Mathematics (Faculty of)
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Coding Strip: A Tool for Supporting Interplay within Abstraction Ladder for Computational Thinking
(University of Waterloo, 20220520)As technologies advance and play an increasingly larger role in our lives, computational thinkingthe ability to understand computing concepts and procedures and their role in the tools we usehas become an important ... 
A Generalized Adversary Method for Quantum Query Complexity
(University of Waterloo, 20220520)Quantum query complexity measures the minimum number of queries a quantum algorithm needs to make to some input string to compute a function of that input. Query complexity models are widely used throughout quantum computing, ... 
MTMAG: Accurate and interpretable machine learning for complete or partial taxonomic assignments of metagenomeassembled genomes
(University of Waterloo, 20220519)We propose MTMAG, a novel machine learningbased software tool for the complete or partial hierarchicallystructured taxonomic classification of metagenomeassembled genomes (MAGs). MTMAG is capable of classifying large ... 
Analysis of a pressurerobust hybridized discontinuous Galerkin method for the stationary NavierStokes equations
(Springer, 20190830)We present wellposedness and an a priori error analysis of the hybridized discontinuous Galerkin method for the stationary form of the NavierStokes problem proposed in (J Sci Comput, 76(3):1484{ 1501, 2018). This scheme ... 
Dispersing representations of semisimple subalgebras of complex matrices
(Elsevier, 20220601)In this paper we consider the problem of determining the maximum dimension of P?(A!B)P, where A and B are unital, semisimple subalgebras of the set Mn of n⇥n complex matrices, and P 2 M2n is a projection of rank n. We ... 
Mathematical Modeling of Kidney Function During Pregnancy
(University of Waterloo, 20220516)During pregnancy major adaptations must occur in the maternal body to be able to support the rapidly developing fetus and placenta. Adaptations occur in almost all tissues and organs. These changes are dynamic, complex, ... 
On First Passage Time Related Problems for Some Insurance Risk Processes
(University of Waterloo, 20220513)For many decades, the study of ruin theory has long been one of the central topics of interest in insurance risk management. Research in this area has largely focused on analyzing the insurer’s solvency risk, which is ... 
Improved Model Poisoning Attacks and Defenses in Federated Learning with Clustering
(University of Waterloo, 20220512)Federated Learning (FL) allows multiple participants to collaboratively train a deep learning model without sharing their private training data. However, due to its distributive nature, FL is vulnerable to various poisoning ... 
Some Mathematical Perspectives of Graph Neural Networks
(University of Waterloo, 20220512)Many realworld entities can be modelled as graphs, such as molecular structures, social networks, or images. Despite coming with such a great expressive power, the complex structure of graphs poses significant challenges ... 
STPASec Applied to Path Planning: QuantumSafe Autonomous Vehicles
(University of Waterloo, 20220512)Autonomous vehicles and quantum computers are two emerging technologies that will transform our world in the nottoodistant future. This thesis examines the safety and security of autonomous vehicles in a world where ... 
A Sparse Random Feature Model for Signal Decomposition
(University of Waterloo, 20220511)Signal decomposition and multiscale signal analysis provide useful tools for timefrequency analysis. In this thesis, an overview of the signal decomposition problem is given and popular methods are discussed. A novel ... 
A TwoTier Storage Interface for LowLatency Kubernetes Deployments
(University of Waterloo, 20220511)Orchestration systems are responsible for automating the management of software deployments on computer systems, managing large numbers of machines. Edge computing is a decentralized compute model describing how compute ... 
Learning Trustworthy Web Sources to Derive Correct Answers and Reduce Health Misinformation in Search
(ACM, 202207)When searching the web for answers to health questions, people can make incorrect decisions that have a negative effect on their lives if the search results contain misinformation. To reduce health misinformation in search ... 
OFFDIAGONAL CORNERS OF SUBALGEBRAS OF L(Cn)
(Elsevier, 20201215)Let n ∈ N, and consider Cn equipped with the standard inner product. Let A ⊆ L(Cn) be a unital algebra and P ∈ L(Cn) be an orthogonal projection. The space L := P ⊥Aran P is said to be an offdiagonal corner of A, and L ... 
MATRIX ALGEBRAS WITH A CERTAIN COMPRESSION PROPERTY I
(Elsevier, 20210715)An algebra A of n × n complex matrices is said to be projection compressible if P AP is an algebra for all orthogonal projections P ∈ Mn(C). Analogously, A is said to be idempotent compressible if EAE is an algebra for all ... 
ALGEBRAIC DEGREE IN SPATIAL MATRICIAL NUMERICAL RANGES OF LINEAR OPERATORS
(American Mathematical Society, 20210720)We study the maximal algebraic degree of principal orthocompressions of linear operators that constitute spatial matricial numerical ranges of higher order. We demonstrate (amongst other things) that for a (possibly ... 
OPERATORS WHICH ARE POLYNOMIALLY ISOMETRIC TO A NORMAL OPERATOR
(American Mathematical Society, 20200115)Let H be a complex, separable Hilbert space and B(H) denote the algebra of all bounded linear operators acting on H. Given a unitarilyinvariant norm k · ku on B(H) and two linear operators A and B in B(H), we shall say ... 
JITGNN: A Deep Graph Neural Network for JustInTime Bug Prediction
(University of Waterloo, 20220510)JustInTime (JIT) bug prediction is the problem of predicting software failure immediately after a change is submitted to the code base. JIT bug prediction is often preferred to other types of bug prediction (subsystem, ... 
A conceptual IoTbased earlywarning architecture for remote monitoring of COVID19 patients in wards and at home
(Elsevier, 202205)Due to the COVID19 pandemic, health services around the globe are struggling. An effective system for monitoring patients can improve healthcare delivery by avoiding inperson contacts, enabling earlydetection of severe ... 
Normal operators with highly incompatible offdiagonal corners
(Polish Academy of Sciences, 20200525)Let H be a complex, separable Hilbert space, and B(H) denote the set of all bounded linear operators on H. Given an orthogonal projection P∈B(H) and an operator D∈B(H), we may write D=[D1D3D2D4] relative to the decomposition ...