Effect of pulsed electromagnetic fields (pemfs) on muscle activity, tissue oxygenation and vo2 during exercise.

PEMF are a medical and non-invasive therapy successfully used for clinical treatments of bone disease, due to the piezoelectric effect that improve bone mass and density, by the stimulation of osteoblastogenesis, with modulation of calcium storages and mineral metabolism. PEMF enhance tissue oxygenation, microcirculation and angiogenesis, in rats and cells erythrocytes, in cells-free assay. Such responses could be caused by a modulation of nitric oxide signal and interaction between PEMF and Ca2+/NO/cGMP/PKG signal. PEMF improve blood flow velocity of smallest vein without changing their diameter. PEMF therapy helpful in patients with diabetes, due to increased microcirculation trough enhance capillary blood velocity and diameter. We investigated the influence of stimulation on muscular activity, tissue oxygenation and pulmonary VO2, during exercise, on different intensity, as heavy or moderate, different subjects, as a athlete or sedentary, and different sport activity, as a cycling or weightlifting. In athletes, we observed a tendency for a greater change and a faster kinetic of HHb concentration. PEMF increased the velocity and the quantity of muscle O2 available, leading to accelerate the HHb kinetics. Stimulation induced a bulk muscle O2 availability and a greater muscle O2 extraction, leading to a reduced time delay of the HHb slow component. Stimulation increased the amplitude of muscle activity under different conditions, likely caused by the effect of PEMF on contraction mechanism of muscular fibers, by the change of membrane permeability and Ca2+ channel conduction. In athletes, we observed an increase of overall activity during warm-up. In sedentary people, stimulation increased the magnitude of muscle activity during moderate constant-load exercise and warm-up. In athletes and weightlifters, stimulation caused an increase of blood lactate concentration during exercise, confirming a possible influence of stimulation on muscle activity and on glycolytic metabolism of type-II muscular fibers.

About stabilization of non-minimum phase systems by output feedback

This thesis work has been motivated by an internal benchmark dealing with the output regulation problem of a nonlinear non-minimum phase system in the case of full-state feedback. The system under consideration structurally suffers from finite escape time, and this condition makes the output regulation problem very hard even for very simple steady-state evolution or exosystem dynamics, such as a simple integrator. This situation leads to studying the approaches developed for controlling Non-minimum phase systems and how they affect feedback performances. Despite a lot of frequency domain results, only a few works have been proposed for describing the performance limitations in a state space system representation. In particular, in our opinion, the most relevant research thread exploits the so-called Inner-Outer Decomposition. Such decomposition allows splitting the Non-minimum phase system under consideration into a cascade of two subsystems: a minimum phase system (the outer) that contains all poles of the original system and an all-pass Non-minimum phase system (the inner) that contains all the unavoidable pathologies of the unstable zero dynamics. Such a cascade decomposition was inspiring to start working on functional observers for linear and nonlinear systems. In particular, the idea of a functional observer is to exploit only the measured signals from the system to asymptotically reconstruct a certain function of the system states, without necessarily reconstructing the whole state vector. The feature of asymptotically reconstructing a certain state functional plays an important role in the design of a feedback controller able to stabilize the Non-minimum phase system.

Non-thermal phenomena in galaxy clusters: the LOFAR revolution

Turbulence introduced into the intra-cluster medium (ICM) through cluster merger events transfers energy to non-thermal components (relativistic particles and magnetic fields) and can trigger the formation of diffuse synchrotron radio sources. Owing to their steep synchrotron spectral index, such diffuse sources can be better studied at low radio frequencies. In this respect, the LOw Frequency ARray (LOFAR) is revolutionizing our knowledge thanks to its unprecedented resolution and sensitivity below 200 MHz. In this Thesis we focus on the study of radio halos (RHs) by using LOFAR data. In the first part of this work we analyzed the largest-ever sample of galaxy clusters observed at radio frequencies. This includes 309 Planck clusters from the Second Data Release of the LOFAR Two Metre Sky Survey (LoTSS-DR2), which span previously unexplored ranges of mass and redshift. We detected 83 RHs, half of which being new discoveries. In 140 clusters we lack a detected RH; for this sub-sample we developed new techniques to derive upper limits to their radio powers. By comparing detections and upper limits, we carried out the first statistical analysis of populations of clusters observed at low frequencies and tested theoretical formation models. In the second part of this Thesis we focused on ultra-steep spectrum radio halos. These sources are almost undetected at GHz frequencies, but are thought to be common at low frequencies. We presented LOFAR observations of two interesting clusters hosting ultra-steep spectrum radio halos. With complementary radio and X-ray observations we constrained the properties and origin of these targets.

Data driven regularization models of non-linear ill-posed inverse problems in imaging

Imaging technologies are widely used in application fields such as natural sciences, engineering, medicine, and life sciences. A broad class of imaging problems reduces to solve ill-posed inverse problems (IPs). Traditional strategies to solve these ill-posed IPs rely on variational regularization methods, which are based on minimization of suitable energies, and make use of knowledge about the image formation model (forward operator) and prior knowledge on the solution, but lack in incorporating knowledge directly from data. On the other hand, the more recent learned approaches can easily learn the intricate statistics of images depending on a large set of data, but do not have a systematic method for incorporating prior knowledge about the image formation model. The main purpose of this thesis is to discuss data-driven image reconstruction methods which combine the benefits of these two different reconstruction strategies for the solution of highly nonlinear ill-posed inverse problems. Mathematical formulation and numerical approaches for image IPs, including linear as well as strongly nonlinear problems are described. More specifically we address the Electrical impedance Tomography (EIT) reconstruction problem by unrolling the regularized Gauss-Newton method and integrating the regularization learned by a data-adaptive neural network. Furthermore we investigate the solution of non-linear ill-posed IPs introducing a deep-PnP framework that integrates the graph convolutional denoiser into the proximal Gauss-Newton method with a practical application to the EIT, a recently introduced promising imaging technique. Efficient algorithms are then applied to the solution of the limited electrods problem in EIT, combining compressive sensing techniques and deep learning strategies. Finally, a transformer-based neural network architecture is adapted to restore the noisy solution of the Computed Tomography problem recovered using the filtered back-projection method.

Spectral asymptotic properties of semi-regular non-commutative harmonic oscillators

The study carried out in this thesis is devoted to spectral analysis of systems of PDEs related also with quantum physics models. Namely, the research deals with classes of systems that contain certain quantum optics models such as Jaynes-Cummings, Rabi and their generalizations that describe light-matter interaction. First we investigate the spectral Weyl asymptotics for a class of semiregular systems, extending to the vector-valued case results of Helffer and Robert, and more recently of Doll, Gannot and Wunsch. Actually, the asymptotics by Doll, Gannot and Wunsch is more precise (that is why we call it refined) than the classical result by Helffer and Robert, but deals with a less general class of systems, since the authors make an hypothesis on the measure of the subset of the unit sphere on which the tangential derivatives of the X-Ray transform of the semiprincipal symbol vanish to infinity order. Abstract Next, we give a meromorphic continuation of the spectral zeta function for semiregular differential systems with polynomial coefficients, generalizing the results by Ichinose and Wakayama and Parmeggiani. Finally, we state and prove a quasi-clustering result for a class of systems including the aforementioned quantum optics models and we conclude the thesis by showing a Weyl law result for the Rabi model and its generalizations.