Digital Commons Network^™

A Theory Of Fundamental Strata For Twisted Formal Connections, Sorawit Viwanthananut

LSU Doctoral Dissertations

Let $G$ be a complex reductive group. A fundamental stratum for $G$ is a triple $(x,r,\beta)$ where $x$ is a point in the Bruhat-Tits building of $G$, $r$ is a nonnegative real number called depth of the stratum, and $\beta$ is a semistable functional on the Moy-Prasad filtration of $\fg$ associated to $x$ at level $r$. Fundamental strata were first introduced to classify admissible representations of a $p$-adic reductive group. More recently, Bremer and Sage have shown that fundamental strata play an important role in the geometric Langlands program and developed a theory of fundamental strata for $G$-connections. In this …

Increasing The Economic And Social Viability Of Carbon Capture Using Biomass Slurry Fracture Injection, Zachary G. Laird

LSU Master's Theses

The climate is changing. This is a fact not a statement, not a theory, and not a falsehood, this is a fact. At the current projections the world’s average temperature is expected to rise by at least 2°C from pre-industrial averages by 2050 (Emissions Pathways to 2100 - Climate Action Tracker, 2024). This temperature rise will be catastrophic for a vast number of communities. What is driving this changing climate? Humans. In particular the carbon emissions caused by human activities. As humans we consume large amounts of meat, causing the need for cattle to increase, generating large amounts …

Strichartz Estimates For Many Particle Dispersive Equations, Tristan Reynoso

LSU Doctoral Dissertations

Dispersive equations are useful for describing a wide variety of phenomena in which solutions disperse through the space as time progresses. These equations show up frequently in physics, especially when studying quantum mechanical and fluid related systems. The single particle variants of equations such as the Schr\"{o}dinger and Wave equations have been studied at great length throughout modern history. Over the last couple decades progress has been made toward extending single particle dispersive equations to cover their many body counterparts. Space-time Strichartz estimates for the homogenous $N$-particle Schr\"{o}dinger equation with small interacting potentials was recently established on both $\mathbb{R}^d$ and …

Predictive Indicators For Graduation Upon Acceptance Into A Naacls-Approved Medical Laboratory Science Program, Warren Hovis

LSU Doctoral Dissertations

The primary purpose of this study was to determine the influence of selected academic and personal demographic characteristics on student success at a NAACLS-accredited medical laboratory science program in the southern portion of the United States.

Both academic and demographic categories were selected on students who entered the medical laboratory science program from 2014 to 2019 (pre-COVID). The sanitized, archived data set was provided by the MLS department and the registrar and student affairs office at the participating school. The extant data set contained academic and demographic variables, collected over a five-year period, of initially over 170 accepted MLS students. …

Source Origins Of Hunter-Harvested Waterfowl In Arkansas And Louisiana, Shannon C. Stemaly

LSU Master's Theses

Understanding variability in breeding origins of harvested waterfowl is important for effective population management and regional conservation. Band-recovery data are often used to estimate harvest derivation and inform resource allocation for cross-seasonal conservation. However, uneven spatial and temporal banding effort across species' breeding ranges may result in an incomplete understanding of summer origins and recruitment, particularly if portions of the breeding range are inaccessible. Analysis of stable-hydrogen isotope ratios in duck feathers (δ²H_f) provides an alternative method for identifying source origins of unmarked populations since environmental deuterium values follow a predictable latitudinal gradient across North …

On Excursions Associated With A Certain Local Time Of Simple Symmetric Random Walks, With Applications, Takahiko Fujita, Naohiro Yoshida

Journal of Stochastic Analysis

In this note, some applications of excursions associated with a certain local time of simple symmetric random walks are presented. Specifically, the excursions are applied to calculate some probability distributions of interest regarding the random walks. Furthermore, a solution of the Skorokhod embedding problem for random walks is obtained through the excursions.

L2-Betti Numbers Of Branched Covers Of Hyperbolic Manifolds, Grigori Avramidi, Boris Okun, Kevin Schreve

Faculty Publications

We show that Gromov–Thurston branched covers satisfy the Singer conjecture whenever the degree of the cover is not divisible by a finite set of primes determined by the base manifold and the branch locus.

