Date of Award
Spring 5-6-2012
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematics and Statistics
First Advisor
Dr. Igor Belykh
Second Advisor
Dr. Guantao Chen
Third Advisor
Dr. Jenny J. Yang
Fourth Advisor
Dr. Vladimir Bondarenko
Abstract
This dissertation aims at analyzing complex problems arising in the context of dynamical networks, proteomics, and disease prevention. First, a new graph-based method for proving global stability of synchronization in directed dynamical networks is developed. This method utilizes stability and graph theories to clarify the interplay between individual oscillator dynamics and network topology. Secondly, a graph-theoretical algorithm is proposed to predict Ca2+-binding site in proteins. The new algorithm enables us to identify previously-unknown Ca2+-binding sites, and deepens our understanding towards disease-related Ca2+-binding proteins at a molecular level. Finally, an optimization model and algorithm to solve a disease prevention problem are described at the population level. The new resource allocation model is designed to assist clinical managers to make decisions on identifying at-risk population groups, as well as selecting a screening and treatment strategy for chlamydia and gonorrhea patients under a fixed budget. The resource allocation model and algorithm can have a significant impact on real treatment strategy issues.
DOI
https://doi.org/10.57709/2768899
Recommended Citation
Zhao, Kun, "Mathematical Methods for Network Analysis, Proteomics and Disease Prevention." Dissertation, Georgia State University, 2012.
doi: https://doi.org/10.57709/2768899