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Examining Committee

Supervisory Committee

Dr. Xuekui Zhang, Department of Mathematics and Statistics, University of Victoria (Supervisor)
Dr. Xiaojian Shao, Department of Mathematics and Statistics, UVic (Co-Supervisor)
Dr. Belaid Moa, Department of Electrical and Computer Engineering, UVic (Outside Member)

External Examiner
Dr. Pingzhao Hu, Department of Biochemistry, Western University

Chair of Oral Examination
Dr. Shengyao Lu, Department of Computer Science, UVic

Abstract

Bronchoalveolar lavage (BAL) provides a unique view to analyze immunological aspects of the human lung. single-cell RNA sequencing data (scRNA-seq) of BAL offers a great potential for immunotherapy of lung diseases. Despite promising, challenges persist in identifying disease-relevant high-resolution subcell types, standardizing annotations across studies, and accurately interpreting bulk RNA-seq data. This dissertation is approached from three perspectives. Chapter one serves as the introduction, while chapter two provides the background.

Chapter three presents scRNA-seq data utilized to characterize macrophage and monocyte populations in chronic obstructive pulmonary disease (COPD). The analysis identified dysfunctional alveolar macrophages and hyperinflammatory monocytes, indicating potential therapeutic targets and emphasizing the modulatory effects of inhaled corticosteroids.

The fourth chapter presents a standardized atlas of human BAL cells through the synthesis multiple scRNA-seq datasets, with ensemble auto-annotation tools and reliable cross-study markers. This atlas deals with discrepancies in previous studies and provides a foundation for BAL research.

Chapter five introduces the first true-paired benchmarking study of cellular deconvolution in BAL. Including 30 human BAL samples, each divided into bulk RNA-seq and matched single-cell libraries. After systematically evaluating 15 popular algorithms across multiple references and cell-type resolutions, this study demonstrates a modestly designed pairing strategy substantially improves both benchmark realism and practical accuracy. Our true-paired data, comparative analyses, and three-step protocol provide a blueprint for future deconvolution studies.

Together, these chapters deliver disease insights, community resources, and methodological frameworks that advance the study of lung immunity through both single-cell and bulk transcriptomics.

Examining Committee

Supervisory Committee
Dr. Xuekui Zhang, Department of Mathematics and Statistics, University of Victoria (Supervisor)
Dr. Xiaojian Shao, Department of Mathematics and Statistics, UVic (Co-Supervisor)
Dr. Belaid Moa, Department of Electrical and Computer Engineering, UVic (Outside Member)

External Examiner
Dr. Pingzhao Hu, Department of Biochemistry, Western University

Chair of Oral Examination
Dr. Michael McGuire, Department of Electrical and Computer Engineering, UVic

Abstract
This dissertation presents a systematic exploration of scalable, interpretable, and high-accuracy computational frameworks for automated cell type classification in scRNA-seq data. The research spans three major contributions, each addressing different trade-offs between simplicity, interpretability, and predictive power:

1. PCLDA (Penalized Component-wise Linear Discriminant Analysis) introduces a highly interpretable and statistically grounded annotation tool.
2. scSorterDL expands on this foundation by combining penalized LDA with ensemble learning and deep neural networks.
3. CellAnnotatorNet represents the culmination of this research by integrating a categorical autoencoder with the Swarm-pLDA framework into a unified, fully differentiable architecture.

Together, these three contributions provide a progressive development from classical interpretable models to fully integrated deep learning pipelines for large-scale single-cell analysis.

