Colleen Farrelly | Searcharxiv

arXiv2026

A Persistent Homology Signature of Knotting

We ask whether knotting can be recognised using persistent homology. Starting from a point-cloud representation of a curve, we compute one-dimensional persistent homology, extract cycle representatives, and assign a hypergraph curvature-based score to these cycles. Motivated by proteins but tested more broadly, the method reveals systematic differences between knotted and unknotted structures in both protein families and synthetic examples. This suggests that knotting leaves a detectable persistent-homology-based signature.

math.AT↗

arXiv2023

Current Topological and Machine Learning Applications for Bias Detection in Text

Institutional bias can impact patient outcomes, educational attainment, and legal system navigation. Written records often reflect bias, and once bias is identified; it is possible to refer individuals for training to reduce bias. Many machine learning tools exist to explore text data and create predictive models that can search written records to identify real-time bias. However, few previous studies investigate large language model embeddings and geometric models of biased text data to understand geometry's impact on bias modeling accuracy. To overcome this issue, this study utilizes the RedditBias database to analyze textual biases. Four transformer models, including BERT and RoBERTa variants, were explored. Post-embedding, t-SNE allowed two-dimensional visualization of data. KNN classifiers differentiated bias types, with lower k-values proving more effective. Findings suggest BERT, particularly mini BERT, excels in bias classification, while multilingual models lag. The recommendation emphasizes refining monolingual models and exploring domain-specific biases.

cs.CY↗