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    Quantifying Structural Uncertainty in Hydrologic Models
    (University of Waterloo, 2026-06-23) Arabzadeh, Rezgar
    Hydrologic models are essential tools for understanding watershed processes and supporting water resource management. However, their predictions are inherently uncertain due to imperfect model structures (structural uncertainty), parameter estimation challenges (parameter uncertainty), and limitations in observational data and model forcings (input uncertainty). Bayesian inference has become a widely used framework for quantifying these uncertainties because it enables probabilistic parameter estimation and prediction while formally incorporating prior information and observational evidence. Despite these advantages, the application of Bayesian methods to complex hydrologic models remains computationally demanding, and the resulting predictive uncertainty often represents a combination of multiple uncertainty sources (including input, parameter, and structural uncertainties) that are difficult to interpret individually. These limitations reduce the effectiveness of Bayesian uncertainty analysis as a diagnostic tool for improving hydrologic models. This thesis develops methodological advances to improve the efficiency and interpretability of Bayesian uncertainty quantification in hydrologic modeling. The research focuses on two challenges: improving the computational feasibility of Bayesian inference for complex models and separating the sources of uncertainty represented within Bayesian predictive distributions. To address these challenges, new methods are developed and evaluated using both regional and continental-scale hydrologic datasets. 1. A machine learning–assisted framework is developed to improve the efficiency of Bayesian joint inference for hydrologic models. The proposed approach integrates machine learning techniques with Bayesian calibration to facilitate exploration of complex posterior parameter distributions and reduce the computational burden associated with traditional sampling methods. The framework is evaluated using twelve watersheds from the MOPEX dataset and demonstrates improved inference performance while maintaining reliable uncertainty quantification. 2. A variance decomposition methodology is introduced to identify and quantify the sources of uncertainty embedded within Bayesian predictions. While Bayesian calibration provides probabilistic estimates of model outputs, it does not directly attribute predictive uncertainty to individual components of the modeling framework. The proposed method decomposes posterior predictive uncertainty into interpretable components, enabling a clearer understanding of how different aspects of the modeling process contribute to overall uncertainty. 3. The proposed uncertainty decomposition framework is applied to a large-scale hydrologic analysis across approximately 3,000 watersheds in North America. This continental-scale application enables the systematic evaluation of spatial patterns in hydrologic model uncertainty and reveals how dominant uncertainty sources vary across hydroclimatic and physiographic regions. Together, the contributions of this thesis improve both the computational efficiency and the interpretability of Bayesian uncertainty estimates in hydrologic modeling. The proposed approaches provide tools for diagnosing uncertainty sources and evaluating model reliability, which can support more transparent hydrological predictions across a range of environmental and water resource applications.
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    Contributions to the model theory of algebraic differential equations
    (University of Waterloo, 2026-06-23) Eagles, Christine
    This thesis deals with semiminimal analyses of finite rank types, primarily in the stable theory of differentially closed fields of characteristic zero (DCF0). The two main themes considered in this thesis are determining when a type is minimal or semiminimal, and understanding what invariants of finite rank types are captured by a semiminimal analysis. In DCF0, a central concern of this thesis is determining when a type is almost internal to the field of constants. Partially generalising a result of Rosenlicht, algebraic criteria are provided in two different contexts: rational vector fields on affine n-space, and pullbacks under the logarithmic derivative of certain types which are internal to the constants. The criteria in the former case answers a question posed by Freitag, Jaoui, Marker and Nagloo about when the Poizat equations are internal to the constants. In both cases, the theory of binding groups in stable theories plays a significant role. Results of Duan and Nagloo are improved upon to completely classify when the generic types of Lotka-Volterra systems are minimal. In the minimal case, a characterization of the possible relations that may exist between solutions of distinct Lotka-Volterra systems is given. In the general setting of a totally transcendental theory, it is shown that the multiplicity with which a minimal type arises in a semiminimal analysis of a finite rank type is invariant, i.e., it is independent of the semiminimal analysis. A conjecture is proposed for the possible ways for two semiminimal analyses of the same finite rank type to differ. Along the way, the connection between semiminimal analyses and domination decompositions, is clarified.
