Graduate Student and Postdoctoral Conference on Applied Inverse Problems

该提案寻求资助初级研究人员参加关于数学逆问题的两年一次的大型会议；应用逆问题(AIP)会议。会议将于2011年5月23日至27日在德克萨斯农工大学校园举行。还将有一个会议前研讨会，专门为研究生和博士后提供批判性的背景材料。正如会议标题所预期的那样，会议的重点是应用，大多数演讲将直接受到物理、生物和工程科学问题的推动。这使得这是一次不容错过的会议，特别是对初级研究员来说，这项提议寻求旅行资金，以允许研究生和博士后参加。这将产生重大的更广泛的影响，因为它让美国初级研究人员在一个快速扩张的领域接触到最先进的应用程序和数学技术，该领域对美国的健康、经济福利和安全具有相当大的技术重要性。AIP-2011是旨在成为偏微分方程逆问题及其应用领域的综合性科学会议的一系列两年期会议中的第六次会议。除了12次全体会议外，还将有大约40次小型会议，外加贡献的会议和海报会议。会议的目的是在分析、计算和为应用程序建模之间取得平衡。逆问题领域在过去十年中有了巨大的增长。虽然基本模型可能是一个偏微分方程式，但需要远远超出这个基础的数学、计算和统计工具。这种情况的一个后果是要求研究人员具有广泛的专业知识，这对新手研究人员的影响尤其大。例如，成像是现代世界中无处不在的工具，由各种形式产生的数学模型会产生逆问题。虽然人们熟悉的CAT扫描来自Radon变换，并产生了(X射线)层析成像领域，但现代成像是极其复杂的。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)，还可以涉及纵波，如声音，或像现在常见的混合版本，以针对扩散和缺乏分辨率这两个邪恶进行优化。虽然这些方法中的许多都是以微分方程为基础的，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。即使是这一子领域也变得如此广泛，以至于没有一个人能在所有方面都成为专家。为此，AIP-2011将举办一个主要面向研究生和博士后的会前讲习班，该讲习班将在主要会议之前举行。讲习班将有来自5位知名专家的10次演讲，并将涵盖了解会议本身的更深入讨论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方法。来自这一奖项的资金也将允许参加研讨会，这本身将在一个对国家技术增长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.