Browse Dissertations and Theses - Mathematics by Contributor "Rapti, Zoi"

• (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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• (2013-05-24)
Using the SISR asymptotic, a classification of a class of scale-separated stochastic differential equations is achieved using combinatorics and formal language theory. This is extended to a topological notion of temperature ...

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• (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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• (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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• (2012-02-06)
A general framework for analyzing finite games will be introduced. The concept of an incentive function will be defined so that it is compatible with the updating protocol defined in Nash's proof of existence of equilibrium ...

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• (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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• (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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• (2012-09-18)
We further generalize the stochastic version of the replicator dynamics due to Fudenberg and Harris. In particular, we add a random jump term to the payo ff function to simulate anomalous events and their e ffects on the ...

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• (2013-02-03)
In this thesis we study the effect of stochastic perturbations on moving boundary value PDE's with Stefan boundary conditions, or Stefan problems, and show the existence and uniqueness of the solutions to a number of ...

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• (2013-08-22)
In this dissertation we are interested in the study of dynamical systems that display rigidity and weak mixing. We are particularly interested in the topological analogue of rigidity, called uniform rigidity. A map $T$ ...

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