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    Some results on hypersymplectic structures
    (University of Waterloo, 2026-04-14) Petcu, Amanda
    A conjecture of Simon Donaldson is that on a compact 4-manifold X⁴ one can flow from a hypersymplectic structure to a hyperkähler structure while remaining in the same cohomology class. To this end the hypersymplectic flow was introduced by Fine–Yao. In this thesis the notion of a positive triple on X⁴ is used to define a hypersymplectic and hyperkähler structure. Given a closed positive triple one can define either a closed G₂ structure or a coclosed G₂ structure on 𝕋³ × X⁴. The coclosed G₂ structure is evolved under the G₂ Laplacian coflow. The coflow descends to a flow of the positive triple on X⁴, which is again the Fine–Yao hypersymplectic flow. In the second part of this thesis we let X⁴ = ℝ⁴ ∖ {0} with a particular cohomogeneity one action. A hypersymplectic structure built from data invariant under this action is introduced. The Riemann and Ricci curvature tensors are computed and we verify in a particular case that this hypersymplectic structure can be transformed to a hyperkähler structure. The notion of a soliton for the hypersymplectic flow in this particular case is introduced and it is found that steady solitons give rise to hypersymplectic structures that can be transformed to hyperkähler structures. Some other soliton solutions are also discussed.
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    Evaluating the Impact of Fan Design and Air Speed on User and Nearby Occupants’ Thermal Comfort in a Shared Office
    (University of Waterloo, 2026-04-13) Bayode, Kehinde
    Personal Comfort Systems (PCS) are increasingly recognized for their potential to improve individual thermal comfort and reduce building energy demand. ASHRAE Standard 55 defines PCS as a device, under the control of the occupant, intended to heat and/or cool individual occupants without affecting the thermal environment of other occupants. Desk fans are common PCS cooling devices, but their use in shared workspaces raises questions about the differential impact on the primary user and nearby occupants. Limited empirical evidence exists on how local air speed and fan technology jointly influence thermal, airflow, and acoustic domains among occupants. To address these gaps, a human-subject experiment involving 40 participants was conducted, paired into 20 pairs: P1 as the fan primary user and P2 as a nearby occupant. Two desk fan designs (conventional-blade and bladeless) were tested at high and low-speed settings. Participants provided repeated comfort assessments at each fan speed condition. The results indicate that both fan technology and operating speed significantly affect the alignment or divergence of comfort between P1 and P2. At low speed, both fan types produced strong convergence, with both occupants reporting neutral thermal sensation, slight satisfaction, and a shared perception of air movement as “just right.” In contrast, at high speed, the bladed fan resulted in divergence: P1 perceived the airflow as “too breezy” and preferred less air movement, while P2 reported no change despite experiencing breezy conditions. Conversely, the bladeless design reduced this asymmetry. At all speeds, both P1 and P2 reported neutral thermal sensation and consistent satisfaction. For primary users, both fan types enhanced thermal comfort at both speeds. The bladed fan was effective only at low speed, as high speed produced a “too breezy” sensation, whereas both speeds were acceptable for the bladeless fan. Despite these advantages, the bladeless fan introduced acoustic disturbance to the environment. High-speed bladeless was perceived as more annoying than the bladed fan, with the P2 group reporting higher annoyance (85%) than the P1 group (65%). This suggests that the high-frequency profile of the air multiplier technology is intrusive, especially for nearby occupants in shared environments. For shared workspaces with mechanical cooling, a low-speed fan setting is recommended. This configuration minimizes acoustic annoyance for both fan technologies (0-5% annoyance) while maintaining high thermal satisfaction for primary users and minimal intrusion into the environment of nearby occupants.
