Physical Sciences and Mathematics Commons^™

The Herzog-Takayama Resolution Over A Skew Polynomial Ring, Linoy Utkina

Theses and Dissertations

Let k be a field, and let I be a monomial ideal in the polynomial ring R = k[x1,..., xn]. In her thesis, Taylor introduced a complex that yields a finite free resolution of R/I as an R-module. Building on Taylor’s work, Ferraro, Martin, and Moore extended this construction to monomial ideals in skew polynomial rings. Because the Taylor resolution is typically not minimal, subsequent research efforts went into identifying specific classes of ideals whose minimal free resolutions can be constructed more simply. In 1990, Eliahou and Kervaire devised an approach for handling minimal resolutions of …

Camassa-Holm Type Equations And Multi-Peakon Solutions, Yonghong Chen

Theses and Dissertations

This thesis investigates the multi-peakon solutions of a class of Camassa-Holm type equations with quadratic nonlinearities, specifically focusing on the differential equation mt +θmu+ amxu+bmux = 0, where m = u−uxx, and θ, a, b are arbitrary constants. We derive the nonlocal form of the equation and explore its peakon dynamics, including the well-known Camassa–Holm, Degasperis–Procesi, and Holm–Staley b-family equations. By employing a practical computational approach, we analyze the N-peakon solutions and present the corresponding dynamical systems, particularly focusing on the two-peakon case. The results will …

Congruences In Arithmetic Progression For Coefficients Of Gaussian Polynomials And Crank Statistics, Joselyne Aniceto

Theses and Dissertations

The study of partition congruences, inspired by Ramanujan’s discoveries for ��(��) over a century ago, remains a central topic in this field. This dissertation examines congruence properties in two restricted partition functions: ��(��,��), which counts partitions of �� into at most �� parts, and ��(��,��,��), which further limits the size of the largest part to be at most ��. Building on Kronholm’s 2007 result, now known as the Interval Theorem, and a recent result by Eichhorn, Engle, and Kronholm, we establish new infinite families of congruences for ��(��,��,��). This dissertation extends not only the recent results of Eichhorn, Engle, …

The Influence Of Solar Energy Infrastructure On Pollinators And Crops, Deisy Garcia

Theses and Dissertations

As the human population grows, demand for agriculture and renewable energy rises. Landuse competition is caused by the expansion of area-intensive solar photovoltaic (PV) facilities. While solar energy is crucial to mitigate climate change, it presents challenges related to land availability and effects on habitats for essential pollinators. In Chapter II, a spatial analysis was conducted to examine the relationship between solar panel density and pollinator diversity, exploring regions with the least interaction between these two factors. Our findings can inform solar siting and management strategies at landscape levels, in conjunction with field studies, that both mitigate potential interaction and …

Implementing And Evaluating An Ai-Powered Visual Decision Support System To Improve Antibiotic Usage Among Physicians With A Built-In Early Warning System, Akua Sekyiwaa Osei-Nkwantabisa

Theses and Dissertations

The widespread misuse and excessive prescription of antibiotics have played a pivotal role in the emergence and proliferation of antibiotic-resistant bacteria, posing a critical global public health crisis. Addressing this challenge necessitates innovative solutions that enhance antimicrobial stewardship. This study presents the development and implementation of a visual decision support system designed to monitor and optimize antibiotic usage among healthcare providers. The proposed system integrates advanced machine learning algorithms with real-time data analytics to provide a dynamic, evidence-based decision support tool. Specifically, a neural network model was developed after evaluating multiple machine learning approaches, including Random Forest, Logistic Regression and …

Spatio-Temporal Pattern Of Nutrient Dynamics In The South Texas Coastal Watershed, Mohammad Sadman Alam

