Date of Award:

12-2025

Document Type:

Dissertation

Degree Name:

Doctor of Philosophy (PhD)

Department:

Mathematics and Statistics

Committee Chair(s)

Kevin R. Moon

Committee

Kevin R. Moon

Committee

D. Richard Cutler

Committee

Daniel Coster

Committee

Matthew W. Harris

Committee

Jacob Gunther

Abstract

This thesis brings together two important research directions: how to compare different sets of data more accurately, and how to better understand how brain cancer cells move and change shape.

In the first part, we look at a problem in statistics: measuring how different two data sources are from each other. Traditional methods often make strong assumptions, which may not always hold in real situations. Our approach avoids those assumptions by using an ensemble method, a way of combining many weak estimators into one stronger result. This makes the method more flexible and reliable, especially when dealing with complex or unknown types of data.

The second part focuses on glioblastoma, a fast-growing and deadly brain tumor. We used computer-based tools to track cancer cells in microscope videos and studied how their shapes change over time. By applying advanced methods to analyze these shapes, we discovered patterns in how different cells behave. Some moved slowly and were more rounded, while others were faster and more stretched out. We also trained a machine learning model to predict how fast a cell moves just by looking at its shape, helping us link cell structure to movement.

Together, these studies improve our ability to analyze both complex data and cancer cell behavior. The results could lead to better tools for scientific discovery and may help future research in cancer treatment and diagnosis.

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