Statistics and Probability Commons^™

Optimized Hiv/Aids Resource Allocation In Ohio: A Linear Programming Approach, Godfred Ahenkroa Kesse

Data Science and Data Mining

This study employs a linear and integer programming approach to optimize HIV resource allocation in Ohio, aiming to minimize new infections and enhance the impact of limited resources. With the advances in HIV prevention and treatment, Ohio faces challenges in addressing disparities in access to healthcare, particularly among high-risk populations. The proposed model integrates data on infection rates, transmission patterns, demographic factors, and cost-effectiveness to provide a decision-support framework for policymakers. Using epidemiological data and equity constraints, the model prioritizes high-risk regions and populations while ensuring fair resource distribution. Results indicate that increased funding allocations significantly enhance the potential to …

Fourier Series For Singular Measures In Higher Dimensions, Chad Berner, John E. Herr, Palle E.T. Jorgensen, Eric S. Weber

Mathematics and Statistics Faculty Research & Creative Works

For multi-variable finite measure spaces, we present in this paper a new framework for non-orthogonal L2 Fourier expansions. Our results hold for probability measures μ with finite support in Rd that satisfy a certain disintegration condition that we refer to as "slice-singular". In this general framework, we present explicit L2(μ)-Fourier expansions, with Fourier exponentials having positive Fourier frequencies in each of the d coordinates. Our Fourier representations apply to every f∈L2(μ), are based on an extended Kaczmarz algorithm, and use a new recursive μ Rokhlin disintegration representation. In detail, our Fourier series expansion for f is in terms of the …

Robust Conic Satisficing, Arjun Ramachandra, Napat Rujeerapaiboon, Melvyn Sim

Working Papers

In practical optimization problems, we typically model uncertainty as a random variable though its true probability distribution is unobservable to the decision maker. Historical data provides some information of this distribution that we can use to approximately quantify the risk of an evaluation function that depends on both our decision and the uncertainty. This empirical optimization approach is vulnerable to the issues of overfitting, which could be overcome by several data-driven robust optimization techniques. To tackle overfitting, Long et al. (2022) propose a robust satisficing model, which is specified by a performance target and a penalty function that measures the …

Visualizing The Rise Of American Women's Soccer, Hoi Wah Tang

Dissertations, Theses, and Capstone Projects

The rise of American women’s soccer is a compelling narrative of determination, talent, and triumph on the global stage. From the inaugural FIFA Women’s World Cup in 1991 to the ongoing dominance of the U.S. Women’s National Team (USWNT), this journey encapsulates not only athletic excellence but also the broader struggles for equality, representation, and respect in sports.

This project aims to bring this story to life by presenting a rich tapestry of data visualizations, timelines, and multimedia elements that showcase key moments, players, and milestones. Through engaging graphics and interactive features, users will explore how the sport evolved, the …

Chatgpt Didn’T Write This: Evaluating The Impact Of Llms With A Case Study In Grading Cuny Language Immersion Program Student Essays, Benjamin Inbar

Dissertations, Theses, and Capstone Projects

This study evaluates the capabilities and limitations of large language models (LLMs), specifically OpenAI’s ChatGPT-4o, in grading essays from students in the City University of New York’s Language Immersion Program. The program serves English language learners with diverse linguistic and demographic backgrounds, offering intensive language instruction to prepare students for academic success in college. Using a dataset of 30 pre- and post-program essays scored by program instructors and ChatGPT-4o under three paradigms, this research explores the alignment between human and AI-generated scores across five rubric-based competency areas. Findings reveal that ChatGPT-4o aligns moderately with human grading, with the strongest agreement …

Childhood Sexual Trauma, Substance Use, And Antiretroviral Therapy Adherence Among Older Adults Living With Hiv: A Mediational Analysis, Monique J. Brown, Josie Zhang, Prince Nii Ossah Addo, Amandeep Kaur, Daniel Amoatika, Elizabeth L. Crouch Ph.D., Steven A. Cohen

Faculty Publications

Childhood sexual abuse (CSA) is linked to substance use and lower antiretroviral therapy (ART) adherence. However, studies examining the mediational role of substance use between CSA and ART adherence are lacking. Therefore, the aim of this study was to determine the potential mediational role of substance use between CSA and ART adherence among older adults living with HIV (OALH) (n = 91). Mediation analyses assessed the direct and indirect relationships between CSA, substance use, and ART adherence. Statistically significant differences existed in substance use by gender (male vs. female: 12.3 vs. 9.97) and ART adherence by race (Black vs. …

Bayesian Belief Networks: Redefining Wholesale Electricity Price Modelling In High Penetration Non-Firm Renewable Generation Power Systems, Martin J. Maticka, Thair S. Mahmoud

Research outputs 2022 to 2026

The transition of electricity generation from firm to non-firm renewable generation is driving changes in wholesale electricity price dynamics that are increasingly challenging to model due to the stochastic nature of wind and solar as the primary energy source. Robust pricing models are essential for optimising financial performance in liberalised electricity markets. The novelty of this paper is the application of Bayesian Belief Networks in the modelling of wholesale electricity price formation, specifically in power systems with a high penetration of non-firm renewable generation. This paper links the mathematical Bayesian representation to established statistical and computational approaches using a functional …

An Investigation Of Travel Distance And Timeliness Of Breast Cancer Treatment Among A Diverse Cohort In The United States, Swann Arp Adams, Oluwole Adeyemi Babatunde, Whitney Zahnd, Peiyin Hung, Karen E. Wickersham, Nathaniel Bell Ph.D., Jan M. Eberth Ph.D.