Interval Spectrum For Electric Quantum Walk And Related Skew-Shift Cmv Matrices, Fan Yang

Faculty Publications

We show that for a family of quantum walk models with electric fields, the spectrum is the unit circle for any irrational field. The result also holds for the associated CMV matrices defined by skew-shifts, as well as a family of the Blattner and Browne model. Generalizations to CMV matrices with skew-shifts on higher dimensional torus are also obtained.

The Jacod-Yor Theorem For Sigma Martingales And The Second Fundamental, Moritz Sohns

Journal of Stochastic Analysis

In this paper, we prove the Jacod-Yor Theorem for sigma martingales, a class of processes that generalize local martingales and play a pivotal role in financial mathematics. While the Jacod-Yor Theorem has been extensively studied for L2-martingales, martingales, and local martingales, no prior version exists for sigma martingales. Our result establishes the connection between sigma martingales and their martingale representation properties, addressing a critical gap in the literature. As an application, we prove the Second Fundamental Theorem of Asset Pricing for markets where price processes are modeled as sigma martingales.

Interfacial Phenomena Of Plastics: From Surface Modifications To Environmental Impacts, Kennedy Guillot

LSU Doctoral Dissertations

Plastic is a ubiquitous part of everyday life since its introduction in the previous century. Global production continues to exponentially increase, establishing plastics as one of the most dominant materials in modern manufacturing. Within the scope of academia, plastic is essential due to its low cost and sterility, particularly for minimizing contamination. Beyond the laboratory, plastic use spans numerous industries, and its use and disposal has since raised many environmental concerns. Once valued for its durability, plastics now pollute the environment in landfills and natural ecosystems. In recent decades, the consequences of this pollution have been investigated, yet the full …

Investigating The Role Of Aerosols In Extreme Precipitation Events Along The Gulf Coast Of The U.S.A., Wenjia Cao

LSU Doctoral Dissertations

Atmospheric aerosols have been found to influence tropical cyclone (TC) and flood event development. In this study, the Weather Research and Forecasting model is applied to investigate specific microphysical impacts and aerosol sensitivity to heavy precipitation and TC events in the U.S. Gulf Coastal area. The Thompson aerosol-aware scheme with regular and adjusted aerosol concentration scenarios is used to quantify precipitation, wind field, horizontal/vertical structures, and track variations, by aerosol mixing ratio. In general, results for the three storms analyzed (the 2016 Baton Rouge, Louisiana, flood event (Chapter 2); Hurricane Harvey in 2017 (Chapter 3); and an idealized storm event …

Passive Vibration Isolation Systems For Mitigating Rotational Forces In Football Helmet Impacts, Julian Lee

LSU Master's Theses

Helmets have been used for centuries to mitigate head injuries, evolving with advancements in materials and design. They are critical in athletics, construction, and military applications, where shock and vibration isolation play a key role in head protection. Helmet performance is currently rated using the Head Injury Criterion (HIC) and Helmet Performance Score (HPS) metrics. HIC is a metric used in sports and automotive industries which focuses on the probability of injury occurring due to the magnitude and duration of linear acceleration of the head [1]. The HPS metric was created by using a linear combination of HIC and a …

The Application Of Syncopated Rhythms In The Development Of Sight-Reading Skills For Non-Keyboard Music Majors, Ronald David Rodriguez Herrera

LSU Doctoral Dissertations

This study investigates the impact of integrating syncopated rhythms into the group piano curriculum for undergraduate music students with varied levels of piano proficiency. Participants (N=76) enrolled in Group Piano II and IV were assigned control and experimental groups across multiple class sections. Three research questions guided the study: (1) How does the introduction of syncopated rhythm patterns affect group piano students’ sight-reading performance? (2) How does consistent practice of syncopated rhythms influence students' ability to sustain a steady pulse? (3) Do students consider exposure to syncopated rhythms a valuable component in their future careers as music educators …

Airfield Pavement Management Framework Using Advanced Modeling Techniques, Heena Dhasmana, Marwa Hassan, Elise Mansour

