I use the Computer Graphics Laboratory (CGL) in my research regarding protein structure. I am pursuing numerous projects that make use of both the computational power and visualization capability of the CGL. One project is to create an unsupervised BCM-based neural network to find principal patterns relating amino acid sequence to phi-psi bond angles. These patterns, when constrained by a limited number of hidden nodes in the model, represent """"""""secondary structures"""""""" ranked by predictability rather than based on bond-angle sequences. A second project is to relate folded proteins to mathematical knots. Rather than simply using the folded structure, I will use an association matrix generated from van der Waals contacts and hydrogen-bond contacts between residues to generate a cyclic non-directed graph, from which a knot can be generated. These knots are embedded in 3-space, and can be visualized using the CGL computers. The goal eventually is to classify these knots using the standard knot invariants (the Alexander polynomial, for example). A third project is to study signal averaged electrocardiograms (SAECG) and conventional 12-lead electrocardiograms. SAECGs are studied in both frequency and time space, but only Fourier transforms are used in the interconversion. I would apply wavelet decomposition to SAECGs, which being limited signals are perfect subjects. 12-lead EKGs, representing repeating oscillations in a 12-dimensional space, can be viewed in projections on the plane that are different from the canonical. These projections may assist in finding subtle features that mark congenital heart disease that are hard to pick up in conventional 12-lead studies.
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