This talk discusses an extention of a Bayesian approach for estimating the ancestry probability, the probability that an inbred line is an ancestor of a given hybrid, to account for genotyping errors. The effect of such errors on ancestry probability estimates is evaluated through simulation. The simulation study shows that if misclassification is ignored, then ancestry probabilities may be slightly overestimated. The sensitivity of ancestry probability calculations to the assumed genotyping error rate is also assessed. Finally we briefly discuss approaches for estimating the error rate from limited data.
We will present several new results about global theorem and asymptotic expansions for the distributions of iid random variables in the domain of attraction of stable laws. Particular attention will be paid to the Cuachy case which exhibits especially interesting features.
I will describe our recent proof of localization at the bottom of the spectrum for Schrodinger operators with Poisson random potentials. Poisson random potentials are the most natural model for describing a material with impurities. This has been a longstanding open problem. I will give a very informal talk on work in progress.
In recent years, I have been thinking about
Mathematical Visualization, and developing a
program that does high quality, customized
visualizations of mathematical objects and
processes. I will demonstrate this program
and discuss some of the interesting and
unexpected ways that certain mathematical
theorems turned out to be just what was
needed to find fast and efficient algorithms
that solve a number of difficult rendering
problems. (Some of these rendering problems
involve seeing 3D objects in stereo, and I
will bring along the red/green glasses needed
for the demonstation.)