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Protein Folding & Global Optimization (1) Protein structure prediction by computer simulations: The one dimensional sequence information of proteins is well understood due to the recent progress of various genome projects. However, it is the three dimensional structural and functional information of proteins that contains the most important and yet unsolved issues of life sciences. We map this protein folding problem to a global optimization problem of a complex energy function which governs the microscopic interactions between atoms. In recent publications, we proposed a systematic protocol to optimize a given potential energy by refining its parameters. This method exploits the high efficiency of the conformal space annealing (CSA) method in finding distinct low energy conformations. Currently, we are studying the application to various available potential energies in order to validate their applicability in the protein folding problem. (2) Protein folding mechanism: Even after extensive investigations both experimentally and theoretically, the microscopic understanding of the folding mechanism is far from being complete. Recently, we proposed an atomistic potential that was specifically optimized to study a few small proteins for the study of the microscopic folding mechanism. This potential is much more useful for the study of folding kinetics in that all possible pair-wise interactions are included. This should be contrasted to the existing approaches where only native interactions are considered. From this study, we conclude that the way a protein folds into its native structure is determined by the convergence point of early folding trajectories relative to the native state. The results agree well with those in the literature and provide new insights on the folding mechanism. (3) Application of CSA method to important global optimization problems: We are currently attacking various global optimization problems, such as the traveling salesman problem (TSP), the Lennard-Jones cluster problem (LJ). For the case of LJ problem, we have shown that the global minimum structure of LJ clusters up to N=201 can be efficiently obtained by the CSA, which is an unbiased optimization method. We have not used any extra information of the problem such as the structures of the known global energy minima. From preliminary tests, we have promising results from various TSP problems. (4) Other research interests: Docking problems, pattern recognition problems (such as secondary structure prediction problem, domain parsing problem, contact prediction), nearest neighbor method for secondary structure problem, multiple sequence alignment, application of action-derived molecular dynamics simulations to carbon clusters and kinetic folding studies, and vortex patterns and infinite degeneracy in the frustrated XY models.