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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)
 6Mizera, Ivan (Mathematical and Statistical Sciences)
 5Hillen, Thomas (Mathematical and Statistical Sciences)

A graphtheoretic approach to the construction of Lyapunov functions for coupled systems on networks
DownloadFall 2010
For coupled systems of differential equations on networks, a graphtheoretic approach to the construction of Lyapunov functions is systematically developed in this thesis. Kirchhoff’s MatrixTree Theorem in graph theory plays an essential role in the approach’s development. The approach is...

A Universal Approximation Theorem for Tychonoff Spaces with Application to Spaces of Probability and Finite Measures
DownloadFall 2022
Universal approximation refers to the property of a collection of functions to approximate continuous functions. Past literature has demonstrated that neural networks are dense in continuous functions on compact subsets of finitedimensional spaces, and this document extends those findings to...

Fall 2021
The theory of convergence structures delivers a promising foundation on which to study general notions of convergence. However, that theory has one striking feature that stands out against all others: it is described using the language of filters. This is contrary to how convergence is used in...

Fall 2017
One main goal of this thesis is to bring forth a systematic and simple construction of a multiwavelet basis on a bounded interval. The construction that we present possesses orthogonality in the derivatives of the multiwavelet basis among all scale levels. Since we are mainly interested in Riesz...

A General Framework of Optimal Stochastic Optimization with Dependent Data: Multiple Optimality Guarantee, Sample Complexity, and Tractability
DownloadSpring 2023
We consider stochastic optimization in settings where the distribution of unknown parameters is observable only through finitely dependent training samples. Using the Sample Averaging Approximation ({SAA}), we specifically study the datadriven procedure in which, instead of receiving samples...

Spring 2014
We introduce two kinds of particle filters, one is weighted particle filter and the other is resampling particle filter. We prove the Strong Law of Large Numbers and Central Limit Theorem for both particle filters. Then, we show that the resampling particle filter is better than the weighted one.

A Bayesian Joint Model Framework for Repeated MatrixVariate Regression with Measurement Error Correction
DownloadSpring 2021
In this thesis, with the purpose of correcting for potential measurement errors in repeatedlyobserved matrixvalued surrogates, and examining the underlying association between latent matrix covariates and a binary response, we propose a Bayesian joint model framework. This joint model method...