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    Parameter Inference and Model Selection for Differential Equation Models with Applications
    (University of Waterloo, 2026-06-23) Zhao, Yuxuan
    Dynamic systems are commonly modelled by differential equations (DEs) in epidemiology and biology, among other fields. The parameters in the DEs are often of scientific interest and required for estimation, given a set of noisy observations. The first and oldest general class of methods for the parameter inference problem in DEs is based on numerical solvers. As a preliminary study, we conduct a comparative study of compartmental models for COVID-19 transmission using such numerical solver-based methods. However, this class of methods can be computationally intensive and may only converge to the local optima due to the sensitivity of the numerical solution to the parameters and initial conditions. This thesis begins by presenting this study, which highlights these limitations and motivates the methodological developments that follow. To address these challenges, Gaussian process-based methods serve as an alternative that bypass the need for numerical solvers. In particular, the recent manifold-constrained Gaussian process inference (MAGI) method demonstrated accurate estimation and fast computational speed. However, the original MAGI method is limited to ordinary differential equations (ODEs), which are inadequate for some dynamic systems, calling for more complex or flexible structures in the specification of the DE model. Motivated by this, this thesis extends the framework of MAGI to facilitate inference for three common but challenging contexts, including (i) delayed differential equations, where system components exhibit time delays in their responses, (ii) mixed-effects ODEs, where experimental data consist of time-course observations on multiple subjects from a population, and (iii) selection of the most appropriate ODE model from a set of candidate models, where there is no true underlying model. The complex structures of these DEs introduce inferential and computational burdens and we address them in this thesis, along with computational and theoretical justifications. We illustrate the efficacy of our methodologies through simulated and real-world applications.
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    Content-Aware Pixel Art Rendering on Pixels of Multiple Shapes
    (University of Waterloo, 2026-06-23) Wang, Zane Z.
    Pixel art is a well studied art form that arose from technical limitations on computing hardware in the early 1980s. Although the discipline itself is often associated with video games, standalone character and landscape portraits in the pixel art style are also popular. Characterized by a deliberately limited resolution and colour palette, pixel art is as an artistic exercise in the conveyance of visual information with a limited number of samples, while avoiding certain unpleasant visual artifacts. In this thesis, we present a first solution to a novel problem in computer graphics: how do we render images in the pixel art style on other tilings of the plane besides the usual squares, all while respecting image features? We formulate the non-square (or "any-shape") pixel art rendering task as an energy minimization problem over tile-shaped filter supports, given a conventional raster image and geometric tiling data as input. We compute tile energy gradients via rasterization of the tiling geometry; using this information, we evolve an optimal filter support shape while imposing geometric constraints to balance between distortion and feature clarity. We then demonstrate that our method produces images with superior qualitative and quantitative properties in comparison with naive methods. Our program can compute finished images in seconds, and allows the user to watch the pixel art evolve in real time. We also provide some basic stylization and interaction features for artists, such as k-means colour quantization, colour palette generation in a perceptually uniform colour space, and brush-based vertex manipulation to adjust the shapes of the filter supports. This method has the potential to be useful in several artistic contexts, such as the creation of highly stylized portraiture and landscapes, and authoring of image and video for real hardware displays that use non-square pixels.