Notice of the Final Oral Examination for the Degree of Master of Science of

SOOJEONG KIM

BSc (Kyungpook National University, 2015)

Permutation in Regression Revisited: The Residual Route Proven Optimal Theoretically

Department of Mathematics and Statistics

Thursday, August 14, 2025
1:00 P.M.
David Turpin Building
Room A203

Supervisory Committee:
Dr. Xuekui Zhang, Department of Mathematics and Statistics, University of Victoria (Supervisor)
Dr. Mary Lesperance, Department of Mathematics and Statistics, UVic (Member)

External Examiner:
Dr. Alex Thomo, Department of Computer Science, UVic

Chair of Oral Examination:
Dr. Jody Klymak, School of Earth and Ocean Sciences, UVic

Abstract

The assumptions for classical linear-model are never met in practice. Recent evidence shows that such violations inflate Type I error as sample size grows, while simple permutation tests can restore control in single-predictor regressions. Yet in multiple regression, practitioners face a confusing menu of residual- and raw-data shuffling schemes, with little theory to guide the choice.

We develop the first closed-form, finite-sample comparison of six widely used permutation strategies for a coefficient of interest in the presence of nuisance covariates. By projecting any full-rank regression onto an equivalent two-predictor "working" model and treating the permutation matrix itself as random, we derive exact means and variances of the permuted estimator, and we establish its asymptotic distribution. The analysis reveals that (i) the three residual-based schemes—permuting response residuals, predictor residuals, or both—are identically distributed; they match the parametric null up to second moments in finite samples and match in distribution as as n approaches infinity, guaranteeing valid Type I error control. (ii) Raw-data permutations behave unpredictably: shuffling the response is overly conservative, shuffling the predictor is liberal when covariates are correlated, and shuffling both can be unstable. Closed-form results quantify how predictor–covariate correlation, error variance, and sample size drive these patterns and specify the Monte-Carlo sample size needed for accurate p- values.

Extensive simulations confirm the theory: residual permutations maintain nominal error and retain power comparable to the classical linear model when assumptions hold, whereas raw-data schemes either inflate or deflate Type I error and sacrifice power. The work reconciles decades of ad-hoc practice, provides actionable guidelines, and equips analysts with a principled, computationally feasible framework for exact inference in large-sample regression.

See announcement (PDF).

Examining Committee

Supervisory Committee
Dr. Yu-Ting Chen, Department of Mathematics and Statistics, University of Victoria (Supervisor)
Dr. Anthony Quas, Department of Mathematics and Statistics, UVic (Member)
Dr. Kristan Jensen, Department of Physics and Astronomy, UVic (Outside Member)

External Examiner
Dr. Clément Cosco, Centre de recherche en mathématiques de la decision, Université Paris-Dauphine

Chair of Oral Examination
Dr. Falk Herwig, Department of Physics and Astronomy, UVic

Abstract
This thesis investigates the mollified versions of the stochastic heat equation (SHE) and the Kardar–Parisi–Zhang (KPZ) equation in high dimensions (d ≥ 3), focusing on their limiting behaviors as the mollification is removed. These limiting behaviors are closely related to a key parameter, known as the coupling constant, which characterizes the strength of the driving noise.

34 The first part of this article analyzes the space-time fluctuations of the mollified SHE and mollified KPZ equation around their stationary states. These rescaled fluctuations, previously considered in [23, 24], provide a new viewpoint for describing the convergence of the above mollified equations. For every coupling constant that is strictly less than a specific critical threshold, called the L2-critical point, we establish Gaussian limits, possibly with additional random perturbations, for these rescaled fluctuations.

The second part of this article investigates the limiting higher moments for the mollified SHE in high dimensions. Motivated by a recent result [21] in two dimensions, a natural question is whether the higher moments also converge at the L2-critical point in high dimensions. Our main theorem gives a negative answer: in high dimensions, the limiting higher moments diverge for all coupling constants in a nontrivial interval containing the L2-critical point. As an application, we derive sharp estimates for quantities, which are believed to be closely related to probability distributions of the limiting partition function of the continuous directed polymer.

As a follow-up investigation, the third part of this article analyzes the above conjecture on the higher moments in three dimensions by considering a specific version of the limiting higher moment at the L2-critical point, referred to as the sub-limiting higher moment. This special limiting higher moment can be regarded as a three-dimensional analogue of the limiting higher moment in two dimensions at the corresponding L2-critical point, established in [21]. Our main result proves the spatial pointwise divergence of this limiting object. This divergence can be related to a well-known phenomenon in quantum physics known as the Efimov effect.

