UVicSpace

# Theses (Mathematics and Statistics)

## Recent Submissions

• (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 ...
• (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 ...
• (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 ...
• (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 ...
• (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 ...
• (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 $A_t = A_{t-1} \cup \{v \in ... • (2022-08-31) Deep Learning (DL) has been broadly applied to solve big data problems in biomedical fields, which is most successful in image processing. Recently, many DL methods have been applied to analyze genomic studies. However, ... • (2022-08-30) Let$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) = ...
• (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. ...
• (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 ...
• (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 ...
• (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 ...
• (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 ( $U_{\text{Schwarzsc ... • (2022-06-06) COVID-19 has affected the lives of millions of people worldwide. This thesis includes two statistical studies on the response to COVID-19. The first study explores the impact of lockdown timing on COVID-19 transmission ... • (2022-05-02) This thesis is devoted to the motion of the incompressible and inviscid flow which is ax- isymmetric and swirl-free in a cylinder, where the hydrostatic approximation is made in the axial direction. It addresses the ... • (2022-04-27) A Pythagorean Triple($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 ...
• (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 ...
• (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 ...
• (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 ...
• (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 ...