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A Staggered Grid-Based Variational Approach for Modeling Elastic Deformation
No full textElastic deformation is often simulated in computer graphics using the Finite Element Method on tetrahedral meshes. However, generating a tetrahedral mesh can be complicated and expensive. When a hierarchy of meshes is needed (for example, with a progressive or multigrid method), generating this set of hierarchical meshes is a time-consuming process. However, in other areas of physics simulation, such as fluid simulation, the use of staggered grids and finite differences is much more common. The application of adaptive or multigrid methods to grid-based simulations is trivial in comparison. By applying the variational method of Batty et al. from fluid simulation to the staggered grid-based elasticity simulation method of Zhu et al., we produce a method that accurately solves the linear elasticity partial differential equations with free boundary conditions solved implicitly.
In this work, we derive a variational formulation for the linear elasticity partial differential equations on a staggered grid. We derive both the static and dynamic forms of the minimization problem, and their subsequent discretizations. Our method only requires an indicator function that specifies the interior and exterior of the solid to be simulated, and does not require any information about the normals of the object’s surface. Furthermore, our method retains the simplicity and sparsity of the basic staggered grid finite difference scheme, but supports non-axis-aligned boundaries without the need for boundary-conforming meshing. We apply our method to several examples of uniform and nonuniform objects under different deformations, demonstrated with both static and quasi-static simulations. We also compare our results with analytical solutions to the linear elasticity partial differential equations to show the accuracy of our method and that our method converges well with grid refinement
Psychosocial Outcomes of Youth with Chronic Physical Illness and Siblings
No full textYouth with chronic physical illness (YwCPI) are more vulnerable to developing psychopathology than their healthy counterparts. Prospective studies show that psychopathology in youth remains stable over time and extends into adulthood. Ongoing symptoms, treatment, and worry about disease progression increase the risk for worsened mental health. Given that health status often impacts physical, mental, and psychosocial health outcomes, health-related quality of life (HRQL) has been a focus in health research. The functional limitations resulting from disability caused by chronic physical illness (CPI) disrupt school participation, peer support, and family relationships, contributing to lower HRQL compared to healthy peers. Existing research on CPI continuity and HRQL is constrained by infrequent assessments and disease-specific approaches, limiting understanding of psychosocial outcomes in YwCPI.
CPI in youth also affects siblings. This is consistent with family systems theory, which posits that emotional functioning results from interactions between an individual and their family members, and the family unit and its contextual circumstances. Research finds that CPI negatively impacts sibling mental, physical, and psychosocial health. Siblings of YwCPI are also at higher risk for internalizing and externalizing symptoms compared to controls. However, studies on sibling mental health and HRQL are limited. Few studies use longitudinal methods, limiting the ability to assess the long-term impact of CPI.
The aim of this research is to assess psychosocial outcomes in YwCPI and siblings. To address the aforementioned literature gaps, the objectives of this dissertation were to:
1) compare the homotypic and heterotypic continuity of psychopathology in YwCPI and siblings over 48 months, 2) model 48-month trajectories and assess predictors of HRQL in YwCPI and siblings, and 3) assess the mediating effect of sibling psychopathology on the association between YwCPI disability and sibling HRQL.
Data come from the Multimorbidity in Children and Youth Across the Life Course Study; data were collected at baseline, 6, 12, 24, and 48 months.
Study 1 utilized cross-lagged panel modelling to assess internalizing and externalizing symptom continuity in YwCPI and siblings. Auto-regressive pathways assessed homotypic continuity and cross-lagged pathways assessed heterotypic continuity. Separate models were computed for YwCPI and siblings. The method of variance estimates recovery (MOVER) assessed how patterns of continuity in YwCPI differed from siblings. Significant (p<0.05) autoregressive pathways were detected between all time points for internalizing and externalizing symptoms in YwCPI and siblings. Few cross-lagged paths were significant in either model. The MOVER showed no significant differences in the magnitude of any path estimates between YwCPI and siblings.