Theses and Dissertations

Eutrophication threatens aquatic ecosystems by altering productivity through excessive nutrient inputs. In some systems, primary productivity is limited by nitrogen (N), phosphorus (P), or both, based on the N:P ratio defined by the "Redfield" ratio. South Texas, facing rapid urban growth and industrialization, is at risk of higher nutrient loads, but research on nutrient dynamics in this region is limited. This study investigates nutrient variations in the freshwater (FW) abandoned distributaries of the Rio Grande and hypersaline saltwater (SW) systems. Results showed a significant decrease in dissolved inorganic nitrogen (DIN) and an increase in dissolved inorganic phosphorus (DIP), shifting the …

Mitigation Of Droughts And Floods From Conjunctive Water Resource Management Using Managed Aquifer Recharge (Mar): Experiments And Numerical Modeling, Sumiaya Amin Preota

Theses and Dissertations

Water supply of Rio Grande Valley in South Texas has been impacted by intensified climate extremes such as droughts and floods. This research assessed the viability of conjunctive water resource management using Managed Aquifer Recharge (MAR) carbon-modified infiltration basins. Multiple environmental variables in the Arroyo Colorado watershed were investigated, i.e., (i) water availability- quantity of floodwater can be repurposed, (ii) storativity and suitability - capacity within the unsaturated aquifer and ideal locations for building infiltration basins, (iii) water quality- contaminant removal using active carbon/biochar.

Unappropriated flow and high magnitude flow (HMF) analysis indicated that excess floodwater can be a …

Relaxation Maximum-Based Iteration Method For Solving The Generalized Absolute Value Equation, Ximing Fang, Zhidong Wang, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

The generalized absolute value equation (GAVE) has wide applications in scientific computing. Establishing a high performance computing method to solve the GAVE is a hot research topic in recent years. In this paper, with the aid of the maximum function, the GAVE is decomposed of two equations, and then we present the relaxation maximum-based (RM) iteration method. To see the feasibility of the method, we discuss the necessary and sufficient conditions for the GAVE to have a unique solution. Next, the convergence analysis of the RM iteration is discussed under some convergence conditions. Moreover, some numerical examples of low and …

Effects Of Environmentally Relevant Concentrations Of Roundup On Oxidative-Nitrative Stress, Cellular Apoptosis, Prooxidant-Antioxidant Homeostasis, Renin And Cyp1a Expressions In Goldfish: Molecular Mechanisms Underlying Kidney Damage During Roundup Exposure, Md Imran Noor, Md Saydur Rahman

School of Earth, Environmental, & Marine Sciences Faculty Publications

Roundup is one of the most widely used glyphosate-based harmful herbicides in the United States as well as globally, which poses a severe risk for terrestrial and aquatic organisms. In order to identify the detrimental effects of Roundup exposure in aquatic organisms, we investigated the environmentally relevant concentrations of Roundup exposure (low dose: 0.5 μg/L and high dose: 5.0 μg/L for 2 weeks) on renin expression, oxidative-nitrative stress biomarkers (e.g., 2,4-dinitrophenol, DNP; and 3-nitrotyrosine protein, NTP), prooxidant-antioxidant enzymes expressions (e.g., superoxide dismutase, SOD; and catalase, CAT), cellular apoptosis, and cytochrome P450 1A (CYP1A) mRNA levels in the kidneys of goldfish …

Microplastics In Coastal And Marine Environments: A Critical Issue Of Plastic Pollution On Marine Organisms, Seafood Contaminations, And Human Health Implications, Rebecca Muñiz, Md. Saydur Rahman

School of Earth, Environmental, & Marine Sciences Faculty Publications

Plastic has quickly become one of the world's most prevalent environmental pollutants. Population growth has only amplified the demand, resulting in 430 million tons of plastic produced annually, with 11 million tons ending up in our oceans. Without intentional intervention, plastic waste in the oceans is expected to triple, posing severe risks for the aquatic ecosystems, animals, and humans dependent on these waters. As plastic accumulates in oceans and other water environments, the non-biodegradable particles break down into micro- and nano-plastics, invading coastal and marine organisms and causing considerable physiological and morphological damage. This is especially concerning for the millions …

