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    Algorithms for Analytic Combinatorics: Positivity Bounds and D-finite Operators
    (University of Waterloo, 2026-08-21) Smith, John
    Analytic combinatorics is concerned with describing limiting behavior of families of combinatorial structures. While this is well-studied in the univariate case, the last two decades have seen the development of analytic combinatorics in several variables (ACSV) treating the same problem in the multivariate case. One advantage of the way ACSV is formulated is that, at least in the simplest cases, its methods are amenable to explicit computation. This thesis contributes to an ongoing effort to automate the results of ACSV by providing developments in two related areas: computing D-finite operators for diagonals of rational functions, and computing explicit error bounds for ACSV in the so-called smooth rational case. First, we provide a SageMath implementation of an algorithm of Lairez for computing periods of rational integrals. Since diagonals of rational functions are rational periods, computing operators of periods is of great importance to practitioners of algebraic and analytic combinatorics. While Lairez gave a MAGMA implementation of his algorithm, our implementation provides full-fledged documentation, robustness, and feature enhancements aimed at combinatorialists -- such as computing diagonal operators for arbitrary directions. Second, we discuss how to find explicit error bounds for asymptotics of rational diagonals, as opposed to the Big-O asymptotics typically provided by ACSV. One motivation for this is the coefficient positivity problem; having explicit bounds allows one to reduce positivity of coefficient sequences to checking asymptotic positivity and finitely many initial sequence terms. We provide fully constructive versions of ACSV arguments in the simplest case, then use these to derive an index N so that positivity of our asymptotic implies positivity of our diagonal for all larger index values, under some small additional assumptions about the form of our asymptotic. We then explore the consequences and caveats of this reduction, exhibiting some classes of functions where asymptotic positivity can be known a priori.
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    “Making sense of the holistic why:” Implementation of sustainable food in healthcare institutions in Ontario, Canada
    (University of Waterloo, 2026-08-21) Blank, Lisa
    Background Health and food systems have deleterious consequences for planetary health. Health systems are responsible for between 4% and 8% of individual countries’ greenhouse gas emissions worldwide, contributing to climate change. Yet, health system emissions not only contribute to warming temperatures but also to poor air and water quality, with cascading effects on health. An estimated 25% of global emissions are attributable to food systems through direct emissions and land clearing, while producing significant waste and pollutants, including fertilizers, pesticides, and plastic packaging. Food systems are also associated with diet-related chronic diseases, leading to increased need for health services and high health costs. Paradoxically, health and food systems not only contribute to environmental change but are also directly impacted by its effects. Environmental change is predicted to increase burdens on health services, while reducing the nutrient quality of agricultural crops. Experts have called for transformations toward more sustainable health and food systems to address the multidimensional impacts on planetary health and increase resilience to future challenges. Foodservice within healthcare institutions is a leverage point for instigating such transformations. Sustainable foodservice would contribute to improving nutrition and health, minimizing environmental impacts, strengthening cultural inclusivity, and promoting local sustainable food systems. Healthcare institutions have begun implementing sustainable food interventions. Yet, progress is small and variable, especially in Canada. The complexity of the healthcare environment creates unique considerations for changing practices. Research on practice change, sustainability, and sustainable food in healthcare indicates multiple barriers and facilitators. There are gaps in understanding the specific factors at play across individual, institutional, and community levels; different political and social contexts; and varying stages of sustainable food implementation, as well as the interactions between different actors and foodservice options within the institutional food environment. Objectives This thesis aimed to 1) explore the barriers and facilitators to sustainable food interventions in the foodservice of an exemplar healthcare institution in Ontario, Canada, and 2) compare barriers and facilitators to two additional institutions at different stages of sustainable food implementation. Methodology