Publications

Travel to and from distant cancer treatment facilities can place a significant burden on cancer patients, particularly rural and minority survivors. Thus, the purpose of our investigation was to examine the association between patient travel distance and delays in types of treatment for breast cancer (surgery, radiation, chemotherapy, and hormonal therapy) and treatment delays. Using a novel linkage between the state cancer registry and administrative data from Medicaid and a private insurance plan, 2155 BC patients were successfully linked to create the cohort. ArcGIS was used to geocode all case residences and treatment facility addresses and calculate network distance between …

Ethnic Disparities In Hba1c And Hypoglycemia Among Youth With Type 1 Diabetes: Beyond Access To Technology, Social Deprivation And Mean Blood Glucose, J. Pemberton, Zhide Fang, Stuart Chalew, S. Uday

School of Public Health Faculty Publications

Introduction The UK national pediatric diabetes audit reports higher HbA1c for children and young people (CYP) with type 1 diabetes (T1D) of Black ethnicity compared with White counterparts. This is presumably related to higher mean blood glucose (MBG) due to lower socioeconomic status (SES) and less access to technology. We aimed to determine if HbA1c ethnic disparity persists after accounting for the above variables. Research design and methods A retrospective analysis of participants who received structured education in continuous glucose monitoring (CGM) use was conducted at a tertiary center. HbA1c was paired with glucose metrics from 90-day CGM data. The …

Racial Disparities Of Type 2 Diabetes Through Exercise: The Multi-Ethnic Study Of Atherosclerosis, Tong Xia, Roch A. Nianogo, Qingzhao Yu, Tamara Horwich, Preethi Srikanthan, Kosuke Inoue, Matthew Allison, Zuo-Feng Zhang, Karol E. Watson, Liwei Chen

School of Public Health Faculty Publications

Introduction: Persistent racial and ethnic disparities exist for Type 2 diabetes in the U.S. Racial and ethnic minorities have a higher risk of Type 2 diabetes, and studies suggest that they engage in less exercise than White population. This study examined whether and to what degree racial differences in Type 2 diabetes were explained by exercise. Methods: Adults aged 45–84 years without Type 2 diabetes at baseline (2000–2002) were included from the Multi-Ethnic Study of Atherosclerosis cohort and followed through 2020. Associations between race and Type 2 diabetes were examined using multivariable Cox proportional hazard regression. The effects of exercise …

Meditation In Qualitative Research For Bracketing And Beyond, Katalin Grajzel

Research Methods and Statistics: Graduate Student Scholarship

In this study, I recounted my experience using mantra meditation during a phenomenological study for the purposes of bracketing. The efficacy and purpose of bracketing have been debated from Husserl (1931), whose aimed was to achieve objectivity, to Heidegger (1962) who advocated for immersion of the researcher, through the French school (Merleau-Ponty, 1964) of middle ground, by whom bracketing was seen as the process to unearth and suspend biases for the better understanding of participants’ experiences (Arsel, 2017; Creswell & Creswell, 2017; Creswell & Poth, 2016; Fischer & Guzel, 2023). In this study, however, I propose another approach to bracketing …

Associations Between Social Determinants Of Health And Mental Health Disorders Among U.S. Population: A Cross-Sectional Study, S. Tanarsuwongkul

Faculty Publications

Aims

The impact of social determinants of health (SDOH) on mental health is increasingly realized. A comprehensive study examining the associations of SDOH with mental health disorders has yet to be accomplished. This study evaluated the associations between five domains of SDOH and the SDOH summary score and mental health disorders in the United States.

Methods

We analyzed data from a diverse group of participants enrolled in the All of Us research programme, a research programme to gather data from one million people living in the United States, in a cross-sectional design. The primary exposure was SDOH based on Healthy …

Kroger Post-Pandemic Customer Segmentation, Mario Mata, Joey Truitt, Renn Spigelmyer, Dhanuja Kasturiratna, Lisa Holden, Nitish Baidya, Hanna Tafari

Posters-at-the-Capitol

The grocery retail industry landscape has changed greatly in the wake of the pandemic. Specifically, delivery and pickup services have become more popular and customer buying habits have evolved. At the same time, improvements in data collection and analysis have allowed grocery marketing strategies to become highly individualized.

