distance. However, to obtain cosmological constraints, additional information is needed to break the degeneracy between parameters in the gravitational waveform. In this thesis, we exploit the latest LIGO-Virgo-KAGRA Gravitational Wave Transient Catalog (GWTC-3) of GW sources to constrain the background cosmological parameters together with the astrophysical properties of Binary Black Holes (BBHs), using information from their mass distribution. We expand the public code MGCosmoPop, previously used for the application of this technique, by implementing a state-of-the-art model for the mass distribution, needed to account for the presence of non-trivial features, i.e. a truncated power law with two additional Gaussian peaks, referred to as Multipeak. We then analyse GWTC-3 comparing this model with simpler and more commonly adopted ones, both in the case of fixed and varying cosmology, and assess their goodness-of-fit with different model selection criteria, and their constraining power on the cosmological and population parameters. We also start to explore different sampling methods, namely Markov Chain Monte Carlo and Nested Sampling, comparing their performances and evaluating the advantages of both. We find concurring evidence that the Multipeak model is favoured by the data, in line with previous results, and show that this conclusion is robust to the variation of the cosmological parameters. We find a constraint on the Hubble constant of H0 = 61.10+38.65−22.43 km/s/Mpc (68% C.L.), which shows the potential of this method in providing independent constraints on cosmological parameters. The results obtained in this work have been included in [1].

Phenomenology of top-philic axion-like particles

Axion like particles (ALPs), i.e., pseudo-scalar bosons interacting via derivative couplings, are a generic feature of many new physics scenarios, including those addressing the strong-CP problem and/or the existence of dark matter. Their phenomenology is very rich, with a wide range of scales and interactions being directly probed at very different experiments, from accelerators to observatories. In this thesis, we explore the possibility that ALPs might indirectly affect precision collider observables. In particular, we consider an ALPs that preferably couple to the top quark (top-philic) and we study new-physics 1- loop corrections to processes involving top quarks in the final state. Our study stems from the simple, yet non-trivial observation that 1-loop corrections are infrared finite even in the case of negligible ALP masses and therefore can be considered on their own. We compute the 1-loop corrections of new physics analytically in key cases involving top quark pair production and then implement and validate a fully general next-to-leading-order model in MadGraph5_aMC@NLO that allows to compute virtual effects for any process of interest. A detailed study of the expected sensitivity to virtual ALPs in ttbar production at the LHC is performed.