• Some results on linear dynamical systems 

  Lee, George (2023-09-07)

  A linear cocycle is an object that arises naturally in the study of dynamical systems and statistics. Oseledets’ multiplicative ergodic theorem [22] guarantees a decompo- sition of a linear space of states into equivariant ...
• Iimi: A novel automated workflow for plant virus diagnostics from high-throughput sequencing data 

  Ning, Haochen (2023-08-31)

  Several workflows have been developed for the diagnostic testing of plant viruses using high-throughput sequencing methods. Most of these workflows require considerable expertise and input from the analyst to perform and ...
• Estimating the Size of the COVID-19 Population in British Columbia Using the Stratified Petersen Estimator 

  Dao, Viet (2023-08-30)

  The presence of undetected COVID-19 cases is a known phenomenon. Mathematical modelling techniques, such as capture-recapture, provide a reliable method for estimating the true size of the infected population. Treating a ...
• Saturation Problems on Graphs 

  Ogden, Shannon (2023-08-25)

  In this thesis, we consider two variations on classical saturation problems in extremal graph theory: rainbow saturation and weak saturation. An edge-coloured graph G is rainbow if every edge in G receives a distinct ...
• The Edwards–Sokal Coupling for the Potts Higher Lattice Gauge Theory on Z^d 

  Shklarov, Yakov (2023-08-25)

  The Edwards–Sokal coupling of the standard Potts model with the FK–Potts (random-cluster) bond percolation model can be generalized to arbitrary-dimension cells. In particular, the Potts lattice gauge theory on Z^d has a ...
• Cross-Sperner Systems 

  Kuperus, Akina (2023-08-22)

  Two sets $A$ and $B$ are \emph{comparable} if $A \subseteq B$ or $B \subseteq A$. A collection of families $(\F_{1}, \F_{2} , \cdots , \F_{k}) \in \mathcal{P}([n])^k$ is \emph{cross-Sperner} if there is no pair $i \not= ...
• Topological Data Analysis: Persistent Homology of Uniformly Distributed Points 

  Sohal, Ranjit (2023-08-09)

  Topological Data Analysis (TDA) is a branch of computational topology that provides methods to extract qualitative information from high dimensional, noisy, and incomplete data. TDA combines techniques from various fields, ...
• A new numerical approach to solve 1D Viscous Plastic Sea Ice Momentum Equation 

  Alam, Fahim (2023-07-20)

  While there has been a colossal effort in the ongoing decades, the ability to simulate ocean ice has fallen behind various parts of the climate system and most Earth System Models are unable to capture the observed adversities ...
• Background Connectivity-Understanding the brain's functional organization 

  Holmes, Mikayla (2023-06-22)

  Task-state fMRI (tfMRI) and rest-state fMRI (rfMRI) surface data from the Human Connectome Project (HCP) was examined with the goal of better understanding the nature of background activation signatures and how they compare ...
• Convex Optimization Methods for Bounding Lyapunov Exponents 

  Oeri, Hans (2023-05-01)

  In dynamical systems, the stability of orbits is quantified by Lyapunov exponents (LEs), which are computed from the average rate of divergence of trajectories. We develop techniques for computing sharp upper bounds on the ...
• A Uniqueness Theorem for C*-algebras of Hausdorff Étale Groupoids 

  Goerke, Gavin (2023-04-27)

  In this thesis we study the ideal intersection property for inclusions of C*-algebras C*(H)↪C*(G) induced from a family of open subgroupoids {H} of a locally compact Hausdorff étale groupoid G. For such a family of open ...
• 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. ...

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