Global Phenomena from Local Rules: Peer-to-Peer Networks and Crystal Steps

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dc.contributor.advisorYorke, James Aen_US
dc.contributor.advisorMargetis, Dionisiosen_US
dc.contributor.authorFinkbiner, Amyen_US
dc.contributor.departmentMathematicsen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.date.accessioned2008-04-22T16:04:32Z
dc.date.available2008-04-22T16:04:32Z
dc.date.issued2007-12-04en_US
dc.description.abstractEven simple, deterministic rules can generate interesting behavior in dynamical systems. This dissertation examines some real world systems for which fairly simple, locally defined rules yield useful or interesting properties in the system as a whole. In particular, we study routing in peer-to-peer networks and the motion of crystal steps. Peers can vary by three orders of magnitude in their capacities to process network traffic. This heterogeneity inspires our use of "proportionate load balancing," where each peer provides resources in proportion to its individual capacity. We provide an implementation that employs small, local adjustments to bring the entire network into a global balance. Analytically and through simulations, we demonstrate the effectiveness of proportionate load balancing on two routing methods for de Bruijn graphs, introducing a new "reversed" routing method which performs better than standard forward routing in some cases. The prevalence of peer-to-peer applications prompts companies to locate the hosts participating in these networks. We explore the use of supervised machine learning to identify peer-to-peer hosts, without using application-specific information. We introduce a model for "triples," which exploits information about nearly contemporaneous flows to give a statistical picture of a host's activities. We find that triples, together with measurements of inbound vs. outbound traffic, can capture most of the behavior of peer-to-peer hosts. An understanding of crystal surface evolution is important for the development of modern nanoscale electronic devices. The most commonly studied surface features are steps, which form at low temperatures when the crystal is cut close to a plane of symmetry. Step bunching, when steps arrange into widely separated clusters of tightly packed steps, is one important step phenomenon. We analyze a discrete model for crystal steps, in which the motion of each step depends on the two steps on either side of it. We find an time-dependence term for the motion that does not appear in continuum models, and we determine an explicit dependence on step number.en_US
dc.format.extent896207 bytes
dc.format.mimetypeapplication/pdf
dc.identifier.urihttp://hdl.handle.net/1903/7682
dc.language.isoen_US
dc.subject.pqcontrolledMathematicsen_US
dc.subject.pqcontrolledComputer Scienceen_US
dc.subject.pqcontrolledPhysics, Condensed Matteren_US
dc.subject.pquncontrolleddistributed hash tablesen_US
dc.subject.pquncontrolledde bruijnen_US
dc.subject.pquncontrolledload balancingen_US
dc.subject.pquncontrolledclassificationen_US
dc.subject.pquncontrolledstep bunchingen_US
dc.subject.pquncontrolledasymptoticsen_US
dc.titleGlobal Phenomena from Local Rules: Peer-to-Peer Networks and Crystal Stepsen_US
dc.typeDissertationen_US

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