REU 2011: Inverse Problems for Electrical Networks

REU电气网络逆问题项目将在2011-13年的每个夏天将八名本科生带到华盛顿大学从事离散逆问题的研究。电力网络的反问题是当边界电流对边界电压的响应(响应矩阵)已知时，求出电力网络中电阻的导电性的问题。阻力可以由有向或无向边函数或顶点函数来指定。学生将研究响应矩阵和网络几何之间的关系。想象这个问题的最好方法是想像一个盒子，里面有一个电路伸出的导线：问题是在不打开盒子的情况下确定电路。学生将学习与其他离散方程的关系，如Helmholtz方程，还将学习排列、图和结--具有类似于电力网络问题的特征的问题。该程序将运行八周。在第一周，将有关于基础材料、已知结果和未解决问题的讲座。然后，学生将利用可用的人力、图书馆和计算机资源，开始他们自己选择的项目。学生们将单独或以两人为一组进行学习。在接下来的几周里，他们将每天与一名顾问会面。学生将提交中级和期末口头和书面报告。

The REU Program on Inverse Problems for Electrical Networks will bring eight undergraduates to the University of Washington in each of the summers 2011-13 to work on discrete inverse problems. The inverse problem for an electrical network is the problem of finding the conductivity of resistors in an electrical network when the boundary current response to boundary voltages (response matrix) is known. Resistances may be specified by directed or undirected edge functions or vertex functions. Students will investigate the relation between the response matrix and the geometry of the network. The best way to imagine the problem is to think of a box that has leads sticking out with an electrical ciruit inside: the problem is to determine the circuit without opening the box. Students will study the relation to other discrete equations such as the Helmholtz equation and will also study permutations, graphs, and knots--problems with similar features to electrical network problems.The program will run for eight weeks. During the first week there will be lectures on foundational material, known results, and open problems. Students will then begin work on projects of their own choosing, using the available human, library, and computer resources. Students will work on their own or in teams of two. They will meet with an advisor daily for the remaining weeks. Students will present intermediate and final oral and written reports.