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One of the core technologies for obtaining protein mixtures is provided by the two dimensional polyacrylamide gel electrophoresis (2D-gel). In order to analyze variations in the protein gels obtained from different groups that account for biological variations we must first eliminate distortions to properly align images. The image alignment is recognized as a major bottleneck in proteomics. We formulate the image alignment problem as a large scale quadratic programming problem, which can be solved in polynomial time by interior point methods. Unlike previous approaches which are based on pairwise alignment, we use the information contained in the whole family of gels for creating an ideal gel and simultaneously determining the transformations that optimally align all images to this ideal gel. The ideal landmarks and the coefficients defining the transformations are the unknowns of the quadratic programming problem. The constraints of the problem ensure smoothness and consistency. Numerical results illustrate the effectiveness of this approach.
Florian Potra earned a Ph.D. in Mathematics from the University of Bucharest, Romania. After an Andrew Mellon Postdoctoral Fellowship at the University of Pittsburgh, he joined the faculty of the University of Iowa, first as an Associate Professor of Mathematics, and then as a Professor of Mathematics and Computer Science. Between 1997-1998, he served as a Program Director in Applied and Computational Mathematics at the National Science Foundation. Since 1998 he has been a Professor of Mathematics and Statistics at the University of Maryland Baltimore County. He is also a Faculty Appointee at the Mathematical and Computational Sciences Division of The National Institute of Standards and Technology. Dr. Potra has published over 120 research papers in prestigious professional journals. He is the Regional Editor for the Americas of the journal "Optimization Methods and Software", and serves on the editorial board of three other well known mathematical journals.