Graduate Student and Postdoctoral Conference on Applied Inverse Problems

该提案旨在为初级研究人员提供资金，以参加关于数学逆问题的大型两年一次的会议;应用逆问题（AIP）会议。 会议将于2011年5月23日至27日在德克萨斯州农工大学校园举行。 还将有一个会前研讨会，专门为研究生和博士后提供重要的背景材料。 正如会议名称所预期的那样，重点是应用，大多数演讲将直接受到物理，生物和工程科学问题的启发。这使得这是一个“不容错过”的会议，特别是对初级研究人员来说，这项提案寻求旅行资金，以允许研究生和博士后出席。 这将产生更广泛的影响，因为它使美国初级研究人员在一个迅速扩大的领域中接触到最先进的应用和数学技术，该领域对国家的健康，经济福利和安全具有相当大的技术重要性。 AIP-2011是一系列两年期会议中的第六次会议，旨在成为偏微分方程及其应用领域反问题的综合科学会议。 除了12场全体会议外，还将有大约40场小型会议和海报会议。 会议的目的是在分析、计算和应用建模之间取得平衡。反问题领域在过去十年中有了巨大的发展。 虽然基本模型可能是偏微分方程，但需要远远超出这一基础的数学、计算和统计工具。 这样做的一个后果是要求研究人员具有广泛的专业知识，这特别影响了开始的研究人员。 例如，成像是现代世界中无处不在的工具，并且由各种模态产生的数学模型引起逆问题。 虽然熟悉的CAT扫描来自Radon变换并产生了（X射线）断层扫描领域，但现代成像非常复杂。 它不仅使用电磁频谱的不同部分（具有非常不同的吸收和分辨率特性），而且还可以涉及诸如声音之类的非线性波，或者像现在常见的那样，混合版本以优化扩散和缺乏分辨率的双重弊端。 虽然这些方法中的许多方法都以微分方程为基础，但重建技术需要密集的计算分析和统计方法来优化数据使用。 即使这个子领域已经变得如此广泛，没有一个人可以在所有方面都是专家。 因此，AIP-2011将在主会议之前举办一个主要针对研究生和博士后的会前研讨会。 研讨会将有5位知名专家的10次演讲，并将涵盖了解会议本身更深入的演讲所需的许多基本工具。 这些方法包括解析/几何方法、贝叶斯技术、逆散射、正则化技术和成像中的层析成像方法。 该奖项的资金也将允许参加研讨会，这本身将在对国家技术发展至关重要的领域产生广泛的教育影响。

This proposal seeks funding for junior researchers to attend the large, biennial meeting on mathematical inverse problems; the Applied Inverse Problems (AIP) conference. The meeting will be held on the campus of Texas A&M University, May, 23-27, 2011. There will also be a pre-conference workshop, specifically tailored to give graduate students and postdocs critical background material. As expected from the conference title, there is an emphasis on applications and most talks will be motivated directly by questions in the physical, biological and engineering sciences. This makes this a "not-to-be-missed" meeting, especially for the junior researcher, and this proposal seeks travel funding to permit graduate student and postdoc attendance. This will have significant broader impact as it exposes US junior researchers to state-of-the-art applications and mathematical techniques in a rapidly expanding area that has considerable technological importance for the health, economic welfare and security of the nation. AIP-2011 is the sixth in a series of biennial meetings that are intended to be the comprehensive scientific conference for the area of inverse problems in partial differential equations and applications. In addition to the 12 plenary talks, there will also be approximately 40 minisymposia plus contributed sessions and poster sessions. The intent of the meeting is to achieve a balance among analysis, computation and modeling for applications.The field of inverse problems has grown enormously within the last decade. While the underlying model may be a partial differential equation, mathematical, computational and statistical tools are required that go far beyond this basis. One consequence of this is the demand put on a researcher to have broad-based expertise and this particularly impacts beginning researchers. For example, imaging is a ubiquitous tool in the modern world and the mathematical models arising from various modalities give rise to inverse problems. While the familiar CAT scan comes from the Radon transform and gave rise to the field of (x-ray) tomography, modern imaging is extremely complex. It not only uses different parts of the electromagnetic spectrum (which have very different absorption and resolution properties) but also can involve longitudonal waves such as sound, or as is now common, hybrid versions to optimize against the twin evils of diffusion and lack of resolution. While many of these methods have differential equations as their basis, reconstruction techniques require intensive computational analysis and statistical methods to optimize data use. Even this sub-field has become so broad that no one individual can be expert on all aspects. For this reason AIP-2011 will feature a pre-conference workshop primarily intended for graduate students and postdocs that will take place immediately prior to the main meeting. The workshop will feature 10 talks from 5 well-known experts and will cover many of the basic tools that will be required for an understanding of the more in-depth talks of the meeting itself. These include analytic/geometrical methods, Baysian techniques, inverse scattering, regularization techniques and tomographic methods in imaging. Funding from this award will also allow attendance at the workshop and this in itself will have a broad educational impact in an area that is critical for the technological growth of the nation.