Scholarly Work - Mathematical Sciences
Permanent URI for this collectionhttps://scholarworks.montana.edu/handle/1/8719
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Item Network topology and interaction logic determine states it supports(Springer Science and Business Media LLC, 2024-08) Gedeon, TomášIn this review paper we summarize a recent progress on the problem of describing range of dynamics supported by a network. We show that there is natural connection between network models consisting of collections of multivalued monotone boolean functions and ordinary differential equations models. We show how to construct such collections and use them to answer questions about prevalence of cellular phenotypes that correspond to equilibria of network models.Item Sleep duration, napping behaviors and restless legs syndrome during pregnancy and the trajectories of ultrasonographic measures of fetal growth: Findings from the NICHD Fetal Growth Studies–Singletons(Elsevier BV, 2024) Na, Muzi; Shetty, Samidha Sudhakar; Niu, Xiaoyue; Hinkle, Stefanie N.; Zhang, Cuilin; Gao, XiangObjectives. Given the plausible mechanisms and the lacking of empirical evidence, the study aims to investigate how gestational sleep behaviors and the development of sleep disorders, such as restless legs syndrome, influence ultrasonographic measures of fetal growth. Methods. The study included 2457 pregnant women from the NICHD Fetal Growth Studies - Singletons (2009-2013), who were recruited between 8-13 gestational weeks and followed up to five times during pregnancy. Women were categorized into six groups based on their total sleep hours and napping frequency. The trajectory of estimated fetal weight from 10-40 weeks was derived from three ultrasonographic measures. Linear mixed effect models were applied to model the estimated fetal weight in relation to self-reported sleep-napping behaviors and restless legs syndrome status, adjusting for age, race and ethnicity, education, parity, prepregnancy body mass index category, infant sex, and prepregnancy sleep-napping behavior. Results. From enrollment to near delivery, pregnant women’s total sleep duration and nap frequency declined and restless legs syndrome symptoms frequency increased generally. No significant differences in estimated fetal weight were observed by sleep-napping group or by restless legs syndrome status. Results remained similar in sensitivity analyses and stratified analyses by women’s prepregnancy body mass index category (normal vs. overweight/obese) or by infant sex. Conclusions. Our data indicate that there is no association between sleep during pregnancy—assessed as total sleep duration and napping frequency, nor restless legs syndrome symptoms—and fetal growth from weeks 10 to 40 in healthy pregnant women.Item Lattice structures that parameterize regulatory network dynamics(Elsevier BV, 2024-08) Gedeon, TomášWe consider two types of models of regulatory network dynamics: Boolean maps and systems of switching ordinary differential equations. Our goal is to construct all models in each category that are compatible with the directed signed graph that describe the network interactions. This leads to consideration of lattice of monotone Boolean functions (MBF), poset of non-degenerate MBFs, and a lattice of chains in these sets. We describe explicit inductive construction of these posets where the induction is on the number of inputs in MBF. Our results allow enumeration of potential dynamic behavior of the network for both model types, subject to practical limitation imposed by the size of the lattice of MBFs described by the Dedekind number.Item Modeling of the daily dynamics in bike rental system using weather and calendar conditions: A semi-parametric approach(Elsevier BV, 2024-06) Odoom, Christopher; Boateng, Alexander; Mensah, Sarah Fobi; Maposa, DanielThis study proposes a more robust methodological approach to modeling the effect of weather and calendar variables on the number of bike rentals. We employ penalized splines quasi-Poisson regression (a semi-parametric model), which involves some form of regularization, like those used in lasso, ridge, and other types of parametric regularization models. We demonstrate that this modeling approach reveals hidden relationships that a pure parametric model fails to identify. The findings show that visibility, windspeed, season, working day, and year all significantly impact bike rentals. Increased rentals are associated with increased visibility and lower wind speed. Rentals are negatively affected by the spring and winter seasons, while working days and the year show positive trends except in a few cases. The analysis of rentals by registered and casual users reveals similar patterns, though the magnitudes of the effects differ. These findings