Study 2 delineated trajectories of change for each domain of HRQL (physical well-being, psychological-being, autonomy and parent relations, peer and social support, school environment) using latent class growth analysis. Models were computed for YwCPI and siblings independently. Backward stepwise regression assessed predictors of trajectory group membership. The number of trajectory groups ranged from two to four, and class size ranged from 5% to 80%. Over half of the models included an increasing, no change, and decreasing group, with most changes occurring at earlier time points. The proportion of siblings having no change in HRQL was greater than YwCPI. Group membership predictors were age, income, and parenting stress.
In Study 3, linear mixed-effect models assessed the mediating effect of sibling psychopathology on the association between YwCPI disability and sibling HRQL. YwCPI disability predicted increased sibling psychopathology, which was associated with lower sibling HRQL on all domains. Mediation effects were statistically significant in all models.
Given the homotypic continuity of symptoms of psychopathology, health services should promote early and routine mental health screening for YwCPI and siblings. Early changes in YwCPI and sibling HRQL trajectories highlight critical opportunities for family-centred approaches to pediatric care. The mediating effect of sibling psychopathology in the association between YwCPI disability and sibling HRQL underscores the importance of integrating siblings into family-centred care, with targeted mental health screening and interventions that aim to mitigate negative psychosocial outcomes
New Methods for Analyzing the Properties of Automatic Sequences
No full textAutomatic sequences and morphic words lie at the intersection of automata theory, logic, and combinatorics on words. Many of their structural properties can be formulated as logical predicates over integer representations and decided using automata. This thesis presents automata-based methods for efficiently constructing and verifying deterministic finite automata corresponding to such predicates, and builds on this foundation to analyze key combinatorial properties of morphic words, including the critical exponent and subword complexity.
In the first part of this thesis, Chapters 2 to 4, we introduce the notion of self-verifying predicates, which are logical predicates capable of verifying their own correctness. We show how this property enables verification of candidate automata through a small set of inductive conditions and allows the corresponding automata to be constructed deterministically rather than through heuristic guessing. Building on Angluin’s L* learning algorithm, we demonstrate that for such predicates, the associated minimal automata can be generated in time polynomial in the size of both the automaton for the underlying sequence and the resulting automaton, thereby avoiding potentially extremely large intermediate automata that sometimes arise in Walnut. In particular, we give effective constructions for the equality-of-factors predicate, which is used extensively in the second half of the thesis, as well as for other self-verifying predicates, including periodicity of factors, addition relations for numeration systems, and summation of synchronized sequences.
The second part, Chapters 5 to 7, applies the previously constructed equality-of-factors predicate to investigate two central combinatorial measures of infinite words: the critical exponent and the subword complexity. Although binary 3-uniform morphisms are used as illustrative examples, the methods generalize naturally to all binary uniform morphisms. For the critical exponent, we present a decision procedure implemented in Walnut that detects whether the exponent is infinite and computes its exact rational value when finite. For subword complexity, we propose two complementary approaches: a constructive method that combines established concepts to produce exact formulas for ρ(n), and a fully deterministic procedure that implements Frid’s approach using Walnut. The new results include explicit subword-complexity formulas for twelve morphisms, and critical-exponent values for ten morphisms.
All algorithms and implementations developed in this thesis are made publicly available on the Github repository Cashew as open-source code to support and facilitate further research in combinatorics on words, and automata theory
The Economics of the Data-driven Economy and the Demand for Antitrust
No full textAntitrust is again in vogue; its long winter has ended. The revival of demand for antitrust is coincident with the advent of a new Gilded Age - this time in the context of an economy built on intangible assets - IP and (later, increasingly) data
Investigating Isotropy in Atmospheric Turbulence Using Large Eddy Simulations
No full textTurbulence plays a key role in many atmospheric and engineering flows, but understanding how it becomes isotropic under different conditions is still a challenge. In this thesis, we use the WRF model in idealized mode to explore how turbulence evolves in four setups: two driven by buoyancy (convective boundary layer and plume) and two by shear (random and bubble-perturbed Shear).
