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.

应用和计算数学的数学和计划部建议购买一个计算集群，该集群将致力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）在磁成像数据中分离独立组件以研究大脑功能的新算法，（2）生物分子如何获得和移动不同构象之间的动态，（3）研究与分析级别在与戈德菲尔德在椭圆形的计算机上的分析等级的研究（3）数字构想（4）数字构想（4）数字构想（4）刺激双曲线的3型manifold。这些项目的每个项目都需要精美大厅目前没有的专用设施。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界面：fMRI项目的信号处理，统计和心理学；第二个项目的应用数学和生物化学； 3个manifold项目的拓扑和几何形状。这些项目的进展将影响几个社区。此外，这些项目将成为PIS持续努力的一部分，以将边境研究带入教室的科学教育，并吸引妇女和其他代表性不足的群体进入数学领域。将组织新的课程和讨论会议，以便数学和科学界的很大一部分将通过拟议的设施访问这些研究项目。