Celebrating Cercignani's conjecture for the Boltzmann equation

Cercignani's conjecture assumes a linear inequality between the entropy and entropy production functionals for Boltzmann's nonlinear integral operator in rarefied gas dynamics. Related to the field of logarithmic Sobolev inequalities and spectral gap inequalities, this issue has been at the core of the renewal of the mathematical theory of convergence to thermodynamical equilibrium for rarefied gases over the past decade. In this review paper, we survey the various positive and negative results which were obtained since the conjecture was proposed in the 1980s.Comment: This paper is dedicated to the memory of the late Carlo Cercignani, powerful mind and great scientist, one of the founders of the modern theory of the Boltzmann equation. 24 pages. V2: correction of some typos and one ref. adde

Exponential decay in time of solutions of the viscous quantum hydrodynamic equations

AbstractThe long-time asymptotics of solutions of the viscous quantum hydrodynamic model in one space dimension is studied. This model consists of continuity equations for the particle density and the current density, coupled to the Poisson equation for the electrostatic potential. The equations are a dispersive and viscous regularization of the Euler equations. It is shown that the solutions converge exponentially fast to the (unique) thermal equilibrium state as the time tends to infinity. For the proof, we employ the entropy dissipation method, applied for the first time to a third-order differential equation

The contribution of iot to the implementation of preventive conservation according to european standards: The case study of the “cannone” violin and its historical copy

One of the main goals of preventive conservation (PC) is to reduce the risk of possible damage produced by the interaction between tangible heritage objects and their conservation environments. This work aims to introduce the European standard EN 15757:2010 as a potential tool for implementing effective museum PC, and it details the potential contributions of both active environmental control and Internet of Things (IoT) technologies in this regard. An application of this strategy is proposed by means of a case study of the conservation of two historical violins, part of a small but significant museum collection in the City of Genoa dedicated to Paganini, whose value is inestimable. According to the standard, monitoring of environmental parameters was carried out for more than four years in the Paganini Hall of Palazzo Doria-Tursi Museum. A remote-control system was implemented, installing digital sensors in the room and in the two showcases. The data were continuously collected through an integrated platform for supervision, monitoring and shared management, based on web-cloud-IoT technology. The analysis of climate data and the assessment of the “historic climate” led to the installation of an active control system on the display cases of the “Cannone” violin and its historical copy. The intervention resulted in a cost-effective improvement in the conservation conditions of the two objects, with an efficient system of warning and safety alarms and a protocol of resolution actions still active and ongoing. The application of IoT systems in monitoring and controlling the indoor climate of heritage collections facilitated the care of the objects at a cost reduction for the institution

Metrics of Gender Differences in Mortality Risk after Diabetic Foot Disease

Background: The aim of this study was to clarify any gender differences in the mortality risk of people with DFD since patients with diabetic foot disease (DFD) are at a high risk of mortality and, at the same time, are more likely to be men. Methods: From regional administrative sources, the survival probability was retrospectively evaluated by the Kaplan-Meier method and using the Cox proportional-hazards model comparing people with DFD to those without DFD across the years 2011-2018 in Tuscany, Italy. Gender difference in mortality was evaluated by the ratio of hazard ratios (RHR) of men to women after initial DFD hospitalizations (n = 11,529) or in a cohort with prior history of DFD hospitalizations (n = 11,246). Results: In both cohorts, the survival probability after DFD was lower among women. Compared to those without DFD, after initial DFD hospitalizations, the mortality risk was significantly (18%) higher for men compared to women. This excess risk was particularly high after major amputations but also after ulcers, infections, gangrene, or Charcot, with a lower reduction after revascularization procedures among men. In the cohort that included people with a history of prior DFD hospitalizations, except for the risk of minor amputations being higher for men, there was no gender difference in mortality risk. Conclusions: In people with DFD, the overall survival probability was lower among women. Compared to those without DFD after a first DFD hospitalization, men were at higher risk of mortality. This excess risk disappeared in groups with a history of previous DFD hospitalizations containing a greater percentage of women who were older and probably had a longer duration of diabetes and thus becoming, over time, progressively frailer than men

Human ether-à-go-go-related potassium channel: exploring SAR to improve drug design

hERG is best known as a primary anti-target, the inhibition of which is responsible for serious side effects. A renewed interest in hERG as a desired target, especially in oncology, was sparked because of its role in cellular proliferation and apoptosis. In this study, we survey the most recent advances regarding hERG by focusing on SAR in the attempt to elucidate, at a molecular level, off-target and on-target actions of potential hERG binders, which are highly promiscuous and largely varying in structure. Understanding the rationale behind hERG interactions and the molecular determinants of hERG activity is a real challenge and comprehension of this is of the utmost importance to prioritize compounds in early stages of drug discovery and to minimize cardiotoxicity attrition in preclinical and clinical studies. We report how the understanding of SAR and the informed use of reliable data and models are pivotal to modulate the interplay with hERG channels