We analyze anisotropy of the eddy dissipation using eddy-viscosity-based metrics, comparing how different forcing mechanisms and spatial resolutions affect the development and isotropization of turbulence. Buoyancy-driven cases showed smoother, more gradual transitions to isotropy, while shear-driven cases featured stronger bursts, persistent anisotropy, and slower convergence in time, especially at low resolution. It can also be understood that vertical velocity is more anisotropic in buoyancy-driven cases, while vertical shear dominates in shear-driven cases.
These results highlight how both physical forcing and resolution shape the anisotropy of turbulence and point to important considerations for model setup in future turbulence studies
Modelling of a Small Electric Aircraft Pipistrel Velis Electro
No full textTransportation electrification has become an active area of research and development in academia and industry, with a strong focus on decarbonizing the sector to move toward a more sustainable environment. As an important player in the global sustainable transportation movement, the aviation industry is also witnessing accelerated efforts towards electrification. This transition comes with many challenges in terms of battery performance, aircraft flight range, and operational safety. Therefore, development of comprehensive simulation models, that replicate the behavior of an actual aircraft, is essential for studying the system’s overall performance. Such models provide invaluable insights into battery health, methods to extend range, and ways to improve flight missions for more efficient battery usage. This thesis aims to develop a mathematical model of the aircraft propeller and a simulation model of the electric powertrain consisting of the battery pack, inverter, and motor. The aircraft under study is the Pipistrel Velis Electro, a two-seater, type-certified, fully electric aircraft. Two methods are proposed to model the propeller behavior: one based on the aircraft equations of motion and the other based on the motor power command. Both methods compute the thrust, motor rotational speed, and load torque for each phase of the flight using different input sets, and these outputs are supplied to the powertrain model. Two modes of operation are considered for the powertrain: an autopilot flight mode and a pilot-controlled mode, with phase detection between powered and glide phases. The simulations are validated by comparing the results with actual Velis Electro flight data obtained from the Waterloo Wellington Flight Center
Correlation-Aware Rendering: Improving Sampling and Denoising for Realistic Image Synthesis
No full textIn realistic image synthesis, Monte Carlo integration is the foundation of most rendering algorithms, but it inevitably introduces noise. To reduce such noise, advanced sampling strategies—such as Markov chain Monte Carlo (MCMC), resampled importance sampling (RIS), and modern denoising techniques—have been proposed. However, these methods of ten introduce correlations that can manifest as new artifacts. This thesis investigates three distinct research directions, spanning from mitigating correlation to actively exploiting it. The first direction tackles correlation in MCMC methods. Traditional MCMC often suffers from low acceptance rates, producing visually “spiky” noise. We propose combining MCMCwithpathguiding techniques to improve acceptance probabilities, thereby reducing correlation artifact and improving image quality. The second direction addresses correlation artifacts in the widely used Reservoir-based Spatiotemporal Importance Resampling (ReSTIR) algorithm. While ReSTIR achieves ef f icient sampling by reusing samples across pixels and frames, this reuse can lead to blotchy artifacts, as many pixels may end up sharing only a few important samples. Observing par allels between ReSTIR and MCMC, we introduce a new spatiotemporal MCMC framework that replaces reservoir resampling. Applied to both direct illumination and path tracing, our approach significantly reduces correlation artifacts while retaining efficiency. The final direction shifts from reducing correlation to exploiting it. We present a gener alized combination framework that leverages spatial, temporal, and multiscale correlations to reduce error. This method enables robust cross-domain fusion, effectively suppressing systematic artifacts and improving temporal coherence—particularly crucial in animation. Through extensive experiments, we demonstrate that our framework enhances temporal stability, visual appearance, and residual error reduction across diverse rendering scenarios
Filter Performance Optimization for Protozoan Pathogen and Particulate Contaminant Removal During Drinking Water Treatment
No full textPhysico-chemical filtration (chemically assisted filtration; CAF) remains a critical barrier for the removal of particulate contaminants, including Cryptosporidium oocysts and emerging contaminants such as microplastics, during drinking water treatment. Ensuring consistent CAF performance becomes particularly challenging for systems reliant on high-quality source waters—those with low turbidity and low dissolved organic carbon concentrations—where traditional performance indicators such as turbidity may provide limited insight into the adequacy of coagulation, as source waters often already meet treated-water turbidity criteria prior to coagulation. Under these conditions, coagulant inadequacy or under-dosing may not be readily apparent, potentially resulting in insufficient particle destabilization and overestimation of Cryptosporidium oocyst removal by CAF and associated regulatory treatment credits.
