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    Risk Sharing with Distortion Risk Measures Beyond Risk Aversion
    (University of Waterloo, 2026-06-30) Ren, Qinghua
    This thesis studies optimal risk sharing among multiple agents whose preferences are represented by distortion risk measures, equivalently Yaari dual utilities. The central question is how to characterize Pareto-optimal risk allocations when agents may have heterogeneous risk preferences, including risk-averse, risk-seeking, and behavioral attitudes toward risk. Particular attention is paid to the dependence structure of optimal allocations and to the geometry of the Pareto frontier. The first part of the thesis develops counter-monotonic risk sharing as a counterpart to the classical comonotonic theory. Comonotonicity represents positive dependence and is fundamental in risk sharing among risk-averse agents, while counter-monotonicity represents an extreme form of negative dependence and arises naturally for risk-seeking agents. Chapters 2 and 3 analyze this counter-monotonic structure for distortion risk measures, moving from a homogeneous setting with a common distortion function to a heterogeneous setting with different distortion functions. Inf-convolution is an important tool for studying Pareto optimality. Using this tool, Chapters 2 and 3 compare the usual formulation with variants that restrict allocations to be comonotonic or counter-monotonic, derive explicit formulas for risk-seeking agents, and illustrate the formulas through a portfolio manager’s problem. Chapter 4 studies markets with mixed risk attitudes, where risk-averse and risk-seeking agents coexist. This setting is more challenging because neither the usual comonotonic arguments for risk-averse agents nor the counter-monotonic arguments for risk-seeking agents apply directly to the whole market. The chapter establishes a reduction theorem showing that the general multi-agent problem can be reduced to a two-agent problem between representative risk-averse and risk-seeking agents. Based on this reduction, the chapter further studies the existence of optimal allocations, identifies cases in which the inf-convolution is unbounded, and derives explicit solutions for piecewise linear distortion functions and Bernoulli-type aggregate risks. Chapter 5 studies Pareto optimality beyond universal risk aversion, with emphasis on constrained allocation problems. Feasibility constraints, such as nonnegative allocations, are natural in insurance and reinsurance, but they change the geometry of the risk-sharing problem and may limit the applicability of weighted-sum methods. The chapter reduces the two-agent Pareto problem to a one-parameter family of constrained optimization problems. For Bernoulli aggregate risks, the Pareto frontier admits a convex-envelope characterization and can be attained by three-atom allocations. For two-point aggregate risks, finite-atom structural results are developed, showing that efficient allocations can be represented by a bounded number of payment levels. These results provide both theoretical insight into non-risk-averse risk sharing and a tractable framework for numerical computation.
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    LLM-Based Frameworks for Information Retrieval Evaluation
    (University of Waterloo, 2026-06-29) Upadhyay, Shivani Jayantkumar
    Evaluating information retrieval (IR) systems requires a reference that captures what correct or relevant output looks like, as well as a mechanism for determining whether a system’s output matches that reference. For lexical retrieval systems, both requirements are relatively straightforward. Systems rank documents by term overlap, pooling produces a judgment file that covers most documents any system is likely to return, and determining relevance reduces to a simple membership test against that file. This evaluation paradigm relies on the assumption that relevance can be detected through surface-form overlap. When retrieval moves beyond that assumption, the framework begins to break down. Retrieval-augmented generation (RAG) systems strain this setup by synthesising free-form natural language responses from retrieved evidence. A gold answer set constructed before system execution cannot anticipate every correct phrasing, so even semantically correct outputs can fail under lexical matching. Dense retrieval systems encode queries and documents as vectors, retrieving relevant documents that might not share vocabulary with the query. Under pooling-based evaluation, these documents never receive human judgments and are instead assigned a default relevance grade of zero. Together, these failures highlight the limits of surface-form evaluation and point to the need for judgment mechanisms that reason directly about meaning. This thesis investigates whether large language models (LLMs) can fill this gap by contributing three frameworks across successive layers of the evaluation pipeline. The first contribution is an open-source QA evaluation framework that combines chain-of-thought (CoT) prompting with self-consistency decoding using instruction-tuned LLMs. When evaluated across 12 systems on NQ-open, it matches zero-shot GPT‑4 in rank correlation with human judgments while using a model more than an order of magnitude smaller, demonstrating that prompting strategy can matter as much as scale. The second contribution is a framework for patching incomplete relevance judgment sets by assigning four-level TREC-style labels to unjudged query-passage pairs via few-shot prompting. When evaluated across five TREC Deep Learning Track collections at removal rates varying from 10 to 90%, it substantially improves system ranking fidelity over the standard practice of treating unjudged documents as non-relevant. The third contribution is UMBRELA, which is a fully automated open-source relevance assessment framework deployed in the TREC 2024 RAG Track across 301 topics, achieving run-level Kendall's tau >= 0.86 against fully manual assessment. All frameworks are released as open-source tools to support reproducible and scalable IR evaluation.
