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    Machine Learning Tight-Binding Hamiltonians for Quantum Transport Simulation in Monolayer and Multilayer 2D Materials
    (University of Waterloo, 2026-08-26) Wong, Justin
    Quantum transport simulation of two-dimensional (2D) semiconductor materials typically relies on a pipeline of density functional theory (DFT), Wannierization, and the non-equilibrium Green's function (NEGF) formalism. The Wannierization step, which transforms the DFT band structure into a real-space tight-binding Hamiltonian, presents a practical bottleneck due to its high computational cost. This thesis adopts the machine learning tight-binding (MLTB) method as a replacement for Wannierization, and extends it to bilayer and multilayer 2D semiconductor systems through a three-stage Hamiltonian construction procedure. The MLTB methodology is first showcased by applying it to monolayer NiN2, a recently synthesized pentagonal 2D semiconductor, providing the first characterization of its quantum transport properties. NiN2 is a direct bandgap semiconductor with pronounced in-plane transport anisotropy arising from its four-fold lattice symmetry. The anisotropic effective mass structure along the 45-degree transport direction is shown to enhance source-to-drain tunneling in p-type devices at short channel lengths, while n-type devices remain largely insensitive to transport orientation. The MLTB framework is then extended to bilayer systems through a three-stage procedure in which independent monolayer Hamiltonians are first constructed for each layer, and interlayer coupling matrices are subsequently fitted to the bilayer DFT band structure with the monolayer blocks held fixed. This approach preserves the layer-resolved structure of the Hamiltonian required for NEGF simulation and avoids the need for a full bilayer Wannierization. The procedure is validated on bilayer MoS2, where the simulated transport characteristics show close agreement with those obtained from a Wannier-derived Hamiltonian. The method is subsequently applied to bilayer Janus MoSSe in the 2AA' and 3AA' stacking configurations. The two configurations are found to exhibit a tradeoff in device performance: the 2AA' configuration shows better DIBL but worse subthreshold swing than 3AA', attributed respectively to its smaller total channel thickness and the more centrally located electron density relative to the gate electrodes. The results demonstrate that the MLTB-based simulation pipeline is applicable to both monolayer and multilayer 2D semiconductor systems, and provides a more automated and scalable alternative to Wannierization for quantum transport simulation of novel materials.
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    From Candidates to Evidence: Diagnostics for Trustworthy Biological Discovery
    (University of Waterloo, 2026-08-26) Zhou, Han
    As biological analysis becomes increasingly mediated by foundation models and automated multi-step workflows, computational methods are used not only to process data, but also to generate outputs that shape downstream biological interpretation. These outputs may include integrated representations, inferred data alignments, similarity scores, retrieval rankings, and other intermediate products of analysis. They are often used to support biological candidates, such as predicted protein functions, putative homologous relationships, candidate cell-state correspondences, proposed gene-regulatory programs, annotations, or hypotheses about molecular interactions and biological mechanisms. However, if the intermediate computational outputs are ambiguous, unstable, or difficult to interpret, then the biological candidates derived from them may not be reliable evidence. This thesis argues that diagnostics are needed to test the meaning, reliability, and failure modes of computational outputs before they are used to support biological interpretation. This diagnostic perspective is developed across two critical layers of AI-driven biological analysis: the data layer and the model layer. First, at the data layer, this thesis presents SONATA, a diagnostic framework designed for diagonal multimodal single-cell data integration. In the absence of shared cells or features, multiple cross-modality alignments can appear computationally coherent yet remain biologically ambiguous. SONATA exposes these alternative integration solutions and quantifies mapping ambiguity, preventing users from treating unstable data alignments as definitive biological facts. Second, at the model layer, the thesis introduces PLM-GUARD, a diagnostic suite that evaluates protein language models (PLMs) used in similarity search. PLM-GUARD scrutinizes model-derived similarity scores across biological fidelity, semantic validity, and manipulation safety. Its evaluations demonstrate that a model’s retrieval utility does not inherently imply evidential reliability, highlighting the need for diagnostic caution before interpreting embedding-space scores as true biological meaning. Finally, this thesis points to a future paradigm at the agent layer. As autonomous AI agents begin to chain together complex analytical workflows, errors and ambiguities from early stages risk propagating silently. Agent-level diagnostics are therefore proposed as an indispensable requirement to ensure that intermediate computational candidates are robust enough to support downstream reasoning. Ultimately, the frameworks developed in this work shift the focus of computational biology from merely accelerating candidate generation to systematically validating outputs as trustworthy scientific evidence.
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    A new shifted Littlewood-Richardson rule and related developments
    (University of Waterloo, 2026-08-26) Estupinan, Santiago
    As Littlewood-Richardson rules compute linear representation theory of symmetric groups and cohomology of ordinary Grassmannians, shifted Littlewood-Richardson rules compute analogous projective representation theory of symmetric groups and cohomology of orthogonal Grassmannians. The first shifted Littlewood-Richardson rule is due to Stembridge (1989). We give a new shifted Littlewood-Richardson rule that is provably more efficient in some cases and is more convenient for hand calculations. Our rule builds on ideas of Lascoux-Schutzenberger (1981), Haiman (1989), and Serrano (2010). Our rule stems from a deeper understanding of the shifted plactic monoid in the form of a new axiomatization. We show that it is the largest monoid satisfying a short list of natural axioms inspired again by work of Lascoux and Schutzenberger. In addition, we obtain the first algebraic proof of Serrano's shifted Littlewood-Richardson rule (2010) and a new proof of the Hiller-Boe shifted Pieri rule (1986). Lastly, we explore the question of constructing a jeu de taquin theory via a rectification algorithm that computes mixed insertion, and find an algorithm that serves that purpose as long as a fixed order of slides is followed. From an algebraic perspective, the search for such a rectification algorithm was formulated by Cho (2013). To be specific, Cho proposed an open problem asking for a satisfactory definition of plactic skew Schur P-functions. We solve that problem using the interaction between the Sagan-Worley jeu de taquin and shifted plactic classes.
