Weighted Inequalities and Lipschitz Spaces

In this thesis I have characterized the trace measures for particular potential spaces of functions defined on R^n, but "mollified" so that the potentials are de facto defined on the upper half-space of R^n. The potential functions are kind Riesz-Bessel. The characterization of trace measures for these spaces is a test condition on elementary sets of the upper half-space. To prove the test condition as sufficient condition for trace measures, I had give an extension to the case of upper half-space of the Muckenhoupt-Wheeden and Wolff inequalities. Finally I characterized the Carleson-trace measures for Besov spaces of discrete martingales. This is a simplified discrete model for harmonic extensions of Lipschitz-Besov spaces.

Spectrum Sensing Algorithms for Cognitive Radio Applications

Future wireless communications systems are expected to be extremely dynamic, smart and capable to interact with the surrounding radio environment. To implement such advanced devices, cognitive radio (CR) is a promising paradigm, focusing on strategies for acquiring information and learning. The first task of a cognitive systems is spectrum sensing, that has been mainly studied in the context of opportunistic spectrum access, in which cognitive nodes must implement signal detection techniques to identify unused bands for transmission. In the present work, we study different spectrum sensing algorithms, focusing on their statistical description and evaluation of the detection performance. Moving from traditional sensing approaches we consider the presence of practical impairments, and analyze algorithm design. Far from the ambition of cover the broad spectrum of spectrum sensing, we aim at providing contributions to the main classes of sensing techniques. In particular, in the context of energy detection we studied the practical design of the test, considering the case in which the noise power is estimated at the receiver. This analysis allows to deepen the phenomenon of the SNR wall, providing the conditions for its existence and showing that presence of the SNR wall is determined by the accuracy of the noise power estimation process. In the context of the eigenvalue based detectors, that can be adopted by multiple sensors systems, we studied the practical situation in presence of unbalances in the noise power at the receivers. Then, we shift the focus from single band detectors to wideband sensing, proposing a new approach based on information theoretic criteria. This technique is blind and, requiring no threshold setting, can be adopted even if the statistical distribution of the observed data in not known exactly. In the last part of the thesis we analyze some simple cooperative localization techniques based on weighted centroid strategies.

Magnetic Resonance Imaging-Derived biomarkers of Isocitrate-Dehydrogenase mutation in diffuse gliomas: a conventional MR and Diffusion Weighted Imaging study.

The introduction of molecular criteria into the classification of diffuse gliomas has added interesting practical implications to glioma management. This has created a new clinical need for correlating imaging characteristics with glioma genotypes, also known as radiogenomics or imaging genomics. Whilst many studies have primarily focused on the use of advanced magnetic resonance imaging (MRI) techniques for radiogenomics purposes, conventional MRI sequences still remain the reference point in the study and characterization of brain tumours. Moreover, a different approach may rely on diffusion-weighted imaging (DWI) usage, which is considered a “conventional” sequence in line with recently published directions on glioma imaging. In a non-invasive way, it can provide direct insight into the microscopic physical properties of tissues. Considering that Isocitrate-Dehydrogenase gene mutations may reflect alterations in metabolism, cellularity, and angiogenesis, which may manifest characteristic features on an MRI, the identification of specific MRI biomarkers could be of great interest in managing patients with brain gliomas. My study aimed to evaluate the presence of specific MRI-derived biomarkers of IDH molecular status through conventional MRI and DWI sequences.