arXiv subjects

David White

Publications and source records attributed to David White.

At least 19 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↗

arXiv2026

Autonomous Subsea Cable Search and Tracking with Graph-Optimised Priors and Visual Tracking

Global communications rely on subsea cable infrastructure that remains vulnerable to damage from natural hazards and human activity. Autonomous underwater vehicles (AUVs) offer an efficient means to inspect long sections of exposed cable, but uncertainty in cable route maps, small cable diameters and partial burial makes continuous tracking a challenge. This paper presents a novel cable search and tracking method that leverages uncertain prior cable route maps. Graph-based optimisation continuously update the cable route to remain consistent with visual observations. Route uncertainty is constrained as a function of distance from observations using physics-based catenary models that account for cable parameters (i.e., lay depth, diameter, and density), bounding the search space to physically feasible regions and improving search efficiency. Cable detection is performed using a semi-supervised classifier running in real-time on-board a camera-equipped AUV. These detections both update the graph-based optimisation and enable visual cable tracking. When tracking is lost due to misclassification, burial or imperfect control, the bounded search space enables efficient recovery. The approach was demonstrated in field trials using the University of Southampton's Smarty200 AUV. The system successfully located the cable despite deliberate errors in it initial cable route map, updating this to be consistent with observations and using visual tracking to inspect up to 59% of a 120m test cable, with successful recovered after tracking loss.

cs.RO↗

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↗

arXiv2025

Modeling Social Systems: Transparency, Reproducibility, and Responsibility

Mathematical models of complex social systems can enrich social scientific theory, inform interventions, and shape policy. From voting behavior to economic inequality and urban development, such models influence decisions that affect millions of lives. Thus, it is especially important to formulate and present them with transparency, reproducibility, and humility. Modeling in social domains, however, is often uniquely challenging. Unlike in physics or engineering, researchers often lack controlled experiments or abundant, clean data. Observational data is sparse, noisy, partial, and missing in systematic ways. In such an environment, how can we build models that can inform science and decision-making in transparent and responsible ways?

math.HO↗

arXiv2024

Homotopical recognition of diagram categories

Building on work of Marta Bunge in the one-categorical case, we characterize when a given model category is Quillen equivalent to a presheaf category with the projective model structure. This involves introducing a notion of homotopy atoms, generalizing the orbits of Dwyer and Kan. Apart from the orbit model structures of Dwyer and Kan, our examples include the classification of stable model categories after Schwede and Shipley, isovariant homotopy theory after Yeakel, and Cat-enriched homotopy theory after Gu. As an application, we give a classification of polynomial functors (in the sense of Goodwillie calculus) from finite pointed simplicial sets to spectra, and compare it to the previous work by Arone and Ching.

math.AT↗

arXiv2024

A statistical analysis of drug seizures and opioid overdose deaths in Ohio from 2014 to 2018

This paper examines the association between police drug seizures and drug overdose deaths in Ohio from 2014 to 2018. We use linear regression, ARIMA models, and categorical data analysis to quantify the effect of drug seizure composition and weight on drug overdose deaths, to quantify the lag between drug seizures and overdose deaths, and to compare the weight distributions of drug seizures conducted by different types of law enforcement (national, local, and drug task forces). We find that drug seizure composition and weight have strong predictive value for drug overdose deaths (F = 27.14, p < 0.0001, R^2 = .7799). A time series analysis demonstrates no statistically significant lag between drug seizures and overdose deaths or weight. Histograms and Kolmogorov-Smirnov tests demonstrate stark differences between seizure weight distributions of different types of law enforcement (p < 0.0001 for each pairwise comparison). We include a discussion of what our conclusions mean for law enforcement and harm reduction efforts.

physics.soc-ph↗

arXiv2024

On Colimits and Model Structures in Various Categories of Manifolds

After explaining the importance of model categories in abstract homotopy theory, we provide concrete examples demonstrating that various categories of manifolds do not have all finite colimits, and hence cannot be model categories. We then consider various enlargements of our categories of manifolds, culminating in categories of presheaves. We explain how to produce model structures on these enlarged categories, culminating with answering an open problem involving Poincar\'{e} spaces.

math.AT↗

arXiv2024

The statistical and dynamic modeling of the first part of the 2013-2014 Euromaidan protests in Ukraine: The Revolution of Dignity and preceding times

