The present work presents a number of contributions to the areas of numerical integration, singular integrals, and boundary element methods. The first contribution is an elemental distortion technique, based on the Duffy transformation, used to improve efficiency for the numerical integration of near hypersingular integrals. Results show that this method can reduce quadrature expense by up to 75 percent over the standard Duffy transformation. The second contribution is an improvement to integration of weakly singular integrals by using regularization to smooth weakly singular integrals. Errors show that the method may reduce errors by several orders of magnitude for the same quadrature order. The final work investigated the use of regularization applied to hypersingular integrals in the context of the boundary element method in three dimensions. This work showed that by using the simple solutions technique, the BEM is reduced to a weakly singular form which directly supports numerical integration. Results support that the method is more efficient than the state-of-the-art.

No description available.

No description available.

No description available.

No description available.

Deep neural language models like GPT-2 is undoubtedly strong at text generation, but often requires special decoding strategies to prevent producing degenerate output - namely repetition. The use of maximum likelihood training objective results in a peaked probability distribution, leading to the over-confidence of neural networks. In this thesis, we explore entropy regularization for a neural language model that can easily smooth peaked output distribution during the fine-tuning process employing GPT-2. We first define the models in three ways: (1) Out of-the box model without fine-tuning process, (2) Fine-tuned model without entropy regularization, and (3) Fine-tuned model with entropy regularization. To investigate the effect of domains on the model, we also divide the dataset into three ways: (1) fine-tuned on heterogeneous dataset, tested on heterogeneous dataset, (2) fine-tuned on homogeneous dataset, tested on homogeneous dataset, and (3) fine-tuned on heterogeneous dataset, tested on homogeneous dataset. In terms of entropy regularization, we experiment controlling the entropy strength parameter (𝛽) in the range of [0.5, 1.0, 2.0, 4.0, 6.0] and annealing the parameter during fine-tuning process. Our findings prove that the entropy-based regularization during fine-tuning process improve the text generation models by significantly reducing the repetition rate without tuning the decoding strategies. As a result of comparing the probabilities of human-generated sentence tokens, it was observed that entropy regularization compensates for the shortcomings of the deterministic decoding method (Beam search) that mostly selects few high-probability words. Various studies have explored entropy regularization in the cold-start training process of neural networks. However, there are not many studies covering the effect of the fine-tuning stage of text generation tasks when employing large scale pre-trained language models. Our findings present strong evidence that one can achieve significant improvement in text generation by way of utilizing entropy regularization, a highly cost-effective approach, during the fine-tuning process.

<p> Magnetic Resonance Imaging (MRI) velocity quantification is addressed in part I of this thesis. In simple MR imaging, data is collected and tissue densities are displayed as images. Moving tissue creates signals which appear as artifacts in the images. In velocity imaging, more data is collected and phase differences are used to quantify the velocity of tissue components. The problem is described and a novel formulation of a regularized, nonlinear inverse problem is proposed. Both Tikhonov and Total Variation Regularization are discussed. Results of numerical simulations show that significant noise reduction is possible.</p> <p> The method is firstly verified with MATLAB. A number of experiments are carried out with different regularization parameters, different magnetic fields and different noise levels. The experiments show that the stronger the complex noise is, the stronger the magnetic field requires for estimating the velocity. The regularization parameter also plays an important role in the experiments. Given the noise level and with an appropriate value of regularization parameter, the estimated velocity converges to ideal velocity very quickly. A proof-of-concept implementation on the Cell BE processor is described, quantifying the performance potential of this platform.</p> <p> The second part of this thesis concerns the evaluation of an elementary function library. Since CBE SPU is designed for compute intensive applications, the well developed Math functions can help developer program and save time to take care other details. Dr. Anand's research group in McMaster developed 28 math functions for CBE SPU. The test tools for accuracy and performance were developed on CBE. The functions were tuned while testing. The functions are either competitive or an addition to the existing SDK1.1 SPU math functions.</p> / Thesis / Master of Applied Science (MASc)

This thesis proposes a large eddy simulation reduced order model (LES-ROM) framework for the numerical simulation of realistic flows. In this LES-ROM framework, the proper orthogonal decomposition (POD) is used to define the ROM basis and a POD differential filter is used to define the large ROM structures. An approximate deconvolution (AD) approach is used to solve the ROM closure problem and develop a new AD-ROM. This AD-ROM is tested in the numerical simulation of the one-dimensional Burgers equation with a small diffusion coefficient ( ν= 10⁻³). / Master of Science

