Normal traces and applications to continuity equations on bounded domains

In this work, we study several properties of the normal Lebesgue trace of vector fields introduced by the second and third author in [18] in the context of the energy conservation for the Euler equations in Onsager-critical classes. Among several properties, we prove that the normal Lebesgue trace satisfies the Gauss-Green identity and, by providing explicit counterexamples, that it is a notion sitting strictly between the distributional one for measure-divergence vector fields and the strong one for $BV$ functions. These results are then applied to the study of the uniqueness of weak solutions for continuity equations on bounded domains, allowing to remove the assumption in [15] of global $BV$ regularity up to the boundary, at least around the portion of the boundary where the characteristics exit the domain or are tangent. The proof relies on an explicit renormalization formula completely characterized by the boundary datum and the positive part of the normal Lebesgue trace. In the case when the characteristics enter the domain, a counterexample shows that achieving the normal trace in the Lebesgue sense is not enough to prevent non-uniqueness, and thus a $BV$ assumption seems to be necessary for the uniqueness of weak solutions

Machine learning of microscopic structure-dynamics relationships in complex molecular systems

In many complex molecular systems, the macroscopic ensemble's properties are controlled by microscopic dynamic events (or fluctuations) that are often difficult to detect via pattern-recognition approaches. Discovering the relationships between local structural environments and the dynamical events originating from them would allow unveiling microscopic level structure-dynamics relationships fundamental to understand the macroscopic behavior of complex systems. Here we show that, by coupling advanced structural (e.g., Smooth Overlap of Atomic Positions, SOAP) with local dynamical descriptors (e.g., Local Environment and Neighbor Shuffling, LENS) in a unique dataset, it is possible to improve both individual SOAP- and LENS-based analyses, obtaining a more complete characterization of the system under study. As representative examples, we use various molecular systems with diverse internal structural dynamics. On the one hand, we demonstrate how the combination of structural and dynamical descriptors facilitates decoupling relevant dynamical fluctuations from noise, overcoming the intrinsic limits of the individual analyses. Furthermore, machine learning approaches also allow extracting from such combined structural/dynamical dataset useful microscopic-level relationships, relating key local dynamical events (e.g., LENS fluctuations) occurring in the systems to the local structural (SOAP) environments they originate from. Given its abstract nature, we believe that such an approach will be useful in revealing hidden microscopic structure-dynamics relationships fundamental to rationalize the behavior of a variety of complex systems, not necessarily limited to the atomistic and molecular scales

Clinical Care Conditions and Needs of Palliative Care Patients from Five Italian Regions: Preliminary Data of the DEMETRA Project

In order to plan the right palliative care for patients and their families, it is essential to have detailed information about patients' needs. To gain insight into these needs, we analyzed five Italian local palliative care networks and assessed the clinical care conditions of patients facing the complexities of advanced and chronic disease. A longitudinal, observational, noninterventional study was carried out in five Italian regions from May 2017 to November 2018. Patients who accessed the palliative care networks were monitored for 12 months. Sociodemographic, clinical, and symptom information was collected with several tools, including the Necesidades Paliativas CCOMS-ICO (NECPAL) tool, the Edmonton Symptom Assessment System (ESAS), and interRAI Palliative Care (interRAI-PC). There were 1013 patients in the study. The majority (51.7%) were recruited at home palliative care units. Cancer was the most frequent diagnosis (85.4%), and most patients had at least one comorbidity (58.8%). Cancer patients reported emotional stress with severe symptoms (38.7% vs. 24.3% in noncancer patients; p = 0.001) and were less likely to have clinical frailty (13.3% vs. 43.9%; p < 0.001). Our study confirms that many patients face the last few months of life with comorbidities or extreme frailty. This study contributes to increasing the general knowledge on palliative care needs in a high-income country

Half-integer Shapiro steps in highly transmissive InSb nanoflag Josephson junctions

We investigate a ballistic InSb nanoflag-based Josephson junction with Nb superconducting contacts. The high transparency of the superconductor-semiconductor interfaces enables the exploration of quantum transport with parallel short and long conducting channels. Under microwave irradiation, we observe half-integer Shapiro steps that are robust to temperature, suggesting their possible non-equilibrium origin. Our results demonstrate the potential of ballistic InSb nanoflags Josephson junctions as a valuable platform for understanding the physics of hybrid devices and investigating their non-equilibrium dynamics.Comment: 37 pages, 14 figure

(Epi)genetic profiling of extraembryonic and postnatal tissues from female monozygotic twins discordant for Beckwith–Wiedemann syndrome

n/

The Diverticular Disease Registry (DDR Trial) by the Advanced International Mini-Invasive Surgery Academy Clinical Research Network: Protocol for a Multicenter, Prospective Observational Study

Diverticular disease is an increasingly common issue, with a variety of clinical presentations and treatment options. However, very few prospective cohort studies explore outcomes between the different presentations and treatments. The Diverticular Disease Registry (DDR Trial) is a multicenter, prospective, observational cohort study on behalf of the Advanced International Mini-Invasive Surgery (AIMS) academy clinical research network. The DDR Trial aims to investigate the short-term postoperative and long-term quality of life outcomes in patients undergoing surgery or medical treatments for diverticular disease. DDR Trial is open to participation by all tertiary-care hospitals. DDR Trial has been registered at ClinicalTriats.gou (NCT 04907383). Data collection will be recorded on Research Electronic Data Capture (REDCap) starting on June 1 , 2021 and will end after 5 years of recruitment. All adult patients with imaging-proven colonic diverticular disease (i.e., symptomatic colonic diverticulosis including diverticular bleeding, diverticulitis, and Symptomatic Uncomplicated Diverticular Disease) will be included. The primary outcome of DDR Trial is quality of life assessment at 12-month according to the Gastrointestinal Quality of Life Index (GIQLI). The secondary outcome is 30-day postoperative outcomes according to the Clavien-Dindo classification. DDR Trial will significantly advance in identifying the optimal care for patients with diverticular disease by exploring outcomes of different presentations and treatments