The goal of this research was to demonstrate the importance of particle destabilization for achieving reliable removal of protozoan pathogens and other particulate contaminants (including microplastics) by CAF for systems reliant on high-quality source waters. While the importance of coagulation in destabilizing particles for effective CAF is well known, its regulatory and operational relevance—particularly for HQSW—needs to be revisited given the public health importance of drinking water treatment. Pilot-scale performance demonstrations were conducted to: (1) demonstrate the inadequacy of filter effluent turbidity as an indicator of coagulant demand required to achieve ≥3-log protozoan removal by CAF; (2) evaluate zeta potential as an operational tool to indicate the sufficiency of particle destabilization needed to maximize protozoan removal by CAF; (3) investigate direct in-line CAF’s ability to achieve ≥3-log protozoan removal; (4) determine whether removal of microplastics exhibit behavior consistent with other colloidal particles during CAF; and (5) evaluate key methodological factors that contribute to variability and uncertainty in performance demonstrations to enhance confidence in interpreting measured CAF performance.
Collectively, the findings reinforce that adequate coagulation and particle destabilization are fundamental drivers of CAF performance across particle types, treatment configurations, and methodological approaches. This work demonstrated that turbidity alone cannot indicate adequacy of coagulant application for high-quality source waters, whereas zeta potential offers a tool to guide coagulant dosing and confirm the particle destabilization needed to achieve ≥3-log protozoan removal by CAF, recognizing that sufficient destabilization range and associated coagulant doses vary with system and water quality specific conditions. At the same time, it also demonstrated performance demonstration methods commonly used to evaluate protozoan removal remain reliable and yield consistent results when particle destabilization is optimized.
This work highlights opportunities to strengthen treatment guidance for the removal of protozoan pathogens by CAF for systems reliant on low-turbidity, low-DOC source waters, provides pilot-scale evidence supporting reconsideration of treatment credits assigned to direct in-line CAF, and offers foundational process understanding needed to inform regulatory policy on microplastics
Riparian vegetation and open water carbon greenhouse gas fluxes of urban stormwater ponds
No full textStormwater ponds (SWPs) are a common stormwater management technology in new urban developments and have been suggested to be significant sources of the carbon greenhouse gases (GHGs); e.g., carbon dioxide (CO2) and methane (CH4). However, they also sequester organic carbon (OC) and reduce the surface runoff of nutrients, hence, altering nutrient limitation patterns, trophic conditions, and GHG exchanges. Although numerous studies have focused on estimating open water GHG emissions in artificial ponds, there are limited studies that evaluate both open water and riparian vegetation fluxes from urban SWP systems comprehensively. This study quantified CO2 and CH4 fluxes from riparian vegetation and open water in two SWPs in the City of Kitchener, Ontario, located in residential (Activa pond) and industrial (Wabanaki pond) catchments.
In Chapter 2, the goal was to compare flux pathways and net source-sink status and assess how land use, spatial variability between forebay and main basin zones, and pond design influence the GHG dynamics. Using vegetation and floating chambers, CO2 and CH4 fluxes were measured bi-weekly across all seasons, capturing net ecosystem exchange (NEE), ecosystem respiration (ER), and gross primary production (GPP) from riparian vegetation, plus the diffusive and ebullitive fluxes from the open water surface.