Publications

Airport authorities constantly collect pavement condition data and utilize life-cycle cost analysis to select construction and maintenance alternatives. The current Federal Aviation Administration (FAA) Advisory Circular 150/5380-7B recommends using Pavement Condition Index (PCI) to assess airfield pavement condition for planning of Maintenance and Rehabilitation (M&R) treatments. However, structural and functional performance might not be fairly represented by solely one indicator, the PCI. The latter might mask the root cause of the pavement deterioration and lead to inadequate M&R recommendations. Furthermore, the regression nature of the existing airfield pavement assessment models is not adequate for establishing pavement performance prediction as a …

Estimating The Future Frequency Of Bonnet Carré Spillway Openings, Kayla Thomas

LSU Master's Theses

In the 2010s, the Bonnet Carré Spillway (BCS) in southeastern Louisiana, U.S.A., experienced an unprecedented uptick in openings to mitigate the possibility of flooding, including a record double-opening in 2019. Both the environmental consequences of BCS openings associated with nutrients that run from the Mississippi River into Lake Pontchartrain and the synoptic-scale meteorological conditions that necessitate these openings are poorly understood. With the unexpectedly frequent openings in recent years and the ever-present threat of climate change, it is vital to consider the future shift of synoptic-scale climate patterns and how it can relate to BCS openings. Understanding the potential for …

Memory-Augmented Llm Agent For Predicting Locomotion Modes In Construction Activities, Ehsan Ahmadi

LSU Doctoral Dissertations

The construction industry faces significant challenges, including labor shortages, high physical demands, and safety risks, necessitating advanced assistive technologies like exoskeletons to enhance worker efficiency and reduce injuries. However, effective exoskeleton control in dynamic construction environments requires accurate locomotion prediction, a task complicated by the diversity of activities and reliance on supervised learning methods that struggle to generalize. This study investigates a multimodal approach to locomotion prediction, leveraging speech commands and visual data from smart glasses to enable adaptive and safe human-exoskeleton interaction. The research unfolds in two stages: the first develops a framework to evaluate the zero-shot capability and …

Use Of Margins Around Small Brain Metastasis Improves Specificity Of Evaluation Methods For Stereotactic Radiosurgery Treatment Plans, Purity Kemunto Bundi

LSU Master's Theses

Purpose: To reduce the high false positive rates (FPRs ≥ 46%) from the evaluation of Gamma Knife stereotactic radiosurgery (SRS) treatment plans for small brain metastases. Specifically, we modified two evaluation indices, Treated Volume Ratio (TVR) and Gradient Index (GI), which exhibited FPRs exceeding 84%. A false positive result incorrectly indicates that an acceptable plan, as determined by a medical physicist and a radiation oncologist, is inacceptable.

Methods: This study utilized training and validation datasets from Gamma Knife treatment plans from The University of Texas MD Anderson Cancer Center (MDACC) and Mary Bird Perkins Cancer Center (MBPCC). Data included doses, …

Integration Of Hydrological Simulations Into The Design Process To Assess The Performance Of Green Infrastructure Designs, Clara Jimenez

Design Research

With the growing threat of flooding in coastal and inland communities, it is necessary to migrate nature-based solutions such as green infrastructure. However, one of the challenges that designers face with this strategy lies in the design phase where it is difficult to quantify the performance with traditional design tools. Thus, there is an incentive to incorporate hydrological models within GIS to aid designers in quantifying performance. The goal of this research is to demonstrate that hydrological simulations can be used as a design tool for designers–such as landscape architects & architects– to analyze the feasibility of green infrastructure designs …

On 2-Superirreducible Polynomials Over Finite Fields, J. W. Bober, L. Du, D. Fretwell, G. S. Kopp, T. D. Wooley

Faculty Publications

We investigate k-superirreducible polynomials, by which we mean irreducible polynomials that remain irreducible under any polynomial substitution of positive degree at most k. Let F be a finite field of characteristic p. We show that no 2-superirreducible polynomials exist in F[t] when p=2 and that no such polynomials of odd degree exist when p is odd. We address the remaining case in which p is odd and the polynomials have even degree by giving an explicit formula for the number of monic 2-superirreducible polynomials having even degree d. This formula is analogous to that given by Gauss for the number …

