Differential Calculus on Manifolds with a Boundary. Applications

This paper contains a set of lecture notes on manifolds with boundary and corners, with particular attention to the space of quantum states. A geometrically inspired way of dealing with these kind of manifolds is presented,and explicit examples are given in order to clearly illustrate the main ideas.Comment: 42 pages, 6 figures, accepted for publication in International Journal of Geometric Methods in Modern Physic

A 1D continuum model for beams with pantographic microstructure: asymptotic micro-macro identification and numerical results

In the standard asymptotic micro-macro identification theory, starting from a De Saint-Venant cylinder, it is possible to prove that, in the asymptotic limit, only flexible, inextensible, beams can be obtained at the macro-level. In the present paper we address the following problem: is it possible to find a microstructure producing in the limit, after an asymptotic micro-macro identification procedure, a continuum macro-model of a beam which can be both extensible and flexible? We prove that under certain hypotheses, exploiting the peculiar features of a pantographic microstructure, this is possible. Among the most remarkable features of the resulting model we find that the deformation energy is not of second gradient type only because it depends, like in the Euler beam model, upon the Lagrangian curvature, i.e. the projection of the second gradient of the placement function upon the normal vector to the deformed line, but also because it depends upon the projection of the second gradient of the placement on the tangent vector to the deformed line, which is the elongation gradient. Thus, a richer set of boundary conditions can be prescribed for the pantographic beam model. Phase transition and elastic softening are exhibited as well. Using the resulting planar 1D continuum limit homogenized macro-model, by means of FEM analyses, we show some equilibrium shapes exhibiting highly non-standard features. Finally, we conceive that pantographic beams may be used as basic elements in double scale metamaterials to be designed in future

A Pedagogical Intrinsic Approach to Relative Entropies as Potential Functions of Quantum Metrics: the qq-zz Family

The so-called $q$-z-\textit{R\'enyi Relative Entropies} provide a huge two-parameter family of relative entropies which includes almost all well-known examples of quantum relative entropies for suitable values of the parameters. In this paper we consider a log-regularized version of this family and use it as a family of potential functions to generate covariant $(0,2)$ symmetric tensors on the space of invertible quantum states in finite dimensions. The geometric formalism developed here allows us to obtain the explicit expressions of such tensor fields in terms of a basis of globally defined differential forms on a suitable unfolding space without the need to introduce a specific set of coordinates. To make the reader acquainted with the intrinsic formalism introduced, we first perform the computation for the qubit case, and then, we extend the computation of the metric-like tensors to a generic $n$-level system. By suitably varying the parameters $q$ and $z$, we are able to recover well-known examples of quantum metric tensors that, in our treatment, appear written in terms of globally defined geometrical objects that do not depend on the coordinates system used. In particular, we obtain a coordinate-free expression for the von Neumann-Umegaki metric, for the Bures metric and for the Wigner-Yanase metric in the arbitrary $n$-level case.Comment: 50 pages, 1 figur

Clinical Features, Cardiovascular Risk Profile, and Therapeutic Trajectories of Patients with Type 2 Diabetes Candidate for Oral Semaglutide Therapy in the Italian Specialist Care

Introduction: This study aimed to address therapeutic inertia in the management of type 2 diabetes (T2D) by investigating the potential of early treatment with oral semaglutide. Methods: A cross-sectional survey was conducted between October 2021 and April 2022 among specialists treating individuals with T2D. A scientific committee designed a data collection form covering demographics, cardiovascular risk, glucose control metrics, ongoing therapies, and physician judgments on treatment appropriateness. Participants completed anonymous patient questionnaires reflecting routine clinical encounters. The preferred therapeutic regimen for each patient was also identified. Results: The analysis was conducted on 4449 patients initiating oral semaglutide. The population had a relatively short disease duration (42%  60% of patients, and more often than sitagliptin or empagliflozin. Conclusion: The study supports the potential of early implementation of oral semaglutide as a strategy to overcome therapeutic inertia and enhance T2D management

