Studies In Applied Mathematics And Statistics

应用数学和统计学研究

• 批准号: 6542182
• 负责人: George H Weiss
• 金额: --
• 依托单位: CENTER FOR INFORMATION TECHNOLOGY
• 依托单位国家: 美国
• 资助国家: 美国
• 起止时间: 至
• 项目状态: 未结题
• 来源: https://reporter.nih.gov/project-details/6542182
• 关键词: bioimaging /biomedical imaging; biophysics; chemical kinetics; computer simulation; electron optics; image enhancement; image processing; ion transport; lasers; light scattering; mathematical model; mathematics; physical model; spectrometry; statistics /biometry

This project involves collaborative work with NIH scientists, in which sophisticated mathematical tools or an acquaintance with theoretical methods in the physical sciences are required for the research. Drs. George Weiss, Marian Bogunya, and Alexander Berezhkovskii (NIDDK) have worked on a variety of problems required to develop the theory of single-molecule spectroscopy. So far an exact solution has been found for the simplest possible two-state system which is an isomerization scheme with first-order transitions. Considerable effort has been spent in developing theoretical approaches to deal with more complicated chemical systems. This requires expansion of the theory of cumulative residence times in one or more states of a multistate system. To date we have published several papers on this subject. A second topic relates to the effects of surfaces on mathematical properties required to describe photon trajectories in tissue, which is relevant to the use of laser light for diagnostic purposes. Many mathematical details of the theory become quite complicated when there is a boundary separating tissue from an external environment. We are currently working on problems in this general area.

该项目涉及与 NIH 科学家的合作，其中研究需要复杂的数学工具或熟悉物理科学的理论方法。博士。 George Weiss、Marian Bogunya 和 Alexander Berezhkovskii (NIDDK) 致力于解决发展单分子光谱学理论所需的各种问题。到目前为止，已经找到了最简单的二态系统的精确解，即具有一阶跃迁的异构化方案。人们花费了大量的精力来开发处理更复杂的化学系统的理论方法。这需要扩展多状态系统的一个或多个状态中的累积停留时间理论。迄今为止，我们已经发表了几篇关于这个主题的论文。第二个主题涉及表面对描述组织中光子轨迹所需的数学特性的影响，这与使用激光进行诊断目的相关。当存在将组织与外部环境分开的边界时，该理论的许多数学细节变得相当复杂。我们目前正在解决这个一般领域的问题。