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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 2022
Field Cancerization is a hypothesis for the formation of cancer in certain types of tissues. It proposes the idea that a tumour can form in a “field” of cells that are predetermined for the development of cancer. Further, it is hypothesized that these fields are mainly caused by the onslaught of...

Sources, sinks, and sea lice: determining patch contribution and transient dynamics in marine metapopulations
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Sea lice are a threat to the health of both wild and farmed salmon and an economic burden for salmon farms. Opennet salmon farms act as reservoirs for sea lice in near coastal areas, which can lead to elevated sea louse levels on wild salmon. With a free living larval stage, sea lice can...

Fall 2022
The Helmholtz equation is a fundamental wave propagation model in the timeharmonic setting, which appears in many applications such as electromagnetics, geophysics, and ocean acoustics. It is challenging and computationally expensive to solve due to (1) its highly oscillating solution and (2)...

Fall 2022
In this dissertation, various problems related to stochastic (partial) differential equations are investigated. These problems include wellposedness, H\"older continuity of the solution, moments of the solution and their asymptotics. This thesis is divided into three parts. The first part...

A Universal Approximation Theorem for Tychonoff Spaces with Application to Spaces of Probability and Finite Measures
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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 2022
Interface problems arise in many applications such as modeling of underground waste disposal, oil reservoirs, composite materials, and many others. The coefficient $a$, the source term $f$, the solution $u$ and the flux $a\nabla u\cdot \vec{n}$ are possibly discontinuous across the interface...

Fall 2022
The topological recursion is a construction in algebraic geometry that takes in the data of a socalled spectral curve, $\mathcal{S}=\left(\Sigma,x,y\right)$ where $\Sigma$ is a Riemann surface and $x,y:\Sigma\to\mathbb{C}_\infty$ are meromorphic, and recursively constructs correlators which, in...

Spring 2022
This work develops numerical methods (finite difference methods) for equations of fluid dynamics and equations of elasticity reformulated in the stress variables (as opposed to natural variables) and applies them to the FluidStructure Interac tion (FSI) problem using a new model based on the...

Fall 2021
This thesis includes 2 parts. Part 1 is: Discretization on High Dimensional Compact Domains. Part 2 is: Polynomial Approximation on High Dimensional Spheres. A special example for part 1 is the result on the unit sphere of highdimensional Euclidean spaces. In chapter 2, we obtained general...

Fall 2021
In this note we present a construction which improves the best known bound on the minimal dispersion of large volume boxes in the unit cube. The dispersion of a subset of the cube is the supremal volume over all axis parallel boxes in the cube which do not intersect the given subset. The minimal...