2014 Summer Undergraduate REU Program

Arizona State University

ASU - School of Mathematical & Statistical Sciences

Topic 1:

Modeling and simulation of cancer treatment - Yang Kuang and Fabio Milner

Project Description:

We will formulate and study cancer treatment models with the aim of evaluating final outcomes of practical alternative treatment plans. For example, we will consider the effects of the ordering and timing of complementing treatments such as surgery, chemotherapy and radiotherapy for brain or ovarian cancers. For prostate cancer, we will also compare the outcomes of intermittent androgen suppression therapy with that of the standard continuous androgen suppression therapy.

Topic 2:

An Inverse Problem in Electrochemical Impedance Spectroscopy - Rosie Renaut

Project Description:

The inverse problem associated with electrochemical impedance spectroscopy requiring the solution of a Fredholm integral equation of the first kind is considered. If the underlying physical model is not clearly determined, the inverse problem needs to be solved using a regularized linear least squares problem that is obtained from the discretization of the integral equation. For this system, it is shown that the model error can be made negligible by a change of variables and by extending the effective range of quadrature. This change of variables serves as a right preconditioner that significantly improves the condition of the system. Still, to obtain feasible solutions the additional constraint of non-negativity is required. Simulations with artificial, but realistic, data demonstrate that the use of non-negatively constrained least squares with a smoothing norm provides higher quality solutions than those obtained without the non-negativity constraint. Using higher-order smoothing norms also reduces the error in the solutions. The L-curve and residual periodogram parameter choice criteria, which are used for parameter choice with regularized linear least squares, have been successfully adapted to be used for the non-negatively constrained problem. Next steps include applying a dictionary learning approach to see whether further improvement in the solutions is possible.