highlight the importance of considering weather and calendar variables when managing and promoting bike-sharing services. The study has implications for bike-sharing system operators and policymakers, suggesting strategies such as improving visibility and wind protection, seasonally tailoring promotional campaigns, targeting non-working days for casual users, and adapting to changing user demands. The study adds to our understanding of the factors that influence bike rentals and provides suggestions for improving the utilization and accessibility of bike-sharing systems.Item Net Primary Production of Ecoregions Across North America in Response to Drought and Wildfires From 2015 to 2022(American Geophysical Union, 2024-04) Potter, Christopher; Pass, Stephanie; Ulrich, RachelEcosystem models are valuable tools to make climate-related assessments of change when ground-based measurements of water and carbon fluxes are not adequate to realistically capture regional variability. The Carnegie-Ames-Stanford Approach (CASA) is one such model based on satellite observations of monthly vegetation cover to estimate net primary production (NPP) of terrestrial ecosystems. CASA model predictions from 2015 to 2022 revealed several notable high and low periods in growing season NPP totals in certain biomes. Both Temperate Broadleaf and Boreal Forest production shifted from relatively high average NPP values in 2015 through 2019 to lower levels in 2020, typically representing a loss of 10%–14% of growing season NPP flux. This rapid decline in growing season NPP from 2019 to 2020–2021 was also estimated for the Temperate Grasslands and Savanna, Temperate Conifer Forest, and Tundra biomes. In contrast to the climate patterns in the temperate biomes that developed into severe widespread drought in 2020 and 2021 due to low precipitation totals and extreme hot temperatures, growing season NPP in the Tundra biome was depressed in these same years by colder temperature induced drought conditions at the high latitudes of North America. Drought severity classes were closely associated with different levels of decline in NPP in most biomes. Trends in NPP in areas of the largest wildfires in North America that burned between 2012 and 2021 were examined to assess recovery of vegetation and the resiliency of ecosystems during extreme drought periods.Item Variable-coefficient parabolic theory as a high-dimensional limit of elliptic theory(Springer Science and Business Media LLC, 2024-01) Davey, Blair; Vega Garcia, Mariana SmitThis paper continues the study initiated in Davey (Arch Ration Mech Anal 228:159–196, 2018), where a high-dimensional limiting technique was developed and used to prove certain parabolic theorems from their elliptic counterparts. In this article, we extend these ideas to the variable-coefficient setting. This generalized technique is demonstrated through new proofs of three important theorems for variable-coefficient heat operators, one of which establishes a result that is, to the best of our knowledge, also new. Specifically, we give new proofs of L2 → L2 Carleman estimates and the monotonicity of Almgren-type frequency functions, and we prove a new monotonicity of Alt–Caffarelli–Friedman-type functions. The proofs in this article rely only on their related elliptic theorems and a limiting argument. That is, each parabolic theorem is proved by taking a high-dimensional limit of a related elliptic result.Item Joint Spatial Modeling Bridges the Gap Between Disparate Disease Surveillance and Population Monitoring Efforts Informing Conservation of At-risk Bat Species(Springer Science and Business Media LLC, 2024-02) Stratton, Christian; Irvine, Kathryn M.; Banner, Katharine M.; Almberg, Emily S.; Bachen, Dan; Smucker, KristinaWhite-Nose Syndrome (WNS) is a wildlife disease that has decimated hibernating bats since its introduction in North America in 2006. As the disease spreads westward, assessing the potentially differential impact of the disease on western bat species is an urgent conservation need. The statistical challenge is that the disease surveillance and species response monitoring data are not co-located, available at different spatial resolutions, non-Gaussian, and subject to observation error requiring a novel extension to spatially misaligned regression models for analysis. Previous work motivated by epidemiology applications has proposed two-step approaches that overcome the spatial misalignment while intentionally preventing the human health outcome from informing estimation of exposure. In our application, the impacted animals contribute to spreading the fungus that causes WNS, motivating development of a joint framework that exploits the known biological relationship. We introduce a Bayesian, joint spatial modeling framework