Stochastic averaging and sensitivity analysis for two scale reaction networks.

In the presence of multiscale dynamics in a reaction network, direct simulation methods become inefficient as they can only advance the system on the smallest scale. This work presents stochastic averaging techniques to accelerate computations for obtaining estimates of expected values and sensitivities with respect to the steady state distribution. A two-time-scale formulation is used to establish bounds on the bias induced by the averaging method. Further, this formulation provides a framework to create an accelerated "averaged" version of most single-scale sensitivity estimation methods. In particular, we propose the use of a centered ergodic likelihood ratio method for steady state estimation and show how one can adapt it to accelerated simulations of multiscale systems. Finally, we develop an adaptive "batch-means" stopping rule for determining when to terminate the micro-equilibration process.

Changing trends in adult facial trauma epidemiology.

OBJECTIVE: The aim of this study was to determine whether the incidence of facial fractures has changed in the United States since 1990. STUDY DESIGN: This study is a retrospective review of all nonpediatric inpatient and outpatient facilities of the Detroit Medical Center from 1990 to 2011 and weighted national inpatient estimates from 1993 to 2010 using the National Inpatient Survey. METHODS: Facial fractures and surgical repairs were grouped according to fracture site and scaled to annual populations. Chow testing determined the year with the most significant change in trend, and regressions were performed before and after the break point. RESULTS: Chow testing showed the year 2000 as the most significant break point across all data sets. National inpatient and institutional data showed a significant decrease in total fractures and most subsites during the 1990s and an increase since 2000. Since 1990, the rate of fracture repairs decreased at our institution and during inpatient stays in the United States. Motor vehicle-related injuries have decreased since the early 1990s. Assault rates have fallen nationally but increased slightly in Detroit. CONCLUSIONS: Evidence from the largest institutional series of adult facial fractures and the largest national inpatient database supports a decrease in fractures and repairs during the 1990s and an increase in fractures despite no change in repairs since 2000. These trends are likely related to increasing use of computed tomographic imaging, decreasing severity of facial injuries, and changing incidences of the major etiologies of facial fractures.