Browse Dissertations and Theses - Mathematics by Contributor "DeVille, Lee"

  • Nawaz, Tayyab (2017-04-07)
    In the first part of this thesis, we will discuss the classical XY model on complete graph in the mean-field (infinite-vertex) limit. Using theory of large deviations and Stein's method, in particular, Cramér and Sanov-type ...

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  • Liu, Shiya (2017-07-11)
    In Part I, we aim to maximize the number of first-quadrant lattice points under a concave (or convex) curve with respect to reciprocal stretching in the coordinate directions. The optimal domain is shown to be asymptotically ...

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  • Kirkoryan, Artur (2018-12-06)
    This thesis consists of two parts. Each of them deals with problems in the design of linear time-invariant systems with certain prescribed properties, such as stability and cost optimality. The first part addresses ...

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  • Ferguson, Timothy (2018-04-13)
    We obtain results for two distinct dynamical models: the Kuramoto model, a general model for coupled oscillator systems, and a model for opinion formation in social networks. Our main focus is on understanding the fixed ...

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  • Berning, Stephen R (2015-07-16)
    We consider here an extension and generalization of the stochastic neuronal network model developed by DeVille et al.; their model corresponded to an all-to-all network of discretized integrate-and-fire excitatory neurons ...

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  • Chung, Jooyeon (2018-05-29)
    In Part I, we study the spectrum of the one-dimensional vibrating free rod equation u′′′′ − τ u′′ = μu under tension (τ > 0) or compression (τ < 0). The eigenvalues μ as functions of the tension/compression parameter τ ...

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  • West, Argen McAllister (2018-07-10)
    We consider a generalization of the linear search problem where the searcher has low sensing capabilities on two rays. We first show the necessary conditions for an optimal search plan to exist. We then investigate ...

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  • Wang, Xiao (2018-12-06)
    Statistical physics, as a branch of modern physics, uses methods of probability theory and statistics to solve physical problems with large populations and approximations. In this thesis, we use numerical simulations to ...

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  • Cong, Lin (2017-04-19)
    In this work we are interested in the stability bifurcations of the dynamical systems defined on graphs, and we use signed graph Laplacians as our tool. In chapter 1, we give the formal definition of the Laplacian matrix ...

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