Breast cancer is one of the most common types of cancer worldwide. Early detection and diagnosis are crucial for improving the chances of successful treatment and survival. In this thesis, many different machine learning algorithms were evaluated and compared to predict breast cancer malignancy from diagnostic features extracted from digitized images of breast tissue samples, called fine-needle aspirates. Breast cancer diagnosis typically involves a combination of mammography, ultrasound, and biopsy. However, machine learning algorithms can assist in the detection and diagnosis of breast cancer by analyzing large amounts of data and identifying patterns that may not be discernible to the human eye. By using these algorithms, healthcare professionals can potentially detect breast cancer at an earlier stage, leading to more effective treatment and better patient outcomes. The results showed that the gradient boosting classifier performed the best, achieving an accuracy of 96% on the test set. This indicates that this algorithm can be a useful tool for healthcare professionals in the early detection and diagnosis of breast cancer, potentially leading to improved patient outcomes.

Graph neural networks (GNN) offer a potential method of bypassing the Kohn-Sham equations in density functional theory (DFT) calculations by learning both the Hohenberg-Kohn (HK) mapping of electron density to energy, allowing for calculations of much larger atomic systems and time scales and enabling large-scale MD simulations with DFT-level accuracy. In this work, we investigate the feasibility of GNNs to learn the HK map from the external potential approximated as Gaussians to the electron density 𝑛(𝑟), and the mapping from 𝑛(𝑟) to the energy density 𝑒(𝑟) using Pytorch Geometric. We develop a graph representation for densities on radial grid points and determine that a k-nearest neighbor algorithm for determining node connections is an effective approach compared to a distance cutoff model, having an average graph size of 6.31 MB and 32.0 MB for datasets with 𝑘 = 10 and 𝑘 = 50 respectively. Furthermore, we develop two GNNs in Pytorch Geometric, and demonstrate a decrease in training losses for a 𝑛(𝑟) to 𝑒(𝑟) of 8.52 · 10^14 and 3.10 · 10^14 for 𝑘 = 10 and 𝑘 = 20 datasets respectively, suggesting the model could be further trained and optimized to learn the electron density to energy functional.

Machine learning is a rapidly growing field, with no doubt in part due to its countless applications to other fields, including pedagogy and the creation of computer-aided tutoring systems. To extend the functionality of FACT, an automated teaching assistant, we want to predict, using metadata produced by student activity, whether a student is capable of fixing their own mistakes. Logs were collected from previous FACT trials with middle school math teachers and students. The data was converted to time series sequences for deep learning, and ordinary features were extracted for statistical machine learning. Ultimately, deep learning models attained an accuracy of 60%, while tree-based methods attained an accuracy of 65%, showing that some correlation, although small, exists between how a student fixes their mistakes and whether their correction is correct.