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- 6Frei, Christoph (Mathematical and Statistical Sciences)
- 6Han, Bin (Mathematical and Statistical Sciences)
- 6Kong, Linglong (Mathematical and Statistical Sciences)
- 6Lewis, Mark (Mathematical and Statistical Sciences)
- 6Mizera, Ivan (Mathematical and Statistical Sciences)
- 5Hillen, Thomas (Mathematical and Statistical Sciences)
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...
A Bayesian Joint Model Framework for Repeated Matrix-Variate Regression with Measurement Error CorrectionDownload
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...
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.
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...
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...
A Universal Approximation Theorem for Tychonoff Spaces with Application to Spaces of Probability and Finite MeasuresDownload
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 finite-dimensional spaces, and this document extends those findings to...
A graph-theoretic approach to the construction of Lyapunov functions for coupled systems on networksDownload
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...