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(20150716)We consider here an extension and generalization of the stochastic neuronal network model developed by DeVille et al.; their model corresponded to an alltoall network of discretized integrateandfire excitatory neurons ...
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Ramanujan's identities, Voronoi summation formula, and zeros of partial sums of zeta and Lfunctions (20150803)The focus of the first part of the thesis commences with an examination of two pages in Ramanujan's lost notebook, pages 336 and 335. A casual, or even more prolonged, examination of the strange formulas on these pages ...
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(20150715)In this thesis we study certain functions on graphs. Chapters 2 and 3 deal with variations on vertex ranking, a type of nodelabeling scheme that models a parallel processing problem. A kranking of a graph G is a labeling ...
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(20150715)Given a $G$toric, foldedsymplectic manifold with coorientable folding hypersurface, we show that its orbit space is naturally a manifold with corners $W$ equipped with a smooth map $\psi: W \to \frak{g}^*$, where ...
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(20150709)We study several problems in graph coloring. In list coloring, each vertex $v$ has a set $L(v)$ of available colors and must be assigned a color from this set so that adjacent vertices receive distinct colors; such a ...
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