iii This thesis reports an unusual and unexpected journey through intellectual territory entirely new to me. Who is prepared for such journeys? I was not. Thus my debt is great to those who have helped me along the way, without whose help I would have been completely lost and uninspired. There is no way to give sufficient thanks to my advisor, John Hopfield. His encouragement for me to get my feet wet, and his advice cutting to the bone of each issue, have been invaluable. John’s policy has been, in his own words, to give his students “enough rope to hang themselves with. ” But he knows full well that a lot of rope is needed to weave macrame. Perhaps the only possible repayment is in kind: to maintain a high standard of integrity, and when my turn comes, to provide a nurturing environment for other young minds. Len Adleman and Ned Seeman have each been mentors during my thesis work. In many ways, my research can be seen as the direct offspring of their work, combining the notion of using DNA for computation with the ability to design DNA structures with artificial topology. Both Len and Ned have provided encouragement, support, and valuable feedback throughout this project. Iwould like additionally to thank Ned Seeman and Xiaoping Yang for teaching me how t
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