Dimensionality reduction techniques (DR) enhance data interpretability and reduce space complexity, though at the cost of information loss. Such methods have been prevalent in the Structural Health Monitoring (SHM) anomaly detection literature. While DR is favorable in supervised anomaly detection, where possible novelties are known a priori, the efficacy is less clear in unsupervised detection. In this work, we perform a detailed assessment of the DR performance trade-offs to determine whether the information loss imposed by DR can impact SHM performance for previously unseen novelties. As a basis for our analysis, we rely on an SHM anomaly detection method operating on input signals' fast Fourier transform (FFT). FFT is regarded as a raw, frequency-domain feature that allows studying various DR techniques. We design extensive experiments comparing various DR techniques, including neural autoencoder models, to capture the impact on two SHM benchmark datasets exclusively. Results imply the loss of information to be more detrimental, reducing the novelty detection accuracy by up to 60\% with autoencoder-based DR. Regularization can alleviate some of the challenges though unpredictable. Dimensions of substantial vibrational information mostly survive DR; thus, the regularization impact suggests that these dimensions are not reliable damage-sensitive features regarding unseen faults. Consequently, we argue that designing new SHM anomaly detection methods that can work with high-dimensional raw features is a necessary research direction and present open challenges and future directions. / M.S. / Structural health monitoring (SHM) aids the timely maintenance of infrastructures, saving human lives and natural resources. Infrastructure will undergo unseen damages in the future. Thus, data-driven SHM techniques for handling unlabeled data (i.e., unsupervised learning) are suitable for real-world usage. Lacking labels and defined data classes, data instances are categorized through similarities, i.e., distances. Still, distance metrics in high-dimensional spaces can become meaningless. As a result, applying methods to reduce data dimensions is currently practiced, yet, at the cost of information loss. Naturally, a trade-off exists between the loss of information and the increased interpretability of low-dimensional spaces induced by dimensionality reduction procedures. This study proposes an unsupervised SHM technique that works with low and high-dimensional data to assess that trade-off. Results show the negative impacts of dimensionality reduction to be more severe than its benefits. Developing unsupervised SHM methods with raw data is thus encouraged for real-world applications.

Gene network modeling is one of the major goals of systems biology research. Gene network modeling targets the middle layer of active biological systems that orchestrate the activities of genes and proteins. Gene network modeling can provide critical information to bridge the gap between causes and effects which is essential to explain the mechanisms underlying disease. Among the network construction tasks, the rewiring of relevant network structure plays critical roles in determining the behavior of diseases. To systematically characterize the selectively activated regulatory components and mechanisms, the modeling tools must be able to effectively distinguish significant rewiring from random background fluctuations. While differential dependency networks cannot be constructed by existing knowledge alone, effective incorporation of prior knowledge into data-driven approaches can improve the robustness and biological relevance of network inference. Existing studies on protein-protein interactions and biological pathways provide constantly accumulated rich domain knowledge. Though novel incorporation of biological prior knowledge into network learning algorithms can effectively leverage domain knowledge, biological prior knowledge is neither condition-specific nor error-free, only serving as an aggregated source of partially-validated evidence under diverse experimental conditions. Hence, direct incorporation of imperfect and non-specific prior knowledge in specific problems is prone to errors and theoretically problematic. To address this challenge, we propose a novel mathematical formulation that enables incorporation of prior knowledge into structural learning of biological networks as Gaussian graphical models, utilizing the strengths of both measurement data and prior knowledge. We propose a novel strategy to estimate and control the impact of unavoidable false positives in the prior knowledge that fully exploits the evidence from data while obtains "second opinion" by efficient consultations with prior knowledge. By proposing a significance assessment scheme to detect statistically significant rewiring of the learned differential dependency network, our method can assign edge-specific p-values and specify edge types to indicate one of six biological scenarios. The data-knowledge jointly inferred gene networks are relatively simple to interpret, yet still convey considerable biological information. Experiments on extensive simulation data and comparison with peer methods demonstrate the effectiveness of knowledge-fused differential dependency network in revealing the statistically significant rewiring in biological networks, leveraging data-driven evidence and existing biological knowledge, while remaining robust to the false positive edges in the prior knowledge. We also made significant efforts in disseminating the developed method tools to the research community. We developed an accompanying R package and Cytoscape plugin to provide both batch processing ability and user-friendly graphic interfaces. With the comprehensive software tools, we apply our method to several practically important biological problems to study how yeast response to stress, to find the origin of ovarian cancer, and to evaluate the drug treatment effectiveness and other broader biological questions. In the yeast stress response study our findings corroborated existing literatures. A network distance measurement is defined based on KDDN and provided novel hypothesis on the origin of high-grade serous ovarian cancer. KDDN is also used in a novel integrated study of network biology and imaging in evaluating drug treatment of brain tumor. Applications to many other problems also received promising biological results. / Ph. D.