High-Order Positivity-Preserving Well-Balanced Discontinuous Galerkin Methods for Euler Equations with Gravitation on Unstructured Meshes

In this paper, we propose a high-order accurate discontinuous Galerkin (DG) method for the compressible Euler equations under gravitational fields on unstructured meshes. The scheme preserves a general hydrostatic equilibrium state and provably guarantees the positivity of density and pressure at the same time. Comparing with the work on the well-balanced scheme for Euler equations with gravitation on rectangular meshes, the extension to triangular meshes is conceptually plausible but highly nontrivial. We first introduce a special way to recover the equilibrium state and then design a group of novel variables at the interface of two adjacent cells, which plays an important role in the well-balanced and positivity-preserving properties. One main challenge is that the well-balanced schemes may not have the weak positivity property. In order to achieve the well-balanced and positivity-preserving properties simultaneously while maintaining high-order accuracy, we carefully design DG spatial discretization with well-balanced numerical fluxes and suitable source term approximation. For the ideal gas, we prove that the resulting well-balanced scheme, coupled with strong stability preserving time discretizations, satisfies a weak positivity property. A simple existing limiter can be applied to enforce the positivity-preserving property, without losing high-order accuracy and conservation. Extensive one- and two-dimensional numerical examples demonstrate the desired properties of the proposed scheme, as well as its high resolution and robustness.     

Do social support and community engagement act as mechanisms in the association between neighbourhood income inequality and the mental health of mothers in Calgary,Canada? A mediation analysis

PurposeAccording to the social determinants of health framework, income inequality is a potential risk factor for adverse mental health. However, few studies have explored the mechanisms suspected to mediate this relationship. The current study addresses this gap through a mediation analysis to determine if social support and community engagement act as mediators linking neighbourhood income inequality to maternal anxiety and depressive symptoms within a cohort of new mothers living in the City of Calgary, Canada.MethodsData collected at three years postpartum from mothers belonging to the All Our Families (AOF) cohort were used in the current study. Maternal data were collected between 2012 and 2015 and linked to neighbourhood socioeconomic data from the 2006 Canadian Census. Income inequality was measured using Gini coefficients derived from 2006 after-tax census data. Generalized structural equation models were used to quantify the associations between income inequality and mental health symptoms, and to assess the potential direct and indirect mediating effects of maternal social support and community engagement.ResultsIncome inequality was not significantly associated with higher depressive symptoms (β = 0.32, 95%CI = −0.067, 0.70), anxiety symptoms (β = 0.11, 95%CI = −0.39, 0.60), or lower social support. Income inequality was not associated with community engagement. For the depression models, higher social support was significantly associated with lower depressive symptoms (β = −0.13, 95%CI = −0.15, −0.097), while community engagement was not significantly associated with depressive symptoms (β = 0.059, 95%CI = −0.15, 0.27). Similarly, for the anxiety models, lower anxiety symptoms were significantly associated with higher levels of social support (β = −0.17, 95%CI = −0.20, −0.13) but not with higher levels of community engagement (β = 0.14, 95%CI = −0.14, 0.41).ConclusionThe current study did not find clear evidence for social support or community engagement mediating the relationship between neighbourhood income inequality and maternal mental health. Future investigations should employ a broader longitudinal approach to capture changes in income inequality, potential mediators, and mental health symptomatology over time.     

A Well-Balanced Positivity-Preserving Quasi-Lagrange Moving Mesh DG Method for the Shallow Water Equations

A high-order, well-balanced, positivity-preserving quasi-Lagrange moving mesh DG method is presented for the shallow water equations with non-flat bottom topography. The well-balance property is crucial to the ability of a scheme to simulate perturbation waves over the lake-at-rest steady state such as waves on a lake or tsunami waves in the deep ocean. The method combines a quasi-Lagrange moving mesh DG method, a hydrostatic reconstruction technique, and a change of unknown variables. The strategies in the use of slope limiting, positivity-preservation limiting, and change of variables to ensure the well-balance and positivity-preserving properties are discussed. Compared to rezoning-type methods, the current method treats mesh movement continuously in time and has the advantages that it does not need to interpolate flow variables from the old mesh to the new one and places no constraint for the choice of a update scheme for the bottom topography on the new mesh. A selection of one- and two-dimensional examples are presented to demonstrate the well-balance property, positivity preservation, and high-order accuracy of the method and its ability to adapt the mesh according to features in the flow and bottom topography.     

Key Social Determinants to Narrow the Gap between Health-adjusted Life Expectancy and Life Expectancy in Megacities

ObjectiveImprovement in the quality of life is reflected in the narrowing of the gap between health-adjusted life expectancy (HALE) and life expectancy (LE). The effect of megacity expansion on narrowing the gap is rarely reported. This study aimed to disclose this potential relationship.MethodsAnnual life tables were constructed from identified death records and population counts from multiple administrative sources in Guangzhou, China, from 2010 to 2020. Joinpoint regression was used to evaluate the temporal trend. Generalized principal component analysis and multilevel models were applied to examine the county-level association between the gap and social determinants.ResultsAlthough LE and HALE in megacities are increasing steadily, their gap is widening. Socio-economic and health services are guaranteed to narrow this gap. Increasing personal wealth, a growing number of newborns and healthy immigrants, high urbanization, and healthy aging have helped in narrowing this gap.ConclusionIn megacities, parallel LE and HALE growth should be highly considered to narrow their gap. Multiple social determinants need to be integrated as a whole to formulate public health plans.     