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    Investigating mitochondrial microRNAs in response to metabolic disruption
    (University of Waterloo, 2026-04-13) Robichaud, Karyn
    Aquatic and terrestrial environments are dynamic due to natural and anthropogenic sources, including pollutants, thermal variability, and hypoxia. These stressors or perturbations can result in changes to energetic demands of animals resulting in metabolic stress. As a major energy transduction site within cells, mitochondria can respond to alterations in environmental conditions and metabolic stress by changing their physiology. Specifically, mitochondrial oxidative phosphorylation may change during stress, resulting in altered oxygen consumption rates and efficiency of energy transduction. These plastic responses of mitochondria can be regulated by post translational modifications to proteins; however post-transcriptional regulation of genes may also alter mitochondrial physiology. Genes can be post-transcriptionally regulated by microRNA; microRNAs are small, non-coding RNA molecules that canonically suppress mRNA expression, and thus protein expression. MicroRNAs regulate nuclear encoded genes in response to a variety of physiological stressors, however microRNA can also redistribute subcellularly into mitochondria. Mitochondria contain their own genome which encodes proteins involved in oxidative phosphorylation, therefore mitochondrial microRNAs (mitomiRs) can also regulate mitochondrial gene expression in response to stress. The overall goal of this thesis was to investigate mitomiRs in animals and predict their potential role in regulating mitochondrial function in response to metabolic stress. Most research on mitomiRs prior to this thesis was conducted in mammals, and with respect to disease. Therefore, this thesis aimed to compare mitomiRs across species, identify whether mitomiRs change in abundance with exposure to different stressors, and predict mitomiR mRNA targets. It was hypothesized that mitomiR abundances differ based on environmental changes (stressor type, stressor duration) and inherent differences (species, sex), resulting in changes to mitochondrial function during metabolic stress. Chapter 2 investigated the mitomiR profiles of zebrafish (Danio rerio) brains under control conditions and during acute exposure to two known metabolic stressors (hypoxia and elevated temperature). Exposure to each stressor resulted in distinct mitomiR profiles, where two mitomiRs were differentially abundant during hypoxia, and another mitomiR had altered abundance during thermal stress. The predicted nuclear targets of these mitomiRs were mainly involved in metabolic pathways, with many distinct predicted targets. Furthermore, brain mitochondrial respiration was only altered during thermal stress, and results indicated a potential decrease in ATP synthesis efficiency. Overall, brain mitochondrial respiration and mitomiR abundances had stressor-specific effects. Chapter 3 investigated whether venlafaxine, an antidepressant commonly found in wastewater effluent, altered zebrafish brain mitochondrial respiration and mitomiR abundances. In vitro, this study first confirmed that venlafaxine suppressed brain mitochondrial respiration. Then, an acute time-course exposure was conducted using zebrafish. In vivo, venlafaxine had minimal effects to brain mitochondrial respiration, however, three mitomiRs were differentially abundant based on exposure, sex, and time sampled. Changes to mitomiR abundance may have been due to their host gene expression, circadian rhythm, and venlafaxine exposure. Chapter 4 utilized three species of wild fish (Etheostoma spp.), to determine if they responded similarly to chronic exposure to wastewater effluent outfall in the Grand River, Waterloo, with respect to mitomiR abundances and mitochondrial function. Wild rainbow (Etheostoma caeruleum), fantail (E. flabellare), and Johnny darters (E. nigrum) were collected from up and down stream of the Waterloo wastewater treatment plant, then liver mitomiR abundances and mitochondrial cytochrome c oxidase activities were measured, and species-specific differences were detected. Results indicated that these darter species had species-specific changes to mitomiR abundances and mitochondrial enzyme activity when living downstream of the Waterloo wastewater treatment plant. Chapter 5 provided a comparative study between vertebrate taxa using a mammal that experiences drastic changes in mitochondrial respiration during torpor and interbout euthermia hibernation states. During torpor, mitochondrial respiration is suppressed and returns to summer values during interbout euthermia. This study profiled mitomiRs in thirteen-lined ground squirrels (Ictidomys tridecemlineatus) during summer and hibernation. Changes in mitomiR abundances were detected during hibernation, and mitomiRs had predicted effects that may indicate their involvement in regulating changes to mitochondrial respiration and function during hibernation. The major finding of this thesis was that mitomiRs are differentially abundant based on stressor, sex, and species, despite some conservation of mitomiRs among species studied. This thesis also predicted targets for differentially abundant mitomiRs within mitochondrial and nuclear genomes, and measured changes in mitochondrial enzyme activities and respiration in fish to provide context for how mitomiRs may aid in regulating mitochondrial function. Overall, this thesis contributed to knowledge of mitomiRs and how they show distinct abundance patterns using a variety of comparative approaches.