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    Saint-Venant Torsion of Functionally Graded Micropolar Beams
    (University of Waterloo, 2026-08-26) Garcha, Chirjivan
    Functionally graded materials (FGMs) are a class of composites that are increasingly used in aerospace, defence, energy, and biomedical applications because their elastic properties and microstructure can be varied continuously in space. These materials can be designed to address specific design requirements at different locations of the material. They provide a clear advantage over traditional composites in that they limit common failure modes such as delamination and de-bonding. FGMs also possess an intrinsic microstructure with non negligible characteristic length relative to the size of the component. Classical elasticity cannot account for independent micro-rotations or couple-stresses caused by the microstructure, and can therefore misrepresent the stiffness and internal stress distribution. Thus, due to the wide range of applications and advantages compared to traditional composites, it is important to study the behaviour of FGMs. This thesis investigates the torsional behaviour of functionally graded micropolar beams. The comprehensive three-dimensional Cosserat continuum framework is used to reduce the problem to a Neumann boundary value problem of anti-plane Cosserat elasticity. The problem is posed on the beam cross-section, accounting for spatially varying elastic moduli within the cross-section. Furthermore, the existence and uniqueness of weak solutions for the resulting system of partial differential equations with variable coefficients is established, using coercivity of the operator and the Lax-Milgram theorem. The general formulation is then specialized to exponentially graded circular and annular cross-section examples to demonstrate practicality. By using the inherent geometric symmetry of the circular and annular beams, the governing boundary value problem reduces to an ordinary differential equation for the radial microrotation amplitude, which is then solved numerically and compared with the corresponding homogeneous and classical cases. The results show that exponential grading on a bounded cross-section satisfies the conditions required for coercivity, so the graded micropolar torsion problem is well-posed. At a fixed level of grading, microstructure relaxes the peak shear stress, since part of the transmitted load is carried by couple-stresses. Grading in turn migrates these couple-stresses toward the stiffer region of the cross-section. Grading and micropolarity also reinforce one another: at the largest grading parameter considered, the normalized torsional rigidity of the graded micropolar bar exceeds the classical homogeneous value. It is therefore clear that grading is a controllable design parameter that can be used to stiffen a beam and redistribute stress concentrations away from critical boundaries. These results establish that functional grading and microstructure must be modelled together, since neither a classical nor a homogeneous micropolar analysis completely captures their combined effect on torsional response.
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    Examining the relationship between loneliness and doctor’s visits for influenza-like symptoms in Canadian older adults
    (University of Waterloo, 2026-08-26) Majoe, Aditi
    Loneliness is the subjective experience of the lack of one’s social belonging in their community which plays an important role in healthy aging. It is a complex phenomenon associated not only with psychological distress, but also negative physiological outcomes. Few studies have examined the association between loneliness and infectious diseases. Infectious respiratory diseases such as influenza disproportionately affect older adults due to the natural weakening of the immune system as we age, as well as the high level of comorbidities in this age group. The purpose of this study is to understand the association between loneliness in older adults and the odds of seeking medical care for flu-related symptoms, after adjusting for demographic variables, social connection, behavioural factors, chronic health conditions and diagnosis of mental health disorders. We also assess whether loneliness is associated with severity of influenza symptoms, and whether there is evidence of the COVID-19 pandemic impacting the association between loneliness and doctor visits for influenza symptoms. We used data from follow-up 1 (FUP1) and follow-up 2 (FUP2) surveys of the CLSA comprehensive and tracking cohorts to understand the association between loneliness and going to the doctor with influenza symptoms in older adults aged 65 and above. FUP1 surveys were administered from 2014 to 2018, while FUP2 surveys were administered from 2018 to 2021. Cross-sectional analyses were conducted separately at FUP1 and FUP2 using a logistic regression model with the binary variable ‘doctor’s visit for influenza symptoms’ as the main outcome, and the categorical variable ‘loneliness status’ as the main explanatory variable. Since follow-up 2 coincided with the COVID-19 pandemic, we used a GEE model to investigate whether the association between loneliness and doctor visits for influenza differed across the two timepoints. In order to investigate the association between loneliness and influenza severity, we used the CLSA COVID-19 exit questionnaire, which was administered in December 2020. We ran a negative binomial regression with ‘number of influenza symptoms’ and ‘loneliness status’ as the primary outcome and explanatory variables respectively. A cumulative log-link GEE was conducted for the association between loneliness and influenza symptom severity. In the cross-sectional analyses, loneliness was associated with higher odds of going to the doctor with influenza symptoms at follow-up 2, but not follow-up 1. Loneliness was also positively associated with experiencing more influenza symptoms, as well as higher levels of symptom severity. While participants who took the CLSA main survey prior to COVID-19 had higher odds of going to the doctor with influenza symptoms compared to participants who took the survey after the commencement of COVID-19, we found no evidence that the relationship between loneliness and healthcare utilization for influenza symptoms was impacted by the COVID-19 pandemic. The number of chronic health conditions, diagnosis of mental health disorders, and social connection were identified as possible confounders of the relationship between loneliness and doctor visits for flu. This study addresses the gap in current scientific evidence around the association between loneliness and seeking healthcare for influenza outcomes, as well as severity of influenza symptoms. Our results highlight the complex interactions between loneliness, social connection, chronic health conditions, mental health, and influenza outcomes as well as health-seeking behaviours. Understanding the association between social connection and health outcome, as well as the factors that impact influenza severity in older adults is instrumental to informing more targeted models of care for this vulnerable age group and preparing for future public health crises.