Ukraine's tug-of-war between Russia and the West has had significant and lasting consequences for the country. In 2013, Viktor Yanukovych, the Ukrainian president aligned with Russia, opted against signing an association agreement with the European Union. This agreement aimed to facilitate trade and travel between the EU and Ukraine. This decision sparked widespread protests that coalesced in Kyiv's Maidan Square, eventually becoming known as the Euromaidan protests. In this study, we analyze the protest data from 2013, sourced from Ukraine's Center for Social and Labor Research. Despite the dataset's limitations and occasional inconsistencies, we demonstrate the extraction of valuable insights and the construction of a descriptive model from such data. Our investigation reveals a pre-existing state of self-excitation within the system even before the onset of the Euromaidan protests. This self-excitation intensified during the Euromaidan protests. A statistical analysis indicates that the government's utilization of force correlates with increased future protests, exacerbating rather than quelling the protest movement. Furthermore, we introduce the implementation of Hawkes process models to comprehend the spatiotemporal dynamics of the protest activity. Our findings highlight that, while protest activities spread across the entire country, the driving force behind the dynamics of these protests was the level of activity in Kyiv. Furthermore, in contrast to prior research that emphasized geographical proximity as a key predictor of event propagation, our study illustrates that the political alignment among oblasts, which are the distinct municipalities comprising Ukraine, had a more profound impact than mere geographic distance. This underscores the significance of social and cultural factors in molding the trajectory of political movements.

physics.soc-ph↗

arXiv2023

An analysis of protesting activity and trauma through mathematical and statistical models

The effect that different police protest management methods have on protesters' physical and mental trauma is still not well understood and is a matter of debate. In this paper, we take a two-pronged approach to gain insight into this issue. First, we perform statistical analysis on time series data of protests provided by ACLED and spanning the period of time from January 1, 2020, until March 13, 2021. We observe that the use of kinetic impact projectiles is associated with more protests in subsequent days and is also a better predictor of the number of deaths in subsequent deaths than the number of protests, concluding that the use of non-lethal weapons seems to have an inflammatory rather than suppressive effect on protests. Next, we provide a mathematical framework to model modern, but well-established psychological and sociological research on compliance theory and crowd dynamics. Our results show that understanding the heterogeneity of the crowd is key for protests that lead to a reduction of social tension and minimization of physical and mental trauma in protesters.

stat.AP↗

arXiv2023

Quasi-tame substitudes and the Grothendieck construction

This paper continues the study of the homotopy theory of algebras over polynomial monads initiated by the first author and Clemens Berger. We introduce the notion of a quasi-tame polynomial monad (generalizing tame ones) and produce transferred model structures (left proper in many settings) on algebras over such a monad. Our motivating application is to produce model structures on Grothendieck categories, which are used in a companion paper to give a unified approach to the study of operads, their algebras, and their modules. We prove a general result regarding when a Grothendieck construction can be realized as a category of algebras over a polynomial monad, examples illustrating that quasi-tameness is necessary as well as sufficient for admissibility, and an extension of classifier methods to a non-polynomial situation, namely the case of commutative monoids.

math.AT↗

arXiv2023

Model structures on operads and algebras from a global perspective

This paper studies the homotopy theory of the Grothendieck construction using model categories and semi-model categories, provides a unifying framework for the homotopy theory of operads and their algebras and modules, and uses this framework to produce model structures, rectification results, and properness results in new settings. In contrast to previous authors, we begin with a global (semi-)model structure on the Grothendieck and induce (semi-)model structures on the base and fibers. In a companion paper, we show how to produce such global model structures in general settings. Applications include numerous flavors of operads encoded by polynomial monads and substitudes (symmetric, non-symmetric, cyclic, modular, higher operads, dioperads, properads, and PROPs), (commutative) monoids and their modules, and twisted modular operads. We also prove a general result for upgrading a semi-model structure to a full model structure.

math.AT↗

arXiv2022

An Optimization Approach to Improve Equitable Access to Local Parks

Local parks are public resources that promote human and environmental welfare. Unfortunately, park inequities are commonplace as historically marginalized groups may have insufficient access. Platforms exist to identify the geographical areas that would benefit from future park improvements. However, these platforms do not optimize decisions nor include key features, such as budget and infrastructure, that are relevant to park location decisions. To support recreational and government agencies in addressing inequities in the distribution and quality of parks, we propose a mixed-integer program that minimizes insufficient access, defined as weighted deviations across multiple categories (distance, capacity, and environmental features). We consider an equity-focused min-max objective and an overall objective to minimize total weighted deviations. We apply the model to a case study of Asheville, North Carolina. We conduct extensive data collection to parameterize the model. In policy analyses, we consider the effects of available budget, planning horizons, strategic demographic priorities, and thresholds of access. The model reflects user-defined criteria and goals, and the results suggest that the framework may be generalizable to other cities. This study serves as a step in the development and incorporation of mathematical modeling to achieve social goals within the recreational setting.

math.OC↗

arXiv2022

User's Guide Project: Looking Back and Looking Forward

In 2014 Luke Wolcott created the User's Guide Project in which a group of algebraic topologists came together to write user's guides to coincide with their research papers in hopes of making their research more accessible. We examine the role of this innovative project within the greater mathematics community. We discuss the structure and history of the project, its impact on the community, and its value to the participants of the project. We end by encouraging the math community to recognize the value of the project and expand the User's Guide Project to other subfields.