that provides inferences about the impact of WNS on measures of relative bat activity and accounts for the uncertainty in estimation of WNS presence at non-surveyed locations. Our simulations demonstrate that the joint model produced more precise estimates of disease occurrence and unbiased estimates of the association between disease presence and the count response relative to competing two-step approaches. Our statistical framework provides a solution that leverages disparate monitoring activities and informs species conservation across large landscapes. Stan code and documentation are provided to facilitate access and adaptation for other wildlife disease applications.Item Coding Code: Qualitative Methods for Investigating Data Science Skills(Informa UK Limited, 2023-11) Theobold, Allison S.; Wickstrom, Megan H.; Hancock, Stacey A.Despite the elevated importance of Data Science in Statistics, there exists limited research investigating how students learn the computing concepts and skills necessary for carrying out data science tasks. Computer Science educators have investigated how students debug their own code and how students reason through foreign code. While these studies illuminate different aspects of students’ programming behavior or conceptual understanding, a method has yet to be employed that can shed light on students’ learning processes. This type of inquiry necessitates qualitative methods, which allow for a holistic description of the skills a student uses throughout the computing code they produce, the organization of these descriptions into themes, and a comparison of the emergent themes across students or across time. In this article we share how to conceptualize and carry out the qualitative coding process with students’ computing code. Drawing on the Block Model to frame our analysis, we explore two types of research questions which could be posed about students’ learning. Supplementary materials for this article are available online.Item Ribosome Abundance Control in Prokaryotes(Springer Science and Business Media LLC, 2023-10) Shea, Jacob; Davis, Lisa; Quaye, Bright; Gedeon, TomasCell growth is an essential phenotype of any unicellular organism and it crucially depends on precise control of protein synthesis. We construct a model of the feedback mechanisms that regulate abundance of ribosomes in E. coli, a prototypical prokaryotic organism. Since ribosomes are needed to produce more ribosomes, the model includes a positive feedback loop central to the control of cell growth. Our analysis of the model shows that there can be only two coexisting equilibrium states across all 23 parameters. This precludes the existence of hysteresis, suggesting that the ribosome abundance changes continuously with parameters. These states are related by a transcritical bifurcation, and we provide an analytic formula for parameters that admit either state.Item Leveraging social networks for identification of people living with HIV who are virally unsuppressed(Wolters Kluwer Health, Inc., 2023-10) Cummins, Breschine; Johnson, Kara; Schneider, John A.; Del Vicchio, Natasha; Moshiri, Niema; Wertheim, Joel O.; Goyal, Ravi; Skaathun, BrittObjectives: This study investigates primary peer-referral engagement (PRE) strategies to assess which strategy results in engaging higher numbers of people living with HIV (PLWH) who are virally unsuppressed. Design: We develop a modeling study that simulates an HIV epidemic (transmission, disease progression, and viral evolution) over 6 years using an agent-based model followed by simulating PRE strategies. We investigate two PRE strategies where referrals are based on social network strategies (SNS) or sexual partner contact tracing (SPCT). Methods: We parameterize, calibrate, and validate our study using data from Chicago on Black sexual minority men to assess these strategies for a population with high incidence and prevalence of HIV. For each strategy we calculate the number of PLWH recruited who are undiagnosed or out-of-care and the number of direct or indirect transmissions. Results: SNS and SPCT identified 256.5 (95% C.I.: [234,279]) and 15 (95% C.I.: [7,27]) PLWH, respectively. Of these, SNS identified 159 (95% C.I.: [142,177]) PLWH out-of-care and 32 (95% C.I.: [21, 43]]) PLWH undiagnosed compared to 9 (95% C.I.: [3,18]) and 2 (95% C.I.: [0,5]) for SPCT. SNS identified 15.5 (95% C.I.: [6,25]) and 7.5 (95% C.I.: [2, 11]]) indirect and direct transmission pairs, while SPCT identified 6 (95% C.I.: [0,8]) and 5 (95% C.I.: [0,8]), respectively. Conclusions: With no testing constraints, SNS is the more effective strategy to identify undiagnosed and out-of-care PLWH. Neither strategy is successful at identifying sufficient indirect or direct transmission pairs to investigate transmission networks.