About

David Glickenstein is a faculty member in the Program in Applied Mathematics at the University of Arizona. His research interests include discrete differential geometry, geometric partial differential equations, convergence and compactness theorems in Riemannian geometry, Delaunay triangulations and their generalizations, and applications of differential geometry. He is engaged in exploring mathematical concepts and their applications within these areas, contributing to the advancement of knowledge in geometric analysis and related fields.

Research topics

• Mathematics
• Pure mathematics
• Mathematical analysis
• Computer science
• Geometry

Selected publications

• 0567 Acceptability of Sleep Interventions Among Firefighters

  SLEEP · 2025-05-01

  articleOpen access

  Abstract Introduction Insufficient sleep disproportionately imposes significant health risks to firefighters. However, access to evidence-based sleep interventions, such as cognitive behavioral therapy for insomnia (CBTi), remains limited in this population. To build a foundation for the implementation of worksite sleep health coaching in fire departments, this study assessed firefighters’ acceptability of nine CBTi-informed sleep interventions. Methods The Patient-Reported Outcomes Measurement Information System–Sleep Disturbance–Short Form 8b was used to screen for firefighters working 24-hour+ shifts who presented sleep disorder symptoms (T score ≥ 55). Eligible participants included 232 firefighters from 20 Arizona fire agencies who completed a cross-sectional online survey, which incorporated the Theoretical Framework of Acceptability measure to assess their perceived sleep intervention acceptability. Results Over half of the firefighters agreed or strongly agreed that the CBTi-informed sleep interventions were likable (percentage: 53%-74%), acceptable (61%-88%), and anticipated to be effective (54%-66%), except for timed exposure to ambient light and darkness, which only 35% liked and 42% perceived as effective. The top three interventions with the highest percentage of firefighters rating them as likable, acceptable, and being anticipated as effective were sleep education (64%, 88%, 58%), sleep extension (69%, 76%, 63%), and recovery sleep enhancement (74%, 80%, 66%). Interestingly, a higher percentage of firefighters also perceived sleep education (34%) and sleep extension (35%) as very effortful compared to other interventions (average: 23%). Firefighters with greater sleep symptoms were less likely to like sleep extension (Odds Ratio = 0.92, 95% CI = 0.87-0.98, p =.017) and recovery sleep enhancement (OR = 0.93, 95% CI = 0.87-0.99, p =.025) whereas more likely to perceive sleep education as effort-intensive (OR = 1.08, 95% CI = 1.02-1.14, p =.018). Conclusion A moderate to high percentage of firefighters demonstrated acceptability of the sleep interventions, with sleep education, sleep extension, and recovery sleep enhancement ranking the highest. Interestingly, sleep education and sleep extension were frequently viewed as acceptable despite being effort-intensive, highlighting the importance of assessing different dimensions of acceptability of sleep interventions. These findings suggest promise in translating these evidence-based interventions to the workplace to improve firefighter sleep health. Support (if any) Funded by the National Institutes of Health (R01HL162799).

  PublisherOA PDFDOI

• Persistent Classification: Understanding Adversarial Attacks by Studying Decision Boundary Dynamics

  Statistical Analysis and Data Mining The ASA Data Science Journal · 2025-01-21 · 2 citations

  articleOpen access

  ABSTRACT There are a number of hypotheses underlying the existence of adversarial examples for classification problems. These include the high‐dimensionality of the data, the high codimension in the ambient space of the data manifolds of interest, and that the structure of machine learning models may encourage classifiers to develop decision boundaries close to data points. This article proposes a new framework for studying adversarial examples that does not depend directly on the distance to the decision boundary. Similarly to the smoothed classifier literature, we define a (natural or adversarial) data point to be ( γ , σ)‐stable if the probability of the same classification is at least for points sampled in a Gaussian neighborhood of the point with a given standard deviation . We focus on studying the differences between persistence metrics along interpolants of natural and adversarial points. We show that adversarial examples have significantly lower persistence than natural examples for large neural networks in the context of the MNIST and ImageNet datasets. We connect this lack of persistence with decision boundary geometry by measuring angles of interpolants with respect to decision boundaries. Finally, we connect this approach with robustness by developing a manifold alignment gradient metric and demonstrating the increase in robustness that can be achieved when training with the addition of this metric.