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    An Ecologically Inspired Constraint-Based Approach to AI System Design: Reshaping Clinical Uncertainty in Paediatric Sepsis
    (University of Waterloo, 2026-04-13) Tennant, Ryan
    In paediatrics, sepsis is a high-stakes, safety-critical challenge for clinicians to recognize and respond to, where a sick child can look stable until they are not, and where diagnostic definitions, symptom baselines, and care pathways vary across children and healthcare settings. This variability creates uncertainty in the clinical environment and limits the extent to which artificial intelligence (AI) and machine learning-based prediction tools can support clinical decision-making when the goal is to classify sepsis. In this dissertation, we position paediatric sepsis as a structurally uncertain domain and argue for an ecologically inspired, constraint-based approach to AI system design that learns and visualizes (1) the boundaries of physiological functioning and (2) the boundaries of the socio-technical system, to support clinically justified decisions under uncertainty in such non-specific contexts. To ground this work, we first synthesize the paediatric sepsis prediction literature through a scoping review. We find substantial heterogeneity in endpoint definitions, datasets, validation practices, prediction timing, and performance reporting. We also find limited attention to human factors considerations, such as workflow integration, interface design, and interaction design, despite their potential for clinical decision support, which fundamentally motivates the research of this dissertation. We then examine how clinicians experience and manage uncertainty about paediatric sepsis. Through semi-structured interviews with registered nurses, respiratory therapists, pharmacists, nurse practitioners and physicians in Canada about their experiences with paediatric sepsis recognition and response, we develop a domain-grounded account of uncertainty conceptualization and a sensemaking-action cycle model. This work extends the established uncertainty constructs from Naturalistic Decision Making by identifying two sources specific to paediatric sepsis: indeterminate clinical trajectories and operational constraints, including how emotional & intuitive anchoring shapes constructing readiness to act. We also describe AI-associated uncertainty concerns, including how and when predictions may reshape clinical judgement. Next, we establish the paediatric sepsis work domain constraints for recognition and response through Cognitive Work Analysis (CWA), conducting a tri-model Work Domain Analysis of the biological, clinical, and AI-augmented clinical work domains, and a Control Task Analysis of decision-making. We also apply this modelling to compare classification- and constraint-based prediction architectures and translate the constraints into an interactive Ecological Interface Design (EID) concept. Our resulting EID includes a configurable display of a baseline-relative trajectory forecast and AI-based uncertainty-aware cues to support the “gut feeling” of early paediatric sepsis recognition and escalation, and how and when to use model predictions at the bedside, respectively. Finally, we formatively evaluate the constraint-based approach in simulated paediatric sepsis scenarios with clinicians in individual and team-based contexts. Across outcomes, including clinical concern, confidence, trust, and sensemaking, our results suggest the trajectory forecast most strongly influences interpretation and action planning and is more validating of preparatory clinical action when the prediction is concordant with clinical reasoning. While AI-based uncertainty elements do not generally yield quantitative differences in outcomes in our evaluation format, they are perceived as potentially valuable for ongoing AI system use; however, mixed perceptions indicate the need for further research to improve their interpretability and usability at the bedside. Taken together, our findings support the promise of further investigating the constraint-based approach toward AI system design in supporting resilience and clinical judgement in paediatric sepsis. Overall, this dissertation demonstrates why the safe integration of AI into high-stakes healthcare cannot be purely data-driven. By conceptualizing uncertainty before introducing predictive algorithms and by applying CWA to anticipate how predictions may reshape clinical judgement, this research provides a framework for more responsible system design. Our approach supports a thorough examination of domain complexity and clinical judgement, informs decisions about whether and how an AI system should be developed and how prediction information should be introduced, and grounds clinical AI in human factors, ensuring these systems respond to genuine clinical needs.
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    Topics in Arithmetic Dynamics
    (University of Waterloo, 2026-04-13) Zhong, Xiao
    This thesis comprises four papers completed during my doctoral studies at the University of Waterloo and is organized into three chapters. The first chapter concerns preimage problems and dynamical cancellation, incorporating the papers “Dynamical Cancellation of Polynomials,” published in the Bulletin of the London Mathematical Society, and “Preimages Question for Surjective Endomorphisms on (P1)^n,” published in the New York Journal of Mathematics. We investigate stabilization phenomena for the set of rational points occurring in the preimages of invariant subvarieties under algebraic dynamical systems. In the special case in which the subvariety is the diagonal subvariety in P1 × P1 and the dynamics is given by a pair of rational functions (f, f), the problem reduces to a dynamical cancellation question. We also obtain a generalization of dynamical cancellation to the setting in which the dynamics are generated by a semigroup of polynomials. The second chapter contains the joint paper with Chatchai Noytaptim, “A Finiteness Result for Common Zeros of Iterates of Rational Functions,” published in International Mathematics Research Notices. Addressing a question posed by Hsia and Tucker concerning finiteness properties of greatest common divisors of polynomial iterates, we prove that if f, g belong to C(X) and are compositionally independent rational functions, and c belongs to C(X), then, apart from a few explicit exceptional families with f and g in Aut(P1_C), there exist only finitely many λ in C for which there is an n satisfying f^n(λ) = g^n(λ) = c(λ). The final chapter presents my recent preprint, “Polynomial Endomorphisms of A2 with Many Periodic Curves.” We show that for any regular polynomial endomorphism of positive degree on P2, every family of curves containing a Zariski dense set of periodic curves must be invariant under some iterate of the map. This establishes a weaker form of the Relative Dynamical Manin-Mumford Conjecture of DeMarco and Mavraki in the setting where the endomorphism is fixed in the family of dynamical systems, and may also be viewed as a dynamical Manin-Mumford statement on the moduli space of divisors. As an application, we classify all regular polynomial endomorphisms of P2 that admit infinitely many periodic curves of bounded degree.