| Title | Date | Views | Brief Description |
|---|
| Visualizing Arctic ice data with optimal transport |
2023 |
87 |
Climate change is a growing concern that causes sea level risings, heatwaves, and loss of habitats, and impacts the ecology. The climate change in the Arctic is specifically important as the Arctic helps reflect a significant amount of sunlight. This... |
| Analyzing the topological properties of 3D STL files |
2024 |
40 |
Part features in 3D objects that are created for the purpose of rapid prototyping and fabrication using methods such as 3D printing or CNC milling often do not match the measurements of the finished product’s features due to tolerancing and clearance... |
| An analysis of racial segregation using topological data analysis |
2022 |
237 |
In recent years, Topological Data Analysis (TDA) has been used to analyze complex data and provide insights that other research techniques cannot. TDA is a newer form of data analysis which analyzes trends of data from a topological perspective by wa... |
| Sampling from the space of persistence diagrams |
2024 |
169 |
The efficacy of using persistent homology as a tool to understand “the shape of data” has been demonstrated in a variety of different machine learning problem domains. Like many other unsupervised techniques within machine learning, the quintessentia... |
| Injective and coarse embeddings of persistence diagrams and Wasserstein space |
2023 |
111 |
In this dissertation we will examine questions related to two fields of mathematics, topological data analysis (TDA) and optimal transport (OT). Both of these fields center on complex data types to which one often needs to apply standard machine lear... |