I Grundlagen der Geometrie

Nel 1899 il matematico David Hilbert pubblicava i Grundlagen der Geometrie, tradotto in italiano con i Fondamenti della geometria. Lo scritto aveva lo scopo di dare una nuova formalizzazione assiomatica alla Geometria, superando i limiti di tutte le trattazioni precedenti. La struttura di questa tesi prevede lo studio dei Fondamenti, anche in un'ottica di confronto con il loro principale antecedente: gli Elementi di Euclide. Si opererà quindi una contestualizzazione storica degli Elementi, del loro autore e della matematica greca in generale; se ne presenterà la struttura generale e si approfondiranno alcuni degli elementi cardine del metodo assiomatico che li ha caratterizzati (postulati e struttura logico-deduttiva), mostrando anche i loro limiti e le loro mancanze, le quali hanno portato, oltre duemila anni dopo, Hilbert a scrivere i suoi Fondamenti. Venendo ai Fondamenti: se ne studierà la particolare struttura assiomatica, confrontandola con quella di Euclide, in particolare nel passaggio da una geometria degli enti ad una delle relazioni. Si studierà il nuovo sistema di assiomi proposto da Hilbert, vedendo in che modo integra, e poi supera, quello degli Elementi. In questo senso si vedrà come siano stati corretti i difetti della trattazione euclidea e di come sia stato possibile allo stesso tempo ricostruire rigorosamente la geometria degli Elementi. Si vedranno poi alcuni aspetti più strettamente logici, come la coerenza, l'indipendenza e la categoricità del nuovo sistema di assiomi, arrivando a toccare anche il progetto del Programma di Hilbert e il suo fallimento a seguito della formulazione dei due teoremi di Gödel

Abrupt Onset of Refractory Heart Failure Associated With Light-Chain Amyloidosis in Hypertrophic Cardiomyopathy

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Multiscale frozen density embedding/molecular mechanics approach for simulating magnetic response properties of solvated systems

: We present a three-layer hybrid quantum mechanical/quantum embedding/molecular mechanics approach for calculating nuclear magnetic resonance (NMR) shieldings and J-couplings of molecular systems in solution. The model is based on the frozen density embedding (FDE) and polarizable fluctuating charges (FQ) and fluctuating dipoles (FQFμ) force fields and permits the accurate ab initio description of short-range nonelectrostatic interactions by means of the FDE shell and cost-effective treatment of long-range electrostatic interactions through the polarizable force field FQ(Fμ). Our approach's accuracy and potential are demonstrated by studying NMR spectra of Brooker's merocyanine in aqueous and nonaqueous solutions

Lattice radiation therapy in clinical practice: a systematic review

Purpose: Lattice radiation therapy (LRT) is an innovative type of spatially fractionated radiation therapy. It aims to increase large tumors control probability by administering ablative doses without an increased toxicity. Considering the rising number of positive clinical experiences, the objective of this work is to evaluate LRT safety and efficacy. Method: Reports about LRT clinical experience were identified with a systematic review conducted on four different databases (namely, Medline, Embase, Scopus, and Cochrane Library) through the August 2022. Only LRT clinical reports published in English and with the access to the full manuscript text were considered as eligible. The 2020 update version PRISMA statement was followed. Results: Data extraction was performed from 12 eligible records encompassing 7 case reports, 1 case series, and 4 clinical studies. 81 patients (84 lesions) with a large lesion ranging from 63.2 cc to 3713.5 cc were subjected to exclusive, hybrid, and metabolism guided LRT. Excluding two very severe toxicity with a questionable relation with LRT, available clinical experience seem to confirm LRT safety. When a complete response was not achieved 3-6 months after LRT, a median lesion reduction approximately ≥50 % was registered. Conclusion: This systematic review appear to suggest LRT safety, especially for exclusive LRT. The very low level of evidence and the studies heterogeneity preclude drawing definitive conclusions on LRT efficacy, even though an interesting trend in terms of lesions reduction has been described

Evaluation of the Classification Accuracy of the Kidney Biopsy Direct Immunofluorescence through Convolutional Neural Networks

