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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)
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Fall 2023
In this thesis, we perform a systematic study of the Allee effect in cancer stem cell (CSC) models with an application to non-small cell lung cancer (NSCLC). Previously, it was shown that an Allee effect exists in mathematical tumor growth models incorporating cancer stem cell (CSC) dynamics....
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Fall 2022
This thesis concerns dynamical systems subject to small noise perturbations. Our purpose is to obtain a deep understanding of how small noise perturbations influence the original unperturbed dynamical system, especially over long but finite time intervals. We consider two special systems, the...
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Monge solutions and uniqueness in multi-marginal optimal transport: costs associated to graphs and a general condition
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This thesis is devoted to the proof of several results on the existence and uniqueness of Monge solutions to the multi-marginal optimal transportation problem. These results are found in Chapters \ref{Chapter3}, \ref{Chapter4} and \ref{Chapter5}, and represent joint work with Brendan Pass. The...
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Fall 2022
The Helmholtz equation is a fundamental wave propagation model in the time-harmonic 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)...
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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...
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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 Fluid-Structure Interac- tion (FSI) problem using a new model based on the...
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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. Open-net 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...
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Reflected Backward Stochastic Differential Equations for Informational Systems with Applications
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The core innovation of this thesis lies in studying reflected backward stochastic differential equations (RBSDE hereafter) for informational systems. An informational system is a system where there is discrepancy in the information received by agents over time. In this thesis, we restrict to the...
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Fall 2022
Numerical methods are one of the most important aspects in the computer modelling of physical phenomena governed by differential equations. In order to study these phenomena precisely and in a timely manner, we need to use robust and efficient numerical methods for solving the underlying...
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Fall 2022
We consider the category of modules over certain subalgebras of the unrolled restricted quantum group associated to any reductive Lie algebra and show some progress towards the proof of an equivalence of categories of this with the category of local representations of a simple current extension.