Enhancing Compton Telescope Imaging With Maximum A Posteriori Estimation A Modified Richardson–Lucy Algorithm For The Compton Spectrometer And Imager, H. Yoneda, T. Siegert, I. Martinez-Castellanos, S. Gallego, C. Karwin, H. Bates, S. E. Boggs, C. Y. Huang, A. Joens, S. Matsumoto, S. Mittal, E. Neights, M. Negro, U. Oberlack, K. Okuma, S. Pike, J. Roberts, F. Rogers, Y. Sheng, T. Takahashi, A. Valluvan, Y. Watanabe, D. Hartmann, C. Kierans, J. Tomsick, A. Zoglauer

Faculty Publications

We present a modified Richardson-Lucy (RL) algorithm tailored for image reconstruction in MeV gamma-ray observations, focusing on its application to the upcoming Compton Spectrometer and Imager (COSI) mission. Our method addresses key challenges in MeV gamma-ray astronomy by incorporating Bayesian priors for sparseness and smoothness while optimizing background components simultaneously. We introduce a novel sparsity term suitable for Poisson-sampled data in addition to a smoothness prior, allowing for flexible reconstruction of both point sources and extended emission. The performance of the algorithm is evaluated using simulated three-month COSI observations of gamma-ray lines of ⁴⁴Ti (1.157 MeV), ²⁶Al (1.809 …

Testing For Normality In Regression Models: Mistakes Abound (But May Not Matter), Stephen Midway, J. Wilson White

Faculty Publications

This study examines the misuse of normality tests in linear regression within ecology and biology, focusing on common misconceptions. A bibliometric review found that over 70% of ecology papers and 90% of biology papers incorrectly applied normality tests to raw data instead of model residuals. To assess the impact of this error, we simulated datasets with normal, interval, and skewed distributions across various sample and effect sizes. We compared statistical power between two approaches: testing the whole dataset for normality (incorrect) versus testing model residuals (correct) to determine whether to use a parametric (t-test) or nonparametric (Mann-Whitney U test) method. …

Advanced Manufacturing Of Multifunctional Shape Memory Polymer Composites And Self-Healing Systems, John B. Konlan

LSU Doctoral Dissertations

The need for multifunctional light weight structures for engineering applications is on the rise. Multifunctional composites are desired because of their ability to combine multiple functionalities into one structure. The advantages of a high strength-to-weight ratio of multifunctional composites make them desirable and suitable for use in energy-efficient applications. Shape-memory polymers (SMPs) have attracted interest over the past several decades because of their multifunctional nature. They have found use in many applications such as aerospace, satellites, automobiles, textiles, and biomedical devices, where lightweight and multifunctionality are key. The self-healing nature of most SMPs makes them suitable for use in lightweight …

Advancing Aerial Survey Techniques For Non-Breeding Waterfowl Populations: A Comprehensive Review And Application In Northeastern Louisiana, Victoria L. Drake

LSU Master's Theses

Aerial surveys play a crucial role in monitoring North America's waterfowl populations and habitat conditions, and consistency across geographies and years allows biologists to track trends through time. The goal of this project was to redesign the northeastern portion of the Louisiana wintering waterfowl survey to align with statistically robust transect surveys conducted in neighboring states within the Mississippi Alluvial Valley. To identify the optimal sampling method, we evaluated three transect weighting schemes: stratified random (unweighted), stratified by watershed, and stratified by expert opinion. Approximately 10% of the total sampling area was randomly selected for each survey period, adhering to …

Global Ocean Bottom Temperature Observation Design: Observing System Simulation Experiments For Strategic Deployment Of Smart Subsea Cables, Karen E. Renninger-Rojas

LSU Master's Theses

Deep-ocean observations below 2000 meters remain limited, restricting our ability to model global ocean processes critical to climate prediction. This thesis evaluates the potential of SMART (Science Monitoring and Reliable Telecommunications) subsea cables to address these observational gaps by conducting Observing System Simulation Experiments (OSSEs) and adjoint sensitivity analyses using the MITgcm ocean model and ECCO outputs.