We worked with 84.51, an analytics firm, to identify customer segments for the Kroger Company based on data from 2023. Using clustering techniques, we organized customers into groups, or segments, based on similar characteristics. We identified and profiled four distinct groups of customers. Three segments were characterized by high frequency and spending …

Supplementary Files For: "Structure Identification For High-Dimensional Data In The Vicinity Of Bear Lake", Ben Shaw, Haley Burger, Brennan Bean, Kevin Moon

Browse all Datasets

This report focuses on seven water quality measurements taken at 43 different depths on the Bear Lake for the months of June - November in the years 2018 - 2023. These measurements create a high-dimensional dataset on which we apply state-of-the-art machine learning (ML) techniques to look for low-dimensional structure in the data. A similar effort was made for weather measurements taken near the lake. Our analysis revealed that water quality measurements tend to cluster (i.e., group together) by year, while weather measurements tend to cluster by time of the year. This suggests that the structure observed in the water …

Massera’S Theorem On Arbitrary Discrete Time Domains, Martin Bohner, Jaqueline G. Mesquita, Sabrina Streipert

Mathematics and Statistics Faculty Research & Creative Works

We present a general version of Massera's theorems for arbitrary discrete domains, based on a newly introduced definition for both linear and nonlinear equations. For scalar nonlinear equations, we identify sufficient conditions that ensure each µ-bounded solution approaches a periodic solution asymptotically. In the case of linear systems, we prove that the presence of a µ-bounded solution necessarily leads to a periodic solution. We also provide some examples to show the practical implications of our findings.

A Monte Carlo Study Of The Efficacy Of The Mantel-Haenszel Method At Detecting Item Bias, Macy Daulton

Masters Theses & Specialist Projects

The Mantel-Haenszel (MH) method is a statistical method used for differential item functioning analysis. Previous differential item functioning (DIF) research of the MH method focused on Type I error rates and statistical power. Not yet studied in the literature is whether excessive numbers of biased items may cause the MH method to fail to identify biased items. The proposed study employed a Monte Carlo design to determine the extent of bias in the match items necessary for the MH method to fail to identify a biased item. Results showed that the threshold was greater than was hypothesized, requiring nearly all …

On The Hölder Continuity Of The Brascamp-Lieb Constant, Ori Friesen

Mathematics, Statistics, and Computer Science Honors Projects

The Brascamp-Lieb inequality is a generalization of many well-known multilinear functional inequalities. The Brascamp-Lieb constant is the best constant that works for the Brascamp-Lieb inequality for a given tuple of input linear maps and powers. If we keep the powers constant while varying the input linear maps, the Brascamp-Lieb constant becomes a function of the linear maps. In this thesis, we explore the Hölder continuity of the Brascamp-Lieb constant. Specifically,we prove that the general 4-linear case of the Brascamp-Lieb inequality is locally Lipschitz continuous. Additionally, we provide an improvement of a previous result on the local Hölder continuity of the …

Estimation And Model Misspecification For Recurrent Event Data With Covariates Under Measurement Errors, Ravinath Alahakoon, Gideon K.D. Zamba, Xuerong Meggie Wen, Akim Adekpedjou

Mathematics and Statistics Faculty Research & Creative Works

For subject i, we monitor an event that can occur multiple times over a random observation window [0, (Formula presented.)). At each recurrence, p concomitant variables, (Formula presented.), associated to the event recurrence are recorded—a subset ((Formula presented.)) of which is measured with errors. To circumvent the problem of bias and consistency associated with parameter estimation in the presence of measurement errors, we propose inference for corrected estimating equations with well-behaved roots under an additive measurement errors model. We show that estimation is essentially unbiased under the corrected profile likelihood for recurrent events, in comparison to biased estimations under a …

Multi-Valued Variational Inequalities For Variable Exponent Double Phase Problems: Comparison And Extremality Results, Siegfried Carl, Vy Khoi Le, Patrick Winkert

Mathematics and Statistics Faculty Research & Creative Works

We prove existence and comparison results for multi-valued variational inequalities in a bounded domain Ω of the form (Formula presented.) where A:W1,H(Ω)→W1,H(Ω)∗ given by (Formula presented.) for u∈W1,H(Ω), is the double phase operator with variable exponents and W1,H(Ω) is the associated Musielak–Orlicz Sobolev space. First, an existence result is proved under some weak coercivity condition. Our main focus aims at the treatment of the problem under consideration when coercivity fails. To this end we establish the method of sub–super-solution for the multi-valued variational inequality in the space W1, H(Ω) based on appropriately defined sub- and super-solutions, which yields the existence …

Existence Results For A Discrete Fractional Boundary Value Problem, David Barilla, Martin Bohner, Giuseppe Caristi, Shapour Heidarkhani, Shahin Moradi

Mathematics and Statistics Faculty Research & Creative Works

In this study, we investigate the existence of at least one solution and the existence of an infinite number of solutions for a discrete fractional boundary value problem. Requiring an algebraic condition on the nonlinear term for small values of the parameter and requiring an additional asymptotical behavior of the potential at zero, we investigate the existence of at least one nontrivial solution for the problem. Moreover, under suitable assumptions on the oscillatory behavior of the nonlinearity at infinity, for exact collections of the parameter, we discuss the existence of a sequence of solutions for the problem. We also present …