  PublisherOA PDFDOI

• 1345 Contextual Predictors of Sleep Coaching Program Acceptability Among Fire Service Workers

  SLEEP · 2025-05-01

  articleOpen access

  Abstract Introduction Sleep disorders are common in the fire service, yet few agencies have adopted evidence-based sleep health workplace wellness programs to address them. As part of the pre-implementation formative assessment, this project aimed to identify theoretically informed contextual factors that predict the acceptability of a new sleep health coaching wellness program among workers in approximately 20 Arizona fire agencies. Methods Cross-sectional survey data were analyzed from non-manager fire service personnel (n=145). Program acceptability was measured via the Acceptability of Intervention Measure. Contextual factors were measured using the Organizational Readiness for Change Assessment (ORCA) subscales, which include culture among captains, culture among senior leadership, leadership, measurement, readiness for change among opinion leaders, and resources. The ORCA instrument aligns with the integrated Promoting Action on Research Implementation in Health Services (i-PARIHS) framework for implementation. Linear regression was used to examine which contextual factors predicted intervention acceptability. Results A total of 145 firefighters and paramedics participated in the survey (M age = 38.89 years, SD = 9.35 years); the average time worked at the current place of employment was 10.17 years (SD = 9.35). Findings indicated that higher readiness for change among opinion leaders was significantly associated with greater program acceptability ratings (β= 0.05, SE = 0.02, p < 0.001). Leadership contextual factors generally did not predict program acceptability, except for culture among senior leadership. Worse evaluations of culture among senior leadership were associated with higher ratings of program acceptability (β = -0.06, SE = 0.03, p < 0.05). Conclusion Opinion leaders, including union members, are key champions for promoting the adoption of sleep health coaching in the fire service. There was no relationship between intervention acceptability and resources or other leadership variables, except for the negative culture of senior leadership. These findings highlight the importance of using measures, such as ORCA, that align with theory-informed implementation frameworks like i-PARIHS, to identify key facilitators and potential barriers to successful implementation in occupational settings. Support (if any) National Heart, Lung, and Blood Institute (R01HL162799)

  PublisherOA PDFDOI

• Persistent Classification: A New Approach to Stability of Data and Adversarial Examples

  arXiv (Cornell University) · 2024-04-11

  preprintOpen access

  There are a number of hypotheses underlying the existence of adversarial examples for classification problems. These include the high-dimensionality of the data, high codimension in the ambient space of the data manifolds of interest, and that the structure of machine learning models may encourage classifiers to develop decision boundaries close to data points. This article proposes a new framework for studying adversarial examples that does not depend directly on the distance to the decision boundary. Similarly to the smoothed classifier literature, we define a (natural or adversarial) data point to be $(γ,σ)$-stable if the probability of the same classification is at least $γ$ for points sampled in a Gaussian neighborhood of the point with a given standard deviation $σ$. We focus on studying the differences between persistence metrics along interpolants of natural and adversarial points. We show that adversarial examples have significantly lower persistence than natural examples for large neural networks in the context of the MNIST and ImageNet datasets. We connect this lack of persistence with decision boundary geometry by measuring angles of interpolants with respect to decision boundaries. Finally, we connect this approach with robustness by developing a manifold alignment gradient metric and demonstrating the increase in robustness that can be achieved when training with the addition of this metric.

  PublisherOA PDFDOI

• An Exact Kernel Equivalence for Finite Classification Models

  arXiv (Cornell University) · 2023-08-01 · 1 citations

  preprintOpen access

  We explore the equivalence between neural networks and kernel methods by deriving the first exact representation of any finite-size parametric classification model trained with gradient descent as a kernel machine. We compare our exact representation to the well-known Neural Tangent Kernel (NTK) and discuss approximation error relative to the NTK and other non-exact path kernel formulations. We experimentally demonstrate that the kernel can be computed for realistic networks up to machine precision. We use this exact kernel to show that our theoretical contribution can provide useful insights into the predictions made by neural networks, particularly the way in which they generalize.

  PublisherOA PDFDOI

• 0023 Circadian fragmentation and stability distinguish employment status

  SLEEP · 2023-05-01 · 1 citations

  articleOpen access1st authorCorresponding

  Abstract Introduction This analysis used data from the Assessing Daily Activity Patterns Through Occupational Transitions (ADAPT) study to compare differences in employment status on activity variability, as an indicator of circadian fragmentation and stability. Circadian fragmentation refers to frequency of alterations between rest and activity relative to the daily rhythm and stability refers to day-to-day similarity. High fragmentation and low stability have been linked to a number of negative health outcomes including depression, obesity, and heightened mortality risk. Methods The sample consisted of 155 participants that included 702 total cases (n = 434 employed, n = 268 unemployed) assessed over 18 months. Participants were required to have involuntarily lost their jobs in the last 90 days. Employment status was determined for all participants at each visit based on demographic surveys. Daily activity patterns were assessed via actigraphy (Actiwatch-Spectrum) at 30 second epochs for 14 days. The nonparametric measures of intradaily variability (IV) and interdaily stability (IS) were used as measures of circadian fragmentation and stability. Several subsampling intervals were considered for IV, ranging from 5 minutes to 4 hours. Results Unemployment was associated with higher IV (for 1 hour subsampling intervals, t=5.23, p < .001) and lower IS than employment (t=2.38, p <.05). The same is true with changes in the subsampling interval for IV, with highest significance at 45 minutes to 1.5 hours. Significant findings remained even for 5 minute (t=2.15, p < .05) and 4 hour (t = 4.07, p<.001) intervals. Conclusion In a sample of adults with variable employment status, employment was associated with less circadian fragmentation and more stability than unemployment. These findings suggest that circadian fragmentation and instability may be two mechanisms by which job loss increases negative health risk. Future planned studies examining prospective changes in circadian fragmentation/stability during employment transitions will help answer this question. Support (if any) NIH #1R01HL117995-01A1, NSF DMS 1937229, NSF CCF 1740858