Notice of the Final Oral Examination for the Degree of Doctor of Philosophy of

YING YING (FAY) YE

MSc (University of Victoria 2019) MSc (University of Victoria 2008) BSc (University of Victoria 2007)

“Chordality of Digraphs, Signed Graphs, and Signed Bigraphs”

Department of Mathematics and Statistics

Tuesday, July 8, 2025
10:00 A.M.
David Turpin Building
Room A203

Supervisory Committee:
Dr. Jing Huang, Department of Mathematics and Statistics, University of Victoria (Supervisor)
Dr. Jonathan Noel, Department of Mathematics and Statistics, UVic (Member)
Dr. Venkatesh Srinivasan, Department of Computer Science, UVic (Outside Member)

External Examiner:
Prof. Shamik Ghosh, Department of Mathematics, Jadavpur University

Chair of Oral Examination:
Dr. David Scoones, Department of Economics, UVic

Abstract
Chordal graphs and chordal bigraphs enjoy beautiful characterizations, in terms of forbidden subgraphs, vertex or edge orderings, and tree-like representations. A digraph analogue of chordal graphs was introduced by Haskins and Rose. Unfortunately, a forbidden subdigraph characterization of chordal digraphs is not known and finding such a characterization seems to be a difficult problem. The study of chordal digraphs has been restricted to various classes of digraphs, such as semicomplete digraphs, quasi-transitive digraphs, extended semicomplete digraphs and locally semicomplete digraphs.

In this dissertation, we introduce the new class of weakly quasi-transitive digraphs as a common generalization of semicomplete digraphs, quasi-transitive digraphs and symmetric digraphs. We show that weakly quasi-transitive digraphs can be obtained from these three classes of digraphs by substitutions. As a consequence, weakly quasitransitive digraphs admit a recursive construction. This construction theorem allows us to find a forbidden subdigraph characterization of weakly quasi-transitive chordal digraphs. In addition, we use it to prove that the small quasi-kernel conjecture holds for weakly quasi-transitive digraphs.

We extend the notion of chordality to signed graphs and signed bigraphs Interestingly, chordal signed graphs are equivalent to strict chordal digraphs studied by Hell and Hernandez-Cruz. Their forbidden subdigraph characterization of strict chordal digraphs can be translated to a forbidden subgraph characterization of chordal signed graphs. We give a forbidden subgraph characterization of chordal signed bigraphs. The forbidden subgraphs for chordal signed bigraphs are analogous to those for chordal signed graphs but the proofs are much more complicated and intriguing.

Examining Committee

Supervisory Committee
Dr. Xuekui Zhang, Department of Mathematics and Statistics, University of Victoria (Supervisor)
Dr. Ke Xu, Department of Economics, UVic (Outside Member)

External Examiner
Dr. Min Tsao, Department of Mathematics and Statistics, UVic

Chair of Oral Examination
Prof. Merrie Klazek, School of Music, UVic

Abstract
This study investigates the pricing efficiency of Chinese convertible bonds and presents evidence of systematic mispricing. To support this analysis, we develop a pricing framework based on the Least Squares Monte Carlo (LSM) method, tailored to reflect contractual features unique to the Chinese market. Using this model, we simulate fair values over the full lifespan of 154 convertible bonds issued between 2015 and 2019 and compare them to observed market prices. The model-predicted price curves generally align well with observed price patterns, demonstrating the robustness and practical value of our approach. However, we also find that trading prices occasionally deviate from model-implied values by more than 10%, with these deviations exhibiting consistent patterns rather than random fluctuations. Furthermore, we demonstrate that simple trading strategies—both at the individual bond level and at the portfolio level—can exploit these discrepancies to generate substantial excess returns. These findings suggest that the Chinese convertible bond market is only partially efficient and highlight persistent arbitrage opportunities, underscoring the importance of market-specific valuation models in emerging financial markets.