The design of this thesis was informed by a critical research paradigm guided by my philosophical assumptions, which value planetary health as the well-being of the whole system, acknowledging that the worth of non-humans is not relative to humans. The thesis was informed by systems science, implementation science, and social science, which contributed to developing a theoretical framework merging the Consolidated Framework for Implementation Research with Institutional Theory, guiding data collection, analysis, and interpretation. I set out to conduct a collective case study of three healthcare institutions in Ontario, Canada, each in different stages of sustainable food implementation: an exemplar institution with multiple sustainable food interventions, a comparative institution with some evidence toward sustainable food, and a second comparative institution with less evidence toward sustainable food. I conducted ten semi-structured interviews with eight participants predominantly working in foodservice. Interviews were complemented by review of 47 documents, including strategic plans and sustainability reports, pertaining to the three institutions. Data were analyzed by institution and across institutions using a systems-based approach and a six-stage framework analysis method. Results Six conceptual themes, including efficiency meets sustainability, making sense of sustainable food, making sense through change management, development from the bottom-up, “the patient voice is at the center of what we do,” and a disconnected food environment, were generated. Themes were mapped to the theoretical framework, highlighting that implementation of sustainable food interventions cuts across all domains of the Consolidated Framework for Implementation Research, and is influenced by multiple pillars of Institutional Theory. The strongest barriers originated from the regulative pillar of Institutional Theory, and the strongest facilitators stemmed from the cultural-cognitive pillar of Institutional Theory. However, barriers and facilitators interacted with one another in complex ways. External partnerships and staff and visitor food options were identified as promising for expanding implementation and potentially weakening negative feedback channels maintaining efficient systems, particularly patient preferences that conflicted with sustainable menus. Accreditation standards incorporating sustainable food indicators were deemed a promising policy direction by participants, with the potential to weaken negative feedback channels by combining normative, cultural-cognitive, and regulative pillars of Institutional Theory to promote change. Conclusions Though there was some alignment with barriers and facilitators identified in prior research, the application of a systems lens in this research identified how barriers and facilitators interacted and seemed to combine into negative and positive feedback channels in a dynamic process, either constraining or reinforcing change toward sustainable food interventions. The findings provide insights into the institutions and individuals slowly shifting norms that dictate everyday practice in healthcare foodservice necessary to move toward sustainable health and food systems that address the negative consequences of such systems for planetary health.
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    ASH: Agents that self-hone via Embodied Learning
    (University of Waterloo, 2026-08-21) Schneider, Benjamin
    Long-horizon embodied tasks remain a fundamental challenge in AI, as current methods rely on hand-engineered rewards or action-labeled demonstrations, neither of which scales. We introduce ASH, an agentic system that learns an embodied policy from unlabeled, noisy internet video, without reward shaping or expert annotation. ASH follows a self improvement loop; when it gets stuck, ASH learns an Inverse Dynamics Model (IDM) from its own trajectories, and uses its IDM to extract supervision from relevant internet video. ASH uses unsupervised learning to identify key moments from large-scale internet video and retains them as long-term memory — allowing it to tackle long-horizon problems. We evaluate ASH on two complementary environments demanding multi-hour planning: Pokémon Emerald, a turn-based RPG, and The Legend of Zelda: The Minish Cap, a real time action-adventure game. In both games, behavioral cloning, retrieval-augmented and zero-shot foundation-model baselines plateau, while ASH sustains progression across our 8-hour evaluation. ASH reaches an average of 11.2/12 milestones in Pokémon Emerald and 9.9/12 in Legend of Zelda, while the strongest baseline gets stuck in both environments at an average of 6.5/12 and 6.0/12 milestones, respectively. We demonstrate that self-improving agents are a scalable recipe for long-horizon embodied learning.
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    When are random regular triangle-free graphs bipartite?
