The concepts for weak-constraint four-dimensional variational data assimilation (w4D-Var) and the mathematical framework to evaluate the sensitivity of model error parameters in w4D-Var are discussed. A novel procedure for adaptive tuning of model error parameters is introduced. Preliminary numerical results are shown to illustrate the potential benefits for practical applications.

We discuss a novel method of obtaining numerical solutions to a particular class of PDE problem: the Dirichlet problem for harmonic functions. Our approach involves solving a finite linear system for the harmonic conjugate of the function on the boundary, and using these data in Cauchy’s integral formula from complex analysis to obtain numerical values for quantities such as the gradient in the interior of the domain. Both smooth and nonsmooth domain boundary cases are considered.

I will share my experience of carving my own small piece of research out of a large, nationwide, NSF (National Science Foundation) funded, multimillion dollar study. The CSPCC (Characteristics of Successful Programs in College Calculus) project was a 5-year study focused on Calculus I instruction at colleges and universities across the United States with overarching goals of identifying the factors that contribute to successful programs. In this presentation, I will discuss the methods I used to analyze student focus group interview data collected from schools that were identified as ‘successful’ by the CSPCC project. The results will characterize the ways in which calculus students talk about their instructors, in an attempt to understand how their perceptions shape their experience.

k-means clustering is a method of sorting a given real dataset into k clusters and determining the center (mean) of each cluster. The standard k-means clustering algorithm converges, but not necessarily to a global solution. The solution depends on the choice of initial guess. We will discuss how the DCA technique for solving a generalized Fermat Torricelli problem can be used to generate an effective starting point for the k-means problem. Empirical testing suggests promising results.