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Skip to Search Results 7Frei, Christoph (Mathematical and Statistical Sciences)
 7Kong, Linglong (Mathematical and Statistical Sciences)
 7Lewis, Mark (Mathematical and Statistical Sciences)
 6Han, Bin (Mathematical and Statistical Sciences)
 6Hillen, Thomas (Mathematical and Statistical Sciences)
 6Mizera, Ivan (Mathematical and Statistical Sciences)

Fall 2012
This thesis is interested in the topological recursion first introduced in \cite{CEO} and generalized to algebraic curves in \cite{Eynard:2007,Eynard:2008}. A presentation of the Hermitian matrix model is given and includes a derivation of this topological recursion. The second part introduces a...

Fall 2021
Topological Recursion began its life as a series of recursive equations aimed at solving constraints which occur in matrix models of Quantum Field Theory. After its inception, Topological Recursion was given a more abstract formulation in terms of Quantum Airy Structures and has since been of...

Spring 2017
We explore the connection between EynardOrantin Topological Recursion (EOTR) and the asymptotic solutions to differential equations constructed with the WKB method (named for its creators Wentzel, Kramers and Brillouin). Using the Airy spectral curve as an initial example, we propose a general...

Fall 2015
Let a locally compact semitopological semigroup S have a separately con tinuous left action on a locally compact Hausdorff X. We define a jointly continuous left action of the measure algebra M(S) on the bounded Borel measure space M(X) which is an analogue of the convolution of measure alge...

Fall 2014
Persistent Homology broadly refers to tracking the topological features of a geometric object. This study aims to use persistent homology to explore the effect of Human Biotherapy on patients suffering from Clotridium Difficile Infection. The data is presented in the form of several distance...

Fall 2017
In this thesis, some topics in convex geometric analysis and discrete tomography are studied. Firstly, let K be a convex body in the ndimensional Euclidean space. Is K uniquely determined by its sections? There are classical results that explain what happens in the case of sections passing...

Fall 2017
In this thesis, we formulate and prove the theorem of quadratic reciprocity for an arbitrary number field. We follow Hecke and base our argument on analytic techniques and especially on an identity of theta functions called theta inversion. From this inversion formula and a limiting argument, we...

Theory of Spectral Sequences of Exact Couples: Applications To Countably And Transfinitely Filtered Modules
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This thesis has two parts. In the first part we start from an arbitrary exact couple of Rmodules and describe completely how the Einfinity terms of the associated spectral sequence relate to adjacent filtration stages of the universal (co)augmenting objects of the exact couple. This advances...

Theoretical and Computational Aspects of Mixture Models, with Applications to Empirical Bayes Methods
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This thesis studies mixture models, in particular the estimation of mixing distributions and their applications to empirical Bayes prediction. The objectives are twofold: to study the largesample property of empirical Bayes estimators; to develop algorithms for the nonparametric estimation of...