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.

Social, economic, and health impact of the respiratory syncytial virus: a systematic search

Background: Bronchiolitis caused by the respiratory syncytial virus (RSV) and its related complications are common in infants born prematurely, with severe congenital heart disease, or bronchopulmonary dysplasia, as well as in immunosuppressed infants. There is a rich literature on the different aspects of RSV infection with a focus, for the most part, on specific risk populations. However, there is a need for a systematic global analysis of the impact of RSV infection in terms of use of resources and health impact on both children and adults. With this aim, we performed a systematic search of scientific evidence on the social, economic, and health impact of RSV infection. Methods: A systematic search of the following databases was performed: MEDLINE, EMBASE, Spanish Medical Index, MEDES-MEDicina in Spanish, Cochrane Plus Library, and Google without time limits. We selected 421 abstracts based on the 6,598 articles identified. From these abstracts, 4 RSV experts selected the most relevant articles. They selected 65 articles. After reading the full articles, 23 of their references were also selected. Finally, one more article found through a literature information alert system was included. Results: The information collected was summarized and organized into the following topics: 1. Impact on health (infections and respiratory complications, mid-to long-term lung function decline, recurrent wheezing, asthma, other complications such as otitis and rhino-conjunctivitis, and mortality; 2. Impact on resources (visits to primary care and specialists offices, emergency room visits, hospital admissions, ICU admissions, diagnostic tests, and treatments); 3. Impact on costs (direct and indirect costs); 4. Impact on quality of life; and 5. Strategies to reduce the impact (interventions on social and hygienic factors and prophylactic treatments). Conclusions: We concluded that 1. The health impact of RSV infection is relevant and goes beyond the acute episode phase; 2. The health impact of RSV infection on children is much better documented than the impact on adults; 3. Further research is needed on mid-and long-term impact of RSV infection on the adult population, especially those at high-risk; 4. There is a need for interventions aimed at reducing the impact of RSV infection by targeting health education, information, and prophylaxis in high-risk populations.