Optimized Filtrations For Stormwater Quality Improvement By Porous Media–Biochar Applications: Column Experiments And Inverse Modeling, Sumiaya Amin Preota, Chu-Lin Cheng, Myung Hwangbo, Jongsun Kim

School of Earth, Environmental, & Marine Sciences Faculty Publications

Stormwater reuse plays a critical role under changing climates and increasing water demands. This study investigates the removal efficacy of lead (Pb2+) and ammonia (NH3) using sand and rice husk (RH) biochar for potential stormwater quality improvements and treatments. Column experiments combined with HYDRUS inverse modeling were conducted to optimize adsorption isotherms from breakthrough curves. Among linear and non-linear models, the Langmuir and Freundlich models performed better for sand and biochar, respectively. RH biochar showed much higher adsorption capacity of both Pb2+ (4.813 mg/g) and NH3 (6.188 mg/g). In contrast, sand showed a relatively limited adsorption capacity for Pb2+ (0.118 …

Fairness And Robustness In Decentralized Federated Learning, Kaichuang Zhang

Theses and Dissertations

Federated Learning (FL) has emerged as a privacy-preserving paradigm that allows multiple clients to collaboratively train a machine learning model without sharing raw data. However, traditional FL relies on a central server for model aggregation, which introduces a single point of failure and makes the system vulnerable to server-side attacks or breakdowns. To address these limitations, Decentralized Federated Learning (DFL) has been proposed, eliminating the need for a central server and enhancing system resilience. Despite these advantages, DFL faces critical challenges related to fairness and robustness, especially under non-i.i.d. data distributions and adversarial conditions. In this thesis, we propose a …

Climate Change And The Field Of Farm Labor In The Lower Rio Grande Valley, Texas, Cody Richard Mortell

Theses and Dissertations

Farm workers in the United States are often vulnerable to adverse impacts of climate change, particularly extreme heat. This study explores farm workers’ climate change perceptions (CCP) as a mediating force in climate adaptation. Using latent class analysis, in-person survey data (n=404) from Lower Rio Grande Valley, TX (2024) and NOAA data were analyzed. Results were interpreted using Bourdieu’s field analysis framework and his notions of capital and symbolic power. Findings include: a social hierarchy with three latent classes of workers based on economic, cultural, social, and symbolic capital, which statistically significantly affected CCP. Workers in higher structural positions were …

A Dg-Algebra Structure With Divided Powers On The Generalized Taylor Resolution, Raul F, Alvarez

Theses and Dissertations

This thesis investigates the construction of a DG Γ-algebra structure on the Generalized Taylor Resolution (GTR) associated with monomial ideals. The classical Taylor resolution is known for providing a free but generally non-minimal resolution, leading to computational challenges and inefficiencies in algebraic analysis. In contrast, the GTR preserves essential algebraic structures while optimizing the resolution process, offering a more efficient and comprehensive framework for studying monomial ideals.

We introduce a novel DG Γ-structure that incorporates divided powers into the GTR, enhancing its multiplicative and homological properties. This structure preserves strict graded commutativity and is fully compatible with the differential graded …

The Improved New Intersection Theorem Revisited, Lars Winther, Luigi Ferraro

School of Mathematical & Statistical Sciences Faculty Publications

We prove a generalized version of Evans and Griffith’s improved new intersection theorem: Let I be an ideal in a local ring R. If a finite free R-complex, concentrated in nonnegative degrees, has I-torsion homology in positive degrees, and the homology in degree 0 has an I-torsion minimal generator, then the length of the complex is at least dimR−dimR/I. This improves the bound htI obtained by Avramov, Iyengar, and Neeman in 2018.

