Mathematical Sciences
Permanent URI for this communityhttps://scholarworks.montana.edu/handle/1/48
Mathematical research at MSU is focused primarily on related topics in pure and applied mathematics. Research programs complement each other and are often applied to problems in science and engineering. Research in statistics encompasses a broad range of theoretical and applied topics. Because the statisticians are actively engaged in interdisciplinary work, much of the statistical research is directed toward practical problems. Mathematics education faculty are active in both qualitative and quantitative experimental research areas. These include teacher preparation, coaching and mentoring for in-service teachers, online learning and curriculum development.
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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 Mapping the number of female sex workers in countries across sub-Saharan Africa(Proceedings of the National Academy of Sciences, 2023-01) Laga, Ian; Niu, Xiaoyue; Rucinski, Katherine; Baral, Stefan; Rao, Amrita; Chen, David; Viswasam, Nikita; Phaswana-Mafuya, Nancy Refilwe; Diouf, Daouda; Sabin, Keith; Zhao, Jinkou; Eaton, Jeffrey W.; Bao, LeFemale sex workers (FSW) are affected by individual, network, and structural risks, making them vulnerable to poor health and well-being. HIV prevention strategies and local community-based programs can rely on estimates of the number of FSW to plan and implement differentiated HIV prevention and treatment services. However, there are limited systematic assessments of the number of FSW in countries across sub-Saharan Africa to facilitate the identification of prevention and treatment gaps. Here we provide estimated population sizes of FSW and the corresponding uncertainties for almost all sub-national areas in sub-Saharan Africa. We first performed a literature review of FSW size estimates and then developed a Bayesian hierarchical model to synthesize these size estimates, resolving competing size estimates in the same area and producing estimates in areas without any data. We estimated that there are 2.5 million (95% uncertainty interval 1.9 to 3.1) FSW aged 15 to 49 in sub-Saharan Africa. This represents a proportion as percent of all women of childbearing age of 1.1% (95% uncertainty interval 0.8 to 1.3%). The analyses further revealed substantial differences between the proportions of FSW among adult females at the sub-national level and studied the relationship between these heterogeneities and many predictors. Ultimately, achieving the vision of no new HIV infections by 2030 necessitates dramatic improvements in our delivery of evidence-based services for sex workers across sub-Saharan Africa.Item A Correlated Network Scale-up Model: Finding the Connection Between Subpopulations(Informa UK Limited, 2023-01) Laga, Ian; Bao, Le; Niu, XiaoyueAggregated relational data (ARD), formed from “How many X’s do you know?” questions, is a powerful tool for learning important network characteristics with incomplete network data. Compared to traditional survey methods, ARD is attractive as it does not require a sample from the target population and does not ask respondents to self-reveal their own status. This is helpful for studying hard-to-reach populations like female sex workers who may be hesitant to reveal their status. From December 2008 to February 2009, the Kiev International Institute of Sociology (KIIS) collected ARD from 10,866 respondents to estimate the size of HIV-related groups in Ukraine. To analyze this data, we propose a new ARD model which incorporates respondent and group covariates in a regression framework and includes a bias term that is correlated between groups. We also introduce a new scaling procedure utilizing the correlation structure to further reduce biases. The resulting size estimates of those most-at-risk of HIV infection can improve the HIV response efficiency in Ukraine. Additionally, the proposed model allows us to better understand two network features without the full network data: 1. What characteristics affect who respondents know, and 2. How is knowing someone from one group related to knowing people from other groups. These features can allow researchers to better recruit marginalized individuals into the prevention and treatment programs. Our proposed model and several existing NSUM models are implemented in the networkscaleup R package.