Scientific Computing Research Environments for the Mathematical Sciences (SCREMS)

数学科学的科学计算研究环境 (SCREMS)

• 批准号: 0421608
• 负责人: Weinan E
• 金额: $ 9.29万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-10-01 至 2007-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0421608&HistoricalAwards=false
• 关键词: Scientific; Computing; Research; Environments; Mathematical

The Department of Mathematics and Program in Applied and Computational Mathematics proposes to purchase a computational cluster which will be dedicated to support computational research in mathematical sciences. This research will be concentrated in particular in the following areas: (1) new algorithms for the separation of independent components in magnetic imaging data to study brain function, (2) the dynamics of how bio-molecules acquire and move between different conformations, (3) study of the analytic rank in connection with the Goldfeld conjecture on elliptic curves (a well-known conjecture in number theory), and (4) computer-assisted enumeration of cusped hyperbolic 3-manifolds.Each of these projects require dedicated facilities that Fine Hall does not have currently. From a scientific and educational point of view, the proposed projects lie at the interfaces between different disciplines: signal processing, statistics and psychology for the fMRI project; applied mathematics and biochemistry for the second project; topology and geometry for the 3-manifold project. Progress on these projects will impact several communities. In addition, these projects will be part of the PIs' continuing effort on bringing frontier research to science education in the classrooms, as well as attracting women and other under-represented groups to the area of mathematics. New courses and discussion sessions will be organized so that a much larger part of the mathematical and scientific community will have access to these research projects through the proposed facility.

数学系和应用与计算数学计划建议购买一个计算集群，专门用于支持数学科学的计算研究。这项研究将特别集中在以下领域：（1）分离磁成像数据中独立分量以研究脑功能的新算法，（2）生物分子如何在不同构象之间获取和移动的动力学，（3）与椭圆曲线上的Goldfeld猜想有关的分析秩的研究（数论中一个著名的猜想），以及（4）尖点双曲3-流形的计算机辅助枚举。这些项目中的每一个都需要Fine Hall目前不具备的专用设施。从科学和教育的角度来看，拟议的项目位于不同学科之间的接口：功能磁共振成像项目的信号处理，统计学和心理学;第二个项目的应用数学和生物化学;三维项目的拓扑学和几何学。这些项目的进展将影响几个社区。此外，这些项目将是PI将前沿研究纳入课堂科学教育以及吸引妇女和其他代表性不足的群体进入数学领域的持续努力的一部分。将组织新的课程和讨论会，以便更大部分的数学和科学界将有机会通过拟议的设施获得这些研究项目。