| In this dissertation we consider fractional and quadratic 0-1 optimization problems with some related applications in biomedicine.; First, we discuss fractional 0-1 programming problems. New results on computational complexity of various classes of fractional 0-1 programming problems, equivalent reformulations as well as some heuristic approaches are reported. In part, this research was motivated by a new fractional 0-1 programming model for biclustering, an important data mining problem, which has a great significance for biomedical applications.; In the second part of the dissertation we investigate quadratic 0-1 optimization problems. We are mostly concerned with two important applications of quadratic 0-1 programming: in silico sequence selection in de novo protein design and epileptic seizure prediction.; In the first application, we focus on the mathematical formulations for in silico sequence selection in de novo protein design. We discuss linear mixed 0-1 reformulations for computational sequence search via quadratic 0-1 programming as well as results on computational complexity of the considered problem.; In the other application, a multi-quadratic 0-1 model is formulated to develop a new automated seizure warning algorithm. The technique was tested on continuous long-term EEG recordings obtained from patients with temporal lobe epilepsy. |
