Efficient matrix determinant calculations have been studied since the 19th century. Computers expand the range of determinants that are practically calculable to include matrices with symbolic entries. However, the fastest determinant algorithms for numerical matrices are often not the fastest for symbolic matrices with many variables. We compare the performance of two algorithms, fraction-free Gaussian elimination and minor expansion, on symbolic matrices with many variables. We show that, under a simplified theoretical model, minor expansion is faster in most situations. We then propose optimizations for minor expansion and demonstrate their effectiveness with empirical data.

Spatial clustering is a crucial field, finding universal use across criminology, pathology, and urban planning. However, most spatial clustering algorithms cannot pull information from nearby nodes and suffer performance drops when dealing with higher dimensionality and large datasets, making them suboptimal for large-scale and high-dimensional clustering. Due to modern data growing in size and dimension, clustering algorithms become weaker when addressing multifaceted issues. To improve upon this, we develop ConstellationNet, a convolution neural network(CNN)-graph neural network(GNN) framework that leverages the embedding power of a CNN, the neighbor aggregation of a GNN, and a neural network's ability to deal with batched data to improve spatial clustering and classification with graph augmented predictions. ConstellationNet achieves state-of-the-art performance on both supervised classification and unsupervised clustering across several datasets, outperforming state-of-the-art classification and clustering while reducing model size and training time by up to tenfold and improving baselines by 10 times. Because of its fast training and powerful nature, ConstellationNet holds promise in fields like epidemiology and medical imaging, able to quickly train on new data to develop robust responses.

Recent years saw an increased interest in modeling and understanding the mechanisms of opinion and innovation spread through human networks. Using analysis of real-world social data, researchers are able to gain a better understanding of the dynamics of social networks and subsequently model the changes in such networks over time. We developed a social network model that both utilizes an agent-based approach with a dynamic update of opinions and connections between agents and reflects opinion propagation and structural changes over time as observed in real-world data. We validate the model using data from the Social Evolution dataset of the MIT Human Dynamics Lab describing changes in friendships and health self-perception in a targeted student population over a nine-month period. We demonstrate the effectiveness of the approach by predicting changes in both opinion spread and connectivity of the network. We also use the model to evaluate how the network parameters, such as the level of `openness' and willingness to incorporate opinions of neighboring agents, affect the outcome. The model not only provides insight into the dynamics of ever changing social networks, but also presents a tool with which one can investigate opinion propagation strategies for networks of various structures and opinion distributions.

We introduce a classification scheme for detecting political bias in long text content such as newspaper opinion articles. Obtaining long text data and annotations at sufficient scale for training is difficult, but it is relatively easy to extract political polarity from tweets through their authorship. We train on tweets and perform inference on articles. Universal sentence encoders and other existing methods that aim to address this domain-adaptation scenario deliver inaccurate and inconsistent predictions on articles, which we show is due to a difference in opinion concentration between tweets and articles. We propose a two-step classification scheme that uses a neutral detector trained on tweets to remove neutral sentences from articles in order to align opinion concentration and therefore improve accuracy on that domain. Our implementation is available for public use at this https URL.