Significant differences in the fluxes between the riparian vegetation and open water surfaces were observed. High photosynthetic activity allowed the riparian zone to function as a net carbon sink (-142.3 mol m-2 yr-1 for Activa and -140.5 mol m-2 yr-1 for Wabanaki). However, higher OC inputs from the industrial Wabanaki catchment enhanced sediment CH4 production, particularly in the forebay, resulting in higher vegetation CH4 emissions that weakened its GHG-sink strength relative to the residential Activa pond., resulting in CO2-equivalent fluxes of -141.4 mol CO2-eq m-2 yr-1 for Activa and only -94.8 mol CO2-eq m-2 yr-1 for Wabanaki. Although Activa had greater per-area vegetation CO2-equivalent uptake, its small riparian zone limited whole-pond removal, whereas Wabanaki’s extensive riparian area provided larger total CO2 uptake (-3.6 mol CO2-eq m-2 yr-1 for Activa and -132.1 mol CO2-eq m-2 yr-1 for Wabanaki).
Open water fluxes were dominated by ebullitive CH4, which accounted for about 88% of the total CO2-equivalent flux (125.6 mol CO2-eq m-2 yr-1 for Activa and 119.6 mol CO2-eq m-2 yr-1 for Wabanaki), making the open water surface a net GHG source. The forebay of the ponds consistently acted as carbon GHG hotspots due to higher carbon loading, nutrient enrichment, and reducing conditions, while larger, deeper main basins mitigated emissions.
Overall, both Activa and Wabanaki ponds ultimately acted as net GHG sources, with annual emissions of 189.6 kmol CO2-eq yr-1 at Activa and 349.9 kmol CO2-eq yr-1 at Wabanaki, driven primarily by CH4 emissions. These findings highlight the combined influence of land-use-driven carbon loading, riparian zone extent, and the contrasting behaviour of forebays and main basins in controlling stormwater pond GHG dynamics.
In Chapter 3, the full dataset collected during the study period were presented. Based on field experience, we outline practical recommendations for municipalities, including linking monitoring objectives to decision-making, applying tiered spatial and temporal sampling, quantifying flux pathways, measuring key water and sediment drivers, integrating hydrologic data, and tracking vegetation cover for upscaling. Together, these approaches create a scalable, transparent framework for incorporating SWPs into city-scale GHG monitoring and management
Associative Memory for Hyperdimensional Spatial Representations with Geodesic Flow Matching
No full textThe ability to recover clean patterns from noisy or partial inputs, known as Associative memory, is a cornerstone of robust computation in both biological and artificial intelligence systems. While well-established for discrete data, implementing this capability for continuous representations remains a challenge. Existing methods typically rely on discretizing the continuous domain into capacity-limited prototypes or performing explicit decoding to the spatial domain, which is often computationally expensive and biologically implausible.
This thesis addresses this gap by reformulating cleanup as a generative transport problem entirely within the embedding space. Geodesic Flow Matching is introduced as a model that learns a continuous time-dependent velocity field to transport corrupted representations back to the valid data manifold. Standard Euclidean Flow matching is shown to be insufficient for high-dimensional normalized representations, as linear interpolants "cut through" the interior of the hypersphere, destroying the vector magnitude and phase relationships required for accurate decoding. By constraining transport dynamics to the intrinsic Riemannian geometry of the hypersphere, the proposed model preserves this structure even under severe corruption.
The framework is validated using Spatial Semantic Pointers (SSPs), a biologically plausible encoding for continuous space. Benchmarks indicate that Geodesic Flow consistently outperforms Euclidean variants and classical baselines, particularly in high-noise regimes. The utility of the approach is further demonstrated through integration into a Spiking Neural SLAM system. As an online stabilizer for the path integrator, the Geodesic model prevents catastrophic drift, reducing path error by up to 72%. Furthermore, it significantly improves resource efficiency by 40%, allowing a neural population of 1,500 neurons to match the tracking accuracy of a baseline system using 2,500 neurons