The investigator together with his co-researchers study and employ a combination of mathematical, statistical, and computational tools which are useful in discovering new orthogonal arrays useful for multifatorial experiments. Proper and relevant small Chebyshev-systems and maximum principles will be developed for identifying and constructing optimal designs for non-linear models. When needed genetic algorithms will be developed for the purpose of explicitly constructing optimal and near optimal designs useful for linear and non-linear models.
This proposal develops new methods and theory for the purpose of collecting informative and cost effective data. Two broad cases are considered. Those cases where data are controlled by many factors, and those cases where medicinal chemists are seeking for natural products with chemotherapeutic and chemopreventive properties among thousands of agents. In both cases the goal is to collect the minimum amount of data with maximum info/cost value. The proposed research has important applications in collecting and analyzing raw optical density data used by medicinal chemists. This research provides a mechanism for integrating, coordinating and expanding interdisciplinary interaction between statisticians and researchers in the areas of pharmaceutical and medical sciences. The emerging uses of natural products in preventing and treating disease add urgency to a portion of the proposed research. The outcomes of this proposal will also assist scientists working on research projects sponsored by NIH Office of Dietary Supplements (DOS) and National Centers for Complementary and Alternative Medicines (NCCAM).
