Convergence of numerical time-averaging and stationary measures via Poisson equations

Numerical approximation of the long time behavior of a stochastic di.erential equation (SDE) is considered. Error estimates for time-averaging estimators are obtained and then used to show that the stationary behavior of the numerical method converges to that of the SDE. The error analysis is based on using an associated Poisson equation for the underlying SDE. The main advantages of this approach are its simplicity and universality. It works equally well for a range of explicit and implicit schemes, including those with simple simulation of random variables, and for hypoelliptic SDEs. To simplify the exposition, we consider only the case where the state space of the SDE is a torus, and we study only smooth test functions. However, we anticipate that the approach can be applied more widely. An analogy between our approach and Stein's method is indicated. Some practical implications of the results are discussed. Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.

Analysis of an asymptotic preserving scheme for linear kinetic equations in the diffusion limit

We present a mathematical analysis of the asymptotic preserving scheme proposed in [M. Lemou and L. Mieussens, SIAM J. Sci. Comput., 31 (2008), pp. 334-368] for linear transport equations in kinetic and diffusive regimes. We prove that the scheme is uniformly stable and accurate with respect to the mean free path of the particles. This property is satisfied under an explicitly given CFL condition. This condition tends to a parabolic CFL condition for small mean free paths and is close to a convection CFL condition for large mean free paths. Our analysis is based on very simple energy estimates. © 2010 Society for Industrial and Applied Mathematics.

Whole-cell-analysis of live cardiomyocytes using wide-field interferometric phase microscopy.

We apply wide-field interferometric microscopy techniques to acquire quantitative phase profiles of ventricular cardiomyocytes in vitro during their rapid contraction with high temporal and spatial resolution. The whole-cell phase profiles are analyzed to yield valuable quantitative parameters characterizing the cell dynamics, without the need to decouple thickness from refractive index differences. Our experimental results verify that these new parameters can be used with wide field interferometric microscopy to discriminate the modulation of cardiomyocyte contraction dynamics due to temperature variation. To demonstrate the necessity of the proposed numerical analysis for cardiomyocytes, we present confocal dual-fluorescence-channel microscopy results which show that the rapid motion of the cell organelles during contraction preclude assuming a homogenous refractive index over the entire cell contents, or using multiple-exposure or scanning microscopy.

Quantifying data quality for clinical trials using electronic data capture.

BACKGROUND: Historically, only partial assessments of data quality have been performed in clinical trials, for which the most common method of measuring database error rates has been to compare the case report form (CRF) to database entries and count discrepancies. Importantly, errors arising from medical record abstraction and transcription are rarely evaluated as part of such quality assessments. Electronic Data Capture (EDC) technology has had a further impact, as paper CRFs typically leveraged for quality measurement are not used in EDC processes. METHODS AND PRINCIPAL FINDINGS: The National Institute on Drug Abuse Treatment Clinical Trials Network has developed, implemented, and evaluated methodology for holistically assessing data quality on EDC trials. We characterize the average source-to-database error rate (14.3 errors per 10,000 fields) for the first year of use of the new evaluation method. This error rate was significantly lower than the average of published error rates for source-to-database audits, and was similar to CRF-to-database error rates reported in the published literature. We attribute this largely to an absence of medical record abstraction on the trials we examined, and to an outpatient setting characterized by less acute patient conditions. CONCLUSIONS: Historically, medical record abstraction is the most significant source of error by an order of magnitude, and should be measured and managed during the course of clinical trials. Source-to-database error rates are highly dependent on the amount of structured data collection in the clinical setting and on the complexity of the medical record, dependencies that should be considered when developing data quality benchmarks.