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.

Developing a radiomic based machine learning model to identify patients with resected non-small-cell lung cancer at high risk of relapse

Background There is a wide variation of recurrence risk of Non-small-cell lung cancer (NSCLC) within the same Tumor Node Metastasis (TNM) stage, suggesting that other parameters are involved in determining this probability. Radiomics allows extraction of quantitative information from images that can be used for clinical purposes. The primary objective of this study is to develop a radiomic prognostic model that predicts a 3 year disease free-survival (DFS) of resected Early Stage (ES) NSCLC patients. Material and Methods 56 pre-surgery non contrast Computed Tomography (CT) scans were retrieved from the PACS of our institution and anonymized. Then they were automatically segmented with an open access deep learning pipeline and reviewed by an experienced radiologist to obtain 3D masks of the NSCLC. Images and masks underwent to resampling normalization and discretization. From the masks hundreds Radiomic Features (RF) were extracted using Py-Radiomics. Hence, RF were reduced to select the most representative features. The remaining RF were used in combination with Clinical parameters to build a DFS prediction model using Leave-one-out cross-validation (LOOCV) with Random Forest. Results and Conclusion A poor agreement between the radiologist and the automatic segmentation algorithm (DICE score of 0.37) was found. Therefore, another experienced radiologist manually segmented the lesions and only stable and reproducible RF were kept. 50 RF demonstrated a high correlation with the DFS but only one was confirmed when clinicopathological covariates were added: Busyness a Neighbouring Gray Tone Difference Matrix (HR 9.610). 16 clinical variables (which comprised TNM) were used to build the LOOCV model demonstrating a higher Area Under the Curve (AUC) when RF were included in the analysis (0.67 vs 0.60) but the difference was not statistically significant (p=0,5147).