• Detecting and distinguishing transitions in ecological systems: model and data-driven approaches 

  Bury, Thomas (University of Waterloo, 2020-01-22)

  There exists a plethora of systems that have the capacity to undergo sudden transitions that result in a significantly different state or dynamic. Consider the collapse of fisheries, outbreak of disease or transition to a ...

• Monte Carlo Simulation of Diffusion Magnetic Resonance Imaging 

  Miao, Ming (University of Waterloo, 2020-01-16)

  The goal of this thesis is to describe, implement and analyse Monte Carlo (MC) algorithms for simulating the mechanism of diffusion magnetic resonance imaging (dMRI). As the inverse problem of mapping the sub-voxel ...

• Mathematical Modeling of C elegans L1 aggregation 

  Avery, Leon (University of Waterloo, 2020-01-16)

  First-stage larvae (L1s) of the nematode Caenorhabditis elegans aggregate after starvation. I develop a mathematical model of this behavior based on the classic Keller-Segel model. In the Keller-Segel model, organisms ...

• Mathematical approaches to the study of cellular heterogeneity, treatment design, and immune response in cancer 

  Pellowe, Moriah Jane (University of Waterloo, 2020-01-09)

  One of the complicating factors in treating cancer patients is the different levels of heterogeneity involved. In this thesis, we use a combination of mathematical methods (in silico experiments) and experimental data (in ...

• Generative Modeling with Neural Ordinary Differential Equations 

  Dockhorn, Tim (University of Waterloo, 2019-12-19)

  Neural ordinary differential equations (NODEs) (Chen et al., 2018) are ordinary differential equations (ODEs) with their dynamics modeled by neural networks. Continuous normalizing flows (CNFs) (Chen et al., 2018; Grathwohl ...

• Robustly Complete Temporal Logic Control Synthesis for Nonlinear Systems 

  Li, Yinan (University of Waterloo, 2019-12-18)

  Modern systems such as spacecrafts and autonomous vehicles are complex yet safety-critical, and therefore the control methods that can deal with different dynamics and constraints while being provably correct are sought ...

• Multiscale models of kidney function and diseases 

  Layton, Anita T. (Elsevier, 2019-09)

  The kidney is a complex system whose function is the result of synergistic operations among a number of biological processes. The spatial and functional scales of those processes span a wide range. To interrogate kidney ...

• Network centrality analysis of eye-gaze data in autism spectrum disorder 

  Sadria, Mehrshad; Karimi, Soroush; Layton, Anita T. (Elsevier, 2019-08)

  Individuals suffering from autism spectrum disorder (ASD) exhibit impaired social communication, the manifestations of which include abnormal eye contact and gaze. In this study, we first seek to characterize the spatial ...

• Optimal Controller and Actuator Design for Nonlinear Parabolic Systems 

  Edalatzadeh, M. Sajjad; Morris, Kirsten (2019-10-08)

  Many physical systems are modeled by nonlinear parabolic differential equations, such as the Kuramoto-Sivashinsky (KS) equation. In this paper, the existence of a concurrent optimal controller and actuator design is ...

• Application of the LANS-alpha Model to Gravity Currents 

  Zhao, Yukun (University of Waterloo, 2019-10-21)

  This thesis aims to investigate how HERCULES performs when running a lock-exchange gravity current case. The LANS-alpha model with stratification is also tested as a subgrid model in HERCULES using the same gravity current ...

• From Gravity to Hopf Algebra Lattice Models 

  Osumanu, Abdulmajid (University of Waterloo, 2019-10-02)

  This thesis addresses three different problems related to quantum gravity. In the first problem we will discuss the two natural ways to encode gravity through geometric structures. One is the much acclaimed Einstein's ...

• Physical Modelling and the Associated Acoustic Behaviour of Trumpets and Trombones 

  Resch, Janelle (University of Waterloo, 2019-09-30)

  Accurately modelling the production of realistic musical notes in brass instruments is no easy task. Compared to woodwind instruments, brass instruments are considerably longer and constructed with bends, valves or coils, ...

• Optimal Actuator Design for Nonlinear Systems 

  Edalatzadeh, M. Sajjad (University of Waterloo, 2019-09-24)

  For systems modeled by partial differential equations (PDE's), the location and shape of the actuators can be regarded as a design variable and included as part of the controller synthesis procedure. Optimal actuator ...

• A walk through quantum noise: a study of error signatures and characterization methods 

  Carignan-Dugas, Arnaud (University of Waterloo, 2019-09-17)

  The construction of large scale quantum computing devices might be one of the most exciting and promising endeavors of the 21st century, but it also comes with many challenges. As quantum computers are supplemented with ...

• The Interactions of Graphene with Ionic Solutions and Their Effects on the Differential Capacitance for Sensing Applications 

  Daniels, Lindsey (University of Waterloo, 2019-08-28)

  Nano-scale devices continue to challenge the theoretical understanding of microscopic systems. Of particular interest is the characterization of the interface electrochemistry of sensors, which operate as field effect ...

• Black Hole to White Hole Quantum Tunnelling 

  Clements, Kate Elizabeth Alexandra (University of Waterloo, 2019-08-26)

  In this thesis, we explore the proposal that near the end of its lifetime, a Schwarzschild black hole will undergo a quantum transition into a 'white hole': an object which is precisely the time-reversal of the black hole. ...

• Numerical Methods for Hamilton-Jacobi-Bellman Equations with Applications 

  Chen, Yangang (University of Waterloo, 2019-08-26)

  Hamilton-Jacobi-Bellman (HJB) equations are nonlinear controlled partial differential equations (PDEs). In this thesis, we propose various numerical methods for HJB equations arising from three specific applications. First, ...

• Model for a cortical circuit associated with childhood absence epilepsy 

  Ahmed, Maliha (University of Waterloo, 2019-08-23)

  Childhood absence epilepsy is suspected to result from mutations in genes which encode ion channels including sodium channels. Our purpose in this thesis is to explore some of the factors that alter the function of neurons ...

• Mathematical Modelling of Cancer Treatments Involving Radiation Therapy and Hypoxia-Activated Prodrugs 

  Meaney, Cameron (University of Waterloo, 2019-08-19)

  Cancer is one of the world's deadliest diseases despite immense investments into oncological research in recent years. Although great strides have been made in our understanding of cancer, much remains unknown regarding ...

• Particle Clustering and Sub-clustering as a Proxy for Mixing in Geophysical Flows 

  Chakraborty, Rishiraj (University of Waterloo, 2019-08-16)

  The Eulerian point of view is the traditional theoretical and numerical tool to describe fluid mechanics. Some modern computational fluid dynamics codes allow for the efficient simulation of particles, in turn facilitating ...

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