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dc.contributor.advisorBERENSTEIN, CARLOS Aen_US
dc.contributor.authorForoozan, Farshaden_US
dc.date.accessioned2006-06-14T05:59:08Z
dc.date.available2006-06-14T05:59:08Z
dc.date.issued2006-04-30en_US
dc.identifier.urihttp://hdl.handle.net/1903/3542
dc.description.abstractThe purpose of this dissertation is to present a mathematical model of network tomography through spectral graph theory analysis. In this regard, we explore the properties of harmonic functions and eigensystems of Laplacians for weighted graphs (networks) with and without boundary. We prove the solvability of the Dirichlet and Neumann boundary value problems. We also prove the global uniqueness of the inverse conductivity problem on a network under a suitable monotonicity condition. As a physical interpretation to the discrete inverse conductivity problem, we define a variant of the chip-firing game (a discrete balancing process) in which chips are added to the game from the boundary nodes and removed from the game if they are fired into the boundary of the graph. We find a bound on the length of the game, and examine the relations between set of spanning weighted forest rooted in the boundary of the graph and the set of critical configurations of the chips.en_US
dc.format.extent494744 bytes
dc.format.mimetypeapplication/pdf
dc.language.isoen_US
dc.titleDISCRETE INVERSE CONDUCTIVITY PROBLEMS ON NETWORKSen_US
dc.typeDissertationen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.contributor.departmentApplied Mathematics and Scientific Computationen_US
dc.subject.pqcontrolledMathematicsen_US


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