NMRA: New Mathematical Methodology for NMR Spectroscopy

描述（由申请人提供）：本项目汇集了一个跨学科的团队，他们拥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之上，并开发核磁共振波谱中出现的特殊类型信号的数学表示。该团队努力的结果将是针对核磁共振信号的特性精心定制的新颖数据表示，并基于坚实的数学基础。这样的表示将为核磁共振界提供一个穿透性的工具，用于定量分析和比较该领域的各种现有算法，包括最近的非线性方法，如滤波对角化和最大熵方法。这种表示也可以大大改进现有的核磁共振波谱技术，无论是在计算速度方面还是在信号/噪声分离方面。更雄心勃勃的是，这样的表示可能会导致创新的光谱算法。过去的经验表明，这种努力将产生反馈效应，在数学领域产生广泛的影响，并将刺激该领域新的、内在的研究。

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.