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    Investigation of Thermal Behavior in Combustion of Al/Fe3O4 Nanothermite Film
    (University of Waterloo, 2026-06-29) Liu, Jingtian
    Aluminum-based nanothermites are promising energetic materials for rapid heat release and microscale combustion applications, but the mechanisms governing their combustion morphology and flame propagation remain incompletely understood. This thesis investigates Al/Fe3O4 nanothermite thin films, focusing on two controlling factors: equivalence ratio (ER) and particle morphology. Al/Fe3O4 thin films provide a suitable nanothermite platform for studying the transition between destructive multiphase burning and near-gasless condensed-phase propagation due to their high energy release and relatively limited gas production. Specifically, the work examines how ER drives the transition between destructive particle-ejection combustion and structurally preserved near-gasless propagation, and how core–shell (CS) and physically mixed (PM) architectures modify the combustion event. Polymer-assisted Al/Fe3O4 thin films were fabricated with controlled ER values and particle morphologies. Their combustion behavior was characterized using synchronized high-speed optical imaging and infrared thermography, combined with post-combustion SEM/EDS analysis and inverse thermal modeling. For PM films, ER < 3 produced destructive combustion with particle ejection, localized hot spots, and partial removal of the energetic layer. In contrast, ER ≥ 3 led to preserved combustion, where the reacted layer remained attached to the substrate and formed a measurable cooling zone. This transition indicates that increasing ER improves condensed-phase continuity and shifts the combustion mechanism from reactive sintering to diffusion-driven reaction. Particle morphology also strongly affected flame propagation. At ER = 3, CS films propagated faster than PM films, with velocities of 11.93 cm/s and 6.11 cm/s, respectively. The inverse-modeled reaction rate of CS films was also more than twice that of PM films, indicating stronger reaction–transport coupling due to improved fuel–oxidizer contact and shorter transport distances. Cooling-zone analysis showed that preserved reacted layers act as thermal reservoirs, redistributing heat toward the reaction and preheating zones and contributing to flame-front stability. Overall, this thesis demonstrates that both ER and particle morphology can be used to tune combustion mechanism, propagation behavior, and post-combustion structure in Al/Fe3O4 nanothermite thin films.
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    A STUDY OF THE CLASSIFICATION AND QUANTIFICATION OF MICROPLASTICS THROUGH RAMAN SPECTROSCOPY AND MACHINE LEARNING
    (University of Waterloo, 2026-06-29) Hogan, Úna Elizabeth
    Synthetic polymers, or ‘plastics’, have become an unavoidable, necessary and ubiquitous part of modern human life. Their low cost, tunable properties, durability and ease of manufacture have led to plastics use in almost every part of day-to-day life including food packaging, car manufacturing and single-use sterile medical equipment. The durability of these plastics, while an advantage in their operational life, results in substantial longevity upon their disposal. After they have been discarded, many plastic particles can exist for up to 1000 years in the environment before their eventual breakdown. Their continued use and disposal as the global population increases have led to a large accumulation of discarded plastics throughout the world. A substantial amount of these exist in sizes of 5 mm or less, and are classified as ‘microplastics’, small pervasive pollutants that have been detected in food, drink, and inside human bodies. It is necessary for researchers to determine suitable ways of characterising and quantifying microplastic particles to increase understanding of their behavior and makeup. Expanding knowledge of the sources, abundance and variety of these particles within the environment can lead to a more comprehensive understanding of the issue of microplastics pollution. The use of Raman spectroscopy as an analytical technique for classification of microplastics particles has emerged as an efficient and accurate tool for characterisation. Traditional validation of Raman spectra using library searches and comparison to reference spectra, however, is often inadequate when the plastics have faced significant environmental degradation, which can alter their Raman spectrum. Alternative validation methods such as machine learning are becoming more widely used as superior techniques to traditional library searches, and have proven fast, effective and cheap ways to identify microplastic particles from their Raman spectra. This thesis describes iterative development of machine learning based methods to semi-automate identification of microplastic particles using Raman spectroscopy.
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    Benthic macroinvertebrate assemblages and freshwater food webs of beaver-impounded streams in the eastern Canadian Arctic
    (University of Waterloo, 2026-06-29) Gao, Katelyn
    As circumpolar warming facilitates the shrubification of Arctic landscapes, the distribution of North American beavers (Castor canadensis) in Canada has been expanding northward, raising concern in Inuit communities. Though ecosystem engineering by beavers in temperate regions is well-documented, there is limited research that examines the effects of beaver impoundments in the tundra. Freshwater streams in the Arctic support subsistence fish populations and it is currently unclear how flow attenuation by dams will affect the habitat quality or prey resources of resident species. This research assesses differences in the benthic macroinvertebrate diversity and trophic structure of beaver-impounded streams above and below the treeline in Nunavik. Invertebrates and consumer stable isotopes were compared downstream and upstream of dams to characterize changes in assemblage composition, basal resource reliance, and Layman’s food web metrics. Shannon-Weiner diversity and the percentage of lotic invertebrates were lower upstream of beaver dams. Filter-feeders and EPT taxa (Ephemeroptera, Plectoptera, Trichoptera) decreased with variables associated with lentic conditions, such as reduced stream velocity, increased depth, and finer substrates. Geomorphic-driven differences in assemblage composition, without exhibiting changes in richness or abundance, suggest restructuring in response to upstream habitat transformation. In subarctic forest sites, reliance on terrestrially derived carbon in consumer diets was greater upstream of beaver dams but no effect was observed in shrub tundra sites. Additionally, upstream averages of consumer carbon were more enriched and similar to riparian vegetation than epilithic algae. Although a resource shift was observed, overall food web metrics were not affected by beaver dams. Collectively, the findings presented in this study demonstrate that beaver dam effects below the treeline generally resemble the lotic taxa replacement and dietary shifts reported within their historical range, while recently colonised streams above the tree line appear to be marginally less affected.