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- 2Department of Biological Sciences
- 2Department of Mechanical Engineering
- 1Department of Civil and Environmental Engineering
- 1Department of Computing Science
- 1Department of Public Health Sciences
- 7Frei, Christoph (Mathematical and Statistical Sciences)
- 7Hillen, Thomas (Mathematical and Statistical Sciences)
- 7Kong, Linglong (Mathematical and Statistical Sciences)
- 7Lewis, Mark (Mathematical and Statistical Sciences)
- 6Han, Bin (Mathematical and Statistical Sciences)
- 6Kashlak, Adam (Mathematical and Statistical Sciences)
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Spring 2013
In this thesis we study operator ideals on ordered Banach spaces such as Banach lattices, $C^*$-algebras, and noncommutative function spaces. The first part of this work is concerned with the domination problem: the relationship between order and algebraic ideals of operators. Fremlin, Dodds and...
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A Bayesian Joint Model Framework for Repeated Matrix-Variate Regression with Measurement Error Correction
DownloadSpring 2021
In this thesis, with the purpose of correcting for potential measurement errors in repeatedly-observed matrix-valued 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...
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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.
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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 data-driven procedure in which, instead of receiving samples...
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A graph-theoretic approach to the construction of Lyapunov functions for coupled systems on networks
DownloadFall 2010
For coupled systems of differential equations on networks, a graph-theoretic approach to the construction of Lyapunov functions is systematically developed in this thesis. Kirchhoff’s Matrix-Tree Theorem in graph theory plays an essential role in the approach’s development. The approach is...
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Fall 2009
This thesis is concerned with the analysis of the control design to the nonlinear networked control systems (NCSs). Ignoring the network connection and cascading actuators, the plant and sensors together, a sampled-data system is obtained. The stabilization problem of nonlinear sampled-data...