Publications (40)
The statistical and dynamic modeling of the first part of the 2013-2014 Euromaidan protests in Ukraine: The Revolution of Dignity and preceding times
Yassin Bahid, Olga Kutsenko, Nancy Rodriguez +1
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 Russ…
User's Guide Project: Looking Back and Looking Forward
Don Larson, Kristen Mazur, David White +1
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…
A Contextual Model Of The Secessionist Rebellion in Eastern Ukraine
Olga Nicoara, David White
This paper explores the possible contextual factors that drove some individuals to lead, and others to join the pro-secessionist rebellion in the 2013-2014 conflict in Eastern Ukra…
Monoidal Bousfield Localizations and Algebras over Operads
David White
We give conditions on a monoidal model category M and on a set of maps C so that the Bousfield localization of M with respect to C preserves the structure of algebras over various…
Bousfield Localization and Algebras over Colored Operads
David White, Donald Yau
We provide a very general approach to placing model structures and semi-model structures on algebras over symmetric colored operads. Our results require minimal hypotheses on the u…
An Optimization Approach to Improve Equitable Access to Local Parks
Anisa Young, Emily L. Tucker, Mariela Fernandez +3
Local parks are public resources that promote human and environmental welfare. Unfortunately, park inequities are commonplace as historically marginalized groups may have insuffici…
Autonomous Subsea Cable Search and Tracking with Graph-Optimised Priors and Visual Tracking
Ibrahim Fadhil Djauhari, Adrian Bodenmann, Samuel Simmons +6
Global communications rely on subsea cable infrastructure that remains vulnerable to damage from natural hazards and human activity. Autonomous underwater vehicles (AUVs) offer an…
Homotopical recognition of diagram categories
Boris Chorny, David White
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 stru…
Traversals of Infinite Graphs with Random Local Orientations
David White
We introduce the notion of a "random basic walk" on an infinite graph, give numerous examples, list potential applications, and provide detailed comparisons between the random basi…
Bousfield Localization and Eilenberg-Moore Categories
Michael Batanin, David White
We prove the equivalence of several hypotheses that have appeared recently in the literature for studying left Bousfield localization and algebras over a monad. We find conditions…
Monoidal Bousfield Localizations and Algebras over Operads: A User's Guide
David White
This paper is a companion for the paper "Monoidal Bousfield Localizations and Algebras over Operads," part of the author's PhD thesis. This paper was written in 2015 for the first…
Model Structures on Commutative Monoids in General Model Categories
David White
We provide conditions on a monoidal model category so that the category of commutative monoids in inherits a model structure from in which…
Processes with inert drift
David White
We construct a stochastic process whose drift is a function of the process's local time at a reflecting barrier. The process arose as a model of the interactions of a Brownian part…
A variant of a Dwyer-Kan theorem for model categories
Boris Chorny, David White
If all objects of a simplicial combinatorial model category \cat A are cofibrant, then there exists the homotopy model structure on the category of small functors $\sS^{\cat A}$, w…
Visualizing Local Maxima of the Ohio overdose epidemic with Vineyards
Nicholas Bermingham, David White, Nathan Willey
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 fro…
Quasi-tame substitudes and the Grothendieck construction
Michael Batanin, Florian De Leger, David White
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 p…
Right Bousfield Localization and Eilenberg-Moore Categories
David White, Donald Yau
We compare several recent approaches to studying right Bousfield localization and algebras over monads. We prove these approaches are equivalent, and we apply this equivalence to o…
A Project Based Approach to Statistics and Data Science
David White
In an increasingly data-driven world, facility with statistics is more important than ever for our students. At institutions without a statistician, it often falls to the mathemati…
Left Bousfield localization without left properness
David White, Michael Batanin
Given a combinatorial (semi-)model category and a set of morphisms , we establish the existence of a semi-model category satisfying the universal property of the lef…
An analysis of protesting activity and trauma through mathematical and statistical models
Nancy Rodriguez, David White
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…
An alternative approach to equivariant stable homotopy theory
Mark Hovey, David White
