Parameter Identification and Applications of Regularization
Friday, June 21st, 2013, 2:00 – 3:00 pM
307 Eberly Hall
ABSTRACT: There are many mathematical difficulties in the area of parameter identification. In one application, brain mapping, we wish to find the correlations of a particular ability (such as walking) to areas of the brain. This understanding has quality of life and financial consequences, as it can be used to detect and prevent early signs of disability. The difficulties are high levels of co-linearity between regions of the brain causing amplification of noise in the walking speeds. Also, current methods of analysis involve many single comparison tests of individual regions to be run. This talk will look at a development of iterated Tikhonov regularization as a defect correction method. Then we offer it as a general method of solving brain mapping problems as opposed to least squares regression, which is the current standard. We will then see how this general method can be applied to a diverse class of problems.
BIO: Nathaniel Mays is an Assistant Professor of Mathematics at Wheeling Jesuit University. He received his Ph.D. in Mathematics from University of Pittsburgh in 2011. His research interests are in iterative regularization methods and their applications.