Masters Degrees (Applied Mathematics)
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- ItemThe use of deep learning to predict HER2 status in breast cancer directly from histopathology slides(Stellenbosch : Stellenbosch University, 2024-03) Smith, Alexandra Nicole; Coetzer, Johannes; Stellenbosch University. Faculty of Science. Dept. of Applied Mathematics.ENGLISH ABSTRACT: The treatment of breast cancer is significantly influenced by the identification of various molecular biomarkers, including Human Epidermal Growth Factor Receptor 2 (HER2). Current techniques for determining HER2 status involve immunohistochemistry (IHC) and in-situ hybridisation (ISH) methods. HER2 testing, which is routinely applied in cases of invasive breast cancer, serves as the primary biomarker guiding HER2-targeted therapies. HE-stained whole slide images, which are more cost-effective, time-efficient, and routinely produced during pathological examinations, present an opportunity for leveraging deep learning to enhance the accuracy, speed, and affordability of HER2 status determination. This thesis introduces a deep learning framework for predicting HER2 status directly from the morphological features observed in histopathological slides. The proposed system has two stages: initially, a deep learning model is employed to differentiate between benign and malignant tissues in whole slide images, using annotated regions of invasive tumours. Following this, the effectiveness of Inception-v4 and Inception-ResNet-v2 architectures in biomarker status prediction is explored, comparing their performance against previous model architectures utilised for this task, namely Inception-v3 and ResNet34. The study utilises a dataset comprising whole slide images from 147 patients, sourced from the publicly available Cancer Genome Atlas (TCGA). Models are trained using 256 ◊ 256 patches extracted from these slides. The best-performing model, Inception-v4, achieved an area under the receiver operating characteristic curve (AUC) of 0.849 (95% confidence interval (CI): 0.845 ≠ 0.853) per-tile and 0.767 (CI:0.556 ≠ 0.955) per-slide in the test set. This research demonstrates the capability of deep learning models to accurately predict HER2 status directly from histopathological whole slide images, offering a more cost- and time-efficient method for identifying clinical biomarkers, with the potential to inform and accelerate the selection of breast cancer treatments.
- ItemModelling blood flow during syringing(Stellenbosch : Stellenbosch University, 2024-03) Goedhals, Jaime Erin; De Villiers, Andie; Smit, Francois; Stellenbosch University. Faculty of Science. Dept. of Applied Mathematics.ENGLISH ABSTRACT: This project investigates modelling blood flow during syringing and the resulting haemol- ysis, which is defined as the breaking open of red blood cells, using numerical simulations in combination with haemolysis models. Haemolysis can be caused by a range of factors, which may be physical, chemical or biological in nature. Physical damage can manifest in scenarios such as emergency rapid blood transfusions conducted through syringing, a practice which may be employed in resuscitation procedures, particularly in rural hospitals. It has been demonstrated that such syringe-based transfusions result in noteworthy haemolysis, significantly surpassing the impact of pressure bag usage. This heightened haemolysis carries potential negative implications for the recipient of the transfusion. Blood flow is modelled, as a Newtonian fluid and as a non-Newtonian fluid, using the open source finite element software deal.II, which is then compared to numerical simulations conducted in Ansys Fluent. Both methods are validated against a known two- dimensional solution. Then, flow through a sudden contraction, which mimics a syringe, is simulated. Lastly, a three-dimensional setup of a hypodermic needle is implemented. The percentage haemolysis is calculated in a post-processing step using the time history of the shear stresses along streamlines. The numerical simulations showed good agreement with the analytical solutions, and the percentage haemolysis results achieved were consistent with published literature.
