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    Characterizing Age- and Contraction-Dependent Mechanical Properties of Lateral Hip Soft Tissues Using Shear Wave Elastography
    (University of Waterloo, 2026-09-01) Peters, Danielle
    Introduction: Hip fractures are a major health concern in Canada, with approximately 95% resulting from falls, and women being 2.9 times more likely than men to sustain one. Muscle contraction influences pelvic stiffness and load distribution, yet ethical constraints limit our understanding of age-related changes in muscle and adipose tissues during falls. Shear wave elastography (SWE) is a non-invasive ultrasound technique that quantifies tissue stiffness using Young's modulus (E), allowing muscle and adipose tissue mechanics to be characterized. Investigating age-related differences in tissue modulus will help bridge gaps in current knowledge, improving hip model biofidelity and supporting hip fracture prevention strategies. Objectives & Hypotheses: There were two main objectives of this thesis. The first objective was to quantify E of muscle and subcutaneous adipose tissue in the lateral hip region across multiple levels of muscle contraction (0, 20, 40, and 60% MVC) in young and older adult women. Based on previous literature, it was hypothesized that: (1) E would increase with increasing levels of muscle contraction in muscle but remain unchanged in adipose tissue; (2) E would be lower in older than younger women; and (3) the increase in E with muscle contraction would be smaller in older women. The second objective was to develop regression equations describing the relationship between muscle contraction level and E for each age group. As this objective was exploratory, no a priori hypotheses were proposed. Methods: Thirty healthy females were recruited and split into groups of younger (18-30) and older (60-70) adults, with inclusion limited to those with a body mass index ≤ 24.9 kg/m². Soft tissue properties were measured using SWE on a research-grade ultrasound system (GE LOGIQ E10) alongside a linear probe (L2-9VN-D). Measurements were taken at the region of peak pressure during lateral falls, posterior-distal to the greater trochanter, while participants performed isometric contractions using visual biofeedback. Two trials per tissue type at each contraction state (0, 20, 40, 60% maximum voluntary contraction) were performed. The ultrasound’s built-in software was used to output E using established acoustoelastic theory. To assess E by muscle contraction and age, tissue-specific two-way mixed measures analysis of variances (ANOVAs) were conducted. Additionally, tissue-specific linear-mixed effects models (LMEMs) were performed to generate exploratory predictive equations for E based on age group and muscle contraction. Results: As hypothesized, muscle E increased significantly with increasing contraction level (p < 0.001). Older adults exhibited lower values overall (p = 0.029), with a significant age × contraction interaction (p = 0.014). Specifically, from rest to 60% MVC, modulus increased by 96.2% in young adults compared to 71.7% in older adults. Age-related differences in muscle E emerged at higher contraction levels (40% and 60% MVC), where younger adults demonstrated greater E. No significant differences were observed in superficial adipose tissue, whereas deep adipose tissue showed a significant increase in E at 60% MVC (p < 0.001). Muscle was modelled using an age × contraction interaction (R²m = 0.56; R²c = 0.85), based on likelihood ratio testing, whereas adipose tissue was modelled using additive effects, as the interaction term did not significantly improve model fit (superficial: R²m = 0.06, R²c = 0.79; deep: R²m = 0.20, R²c = 0.56). Discussion & Conclusions: Lower muscle E in older adults may reflect age-related changes in actin–myosin cross-bridge formation and motor unit recruitment. The observed age-related divergence at higher contraction intensities, may reflect underlying differences in muscle composition or recruitment strategies that alter the relationship between contraction level and muscle stiffness with age. This highlights the importance of accounting for both age and contraction intensity when interpreting muscle mechanical behaviour. The corresponding increase in deep adipose tissue modulus likely results from its position between the contracting gluteus maximus and overlying superficial adipose layer, where muscle thickening at high contraction transmits compressive stress into the deep layer. Together, these findings suggest that age- and contraction-dependent changes in muscle propagate mechanically into adjacent soft tissue layers. The regression equations generated provide a framework for improving the biofidelity biomechanical hip models and enhancing the physiological representation of soft tissue behaviour.
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    Weighted graph based ordering techniques for preconditioned conjugate gradient methods
    (University of Waterloo, 1993-08-17) Clift, Simon S.; Tang, Wei-Pai
    We describe the basis for a matrix ordering heuristic for improving incomplete factorization for preconditioned conjugate gradient techniques applied to anisotropic PDE's. Several new matrix ordering techniques, derived from well-known algorithms in combinatorial graph theory, which attempt to implement this heuristic, are described. These ordering techniques are tested against a number of matrices arising from linear anisotropic PDE's, and compared with other matrix ordering techniques. A variation of RCM is shown to generally improve the quality of incomplete factorization preconditioners.