math.HO↗

arXiv2022

Exploring the Intersection between Neural Architecture Search and Continual Learning

Despite the significant advances achieved in Artificial Neural Networks (ANNs), their design process remains notoriously tedious, depending primarily on intuition, experience and trial-and-error. This human-dependent process is often time-consuming and prone to errors. Furthermore, the models are generally bound to their training contexts, with no considerations to their surrounding environments. Continual adaptiveness and automation of neural networks is of paramount importance to several domains where model accessibility is limited after deployment (e.g IoT devices, self-driving vehicles, etc.). Additionally, even accessible models require frequent maintenance post-deployment to overcome issues such as Concept/Data Drift, which can be cumbersome and restrictive. By leveraging and combining approaches from Neural Architecture Search (NAS) and Continual Learning (CL), more robust and adaptive agents can be developed. This study conducts the first extensive review on the intersection between NAS and CL, formalizing the prospective Continually-Adaptive Neural Networks (CANNs) paradigm and outlining research directions for lifelong autonomous ANNs.

cs.AI↗

arXiv2022

A Generalization of Ripley's K Function for the Detection of Spatial Clustering in Areal Data

Spatial clustering detection has a variety of applications in diverse fields, including identifying infectious disease outbreaks, assessing land use patterns, pinpointing crime hotspots, and identifying clusters of neurons in brain imaging applications. While performing spatial clustering analysis on point process data is common, applications to areal data are frequently of interest. For example, researchers might wish to know if census tracts with a case of a rare medical condition or an outbreak of an infectious disease tend to cluster together spatially. Since few spatial clustering methods are designed for areal data, researchers often reduce the areal data to point process data (e.g., using the centroid of each areal unit) and apply methods designed for point process data, such as Ripley's K function or the average nearest neighbor method. However, since these methods were not designed for areal data, a number of issues can arise. For example, we show that they can result in loss of power and/or a significantly inflated type I error rate. To address these issues, we propose a generalization of Ripley's K function designed specifically to detect spatial clustering in areal data. We compare its performance to that of the traditional Ripley's K function, the average nearest neighbor method, and the spatial scan statistic with an extensive simulation study. We then evaluate the real world performance of the method by using it to detect spatial clustering in land parcels containing conservation easements and US counties with high pediatric overweight/obesity rates.

stat.ME↗

arXiv2021

Substitudes, Bousfield localization, higher braided operads, and Baez-Dolan stabilization

This short note reports on joint work with Michael Batanin towards a general machine for proving Baez-Dolan Stabilization Theorems for various models of higher categories, based on substitudes, Bousfield localization, and homotopical Beck-Chevalley squares. I provide a road map to our recent papers, and include new results proving Baez-Dolan Stabilization Theorems for Tamsamani weak $n$-categories, higher Segal categories, Ara's $n$-quasi-categories, and cartesian models of Segal and complete Segal objects due to Bergner and Rezk. I also attempt to clarify the connection to higher braided operads, and our more general stabilization machinery.

math.AT↗

arXiv2020

Homotopy theory of algebras of substitudes and their localisation

We study the category of algebras of substitudes (also known to be equivalent to the regular patterns of Getzler) equipped with a (semi)model structure lifted from the model structure on the underlying presheaves. We are especially interested in the case when the model structure on presheaves is a Cisinski style localisation with respect to a proper Grothendieck fundamental localiser. For example, for $\mathtt{W}=\mathtt{W}_{\infty}$ the minimal fundamental localiser, the local objects in such a localisation are locally constant presheaves, and local algebras of substitudes are exactly algebras whose underlying presheaves are locally constant. We investigate when this localisation has nice properties. We single out a class of such substitudes which we call left localisable and show that the substitudes for $n$-operads, symmetric, and braided operads are in this class. As an application we develop a homotopy theory of higher braided operads and prove a stabilisation theorem for their $\mathtt{W}_k$-localisations. This theorem implies, in particular, a generalisation of the Baez-Dolan Stabilisation Hypothesis for higher categories.

math.CT↗

arXiv2020

Left Bousfield localization without left properness

Given a combinatorial (semi-)model category $M$ and a set of morphisms $C$, we establish the existence of a semi-model category $L_C M$ satisfying the universal property of the left Bousfield localization in the category of semi-model categories. Our main tool is a semi-model categorical version of a result of Jeff Smith, that appears to be of independent interest. Our main result allows for the localization of model categories that fail to be left proper. We give numerous examples and applications, related to the Baez-Dolan stabilization hypothesis, localizations of algebras over operads, chromatic homotopy theory, parameterized spectra, $C^*$-algebras, enriched categories, dg-categories, functor calculus, and Voevodsky's work on radditive functors.

math.AT↗