Vertical decorrelation analysis showed that temperature and salinity in key regions decouple from the upper ocean beyond 2000 m. Over 60% of the proposed SMART cable sites exhibited decorrelation depths exceeding Argo’s maximum sampling depth, highlighting their strategic value for deployment.

A comparison …

Impacts Of Extreme Weather Conditions On Coastal Fisheries Near Bayou Teche, Louisiana From 2019–2023, Georgia C. Davis

LSU Master's Theses

The region of Southcentral Louisiana, particularly around Bayou Teche, thrives on its commercial and recreational fisheries. These fisheries are occasionally subject to events like extreme weather that cause sudden and unexpected losses (NOAA Fisheries, 2024a). Between 2019 and 2023, a series of extreme weather events impacted southcentral Louisiana near Bayou Teche. This series of extreme events includes Hurricane Barry (2019), Hurricane Laura (2020), Hurricane Delta (2020), Hurricane Zeta (2020), Hurricane Ida (2021), and a United States Drought Monitor (USDM) D4 drought (2023). This study analyzes the impacts of the extreme weather series on coastal fish observed species richness (SR) in …

Multiparticle Quantum Plasmonics: Fundamentals And Applications, Mingyuan Hong

LSU Doctoral Dissertations

Quantum plasmonics explores the interaction between light and collective charge oscillations at metal-dielectric interfaces, enabling strong light confinement and enhanced quantum effects at the nanoscale. While traditional quantum optics has primarily focused on single-photon systems, an intermediate regime exists between classical and single-photon optics - multiparticle (or multiphoton) quantum optics. In this regime, classical light sources, when analyzed through techniques such as photon-number-resolving (PNR) detection and projective measurement, can reveal nontrivial quantum correlations. This thesis investigates how multiparticle quantum plasmonics harnesses these correlations to control quantum statistical properties, enhance coherence, and enable novel applications in quantum technologies.

In this thesis, …

Decadal To Millennial-Scale Morphodynamic Evolution Of Microtidal Marshes, Samuel Mason Zapp

LSU Doctoral Dissertations

Tidal marshes are susceptible to rapidly converting to open water due to their low elevations within the tidal frame. A continuous supply of externally supplied mineral sediment and in situ organic material production is necessary to offset elevation losses from relative sea level rise and erosion. Complex feedbacks between hydrodynamics, the erosion, transport, and deposition of sediment, and physical modification of the landscape by the establishment of intertidal vegetation govern the spatial and temporal patterns of elevation response. This dissertation focuses on modeling how these dynamics drive marsh landscape evolution in the past, present, and into the future under changing …

Disentanglement In Representation Learning: Interpretability In Dimension Reduction With Vae, Minh Hong Vu

LSU Doctoral Dissertations

This research explores both theoretical and practical aspects of disentangled representation learning by extending the VAE framework. We address the core challenge of extracting independent generative factors from observed data while preserving high reconstruction fidelity. To this end, we propose two novel VAE variants: (i) the $\lambda\beta$-VAE, which incorporates an additional $\ell^2$-norm reconstruction loss to improve accuracy, and (ii) the $\gamma\beta$-VAE, which introduces a mutual information regularization term to encourage independence across latent dimensions.

Our theoretical analysis is conducted in a linear Gaussian setting, where we derive optimal solutions for these VAE-based models. We further examine how varying levels of …

Ai-Based Accessibility Widget (Aibaw) Shortcomings For Blind Web Users, Joshua A. Rovira

LSU Master's Theses

With legal, ethical, and financial motivations to make their websites more accessible, many businesses and sites have begun to employ the use of artificial intelligence (AI) based widgets to automatically make necessary modifications to their sites' pages and subdomains. In this work, we conduct a qualitative case study to determine the efficacy of these AI tools as they pertain specifically to blind users. We analyze pages from twelve websites using accessiBe's AI accessibility widget and provide a taxonomy of their violations against the Web Content Accessibility Guidelines (WCAG) 2.1 level AA compliance. We found each website to bear numerous violations …

My Tunisia Encounters: Inspiration For Some Mathematical Ideas, Hui-Hsiung Kuo

Journal of Stochastic Analysis

No abstract provided.