• Numerical Blowup Solutions for Boundary Value Models 

  Hoang, Duyen (2023-01-30)

  In this thesis, we discuss several numerical methods to approximate singular solutions for some partial differential equations such as Burgers’ equation, Prandtl’s equations, and the inviscid primitive equations. The ...
• The i-Graph and Other Variations on the γ-Graph 

  Teshima, Laura Elizabeth (2023-01-03)

  In graph theory, reconfiguration is concerned with relationships among solutions to a given problem. For a graph G, the γ-graph of G, G(γ), is the graph whose vertices correspond to the minimum dominating sets of G, and ...
• Algebraic Cycles on Products of Generically Smooth Quadrics 

  Guangzhao, Zhu (2022-12-21)

  In this thesis, we study rationality questions for algebraic cycles (modulo 2) on products of generically smooth projective quadrics over fields of any characteristic. More specifically, let $X_{1},\cdots,X_{n}$ be generically ...
• Boundary Independent Broadcasts in Graphs 

  Hoepner, Jules (2022-12-08)

  A \textit{broadcast} on a connected graph $G$ with vertex set $V(G)$ is a function $f:V(G)\rightarrow \{0, 1, ..., \text{diam}(G)\}$ such that $f(v)\leq e(v)$, where $e(v)$ denotes the eccentricity of $v$. A vertex $v$ is ...
• Random forests on trees 

  Xiao, Ben (2022-09-02)

  This thesis focuses a mathematical model from statistical mechanics called the Arboreal gas. The Arboreal gas on a graph $G$ is Bernoulli bond percolation on $G$ with the conditioning that there are no ``loops". This model ...
• Tight Bounds on 3-Neighbor Bootstrap Percolation 

  Romer, Abel (2022-08-31)

  Consider infecting a subset $A_0 \subseteq V(G)$ of the vertices of a graph $G$. Let an uninfected vertex $v \in V(G)$ become infected if $|N_G(v) \cap A_0| \geq r$, for some integer $r$. Define $A_t = A_{t-1} \cup \{v \in ...
• Deep Learning Methods Cannot Outperform Other Machine Learning Methods on Analyzing Genome-wide Association Studies 

  Zhou, Shaoze (2022-08-31)

  Deep Learning (DL) has been broadly applied to solve big data problems in biomedical fields, which is most successful in image processing. Recently, many DL methods have been applied to analyze genomic studies. However, ...
• Erdős-Deep Families of Arithmetic Progressions 

  Gaede, Tao (2022-08-30)

  Let $A \subseteq \Z_n$ with $|A| = k$ for some $k \in \Z^+$. We consider the metric space $(\Z_n,\delta)$ in which $\delta$ is the distance metric on $\Z_n$ defined as follows: for every $x,y \in \Z_n$, $\delta(x,y) = ...
• C*-algebras constructed from factor groupoids and their analysis through relative K-theory and excision 

  Haslehurst, Mitch (2022-08-30)

  We address the problem of finding groupoid models for C*-algebras given some prescribed K-theory data. This is a reasonable question because a groupoid model for a C*-algebra reveals much about the structure of the algebra. ...
• Sub-phenotypes of Macrophages and Monocytes in COPD and Molecular Pathways for Novel Drug Discovery 

  Yan, Yichen (2022-08-22)

  Chronic obstructive pulmonary disease (COPD) is a common respiratory disorder and the third leading cause of mortality. In this thesis we performed a clustering analysis of four specific immune cells in the GSE136831 ...
• scAnnotate: An Automated Cell Type Annotation Tool for Single-cell RNA-Sequencing Data 

  Ji, Xiangling (2022-08-11)

  Single-cell RNA-sequencing (scRNA-seq) technology enables researchers to investigate a genome at the cellular level with unprecedented resolution. An organism consists of a heterogeneous collection of cell types, each ...
• Optimality Conditions for Cardinality Constrained Optimization Problems 

  Xiao, Zhuoyu (2022-08-11)

  Cardinality constrained optimization problems (CCOP) are a new class of optimization problems with many applications. In this thesis, we propose a framework called mathematical programs with disjunctive subspaces constraints ...
• Dynamical Classification of the Two-body and Hill’s Lunar Problems with Quasi-homogeneous Potentials 

  Qian, Lingjun (2022-07-20)

  As seen in many examples, higher order correction added to the Newtonian potential often provides more realistic and accurate model in astrophysics. Such examples include the Schwarzschild potential ( $U_{\text{Schwarzsc ...
• Statistical Research on COVID-19 Response 

  Huang, Xiaolin (2022-06-06)

  COVID-19 has affected the lives of millions of people worldwide. This thesis includes two statistical studies on the response to COVID-19. The first study explores the impact of lockdown timing on COVID-19 transmission ...
• Well-posedness and blowup results for the swirl-free and axisymmetric primitive equations in a cylinder 

  SadatHosseiniKhajouei, Narges (2022-05-02)

  This thesis is devoted to the motion of the incompressible and inviscid flow which is ax- isymmetric and swirl-free in a cylinder, where the hydrostatic approximation is made in the axial direction. It addresses the ...
• The dynamics of Pythagorean Triples 

  Acar, Nazim (2022-04-27)

  A Pythagorean Triple($PT$) is a triple of positive integers $(a,b,c)$, that satisfies\\ $a^2+b^2=c^2$. By requiring two of the entries being relatively prime, $(a,b,c)$ becomes a Primitive Pythagorean Triple($PPT$). This ...
• Splitting factor maps into s- and u-bijective maps 

  Buric, Dina (2022-01-04)

  We model hyperbolic toral automorphisms by two types of Smale spaces; shifts of finite type and substitution tilings spaces. Smale spaces are dynamical systems with local hyperbolic product structure. In 1970, Bowen ...
• Complexity of frugal homomorphisms 

  Bard, Stefan (2021-12-20)

  Let t >= 1 be an integer. A k-colouring of a graph G is called t-frugal if no colour is assigned to more than t vertices in the neighbourhood of any vertex. Similarly, a homomorphism of G to H is t-frugal if no vertex of ...
• A multistate extension of the Jolly-Seber model: combining adult mark-recapture data with juvenile data 

  Halverson-Duncan, Brittany (2021-10-28)

  The Laskeek Bay Conservation Society has been collecting data on the East Limestone Island population of Ancient Murrelets since 1990. For the first 15 years of this decades-long study, mark-recapture data was collected ...
• Statistical methods for imaging data, imaging genetics and sparse estimation in linear mixed models 

  Opoku, Eugene A. (2021-10-21)

  This thesis presents research focused on developing statistical methods with emphasis on techniques that can be used for the analysis of data in imaging studies and sparse estimations for applications in high-dimensional ...

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