- Item3D reconstruction of naturally fragmenting warhead fragments(Stellenbosch : Stellenbosch University, 2024-03) Sequeira, Jose; Smit, Francois; Coetzer, Johannes; Stellenbosch University. Faculty of Science. Dept. of Applied Mathematics.ENGLISH ABSTRACT: This study starts with a brief introduction to the South African armaments and ammunition technology industry, highlighting the historical alignment with NATO standards. The focal point is the investigation into the potential of an existing NATO-compliant icosahedral imaging system to ascertain additional geometric features of fragments, such as mass and volume. Building on prior work, the author proposes leveraging extensive image data sets acquired through the icosahedral imaging system to determine these features. The literature study explores two key approaches: stereo vision and shape-from-silhouette 3D reconstruction. The latter emerges as the favored method, particularly due to how well the technique complements the icosahedral camera arrangement. Subsequently, attention is directed toward the electro-mechanical design of the icosahedral imaging instrument and the creation of shape-from-silhouette reconstruction software. Challenges in calibrating the multi-imaging system are addressed through hardware upgrades. The study advances to experimental results, involving the analysis of fragments recovered from a warhead arena test. Average presented areas are determined, and 3D reconstructed models are obtained using the shape-from-silhouette technique, with errors ranging from 2% to 54%. A detailed discussion follows, highlighting the similar average presented area measurements for different icosahedral imaging systems. The inclusion of shadow regions is noted to significantly impact the accuracy of the 3D reconstruction process. Furthermore, slender fragments exhibit smaller errors compared to non-slender counterparts. The study concludes by affirming the achievement of the primary objectives, namely, the ability to use fragment silhouettes obtained during average presented area measurements to produce close-fit 3D models of fragments. Future work is underscored, building upon the strong foundation laid by this investigation. Recommendations, improvements, and suggestions for future research are provided, emphasizing the potential for enhanced reconstruction accuracy, particularly for non-slender fragments, with increased camera deployment.
- ItemMitigation of control errors in quantum annealing(Stellenbosch : Stellenbosch University, 2024-03) Dlamini, Thembelihle Rose; Touchette, Hugo; Sanders, Barry C.; Nickelsen, Daniel; Stellenbosch University. Faculty of Science. Dept. of Applied Mathematics.ENGLISH ABSTRACT: Quantum annealing is a form of quantum computing that incorporates algorithms and hardware design to solve optimization problems. Evidence suggests that quantum an- nealing can be superior to classical solvers for certain optimizations. However, quantum computers including quantum annealing devices are more susceptible to errors than clas- sical computers hence the inclusion of some form of protection against errors in quantum annealing is important to ensure scalability. In this thesis, we address the issue of control errors in the accuracy of solutions obtained via a quantum annealer through optimiza- tion of the control fields v ia t he K rotov m ethod. C ontrol fi elds op timized in th is way for a problem with known solutions can be used to mitigate control errors of a similar problem.
- ItemIntelligent control for processing solar photovoltaic energy(Stellenbosch : Stellenbosch University, 2023-12) Wacira, Joseph Muthui; Bah, Bubacarr; Vargas, Alessandro; Stellenbosch University. Faculty of Science. Dept. of Applied Mathematics.ENGLISH ABSTRACT: Maximum Power Point Tracking (MPPT) techniques play a pivotal role in optimizing the performance of photovoltaic systems within renewable energy. Traditional MPPT methods, often reliant on Proportional Integral and Derivative (PID) controllers, face challenges when applied to nonlinear systems with dynamic operating conditions, typical in photovoltaic systems where temperature and irradiance continually fluctuate. The inherent static nature of the PID parameters leads to power losses, thereby reducing their efficiency. Additionally, they rely on trial-and-error approaches to determine the actual Maximum Power Point (MPP). This study introduces two novel MPPT approaches: the Gradient Descent Approach and the Deep Q-Network (DQN) approach. These methods share a common feature: they require knowledge of the maximum power point (MPP). An ANN was employed to predict the MPP under current operating conditions. Once the MPP is known, the Gradient Descent Approach aims to minimize the mean squared error by adjusting the duty cycle, whereas the DQN Approach employs a state-action-reward system that penalizes deviations from the MPP and large actions. To evaluate the effectiveness o f t hese a pproaches, s imulations were conducted under uniform operating conditions using MATLAB/Simulink, with data sourced from the NSRBD website for Brazil. The results were compared with those of the conventional Perturb and Observe algorithm with a PI controller tuned using the Ziegler-Nichols method under Standard Test Conditions. Simulations revealed that the proposed methodologies exhibited significantly higher efficiency than the benchmark algorithm. Furthermore, they demonstrate fast response times and minimal steady-state errors. Although these findings underscore the promise of the proposed approaches, further validation in real-world environments is necessary to confirm their superiority and practical applicability.