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    A query sampling method for estimating local cost parameters in a multidatabase system
    (University of Waterloo, 1993) Zhu, Qiang; Larson, Per-Ake
    In a multidatabase system (MDBS), some query optimization information related to local database systems may not be available at the global level because of local authority. To perform global query optimization, a method is required to derive the necessary local information. This paper presents a new method that employs a query sampling technique to estimate the cost parameters of an autonomous local database system. We introduce a classification for grouping local queries and suggest a cost estimation formula for the queries in each class. We present a procedure to draw a sample of queries from each class and use the observed costs of sample queries to determine the cost parameters by multiple regression. Experimental results indicate that the method is quite promising for estimating the cost of local queries in an MDBS.
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    Dynamic Dual-Camera Visual Servo Tracking for Mobile Manipulators
    (University of Waterloo, 2026-09-01) Cazes, Corey
    Mobile manipulators combine the extended workspace of a mobile platform with the dexterity of a robotic arm, making them well suited to vision-guided tasks in dynamic environments. However, conventional Image-Based Visual Servoing (IBVS) commonly relies on a single camera and is therefore vulnerable to tracking interruptions when the camera–target line of sight becomes obstructed. Dual-camera systems provide complementary viewpoints, but existing approaches often fuse their measurements, switch between them reactively, or assign fixed sensor roles, limiting their ability to coordinate both viewpoints proactively. This thesis presents a dynamic dual-camera visual servoing framework using an end-effector-mounted camera and a base-mounted camera. A real-time visibility score assigns the cameras to active and auxiliary roles according to the quality of their target observations. The active camera generates the primary IBVS tracking command, while the auxiliary camera uses target segmentation, depth measurements, and predicted image-plane occluder motion to generate a visibility-maintenance command. When the active observation becomes unreliable and the alternate camera provides a better view, the camera roles are exchanged. A two-level Hierarchical Quadratic Programming (HQP) controller maps both camera commands to the generalized velocity of the mobile manipulator. The first level determines the best feasible motion for active-camera tracking, while the second level optimizes auxiliary-camera repositioning while preserving the active-camera velocity achieved at the first level. The framework is evaluated in two simulated dynamic-occlusion scenarios and in a physical experiment on a 10-DOF mobile manipulator equipped with two RGB-D cameras. In simulation, the proposed controller produced a frame total-occlusion percentage of 1.84%, compared with 9.85% for a fixed-role multi-camera controller, 21.30% for Control Barrier Function visual servoing, and 54.58% for visibility-aware Model Predictive Control. During physical validation, the end-effector and base-camera observations were individually unavailable for 24.58% and 34.58% of the trial, respectively, however, camera coordination limited simultaneous observation loss to 11.67%. The mean active-camera tracking error was 78.41 pixels and the HQP solver required an average of 4.95 ms per control cycle. These results indicate that dynamic camera-role assignment and prioritized viewpoint control can improve camera coordination during target tracking tasks for mobile manipulators.
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    Backedge Graphs of Tournaments: Algorithms and Complexity
    (University of Waterloo, 2026-09-01) Evangelista, David
    A tournament $T=(V,A)$ on $n$ vertices is an orientation of the complete graph $K_n$. The backedge graph of $T$ with respect to an ordering of $V$ is the undirected graph on vertex set $V$ whose edge set corresponds to the arcs directed from a later vertex to an earlier vertex in the ordering. Tournaments are dense digraphs, and an appropriate choice among the $n!$ orderings of $V$ can yield a backedge graph that provides a concise representation of the tournament. However, the algorithmic problem of determining whether a tournament admits a backedge graph in a given class of undirected graphs varies in complexity. Moreover, this problem is often closely tied to computing existing parameters of tournaments, such as the dichromatic number, clique number \cite{Aboulker et al., 2023}, and degreewidth \cite{Davot et al., 2023} of a tournament. We extend the notion of degreewidth by introducing directional degreewidth, which separately bounds the left-degrees and right-degrees of vertices in addition to bounding the total degrees in the backedge graph. We investigate the algorithmic complexity of verifying bounds on directional degreewidth and obtain an algorithm which runs in polynomial time when the total degree is unbounded, or in fixed-parameter tractable time parameterized by the total degree bound otherwise. We also provide a polynomial-time algorithm for computing a $P_3$-free backedge graph of a tournament, if it exists. Together with existing results, this settles the complexity of determining whether a tournament admits an $H$-free backedge graph for every graph $H$ on three vertices.