3:45 - 4:15 :
Ahmed, S. Ejaz
(Department of Mathematics & Statistics, University of Windsor)
-Title: Improved Estimation Strategies for Tumor Growth Rate
-Abstract: From tumor to tumor, there is a great variation in the proportion of cancer cells growing and making daughter cells that ultimately metastasize. The differential growth within a single tumor, however, has not been studied extensively and this may be helpful in predicting the aggressiveness of a particular cancer type. The estimation problem of tumor growth rates from several populations is studied. The baseline growth rate estimator is based on a family of interacting particle system models which generalize the linear birth process as models of tumor growth. These interacting models incorporate the spatial structure of the tumor in such a way that growth slows down in a crowded system. Approximation-assisted estimation strategy is proposed when initial values of rates are known from the previous study. Some alternative estimation strategies are suggested and the relative dominance picture to the benchmark estimator is investigated. The analytical and numerical results demonstrate that our suggested estimator outperforms the classical estimator.
4:15 - 4:45 :
Tian, Jianjun Paul
(Mathematics, College of William and Mary)
-Title: A challenging problem in the competition between two stem cells
In this talk, I will briefly introduce a difficult problem arising from two germline stem cell competition process. In the female germline stem cell niche, there are 2 or 3 stem cells. Recent biological experiments showed that there is a competition for the niche space occupancy among stem cells. Stem cells compete by means of physical interaction. This is a new mechanism of cell interactions, and it is different from the well-understood cell interaction via sending and receiving chemical signals. The stem cell physical interaction involves a series of biochemical and biophysical processes. It is difficult to understand without considering these processes in molecular level. We propose a model that is a reaction-diffusion system over cell surfaces with two free boundaries. I will report the model and some research on simplified version of the model.