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This work originates from my PhD thesis at the London School of Economics and Political Science. I am indebted to Bemhard von Stengel for his excellent supervision. He introduced me to the questions addressed in this work. I am thankful for the many hours of discussions, and also for his guidance and patience in times when results seemed far away. Also, I am grateful to Srihari Govindan and Robert Wilson for useful ad- vice and encouragement. Furthermore, I would like to thank the members of the Mathematics De- partment for their general support. In particular, I thank Jackie Everid, David Scott and Mark Baltovic for their assistance, as well as Nic Georgiou and Luis Cereceda for their help on the final draft. There were many people who supported me personally. Foremost, I would like to thank my parents and Ane S. Flaatten for always being there for me. I am also beholden to Philipp Beckmann for his advice, and to Philip Hochstrate for his inspiration. Finally, I would like to thank the London School of Economics and Po- litical Science (LSE), the Department of Mathematics at LSE and the UK Engineering and Physical Sciences Research Council (EPSRC) for financial support.