Investigation Into The Effectiveness Of G-C3n4 For The Degradation Of Indigo Dye In Aqueous Solution Via Electrocatalysis, Rolando R. Barron Jr

Theses and Dissertations

Indigo dye (IUPAC 2-(3-hydroxy-1H-indol-2-yl)indol-3-one) is one of the most used dyes in the textile industry worldwide with more than 40,000 tons produced each year. It can elicit adverse physiological responses in humans including vomiting, diarrhea, and other gastrointestinal conditions, and it is toxic in large amounts. There is also evidence to suggest that indigo is a teratogen and genotoxic in aquatic life. Environmentally, the enormous amount of indigo used in the textile industry has caused rivers and waterways to run blue as well as severely impacting aquatic and plant ecosystems. The chemicals used in its synthesis are also …

Joint Modelling Of Longitudinal Egfr Trajectory And Time To Acute Kidney Injury In Lung Transplant Patients, Samiha Zakir

Theses and Dissertations

Progressive declines in estimated glomerular filtration rate (eGFR) often precede acute kidney injury (AKI), yet the relationship between eGFR trends and AKI risk remains unclear. This study investigates longitudinal eGFR changes and their association with AKI in 459 lung transplant patients followed for up to 7 years (n = 6419). We applied a piecewise linear mixed-effects model to evaluate eGFR trajectories and a Cox proportional hazards model to assess time to AKI. A joint model was used to explore the interplay between longitudinal and survival processes. Key covariates included gender, age at transplantation, antibody-mediated rejection (AMR), and pre-transplant eGFR. Males …

The Dialogue Dilemma: The Role Of Patient-Clinician Communication For Low-Income People Who Smoke And Manage Multiple Conditions, Monique T. Cano, Michael R. Lindstrom, Ricardo F. Muñoz

School of Mathematical & Statistical Sciences Faculty Publications

Introduction: Adults from low-income backgrounds who smoke face significant health disparities related to tobacco use, often at disproportionately high rates. These individuals are more likely to endure multiple mental and physical (MP) health conditions, which can negatively influence their self-rated health (SRH). The quality and effectiveness of patient-clinician communication (PCC) can influence how patients perceive their own health. Understanding how PCC influences SRH among low-income adults who smoke and suffer from multiple MP conditions is essential for clinical care as multimorbidity is on the rise. This study examines how PCC may influence the health perceptions of low-income adults who smoke …

Quantization For A Condensation System, Shivam Dubey, Mrinal Kanti Roychowdhury, Saurabh Verma

School of Mathematical & Statistical Sciences Faculty Publications

For a given r∈(0,+∞), the quantization dimension of order r, if it exists, denoted by Dr(μ), represents the rate at which the nth quantization error of order r approaches zero as the number of elements n in an optimal set of n-means for μ tends to infinity. If Dr(μ) does not exist, we define D−−r(μ) and ¯¯¯Dr(μ) as the lower and the upper quantization dimensions of μ of order r, respectively. In this paper, we investigate the quantization dimension of the condensation measure μ associated with a condensation system ({Sj}Nj=1, (pj)Nj=0,ν). We provide two examples: one where ν is an …

Ai Meets Economics: Can Deep Learning Surpass Machine Learning And Traditional Statistical Models In Inflation Time Series Forecasting?, Ezekiel N.N. Nortey, Edmund F. Agyemang, Enoch Sakyi-Yeboah, Obu-Amoah Ampomah, Louis Agyekum

School of Mathematical & Statistical Sciences Faculty Publications

This study examined the forecasting ability of deep learning (DL) and machine learning (ML) models against benchmark traditional statistical models for the monthly inflation rates in the USA. The study compared various DL and ML models like transformers, linear regression, gradient boosting (GB), extreme gradient boosting (XGBoost), and adaptive boosting (AdaBoost) with traditional baseline time-series models like autoregressive integrated moving averages (ARIMA) and exponential smoothing (ETS) with Holt-Winters seasonal method utilizing data sourced from the Federal Reserve Bank of St. Louis. The study consistently showed that all DL and ML models outperformed the traditional approaches. In particular, the Transformer (RMSE …