Building on the work of Martin Stolz, we develop the basics of equivariant stable homotopy theory starting from the simple idea that a G- spectrum should just be a spectrum with an…
Arrow Categories of Monoidal Model Categories
David White, Donald Yau
We prove that the arrow category of a monoidal model category, equipped with the pushout product monoidal structure and the projective model structure, is a monoidal model category…
Encoding Equivariant Commutativity via Operads
Javier J. Gutiérrez, David White
In this paper, we prove a conjecture of Blumberg and Hill regarding the existence of -operads associated to given sequences $\mathcal{F} = (\mathcal{F}_n)_{n \in \mathbb{…
Comonadic Coalgebras and Bousfield Localization
David White, Donald Yau
For a model category, we prove that taking the category of coalgebras over a comonad commutes with left Bousfield localization in a suitable sense. Then we prove a general existenc…
The user's guide project: giving experiential context to research papers
Cary Malkiewich, Mona Merling, David White +2
This paper was written in 2015, and published in the Journal of Humanistic Mathematics. This paper announces the first issue (2015) of Enchiridion: Mathematics User's Guides, a pro…
Homotopy theory of algebras of substitudes and their localisation
Michael Batanin, David White
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 struct…
Right Bousfield Localization and Operadic Algebras
David White, Donald Yau
It is well known that under some general conditions right Bousfield localization exists. We provide general conditions under which right Bousfield localization yields a monoidal mo…
An Overview of Schema Theory
David White
The purpose of this paper is to give an introduction to the field of Schema Theory written by a mathematician and for mathematicians. In particular, we endeavor to to highlight are…
Homotopical Adjoint Lifting Theorem
David White, Donald Yau
This paper provides a homotopical version of the adjoint lifting theorem in category theory, allowing for Quillen equivalences to be lifted from monoidal model categories to catego…
A statistical analysis of drug seizures and opioid overdose deaths in Ohio from 2014 to 2018
Lin Ma, Lam Tran, David White
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 an…
Curriculum Guidelines for Undergraduate Programs in Data Science
Richard De Veaux, Mahesh Agarwal, Maia Averett +22
The Park City Math Institute (PCMI) 2016 Summer Undergraduate Faculty Program met for the purpose of composing guidelines for undergraduate programs in Data Science. The group cons…
Markov processes with product-form stationary distribution
Krzysztof Burdzy, David White
We study a class of Markov processes with finite state space and continuous time that have product form stationary distributions. We obtain a number of examples that can generate c…
Tracking the Spatiotemporal Spread of the Ohio Overdose Epidemic with Topological Data Analysis
Nicholas Bermingham, David White, Nathan Willey
In recent years, techniques from Topological Data Analysis (TDA) have proven effective at capturing spatial features of multidimensional data. However, applying TDA to spatiotempor…
On Colimits and Model Structures in Various Categories of Manifolds
David White
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 fin…
Smith Ideals of Operadic Algebras in Monoidal Model Categories
David White, Donald Yau
Building upon Hovey's work on Smith ideals for monoids, we develop a homotopy theory of Smith ideals for general operads in a symmetric monoidal category. For a sufficiently nice s…
A Generalization of Ripley's K Function for the Detection of Spatial Clustering in Areal Data
Stella Self, Anna Overby, Anja Zgodic +3
Spatial clustering detection has a variety of applications in diverse fields, including identifying infectious disease outbreaks, assessing land use patterns, pinpointing crime hot…
Model structures on operads and algebras from a global perspective
Michael Batanin, Florian De Leger, David White
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 o…
Substitudes, Bousfield localization, higher braided operads, and Baez-Dolan stabilization
David White
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…
Modeling Social Systems: Transparency, Reproducibility, and Responsibility
Maximino Aldana, Roni Barak Ventura, Heather Z. Brooks +13
Mathematical models of complex social systems can enrich social scientific theory, inform interventions, and shape policy. From voting behavior to economic inequality and urban dev…
Exploring the Intersection between Neural Architecture Search and Continual Learning
Mohamed Shahawy, Elhadj Benkhelifa, David White
Despite the significant advances achieved in Artificial Neural Networks (ANNs), their design process remains notoriously tedious, depending primarily on intuition, experience and t…