Background and objectives: Immunohistopathology is an essential technique in the diagnostic workflow of a kidney biopsy. Deep learning is an effective tool in the elaboration of medical imaging. We wanted to evaluate the role of a convolutional neural network as a support tool for kidney immunofluorescence reporting. Design, setting, participants, & measurements: High-magnification ( 7400) immunofluorescence images of kidney biopsies performed from the year 2001 to 2018 were collected. The report, adopted at the Division of Nephrology of the AOU Policlinico di Modena, describes the specimen in terms of \u201cappearance,\u201d \u201cdistribution,\u201d \u201clocation,\u201d and \u201cintensity\u201d of the glomerular deposits identified with fluorescent antibodies against IgG, IgA, IgM, C1q and C3 complement fractions, fibrinogen, and \u3ba- and \u3bb-light chains. The report was used as ground truth for the training of the convolutional neural networks. Results: In total, 12,259 immunofluorescence images of 2542 subjects undergoing kidney biopsy were collected. The test set analysis showed accuracy values between 0.79 (\u201cirregular capillary wall\u201d feature) and 0.94 (\u201cfine granular\u201d feature). The agreement test of the results obtained by the convolutional neural networks with respect to the ground truth showed similar values to three pathologists of our center. Convolutional neural networks were 117 times faster than human evaluators in analyzing 180 test images. A web platform, where it is possible to upload digitized images of immunofluorescence specimens, is available to evaluate the potential of our approach. Conclusions: The data showed that the accuracy of convolutional neural networks is comparable with that of pathologists experienced in the field

Fluorescence-guided lung nodule identification during minimally invasive lung resections

In the last few years, minimally invasive surgery has become the standard routine practice to manage lung nodules. Particularly in the case of robotic thoracic surgery, the identification of the lung nodules that do not surface on the visceral pleura could be challenging. Therefore, together with the evolution of surgical instruments to provide the best option in terms of invasiveness, lung nodule localization techniques should be improved to achieve the best outcomes in terms of safety and sensibility. In this review, we aim to overview all principal techniques used to detect the lung nodules that do not present the visceral pleura retraction. We investigate the accuracy of fluorescence guided thoracic surgery in nodule detection and the differences among the most common tracers used

Effective Field Theory and Integrability in Two-Dimensional Mott Transition

We study the Mott transition in a two-dimensional lattice spinless fermion model with nearest neighbors density-density interactions. By means of a two-dimensional Jordan-Wigner transformation, the model is mapped onto the lattice XXZ spin model, which is shown to possess a Quantum Group symmetry as a consequence of a recently found solution of the Zamolodchikov Tetrahedron Equation. A projection (from three to two space-time dimensions) property of the solution is used to identify the symmetry of the model at the Mott critical point as U_q(sl(2))xU_q(sl(2)), with deformation parameter q=-1. Based on this result, the low-energy Effective Field theory for the model is obtained and shown to be a lattice double Chern-Simons theory with coupling constant k=1 (with the standard normalization). By further employing the Effective Filed Theory methods, we show that the Mott transition that arises is of topological nature, with vortices in an antiferromagnetic array and matter currents characterized by a d-density wave order parameter. We also analyze the behavior of the system upon weak coupling, and conclude that it undergoes a quantum gas-liquid transition which belongs to the Ising universality class.Comment: 36 page

Prevalence of anxiety and depression symptoms in a sample of outpatients with ATTR cardiac amyloidosis

Patients with ATTR cardiac amyloidosis (ATTR-CA) face rare disease that could negatively influence psychological well-being with consequences on the course of the disease and quality of life. However, to date, no study analyzed the prevalence of anxiety and depression in patients with ATTR-CA and which clinical and sociodemographic characteristics are linked with these psychopathological conditions. A total of 109 consecutive patients (83% males) aged 62–90 years with ATTR-CA were recruited. In order to better understand the prevalence of anxiety and depression in ATTR-CA, a control group composed by 33 individuals equaling gender, education, and age were recruited. The level of anxiety and depression was measured using the Italian version of the Hospital Anxiety and Depression Scale (HADS). Sociodemographic and clinic characteristics were registered. Almost half of patients (49%) reported a clinical level of depression or anxiety, or both. ATTR-CA patients reported higher levels of anxiety and depression than control group. Results showed that older patients with ATTR-CA, especially females, with more advanced disease could be more at risk to develop an anxious disorder. Furthermore, being a woman, and presenting with a greater severity of symptoms, would appear to be a risk factor for developing a depressive disorder. Overall, these results highlighted the high presence of anxiety and depression in ATTR-CA patients, suggesting to physicians to pay attention to the psychological well-being of ATTR-CA patients. In fact, a psychological support for patients with high level of psychopathological disease could reduce disease burden and improve quality of life in ATTR-CA population