NMRA: New Mathematical Methodology for NMR Spectroscopy

描述（由申请人提供）：该项目组建了一支跨学科团队，拥有前所未有的技能和经验组合。该团队的目标是利用信号数学表示方面的最新进展，开发核磁共振波谱中出现的特殊信号的数学表示。该团队努力的成果将是针对 NMR 信号的新颖数据表示，这些数据表示是根据此类信号的属性精心定制的，并且基于坚实的数学基础。这种表示将为 NMR 界提供一个深入的工具，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，如滤波器对角化和最大熵方法。这种表示还可以显着改进现有的核磁共振波谱技术，无论是在计算速度还是信号/噪声分离方面。更雄心勃勃的这种表示可能会带来创新的光谱算法。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，并将刺激该领域新的、内在的研究。 跨学科研究常常受到不同科学语言以及分隔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取决于制定一个以深思熟虑和现实的方式解决跨学科协作问题的管理计划。 该项目的管理计划借鉴了团队成员过去的经验，被认为是高效且有效的。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模型，以及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.