• Topics in early and late Universe cosmology 

  Sarma Boruah, Supranta (University of Waterloo, 2020-08-11)

  In this thesis, we explore different problems in various areas of cosmology. The inflationary paradigm has been very successful in explaining cosmological observations. However, some problems still linger on. In the ...

• Feature Identification 

  Shaw, Justin (University of Waterloo, 2020-08-04)

  We present several methods for identifying time periods of interest (features) in a wide range of data sets. The gamma method is a computationally inexpensive, flexible feature identification method which uses a comparison ...

• Late-lumping backstepping control of partial differential equations 

  Auriol, Jean; Morris, Kirsten A.; Di Meglio, Florent (Elsevier, 2019-02)

  We consider in this paper three different partial differential equations (PDEs) that can be exponentially stabilized using backstepping controllers. For implementation, a finite-dimensional controller is generally needed. ...

• Numerical Simulation of Nonlinear and Dispersive Wave Equations using Adaptive Mesh Refinement (AMR) 

  Rahman, G M Ashikur (University of Waterloo, 2020-06-24)

  Numerical solution of time dependent Partial Differential Equations plays an important role in different fluid flow modelling problems. Sometimes a little portion of the computational domain needs high grid resolution in ...

• Zero dynamics for networks of waves 

  Jacob, Birgit; Morris, Kirsten A.; Zwart, Hans (Elsevier, 2019-05)

  The zero dynamics of infinite-dimensional systems can be difficult to characterize. The zero dynamics of boundary control systems are particularly problematic. In this paper the zero dynamics of port-Hamiltonian systems ...

• Modelling resilience and sustainability of complex human-environment systems in agriculture and ecology 

  Fair, Kathyrn (University of Waterloo, 2020-06-01)

  As we move further into the Anthropocene, numerous challenges to sustainable development present themselves. Questions abound: How do we feed a growing population? What steps must we take to conserve ecologically valuable ...

• From Fundamentals to Spectroscopic Applications of Density Functional Theory 

  Lyon, Keenan (University of Waterloo, 2020-05-29)

  Density functional theory (DFT) and its time-dependent counterpart (TDDFT) are crucial tools in material discovery, drug design, biochemistry, catalysis, and nanoscience. However, despite its exact theoretical basis, ...

• Stochastic synchronization of semi-Markovian jump chaotic Lur’e systems with packet dropouts subject to multiple sampling periods 

  Li, Qian; Liu, Xinzhi; Zhu, Qingxin; Zhong, Shouming; Cheng, Jun (Elsevier, 2019-09)

  This paper is concerned with the problem of stochastic synchronization for semi-Markovian jump chaotic Lur’e systems. Firstly, packet dropouts and multiple sampling periods are both considered. By input-delay approach and ...

• Synchronization of coupled reaction-diffusion neural networks: Delay-dependent pinning impulsive control 

  Xie, Xiang; Liu, Xinzhi; Xu, Honglei; Luo, Xiaobing; Liu, Genfan (Elsevier, 2019-12)

  This paper studies the synchronization problem of coupled reaction-diffusion neural networks with time-varying delays. A novel pinning impulsive controller is proposed, where distributed delays and discrete delays are taken ...

• Stability analysis by contraction principle for impulsive systems with infinite delays 

  Liu, Xinzhi; Ramirez, Cesar (Elsevier, 2020-03)

  This paper studies a class of quasi-linear impulsive systems of functional differential equations with infinite time delay. By employing the contraction principle, several criteria on uniform stability and asymptotic ...

• Impulsive observer design for a class of switched nonlinear systems with unknown inputs 

  Zhan, Tao; Ma, Shuping; Liu, Xinzhi; Chen, Hao (Elsevier, 2019-08)

  This paper investigates hybrid observer design of a class of unknown input switched nonlinear systems. The distinguishing feature of the proposed method is that the stability of all subsystems of the error switched systems ...

• A Novel Class of Intensity-based Metrics for Image Functions which Accommodate a Generalized Weber's Model of Perception 

  Li, Dongchang (University of Waterloo, 2020-04-29)

  Even though the usual L2 image fidelity measurements, such as MSE and PSNR, characterize the mean error for each pixel of the images, these traditional measurements are not designed to predict human visual perception of ...

• Multi-scale entropy analysis and Hurst exponent 

  Mollaei, Saeid; Darooneh, Amir Hossein; Karimi, Somaye (Elsevier, 2019-08-15)

  Several methods exist for measuring the complexity in a system through analysis of its associated time series. Multi-scale entropy appears as a successful method on this matter. It has been applied in many disciplines with ...

• Feature identification in time series data sets 

  Shaw, Justin; Stastna, Marek; Coutino, Aaron; Walter, Ryan K.; Reinhardt, Eduard (Elsevier, 2019-05)

  We present a computationally inexpensive, flexible feature identification method which uses a comparison of time series to identify a rank-ordered set of features in geophysically-sourced data sets. Many physical phenomena ...

• 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 ...

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