A Performance Comparison Between Two Speech-To-Asl-Gesture-Projection Translation Implementations, Alexandra Kashani Motlagh, Shikha Mehta, Ishfaq Ahmad, Addison Clark, Hansheng Lei

Informatics and Engineering Systems Faculty Publications

Millions of people with hearing disabilities use sign language for communication, creating a communication gap with those who are not fluent in ASL (American Sign Language). This paper aims to introduce an ASL interpreter system using a smart-glasses-based augmented reality system. We begin by introducing and comparing two models that translate spoken language into ASL poses. The first system translates spoken text to ASL Gloss, an intermediate representation, before generating ASL poses. The second system directly translates the text to ASL poses. Our analysis shows that using ASL Gloss as an intermediate step significantly improves the translation speed. We then …

Trimming Five Generated Gorenstein Ideals, Luigi Ferraro, W. Frank Moore

School of Mathematical & Statistical Sciences Faculty Publications

Let (𝑅,𝔪,𝕜) be a regular local ring of dimension 3. Let I be a Gorenstein ideal of R of grade 3. It follows from a result of Buchsbaum and Eisenbud that there is a skew-symmetric matrix of odd size such that I is generated by the sub-maximal pfaffians of this matrix. Let J be the ideal obtained by multiplying some of the pfaffian generators of I by 𝔪; we say that J is a trimming of I. In a previous work, the first author and A. Hardesty constructed an explicit free resolution of 𝑅/𝐽 and computed a DG algebra …

Shaping Mathematics Identity: An Exploratory Study On Specifications Grading In Calculus I At A Hispanic-Serving Institution, Luis M. Fernandez, Kaitlyn Stephens Serbin, Cristina Villalobos, Shaghayegh Azadi Setayesh, Guillermo Garza

School of Mathematical & Statistical Sciences Faculty Publications

Calculus I courses play a pivotal role in shaping students' STEM pathways, making it essential to adopt pedagogies that foster both achievement and mathematics identity development, particularly among underserved groups such as Hispanic students. This study explores the impact of Specifications Grading, an alternative assessment method where students meet specific course learning objectives through multiple attempts, on students’ mathematics identity development. Through a comparative case study of two Calculus I students at a Hispanic-Serving Institution, one enrolled in a specification graded course and the other in a traditionally-graded course, we examine shifts in their self-perceptions of competence, interest, recognition in …

Data-Driven Survival Modeling For Breast Cancer Prognostics: A Comparative Study With Machine Learning And Traditional Survival Modeling Methods, Theophilus Gyedu Baidoo, Hansapani Rodrigo

School of Mathematical & Statistical Sciences Faculty Publications

Background This investigation delves into the potential application of data-driven survival modeling approaches for prognostic assessments of breast cancer survival. The primary objective is to evaluate and compare the ability of machine learning (ML) models and conventional survival analysis techniques, to identify consistent key predictors of breast cancer survival outcomes.

Methods This study employs data-driven survival modeling approaches to predict breast cancer survival, including survival-specific methods such as the Cox Proportional Hazards (CPH) model, Random Survival Forests (RSF), and Cox Proportional Deep Neural Networks (DeepSurv), as well as machine learning models like Random Forests (RF), XGBoost, Support Vector Machines (SVM) …

Search For Continuous Gravitational Waves From Known Pulsars In The First Part Of The Fourth Ligo-Virgo-Kagra Observing Run, A. G. Abac, R. Abbott, I. Abouelfettouh, F. Acernese, Teviet Creighton, Mario C. Diaz, Francisco Llamas Villarreal, Soma Mukherjee, Volker Quetschke, Wenhui Wang

Physics & Astronomy Faculty Publications

Continuous gravitational waves (CWs) emission from neutron stars carries information about their internal structure and equation of state, and it can provide tests of general relativity. We present a search for CWs from a set of 45 known pulsars in the first part of the fourth LIGO–Virgo–KAGRA observing run, known as O4a. We conducted a targeted search for each pulsar using three independent analysis methods considering single-harmonic and dual-harmonic emission models. We find no evidence of a CW signal in O4a data for both models and set upper limits on the signal amplitude and on the ellipticity, which quantifies the …

