Topics in Design of Scientific Experiments

摘要DMS 0103727 S. Hedayat研究人员与他的合作研究人员一起研究并使用数学，统计和计算工具的组合，这些工具有助于发现新的正交表用于多因素实验。 适当的和相关的小切比雪夫系统和最大值原理将被开发用于识别和构建非线性模型的最优设计。当需要时，遗传算法将被开发用于明确构建线性和非线性模型有用的最优和接近最优的设计。该建议开发了新的方法和理论，用于收集信息和成本效益的数据。 两个广泛的情况下考虑。 数据受多种因素控制的情况，以及药物化学家在数千种药物中寻找具有化疗和化学预防特性的天然产物的情况。 在这两种情况下，目标都是以最大的信息/成本价值收集最少量的数据。 所提出的研究在收集和分析药物化学家使用的原始光密度数据方面具有重要的应用。 这项研究提供了一个机制，整合，协调和扩大统计人员和研究人员在制药和医学领域的跨学科互动。 天然产品在预防和治疗疾病方面的新用途增加了部分拟议研究的紧迫性。该提案的结果还将有助于从事由NIH膳食补充剂办公室（DOS）和国家补充和替代药物中心（NCCAM）赞助的研究项目的科学家。

ABSTRACTDMS 0103727S. HedayatThe 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).