  PublisherOA PDFDOI

• Effects of sleep on breakfast behaviors in recently unemployed adults

  Sleep Health · 2023-11-14 · 3 citations

  articleOpen access
  PublisherOA PDFDOI

• Geometric triangulations and discrete Laplacians on manifolds: An update

  Computational Geometry · 2023-10-29 · 2 citations

  article1st authorCorresponding
  PublisherDOI

• The impact of social rhythm and sleep disruptions on waist circumference after job loss: A prospective 18‐month study

  Obesity · 2022-09-05 · 1 citations

  articleOpen access

  OBJECTIVE: This study prospectively examined change in waist circumference (WC) as a function of daily social rhythms and sleep in the aftermath of involuntary job loss. It was hypothesized that disrupted social rhythms and fragmented/short sleep after job loss would independently predict gains in WC over 18 months and that resiliency to WC gain would be conferred by the converse. METHODS: Eligible participants (n = 191) completed six visits that included standardized measurements of WC. At the baseline visit, participants completed the social rhythm metric and daily sleep diary and wore an actigraph on their nondominant wrist each day for a period of 2 weeks. RESULTS: When controlling for obesity and other covariates, WC trajectories decreased for individuals with more consistent social rhythms, more activities in their sdiocial rhythms, and higher sleep quality after job loss. WC trajectories did not change for individuals with lower scores on these indicators. CONCLUSIONS: The frequency and consistency of social rhythms after job loss play a key role in WC loss. These findings support the implementation of social rhythm interventions after job loss, a potentially sensitive time for the establishment of new daily routines that have an impact on metabolic health.

  PublisherOA PDFDOI

• 0139 Work Duration Affects How Prior-Night Sleep Predicts Next-Day Energy Expenditure in Emergency Response System Telecommunicators

  SLEEP · 2022-05-25

  articleOpen access

  Abstract Introduction ERS telecommunicators are the first of the first responders challenged with solving complex, time-sensitive problems while managing workplace presence. Very little is known about sleep, work, and lifestyle factors among workers in this industry. One study demonstrated that 85% of ERS telecommunicators are overweight, suggesting that job-related factors may place these workers at risk for sedentary lifestyles. To test this hypothesis, we examined whether 14 day total work duration moderated the daily relationship between prior-night total sleep time and next day energy expenditure. Methods Over the course of 14 days (M = 6.9 days on-shift; SD = 1.9 days), 47 ERS telecommunicators were instructed to (a) wear actigraphs on their waist to gather estimates of average energy expenditure (EE, kcal/hour), (b) wear actigraphs on their wrist to gather estimates of total sleep time (min), and (c) complete daily shift logs to gather information about work duration (hours). Mixed linear modeling was employed to examine whether prior night within-subject total sleep time (TST) predicted next day energy expenditure, as moderated by between-subject work hours (n = 525 cases). Results A significant cross-level Work Duration x TST interaction (Estimate = .007, SE = .002, p < .001, 95% CI [.003, .011]) indicated that less prior-night TST was associated with less next-day EE among telecommunicators who worked more hours over the last 14 days. Conversely, telecommunicators who worked fewer hours expended more energy per hour the next day when they slept less than usual. Simple effects indicated that for each extra 102 minutes sleep (+1 SD), telecommunicators expended 5 kcal/hr (90 kcal over 18 hours awake). These results remained stable when controlling for between-subject differences in sleep and within-subject changes in work duration, night-shift work, and other relevant covariates. Conclusion The effect of total sleep time on next-day EE is unique to each telecommunicator’s typical sleep levels and the total hours worked over the course of two weeks. These two risk factors operate on EE as a function of one another. Findings provide support for the implementation of policy-level intervention to minimize chronic overwork and individual-level intervention to support sleep prioritization. Support (If Any) UA Canyon Ranch Center for Health Promotion and Treatment

  PublisherOA PDFDOI

Recent grants

• CAREER: Discrete and Generalized Riemannian Geometry and Curvature Flows

  NSF · $402k · 2008–2016

• FRG: Collaborative Research: Geometric and Topological Methods for Analyzing Shapes

  NSF · $284k · 2018–2024

Frequent coauthors

• Bennett Chow

  53 shared

• Tom Ivey

  College of Charleston

  48 shared

• James Isenberg

  University of Oregon

  48 shared

• Christine Guenther

  Pacific University

  48 shared

• Dan Knopf

  48 shared

• Sun-Chin Chu

  National Chung Cheng University

  47 shared

• Lei Ni

  40 shared

• Feng Luo

  East China University of Technology

  23 shared

Labs

• Program in Applied MathematicsPI