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    Exploring Inuvialuit youth food security experiences and supports in the Inuvialuit Settlement Region
    (University of Waterloo, 2026-06-23) Ramirez Prieto, Maria
    Background: The Inuvialuit Settlement Region (ISR) is in the Northwest Territories, Canada, and is the westernmost of the four Canadian Inuit regions. The ISR covers 906,430 km2 and includes six communities: Aklavik, Inuvik, Paulatuk, Sachs Harbour, Tuktoyaktuk, and Ulukhaktok. Today, Inuvialuit in the ISR are closely connected to and dependent on-the-land for physical, mental, spiritual, and emotional nourishment, which supports food security and well-being. Yet Inuvialuit youth face numerous barriers to participating in subsistence harvesting, and a growing body of literature documents a dietary shift away from country foods (CF) among younger generations. This is especially concerning as 69% of individuals aged 15 years or older in the ISR experience food insecurity. However, few studies have examined how Inuvialuit, including Inuvialuit youth, engage with CF and their relationships within the food web in relation to food security and well-being. While youth are the focus of the overall dissertation, Elders and families are also participants in this dissertation. Objectives: The purpose of this dissertation is to explore the web of relationships and experiences that shape the participation of Inuvialuit youth in the CF system, including the connection to the natural world, culture, and others, in order to generate community-driven evidence that fills gaps in the literature. Moreover, this dissertation aims to centre Inuvialuit knowledge holders through the co-production of knowledge, and use community based participatory action research (CBPAR) to conduct equitable and community-driven research. Methods: Using CBPAR, the studies in this dissertation employ diverse qualitative methods to conduct research with community members, including Community Research Leads (CRLs). Using a CBPAR approach provides an opportunity for research to move away from research on Indigenous communities to research with and for Indigenous communities and aligns itself with the National Inuit Strategy on Research. Photovoice, talking circles, and semi-structured interviews were used with purposive and snowball sampling of 11 Inuvialuit youth across all six ISR communities, 19 Elders in Aklavik, Paulatuk, Tuktoyaktuk, and Ulukhaktok, and nine families in Aklavik, Tuktoyaktuk and Ulukhaktok. Reflexive thematic analysis, using co-analysis methods, was used for all three studies. Results: Study 1 (Chapter 2) employed photovoice methodology, working with 11 youth participants who captured photographs of their CF experiences and shared ~5 photographs during semi-structured interviews. Through reflexive thematic analysis, our research team co-created five themes from the data: 1) CF supports Inuvialuit youth well-being; 2) preference for CF despite varied consumption and activity frequencies; 3) network of CF within communities; 4) strong foundational cultural knowledge and skills; and 5) cultural continuity. Study 2 (Chapter 3) brought together 10 youth from Study 1 and 19 Elders through talking circles to explore the relationship between youth, Elders, and intergenerational Inuvialuit knowledge (IK) transmission in relation to CF, food security, and well-being. In addition to semi-structured questions, photo-elicitation was used to initiate conversation between Elders and youth about the photograph’s subject matter and to invite storytelling (e.g., caribou harvest, goose roast for dinner). Our research team co-created four themes from the data: 1) fostering cultural connection and knowledge transmission through CF and family time; 2) emphasizing oral teachings as essential for well‑being; 3) recognizing the true cost of store‑bought food and goods; and 4) working together for community food security In Studies 1 and 2, family was identified as a crucial aspect of youth connection to CF and IK, in turn, supporting food security and well-being. As such, in Study 3 (Chapter 4), nine families (n = 28 participants) from Aklavik, Tuktoyaktuk, and Ulukhaktok were interviewed through semi-structured group interviews to explore the role of CF and family in the transmission of IK to support youth food security and well-being in the ISR. Our research team co-created four themes from the data: 1) learning on-the-land through experiences; 2) nourished by the land; 3) navigating barriers; and 4) the guiding principles for present and future generations’ well-being. Conclusion: Together, these studies examine Inuvialuit youth, Elders, and families’ experiences in the CF system, including identifying facilitators and barriers to accessing CF and IK. These studies make substantive contributions to the literature by documenting what Inuvialuit have long known – that CF is essential for youth, family, and community food security and well-being. Concurrently, these studies offer critical qualitative evidence that broadens the predominantly quantitative and store-bought-food-centered literature in the ISR. Adding to a growing body of literature, this research highlights that CF, along with the relationships it fosters with people, the land, culture, and community, supports food security while also nourishing the mind, body, and soul. This research employed a CBPAR approach, engaging community members at all stages of the research process and aligning with Inuit Tapiriit Kanatami’s National Inuit Strategy on Research and the Inuvialuit Regional Corporation’s ISR Research Data Strategy to ensure that Inuvialuit are included and respected as knowledge holders, thereby fostering respectful and beneficial research for Inuvialuit communities.