Graduate Student and Postdoctoral Conference on Applied Inverse Problems

该提案寻求资助初级研究人员参加两年一次的大型数学逆问题会议；应用逆问题（AIP）会议会议将于2011年5月23日至27日在德州农工大学校园举行。会议前还将有一个专门为研究生和博士后提供重要背景材料的研讨会。正如会议名称所预期的那样，会议强调应用，大多数会谈将直接受到物理、生物和工程科学问题的推动。这使得这是一个“不容错过”的会议，特别是对初级研究员来说，该提案寻求旅行资金，以允许研究生和博士后参加。这将产生更广泛的影响，因为它使美国的初级研究人员在一个快速发展的领域接触到最先进的应用和数学技术，这对国家的健康、经济福利和安全具有相当大的技术重要性。AIP-2011是一系列两年一次的会议中的第六届会议，旨在成为偏微分方程反问题及其应用领域的综合科学会议。除了12场全体会议外，还将举行大约40场小型专题讨论会和专题讨论会。会议的目的是实现应用程序的分析、计算和建模之间的平衡。反问题领域在过去十年中有了巨大的发展。虽然基础模型可能是一个偏微分方程，但需要远远超出这个基础的数学、计算和统计工具。这样做的一个后果是要求研究人员拥有广泛的专业知识，这对初级研究人员的影响尤其大。例如，成像在现代世界是一种无处不在的工具，而由各种模态产生的数学模型会产生逆问题。虽然我们熟悉的CAT扫描来自于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（它们具有非常不同的吸收和分辨率特性），而且还可以涉及像声音这样的纵波，或者像现在常见的那样，混合版本来优化扩散和缺乏分辨率的双重弊端。虽然许多这些方法以微分方程为基础，但重建技术需要密集的计算分析和统计方法来优化数据的使用。甚至这个子领域已经变得如此广泛，以至于没有一个人可以成为所有方面的专家。因此，AIP-2011将在主要会议之前举行一个主要面向研究生和博士后的会前研讨会。讲习班将有5位知名专家的10场演讲，并将涵盖许多基本工具，这些工具将是理解会议本身更深入的演讲所必需的。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。来自该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.