An Exponential Time Differencing Scheme with a Real Distinct Poles Rational Function for Advection-Diffusion Reaction Equations

A second order Exponential Time Differencing (ETD) scheme for advection-diffusion reaction systems is developed by using a real distinct poles rational function for approximating the underlying matrix exponential. The scheme is proved to be second order convergent. It is demonstrated to be robust for reaction-diffusion systems with non-smooth initial and boundary conditions, sharp solution gradients, and stiff reaction terms. In order to apply the scheme efficiently to higher dimensional problems, a dimensional splitting technique is also developed. This technique can be applied to all ETD schemes and has been found, in the test problems considered, to reduce computational time by up to 80%

An Efficient Methodology for Learning Bayesian Networks

Statistics from the National Cancer Institute indicate that 1 in 8 women will develop Breast cancer in their lifetime. Researchers have developed numerous statistical models to predict breast cancer risk however physicians are hesitant to use these models because of disparities in the predictions they produce. In an effort to reduce these disparities, we use Bayesian networks to capture the joint distribution of risk factors, and simulate artificial patient populations (clinical avatars) for interrogating the existing risk prediction models. The challenge in this effort has been to produce a Bayesian network whose dependencies agree with literature and are good estimates of the joint distribution of risk factors. In this work, we propose a methodology for learning Bayesian networks that uses prior knowledge to guide a collection of search algorithms in identifying an optimum structure. Using data from the breast cancer surveillance consortium we have shown that our methodology produces a Bayesian network with consistent dependencies and a better estimate of the distribution of risk factors compared with existing method