Constrained empirical-likelihood confidence regions in nonignorable covariate-missing data problems

Missing covariates in regression analysis are a pervasive problem in medical, social, and economic researches. We study empirical-likelihood confidence regions for unconstrained and constrained regression parameters in a nonignorable covariate-missing data problem. For an assumed conditional mean regression model, we assume that some covariates are fully observed but other covariates are missing for some subjects. By exploitation of a probability model of missingness and a working conditional score model from a semiparametric perspective, we build a system of unbiased estimating equations, where the number of equations exceeds the number of unknown parameters. Based on the proposed estimating equations, we introduce unconstrained and constrained empirical-likelihood ratio statistics to construct empirical-likelihood confidence regions for the underlying regression parameters without and with constraints. We establish the asymptotic distributions of the proposed empirical-likelihood ratio statistics. Simulation results show that the proposed empirical-likelihood methods have a better finite-sample performance than other competitors in terms of coverage probability and interval length. Finally, we apply the proposed empirical-likelihood methods to the analysis of a data set from the US National Health and Nutrition Examination Survey.     

Continuous electroencephalography characteristics and acute symptomatic seizures in COVID-19 patients

ObjectiveAs concerns regarding neurological manifestations in COVID-19 (coronavirus disease 2019) patients increase, limited data exists on continuous electroencephalography (cEEG) findings in these patients. We present a retrospective cohort study of cEEG monitoring in COVID-19 patients to better explore this knowledge gap.MethodsAmong 22 COVID-19 patients, 19 underwent cEEGs, and 3 underwent routine EEGs (<1 h). Demographic and clinical variables, including comorbid conditions, discharge disposition, survival and cEEG findings, were collected.ResultscEEG was performed for evaluation of altered mental status (n = 17) or seizure-like events (n = 5). Five patients, including 2 with epilepsy, had epileptiform abnormalities on cEEG. Two patients had electrographic seizures without a prior epilepsy history. There were no acute neuroimaging findings. Periodic discharges were noted in one-third of patients and encephalopathic EEG findings were not associated with IV anesthetic use.ConclusionsInterictal epileptiform abnormalities in the absence of prior epilepsy history were rare. However, the discovery of asymptomatic seizures in two of twenty-two patients was higher than previously reported and is therefore of concern.SignificancecEEG monitoring in COVID-19 patients may aid in better understanding an epileptogenic potential of SARS-CoV2 infection. Nevertheless, larger studies utilizing cEEG are required to better examine acute epileptic risk in COVID-19 patients.     

Long-term health and socioeconomic outcome of obstructive sleep apnea in children and adolescents

BackgroundThere is limited information about the long-term outcome of obstructive sleep apnea (OSA) diagnosed in children and adolescents for educational and social factors. Here, we estimate the long-term socioeconomic outcome and health care costs of OSA.MethodsThe historical case-control cohort study included Danish individuals with OSA diagnosed in childhood or adolescence between 1994 and 2015. Health care costs and socioeconomic data were obtained from nationwide administrative and health registers. A total of 5419 were diagnosed during this period; of these we traced 1004 patients who we compared with 4085 controls (mean index age, 10.2 years; Standard Deviation (SD), 5.6 years) until the age of 20 years. Controls were matched for age, gender, and residency.ResultsComparing the OSA patient and control groups at age 20 years we found: 1) lower parental educational level; 2) significantly lower educational level also after adjustment for parental educational level; 3) lower school grade-point averages; 4) lower employment rate and lower income, which was not fully compensated when transfer payments were considered; and 5) patients' initial health care costs were higher due to higher morbidity. Patients showed higher mortality rates than controls (Hazard Ratio (HR) = 7.63, 95% CI = 4.87–11.95, P < 0.001).ConclusionsOSA in children and adolescent is associated with a significant influence on morbidity, mortality, educational level, grading, social outcome, and welfare consequences.     

Partial Youden index and its inferences

In medical diagnostic research, medical tests with continuous values are widely employed to distinguish between diseased and non-diseased subjects. The diagnostic accuracy of a medical test can be assessed by using the receiver operating characteristic (ROC) curve of the test. To summarize the ROC curve and determine an optimal cut-off point for test results, the Youden index is commonly used. In particular, the Youden index is optimized over the entire range of values for sensitivity and specificity, which determine the ROC space. However in clinical practice, one may only be interested in the regions of the ROC curve that correspond to low false-positive rates or/and high sensitivities. In this paper, a new summary index for the ROC curve, called the “partial Youden index”, is defined on regions of the ROC space in which sensitivity/specificity values are of practical interest. The traditional Youden index is a special case of the partial Youden index. Various parametric and non-parametric interval estimation methods are proposed for the partial Youden index. Extensive simulation studies are conducted to evaluate the finite sample performances of the proposed methods. A real example is used to illustrate the application of the new methods.     

Fifteen-year follow-up of a patient with a DHDDS variant with non-progressive early onset myoclonic tremor and rare generalized epilepsy

BackgroundGeneralized epilepsy and tremor phenotypes have been reported in some genetic disorders. Among them benign adult familial myoclonus epilepsy (BAFME) has been confirmed as a clearly defined clinical and genetic entity. On the other hand, non-progressive tremor and generalized epilepsy phenotypes have also been reported in patients with DHDDS variants.Case presentation.We report on a long term follow-up of patient with de novo missense variant of DHDDS, who revealed non progressive nature. This 18-year-old woman presented non-progressive tremor since her early infancy. She had rare seizures. Her tremor was considered as cortical myoclonic tremor with giant somatosensory evoked potentials.ConclusionIn patients with early onset, non-progressive tremor and rare generalized epilepsy phenotypes, DHDDS variants may be considered in the genetic differential diagnosis.