Associations between depressive symptoms and disease progression in older patients with chronic kidney disease: results of the EQUAL study

Background Depressive symptoms are associated with adverse clinical outcomes in patients with end-stage kidney disease; however, few small studies have examined this association in patients with earlier phases of chronic kidney disease (CKD). We studied associations between baseline depressive symptoms and clinical outcomes in older patients with advanced CKD and examined whether these associations differed depending on sex. Methods CKD patients (>= 65 years; estimated glomerular filtration rate <= 20 mL/min/1.73 m(2)) were included from a European multicentre prospective cohort between 2012 and 2019. Depressive symptoms were measured by the five-item Mental Health Inventory (cut-off <= 70; 0-100 scale). Cox proportional hazard analysis was used to study associations between depressive symptoms and time to dialysis initiation, all-cause mortality and these outcomes combined. A joint model was used to study the association between depressive symptoms and kidney function over time. Analyses were adjusted for potential baseline confounders. Results Overall kidney function decline in 1326 patients was -0.12 mL/min/1.73 m(2)/month. A total of 515 patients showed depressive symptoms. No significant association was found between depressive symptoms and kidney function over time (P = 0.08). Unlike women, men with depressive symptoms had an increased mortality rate compared with those without symptoms [adjusted hazard ratio 1.41 (95% confidence interval 1.03-1.93)]. Depressive symptoms were not significantly associated with a higher hazard of dialysis initiation, or with the combined outcome (i.e. dialysis initiation and all-cause mortality). Conclusions There was no significant association between depressive symptoms at baseline and decline in kidney function over time in older patients with advanced CKD. Depressive symptoms at baseline were associated with a higher mortality rate in men

Association of kidney disease measures with risk of renal function worsening in patients with type 1 diabetes

Background: Albuminuria has been classically considered a marker of kidney damage progression in diabetic patients and it is routinely assessed to monitor kidney function. However, the role of a mild GFR reduction on the development of stage 653 CKD has been less explored in type 1 diabetes mellitus (T1DM) patients. Aim of the present study was to evaluate the prognostic role of kidney disease measures, namely albuminuria and reduced GFR, on the development of stage 653 CKD in a large cohort of patients affected by T1DM. Methods: A total of 4284 patients affected by T1DM followed-up at 76 diabetes centers participating to the Italian Association of Clinical Diabetologists (Associazione Medici Diabetologi, AMD) initiative constitutes the study population. Urinary albumin excretion (ACR) and estimated GFR (eGFR) were retrieved and analyzed. The incidence of stage 653 CKD (eGFR < 60 mL/min/1.73 m2) or eGFR reduction > 30% from baseline was evaluated. Results: The mean estimated GFR was 98 \ub1 17 mL/min/1.73m2 and the proportion of patients with albuminuria was 15.3% (n = 654) at baseline. About 8% (n = 337) of patients developed one of the two renal endpoints during the 4-year follow-up period. Age, albuminuria (micro or macro) and baseline eGFR < 90 ml/min/m2 were independent risk factors for stage 653 CKD and renal function worsening. When compared to patients with eGFR > 90 ml/min/1.73m2 and normoalbuminuria, those with albuminuria at baseline had a 1.69 greater risk of reaching stage 3 CKD, while patients with mild eGFR reduction (i.e. eGFR between 90 and 60 mL/min/1.73 m2) show a 3.81 greater risk that rose to 8.24 for those patients with albuminuria and mild eGFR reduction at baseline. Conclusions: Albuminuria and eGFR reduction represent independent risk factors for incident stage 653 CKD in T1DM patients. The simultaneous occurrence of reduced eGFR and albuminuria have a synergistic effect on renal function worsening

On the representation of wavefronts localized in space-time and wavenumber-frequency domains

This Letter reports evidence suggesting a representation system for transient waves with band limited spectra, referred to here as localized waves in the space-time and wavenumber-frequency domains. A theoretical analysis with a transient monopole shows that the wavenumber-frequency pressure spectrum is distributed over hyperbolic regions of propagating waves and evanescent waves. An experimental analysis is performed, applying dictionary learning to reverberant sound fields measured with a microphone array in three rooms. The learned components appear to be related by analytical transformations in the spectra, suggesting a partitioning characterized by hyperbolic dispersion curves and multiple directions and times of arrival.QC 20210525QC 20210525</p

