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In this paper we introduce a general framework for defining and studying essentially non-oscillatory reconstruction procedures of arbitrarily high order accuracy, interpolating data in a central stencil around a given computational cell (CWENO). This technique relies on the same selection mechanism of smooth stencils adopted in WENO, but here the pool of candidates for the selection includes polynomials of different degrees. This seemingly minor difference allows to compute an analytic expression of a polynomial interpolant, approximating the unknown function uniformly within a cell, instead of only at one point at a time. For this reason this technique is particularly suited for balance laws for finite volume schemes, when averages of source terms require high order quadrature rules based on several points; in the computation of local averages, during refinement in h-adaptive schemes; or in the transfer of the solution between grids in moving mesh techniques, and in general when a globally defined reconstruction is needed. Previously, these needs have been satisfied mostly by ENO reconstruction techniques, which, however, require a much wider stencil then the CWENO reconstruction studied here, for the same accuracy.MSC 65M08, 65M12.

IntroductionThe elderly, who suffer from multiple chronic diseases, represent a substantial proportion of Emergency Department (ED) frequent users, thus contributing to ED overcrowding, although they could benefit from other health care facilities, if those were available. The aim of this study was to evaluate and characterize hospital visits of older patients (age 65 or greater) to the ED of a university teaching hospital in Rome from the 1st of January to the 31st of December 2014, in order to identify clinical and social characteristics potentially associated with “elderly frequent users”.Material and MethodsA retrospective study was performed during the calendar year 2014 (1st January 2014 – 31st December 2014) analyzing all ED admissions to the University Hospital of Rome Tor Vergata. Variables collected included age, triage code, arrival data, discharge diagnosis, and visit outcome. We performed a risk analysis using univariate binary logistic regression models.ResultsA total number of 38,016 patients accessed the ED, generating 46,820 accesses during the study period, with an average of 1.23 accesses for patient. The elderly population represented a quarter of the total ED population and had an increased risk of frequent use (OR 1.5: CI 1.4–1.7) and hospitalization (OR 3.8: CI 3.7–4). Moreover, they showed a greater diagnostic complexity, as demonstrated by the higher incidence of yellow and red priority codes compared to other ED populations (OR 3.1: CI 2.9–3.2).DiscussionOlder patients presented clinical and social characteristics related to the definition of “elderly frail frequent users”. The fact that a larger number of hospitalizations occurred in such patients is indirect evidence of frailty in this specific population, suggesting that hospital admissions may be an inappropriate response to frailty, especially when continued care is not established.ConclusionEnhancement of continuity of care, establishment of a tracking system for those who are at greater risk of visiting the ED and evaluating fragile individuals should be the highest priority in addressing ED frequent usage by the elderly.

The purpose of this paper is to study the properties of kinetic models for traffic flow described by a Boltzmann-type approach and based on a continuous space of microscopic velocities. In our models, the particular structure of the collision kernel allows one to find the analytical expression of a class of steady-state distributions, which are characterized by being supported on a quantized space of microscopic speeds. The number of these velocities is determined by a physical parameter describing the typical acceleration of a vehicle and the uniqueness of this class of solutions is supported by numerical investigations. This shows that it is possible to have the full richness of a kinetic approach with the simplicity of a space of microscopic velocities characterized by a small number of modes. Moreover, the explicit expression of the asymptotic distribution paves the way to deriving new macroscopic equations using the closure provided by the kinetic model