    (University of Waterloo, 2026-08-21) DeCamillis, Gregory
    Let $\mathcal T_{n,m}$ denote the set of triangle-free graphs on $n$ vertices with $m$ edges where $m = m(n)$. A natural and well-studied question in random graph theory is ``for large $n$, how large is $\mathcal T_{n,m}$?" This question has been answered when $m \le n^{3/2-\eps}$ for some $\eps>0$, or $m \geq \frac{13}{56}n^{3/2}\sqrt{\log n}$. These results depend on the typical structure of graphs in $\mathcal T_{n,m}$, where in the sparse regime these graphs are unstructured and in the dense regime these graphs are rigidly structured. One such result is that $m = \frac{\sqrt 3}{4}n^{3/2}\sqrt{\log n}$ is the tight threshold for a graph chosen uniformly at random from $\mathcal T_{n,m}$ to be bipartite. Another popular topic in random graph theory is the study of random regular graphs. Let $G'$ be random graph chosen uniformly from all $d$-regular graphs on $n$ vertices. Let $X$ be the number of triangles in $G'$. One particular question that has been considered recently is ``what is the distribution of $X$?'' The answer to this question is well understood when $X$ is near its mean for certain values of $d$, but is not well understood in the lower or upper tail of the distribution; in particular, when $X=0$. In this thesis, we establish that $d = \frac{\sqrt 3}{2} \sqrt{n\log n}$ is the sharp threshold for random $d$-regular triangle-free graphs being bipartite, which implies an asymptotic enumeration of $d$-regular triangle-free graphs when $(1 + \eps)\frac{\sqrt 3}{2}\sqrt{n \log n} \leq d \leq \mu_0 n$ for any $\eps > 0$ and sufficiently small $\mu_0 > 0$ (the restriction of $d\le \mu_0 n$ is due to some technical considerations). This extends the enumeration of triangle-free graphs to the regular setting and broadens our understanding of the extreme lower tail of the distribution of the number of triangles in a random regular graph.
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    From Geometry-Aware Planning to Cooperative Infrastructure Sensing: Toward Robust Autonomous Mobility
    (University of Waterloo, 2026-08-21) Ning, Minghao
    Safe autonomous mobility requires perception and motion planning systems that can operate reliably under limited sensor coverage, occlusion, adverse environmental conditions, and communication delay. This thesis investigates this problem in both onboard and infrastructure-supported autonomous mobility. It first develops geometry-aware perception and motion planning methods for autonomous vehicles using onboard sensor data, and then extends the framework to cooperative infrastructure sensing for outdoor vehicle-infrastructure cooperation and indoor robotic mobility. The first part of the thesis focuses on onboard perception and planning. A point-cloud-based motion planning framework is developed by constructing a potential field directly from LiDAR observations and integrating it into a Model Predictive Control formulation. Instead of relying only on object-level detections or predefined object categories, the method uses geometric drivable-area boundaries extracted from point clouds to support real-time trajectory generation around irregular and previously unseen obstacles. This framework is further elaborated by a multi-modal drivable-space perception method that fuses LiDAR, camera, and HD map information. The perception pipeline combines adaptive ground removal, adaptive clustering, and robust LiDAR-camera association to extract safe drivable areas. The perception module has been validated in real autonomous-shuttle tests, confirming its reliability and efficiency, and simulations demonstrate robust and efficient motion planning under challenging conditions. The second part of the thesis addresses the limitations of onboard sensing by developing cooperative infrastructure perception systems. For outdoor autonomy, the thesis presents CoInfra, a large-scale cooperative infrastructure perception system and dataset for vehicle-infrastructure cooperation. The system deploys multiple synchronized infrastructure sensor nodes equipped with cameras, LiDAR, edge computing, and 5G communication. A delay-aware fusion strategy is introduced to aggregate multi-node observations into a shared global representation while accounting for communication latency and late-arriving data. The resulting dataset provides synchronized multi-modal infrastructure data with globally consistent 3D annotations and diverse weather coverage, supporting evaluation of cooperative perception under realistic urban conditions. The third part extends cooperative infrastructure sensing to indoor human-centric mobility. A delay-aware indoor perception framework is developed using ceiling-mounted infrastructure sensor nodes, local multi-modal perception, central fusion, and latency-compensated tracking. The system supports real-time estimation of robot, pedestrian, and obstacle states in crowded indoor spaces. An infrastructure-supported 3D human pose estimation method is further developed to improve human position and orientation estimation under occlusion. The fused indoor perception output is integrated with the proposed MPC-based planner and evaluated in closed-loop experiments with a mobile robot platform. Together, these contributions show how explicit geometric representations, multi-modal sensing, and delay-aware infrastructure perception can improve the robustness and deployability of autonomous mobility systems. By progressing from onboard perception and planning to outdoor and indoor cooperative infrastructure sensing, this thesis provides algorithms, system implementations, datasets, and real-world evaluations for reliable autonomous mobility in complex environments.