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Fall 2024

Venegas Garcia, Pablo

Increased anthropogenic greenhouse gas emissions have gained attention from researchers and world leaders due to the potential for global warming. Part of the primary greenhouse gas emitters come from the agriculture and oil and gas industrial sectors. The sources of two prioritized greenhouse...

Fall 2024

Fan, Xinyi

In the field of sleep research, the quantitative analysis of electroencephalography (EEG) data acquired during sleep offers invaluable insights. However, the presence of artifacts in such data can severely distort analytical outcomes. Therefore, this study aims to develop an innovative artifact...

Fall 2024

Wagner, Connor J

We begin with a survey of mathematical epidemic modelling from its inception to present day. We present up-to-date research on the field of variable susceptibility SIR (Susceptible-Infected-Removed system of differential equations model), which takes the classic SIR model and adds another...

Fall 2024

Biswas, Amitakshar

Motivated by Elizabeth Meckes’ work on concentration inequalities using the group SO(n) (see [9]), this thesis explores the use of random rotations for detecting autocorrelation in time series data. Traditional tests like the Durbin Watson test assess autocorrelation by analyzing quadratic forms...

Fall 2024

Milanes Perez, Daniel Enrique

We consider the problem of a firm that wants to maximize its earnings. Production generates pollution as a by-product and has a negative impact on the environment. This negative impact causes disutility. The firm determines the optimal production rate and chooses between two types of technologies...

Fall 2024

Goldthorpe, Zachariah PL

Let Cat(oo,oo) denote the (oo,1)-category of (oo,oo)-categories with weakly inductive equivalences. The main objective of this thesis is to demonstrate that Cat(oo,oo) satisfies universal properties with respect to homotopy-coherent internalisation and enrichment. To achieve these universal...

Fall 2024

Baabdulla, Arwa Abdulla

In this thesis, we explore the spatial dynamics of viral infection within tissue through mathematical modelling, aiming to understand the impact of virus spread on both cancerous and healthy tissue. Specifically, we investigate how spatial patterning and heterogeneity influence viral infection...

Fall 2024

Chang, Xiaotian

We study the Severi varieties of Atiyah ruled surfaces over generic elliptic curves. In particular, we prove that general members of such varieties have at worst ordinary triple points.

Fall 2024

Yu, Peng

The evolution of data acquisition technologies and the exponential growth in computing capabilities have inaugurated an epoch wherein researchers are empowered to procure data of unprecedented dimensionality and complexity. Simultaneously, Bayesian hierarchical models distinguish themselves as...

Fall 2024

Liu, Meichen

Functional regression is a cornerstone for understanding complex relationships where predictors or responses (or both) are functions. A particularly powerful framework within this domain is the Reproducing Kernel Hilbert Space (RKHS), which facilitates the handling of infinite-dimensional data...