Detection And Parameter Estimation Of Supermassive Black Hole Ringdown Signals Using A Pulsar Timing Array, Xuan Tao, Yan Wang, Soumya D. Mohanty

Physics & Astronomy Faculty Publications

Gravitational wave (GW) searches using pulsar timing arrays (PTAs) are commonly assumed to be limited to a GW frequency of ≲4 ×10−7  Hz given by the Nyquist rate associated with the average observational cadence of 2 weeks for a single pulsar. However, by taking advantage of asynchronous observations of multiple pulsars, a PTA can detect GW signals at higher frequencies. This allows a sufficiently large PTA to detect and characterize the ringdown signals emitted following the merger of supermassive binary black holes (SMBBHs), leading to stringent tests of the no-hair theorem in the mass range of such systems. Such large-scale …

Ligo Detector Characterization In The First Half Of The Fourth Observing Run, S. Soni, B. K. Berger, D. Davis, F. Di Renzo, A. Effler, T. Ferreira, E. Goetz, Francisco Llamas Villarreal, Volker Quetschke, J. Glanzer

Physics & Astronomy Faculty Publications

Progress in gravitational-wave (GW) astronomy depends upon having sensitive detectors with good data quality. Since the end of the Laser Interferometer Gravitational-Wave Observatory-Virgo-KAGRA third Observing run in March 2020, detector-characterization efforts have lead to increased sensitivity of the detectors, swifter validation of GW candidates and improved tools used for data-quality products. In this article, we discuss these efforts in detail and their impact on our ability to detect and study GWs. These include the multiple instrumental investigations that led to reduction in transient noise, along with the work to improve software tools used to examine the detectors data-quality. We end …

On The Determinant Of Up On Mk(P,Χ), Xingyu Huang, Timothy J. Huber, Dongxi Ye

School of Mathematical & Statistical Sciences Faculty Publications

In this work, for p a prime, we compute the absolute value of the determinant of the UpUp-operator on the vector space Mk(p,χ)Mk(p,χ) of holomorphic modular forms of weight k and level Γ0(p)Γ0(p) with character χχ. As an implication, we confirm a number of conjectures of the second author.

Utilizing Machine Learning To Predict The Charge Storage Capability Of Lithium-Ion Battery Materials, Manoj Chhetri, Karen S. Martirosyan

Physics & Astronomy Faculty Publications

With the increasing demand for high-performance batteries in applications such as electric vehicles and portable electronics, accurately predicting the charge storage capacity of battery materials is crucial for developing more efficient and reliable energy storage systems. Machine Learning (ML) and data-driven approaches, plays a vital role in enhancing our understanding of Li-ion battery performance, guiding materials design, optimizing system efficiency, and accelerating innovation in energy storage technologies. In this study, an ML-based approach was applied to a dataset of 2345 rechargeable Li-ion battery materials, obtained from the Materials Project online portal, to predict gravimetric charge storage capacity ─ a key …

Three New 2+2 Quadruple Systems With Changing Inclination, Petr Zasche, Z. Henzl, M. Mašek, Jan Kára, H. Kučáková, J Merc, R. Uhlař

Physics & Astronomy Faculty Publications

We present a unique discovery of three new detected systems showing two different phenomena together. These are 2+2 quadruple stellar systems showing two eclipsing binaries as the inner pairs. And besides that, these systems were also found to exhibit the precession of the inner orbits causing the inclination changes manifesting themselves through the eclipse depth variations. We are not aware of any similar known system on the sky nowadays, hence our discovery is really unique. In particular these systems are: CzeV4315 = HD 228777 (periods 6.7391 and 0.91932 d, inclination change of pair B of about 1.4∘ yr−1); ASASSN-V J075203.23−323102.7 …