Identification of localised water surface patterns using unsupervised learning

Water surface deformations in rivers can have very different shapes and dynamics depending on which mechanism drives them: turbulence, wind, and/or bed morphology. While some surface patterns can be treated as effective tracers for image-based velocimetry, others, such as gravity waves, affect the accuracy of the measurements. Emerging analysis techniques attempt to filter out the contribution of waves, or conversely to enhance them in order to infer the flow properties based on their dynamics. These approaches are typically based on Fourier analysis, which decomposes the images in a homogeneous distribution of sinusoidal waves. In contrast, water surface patterns such as vortices, scars, wakes, or even groups of ripples, are localised in space and in time. Identifying them, or distinguishing them from other types of waves, requires a more targeted approach. This work proposes the use of unsupervised machine learning to identify a collection of wave patterns that can represent the water deformations. Unlike Fourier bases, the wave patterns learned are able to capture more sophisticated dynamics with increased efficiency. Provided enough training data, it is in principle possible to distinguish different types of surface deformations, and to determine their scale and speed with a higher resolution than is currently allowed by Fourier analysis. This work shows preliminary results including learned components from two video recordings of the river Sheaf (Sheffield, UK) obtained with a fixed camera at different flow conditions. The learned components resemble a combination of wave-groups localised in space-time, confirming the importance of moving beyond the assumption of stationarity.QC 20220404</p

Identification of localised water surface patterns using unsupervised learning

Water surface deformations in rivers can have very different shapes and dynamics depending on which mechanism drives them: turbulence, wind, and/or bed morphology. While some surface patterns can be treated as effective tracers for image-based velocimetry, others, such as gravity waves, affect the accuracy of the measurements. Emerging analysis techniques attempt to filter out the contribution of waves, or conversely to enhance them in order to infer the flow properties based on their dynamics. These approaches are typically based on Fourier analysis, which decomposes the images in a homogeneous distribution of sinusoidal waves. In contrast, water surface patterns such as vortices, scars, wakes, or even groups of ripples, are localised in space and in time. Identifying them, or distinguishing them from other types of waves, requires a more targeted approach. This work proposes the use of unsupervised machine learning to identify a collection of wave patterns that can represent the water deformations. Unlike Fourier bases, the wave patterns learned are able to capture more sophisticated dynamics with increased efficiency. Provided enough training data, it is in principle possible to distinguish different types of surface deformations, and to determine their scale and speed with a higher resolution than is currently allowed by Fourier analysis. This work shows preliminary results including learned components from two video recordings of the river Sheaf (Sheffield, UK) obtained with a fixed camera at different flow conditions. The learned components resemble a combination of wave-groups localised in space-time, confirming the importance of moving beyond the assumption of stationarity.QC 20220404</p

Buckling critical pressures in collapsible tubes relevant for biomedical flows

Abstract The behaviour of collapsed or stenotic vessels in the human body can be studied by means of simplified geometries like a collapsible tube. The objective of this work is to determine the value of the buckling critical pressure of a collapsible tube by employing Landau’s theory of phase transition. The methodology is based on the implementation of an experimentally validated 3D numerical model of a collapsible tube. The buckling critical pressure is estimated for different values of geometric parameters of the system by treating the relation between the intramural pressure and the area of the central cross-section as the order parameter function of the system. The results show the dependence of the buckling critical pressures on the geometric parameters of a collapsible tube. General non-dimensional equations for the buckling critical pressures are derived. The advantage of this method is that it does not require any geometric assumption, but it is solely based on the observation that the buckling of a collapsible tube can be treated as a second-order phase transition. The investigated geometric and elastic parameters are sensible for biomedical application, with particular interest to the study of the bronchial tree under pathophysiological conditions like asthma