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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 2020
In movement ecology, many methods currently exist for analyzing and estimat ing animal movement patterns and selection for habitat types. However, the accuracy of the estimates for quantifying animal movement and selection are difficult to determine, especially when data is missing. In the...

Fall 2020
In this thesis, we study some aspects of algebraic geometry that have had a significant influx of ideas from physics. The first part focuses on the Eynard Orantin topological recursion and its variants as a theory of enumerative ge ometry. We investigate the conjectural relationship between the...

Spring 2020
This thesis studies various aspects of the theory of vertex algebras. It has been shown that the moonshine module for Conway’s group C0 has close ties to the equivariant elliptic genera of sigma models with a K3 surface as target space. This is taken as a motivation to investigate conditions...

Fall 2020
Formation of singularities in physical phenomena has always fascinated scientists and stimulated both development of mathematical theories accounting for observations and further experimental scrutiny of the governing physics with the goal to resolve the singular behavior. The underlying theme of...

Spring 2020
Abstract harmonic analysis is well established on compact Hausdorff admissible right topological (CHART) groups. Specifically these groups are onesided analogues of topological groups, where the elements that multiply continuously on the other side are dense in the group. The analytic theory of...

Fall 2020
The kinetic chemotaxis equations have long been used to model biological processes. We will analyze a volume filling variant of the kinetic chemotaxis equations on the torus. Since the kinetic chemotaxis systems have well known blowup solutions, we spend a considerable amount of time showing...

Categories of Weight Modules for Unrolled Quantum Groups and Connections to Vertex Operator Algebras
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Recently, numerous connections between the categories of modules $\mathrm{Rep}{\langle s \rangle} \mcM(r)$ for the singlet vertex operator algebra $\mcM(r)$ and $\mathrm{Rep}{wt}\overline{U}q^H(\mathfrak{sl}2)$ for the unrolled restricted quantum group $\overline{U}q^H(\mathfrak{sl}2)$ at $2r$th...

Comparison of Sleep State Classification Performance Using Random Forests, Hidden Markov Models, and Nonhomogeneous Hidden Markov Models
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In this work, the CF00N polysomnograph data of 75 patients, with ranging severeties of Obstructive Sleep Apnea (OSA), is presented and analyzed in terms of sleep state classification. The preprocessing and cleaning of each polysomnograph recording were performed in R (R Core Team, 2019) using...

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...