arXiv subjects

Nicholas Bermingham

Publications and source records attributed to Nicholas Bermingham.

3 recordsLinked to original sources

arXiv2026

Visualizing Local Maxima of the Ohio overdose epidemic with Vineyards

Understanding how spatial patterns evolve over time is a complex task that often arises in the analysis of public health data. In this work, we investigate the use of vineyards from topological data analysis (TDA) in this setting by applying them to time series data related to the overdose epidemic in the state of Ohio. We begin by proposing statistical tests that can be used in order to evaluate whether vineyards are a reasonable technique to study a spatiotemporal dataset. We then apply these tests to the data of drug overdose deaths in Ohio and, finding the data suitable, perform a subsequent analysis using vineyards to visualize the evolution of local maxima of death rates throughout the Ohio overdose epidemic. We conclude by developing statistical methods to quantify the significance and uncertainty of vineyard features and by exploring how vineyard-derived summaries can be used for forecasting.

math.AT↗

arXiv2025

Tracking the Spatiotemporal Spread of the Ohio Overdose Epidemic with Topological Data Analysis

In recent years, techniques from Topological Data Analysis (TDA) have proven effective at capturing spatial features of multidimensional data. However, applying TDA to spatiotemporal data remains relatively underexplored. In this work, we extend previous studies of disease spread by using the Mapper algorithm to analyze the Ohio drug overdose epidemic from 2007 to 2024. We introduce a novel method for constructing covers in Mapper graphs of spatiotemporal data that respects geographic structure and highlights the time-dependent variables. Finally, we generate a Mapper visualization of regional demographics to examine how these factors relate to overdose deaths. Our approach effectively reveals temporal trends, overdose hotspots, and time-lagged patterns in relation to both geography and community demographics.

stat.AP↗

arXiv2023

Planar Symmetry Detection and Quantification using the Extended Persistent Homology Transform

Symmetry is ubiquitous throughout nature and can often give great insights into the formation, structure and stability of objects studied by mathematicians, physicists, chemists and biologists. However, perfect symmetry occurs rarely so quantitative techniques must be developed to identify approximate symmetries. To facilitate the analysis of an independent variable on the symmetry of some object, we would like this quantity to be a smoothly varying real parameter rather than a boolean one. The extended persistent homology transform is a recently developed tool which can be used to define a distance between certain kinds of objects. Here, we describe how the extended persistent homology transform can be used to visualise, detect and quantify certain kinds of symmetry and discuss the effectiveness and limitations of this method.

math.AT↗