NMRA: New Mathematical Methodology for NMR Spectroscopy

描述（由申请人提供）：该项目汇集了一个跨学科的团队，具有前所未有的技能和经验。该团队的目标是建立在信号数学表示的最新进展的基础上，并开发核磁共振光谱中发生的特殊类型信号的数学表示。该团队的努力成果将是NMR信号的新数据表示，这些数据表示根据此类信号的特性精心定制，并基于坚实的数学基础。这种表示将提供NMR社区与穿透工具的定量分析和比较的各种现有的算法在这一领域，包括最近的非线性方法，如过滤器对角化和最大熵方法。这样的表示还可以在计算速度或信号/噪声分离方面实质上改进现有的NMR光谱技术。更雄心勃勃的是，这种表示可能会导致创新的光谱算法。过去的经验表明，这一努力将产生反馈效应，在数学领域产生广泛的影响，并将刺激这一领域新的内在研究。 跨学科的研究往往受到不同科学语言以及分离合作学科的科学文化障碍的阻碍。因此，这项工作的成功关键在于有一个管理计划，以深思熟虑和现实的方式解决跨学科合作问题。 该项目的管理计划借鉴了团队成员过去的经验，被认为是高效和有效的。因此，该项目可能成为数学家和生物学家之间成功建立和管理伙伴关系的典范，也可能成为克服上述障碍的有效方法。

DESCRIPTION (provided by applicant): This project assembles an inter-disciplinary team with an unprecedented combination of skills and experience. The team aims to build on recent advances in mathematical representation of signals, and to develop mathematical representation to the special kinds of signals occurring in Nuclear Magnetic Resonance Spectroscopy. The outcome of this team effort will be novel data representations for NMR signals that are carefully tailored to the properties of such signals, and are based on a solid mathematical foundation. Such representations will provide the NMR community with a penetrating tool for quantitative analysis and comparison of the various existing algorithms in this area, including the recent nonlinear methods such as filter diagonalization and maximum entropy methods. Such representations can also substantially improve existing NMR spectroscopy techniques, either with regards to computational speed or signal/noise separation. More ambitiously such representations may lead to innovative spectroscopic algorithms. Past experience suggests the effort will have feedback effects, with wide-spread ramifications within mathematics, and will stimulate new, intrinsic studies in this field. Inter-disciplinary research is often hampered by differing scientific languages as well as by scientific cultural barriers that separate the collaborating disciplines. Therefore, success in the effort hinges critically on having a management plan which addresses inter-disciplinary collaboration issues in a thoughtful and realistic way. The management plan of this project draws from the past experience of the team's members, and is believed to be efficient and effective. As such, the project may emerge as a model for a successful creation and management of partnerships between mathematicians and biologists, as well as for an effective approach for bridging over the aforementioned barriers.