Acknowledgments

There are many people that have earned my gratitude for their contribution to my life and especially during my graduate school at the University of Minnesota. In particular, I would like to express my sincere thanks to Professor Gilad Lerman, my adviser in the school of mathematics, who showed me the way and supported my academic endeavors with patience and care. I am indebted to my PhD adviser Professor Efi Foufoula-Georgiou in the department of civil engineering. I would like to express my utmost gratitude to her, who paved the way and my academic accomplishments would not have been possible without her generous support and guidance. My appreciations are also extended to Professor Arnd Scheel, a dedicated teacher, who kindly admitted to serve as a committee member of this thesis and I owe him fundamental parts of my knowledge in linear algebra.