Search of symmetric composition methods of symmetric integrators

Composition methods are useful when solving Ordinary Differential Equations (ODEs) as they increase the order of accuracy of a given basic numerical integration scheme. We will focus on sy-mmetric composition methods involving some basic second order symmetric integrator with different step sizes [17]. The introduction of symmetries into these methods simplifies the order conditions and reduces the number of unknowns. Several authors have worked in the search of the coefficients of these type of methods: the best method of order 8 has 17 stages [24], methods of order 8 and 15 stages were given in [29, 39, 40], 10-order methods of 31, 33 and 35 stages have been also found [24, 34]. In this work some techniques that we have built to obtain 10-order symmetric composition methods of symmetric integrators of s = 31 stages (16 order conditions) are explored. Given some starting coefficients that satisfy the simplest five order conditions, the process followed to obtain the coefficients that satisfy the sixteen order conditions is provided.

Undertreatment of human immunodeficiency virus in psychiatric inpatients: a cross-sectional study of seroprevalence and associated factors

Background: The aims of this study were to evaluate the prevalence of HIV and its associated demographic and clinical factors among psychiatric inpatients of a general hospital. Methods: This was a single-center, observational, cross-sectional study that included patients consecutively admitted to our unit aged 16 years or older and with no relevant cognitive problems. The patients were evaluated using a semistructured interview and an appropriate test for HIV infection. Results: Of the 637 patients who were screened, 546 (86%) who consented to participate were included in the analyses. Twenty-five (4.6%, 95% confidence interval [CI] 3.0-6.8) patients were HIV-positive. The prevalence was higher among patients with substance misuse (17.4%, 95% CI 9.7-28.8). All except one of the 25 patients knew of their seropositive condition prior to participation in the study. Only 14 (56%) of the 25 seropositive patients had previously received pharmacological treatment for their infection. According to the multiple logistic regression analysis, the likelihood of HIV infection was lower in patients with higher levels of education and higher among patients who were single, had history of intravenous drug use, and had an HIV-positive partner, particularly if they did not use condoms. Among the patients with HIV infection, 18 (72%) had a history of suicide attempts compared with 181 (34.7%) of the patients without HIV infection (relative risk 2.1, 95% CI 1.6-2.7; P<0.001). Conclusion: HIV infection is highly prevalent in patients admitted to a psychiatric unit, especially those with a diagnosis of substance misuse. Seropositive patients show very poor treatment adherence. The risk of suicide seems to be very high in this population. Implementing interventions to reduce the suicide risk and improve adherence to antiretroviral therapy and psychotropic medications seems crucial.