There are plenty of people that I want to offer my sincere gratitude to. Without them, I may not reach what I have achieved during my PhD. My supervisors, Prof. Yang Liu and Prof. Jie Zhang, have been playing a crucial role in leading me to a qualified researcher. I remember the very beginning of my PhD study, when I was quite new to doing research. Prof. Liu did not force me to study some specific problems immediately. Instead, he provided me freedom to get a wide horizon of the area first. And he allowed me to choose the research problems I like to solve. Prof. Zhang always provide very valuable opinions in evaluating my ideas and paper drafts. He offers me significant guidance on how to make my research more valuable and recognizable. Besides, he is very generous in spending his time on us: from discussing ideas and plans, to helping fix some writing problems. I am very grateful for both Profs supervision in the last four years. Whenever I get myself too relaxed, they remind me that I can do better, without which, I cannot be productive in research. Tim, who was a post-doc when cooperating with me (and now is a lecturer in Oxford), has been very supportive. When I got stuck in small questions or technical problems, he helped to drag me out and taught me how to think in a higher level. As a mentor, he has been showing considerable patience. He would never feel troubled to discuss with me, or teach me how to fix even tedious problems. He has influenced me not only on the way of thinking, but also on exploring for meaningful research. Tim is also a very nice friend, he often invited us to cook, BBQ or have some drinks, and we really enjoyed the time. In a word, it has been my great pleasure to be a friend with him. I also want to thank my TAC members, Prof. Alwen Tiu, Prof. Bo An, and Prof. Rongxin Lu. They supervised my research progress regularly, and brought up questions to help me reflect on my solutions or methods. vii viii During the last four years, I have been surrounded by a group of nice fellows, who are also my friends. I appreciate their company, which enriches my PhD life and brings me beautiful memories. They are