Physical Sciences and Mathematics Commons^™

Learning Problems Related To Stochastic Differential Equations, Jinpu Zhou

LSU Doctoral Dissertations

Stochastic differential equations (SDEs) are essential for modeling systems influenced by both deterministic dynamics and random fluctuations, with applications in a wide variety of disciplines. This thesis develops a Bayesian framework for nonparametric learning in SDEs, addressing key challenges in inference, particularly when dealing with complex systems and incomplete data. The thesis begins by establishing a theoretical foundation in optimization over Hilbert spaces, including a generalized representer theorem to address infinite-dimensional optimization problems encountered in nonparametric inference. Building on this, we introduce a Bayesian framework with shrinkage priors to learn drift functions from high-frequency data. Bayesian approach incorporates low-cost sparse …

Coloring Trivalent Graphs: A Defect Tft Approach, Amit Kumar

LSU Doctoral Dissertations

We show that the combinatorial matter of graph coloring is, in fact, quantum in the sense of satisfying the sum over all the possible intermediate state properties of a path integral. In our case, the topological field theory (TFT) with defects gives meaning to it. This TFT has the property that when evaluated on a planar trivalent graph, it provides the number of Tait-Coloring of it. Defects can be considered as a generalization of groups. With the Klein-four group as a 1-defect condition, we reinterpret graph coloring as sections of a certain bundle, distinguishing a coloring (global-sections) from a coloring …

Effects Of Longitudinal Training Walls On Two-Dimensional Flow Structure, Sediment Transport, And Bed Aggredation Using Numerical Methods And Sediment Core Analyses In Grand River, Michigan, Sumaiya Tul Siddique

LSU Doctoral Dissertations

Longitudinal training walls (LTWs) are structures oriented parallelly with the main flow and separate the channel into two sub-channels. One channel acts as the main navigational channel and the other is considered a secondary side channel. The long-term effects of the LTWs on morphodynamics and deposition remain poorly understood. This study investigated the long-term effects of the LTWs on flow, sediment transport and long-term deposition of the Grand River using numerical approaches and sediment core analysis. The effects of LTWs on 2D flow dynamics and sediment transport were investigated by using numerical approaches. The long-term deposition under the influence of …

Modern Lakeshore Processes And Historic Lake And Glacial Changes In Taylor Valley, Antarctica, Michael Stanley Stone

LSU Doctoral Dissertations

Taylor Valley, which opens to the Ross Sea, is one of several ice-free valleys comprising the McMurdo Dry Valleys, Antarctica. The valley is home to several close-basin, perennially ice-covered lakes, whose lake levels largely reflect a balance between meltwater inputs and lake ice ablation; both being driven by climate. A dynamic environment exists where the lake ice covers meet the lakeshore, with the ice grounding to the substrate throughout the cold and dark of winter, and melting to form a perimeter of thin-to-no ice around the lake during the summer. These marginal freeze-thaw regions are known as moats. Here, physical, …

Effect Of Electronegativity On Environmentally Persistent Free Radical (Epfr) Formation, Persistence, And Toxicity On Transition Metal Oxides, Syed Monjur Ahmed

LSU Doctoral Dissertations

Environmentally persistent free radicals (EPFRs) are a group of emerging environmental pollutants. Owing to their resonance structures, EPFRs have significantly higher lifetimes than typical free radicals, and can induce the formation of reactive oxygen species (ROS) known to cause pulmonary and cardiovascular dysfunction. EPFRs form by the adsorption of organic precursors on a transition metal oxide (TMO) surface and exhibit enough stability to cause negative health and environmental effects. While aromatic and substituted aromatic precursors form EPFRs on TMO surface at elevated temperatures and numerous substituted organics are ubiquitous in various industrial processes and household products, studies have largely overlooked …

Coastal Sedimentary Records Of Extreme Events And Human Activity: Examples From Hurricanes And Microplastics, Nicholas T. Culligan

LSU Doctoral Dissertations

Coastal regions are uniquely vulnerable to a myriad of natural and anthropogenically caused stresses such as hurricane strikes and chronic microplastic pollution. Both hurricanes and microplastics have major negative effects on global coastlines and are forecast to become more damaging in the future. However, current model trends are based on limited modern data and may not provide an accurate or comprehensive view of the future. Therefore, this dissertation investigates coastal stratigraphic records to determine long-term past trends of these presses and pulses so that researchers, stakeholders, and policy makers can use them to enact strategies to mitigate damages from worsening …

A Coarse-Grained Molecular Dynamics Study Of Gas Hydrate Formation And Dissociation, Meisam Adibifard

LSU Doctoral Dissertations

The study of gas hydrates has increased significantly over the last two decades because of their potential application in energy storage, production and transportation, water desalination, refrigeration, gas separation, etc. There is a significant interest in commercially developing natural gas hydrates because the energy content of methane hydrate reservoirs (MHRs) is at least twice that of all conventional fossil fuels combined. Additionally, due to the higher storage capacity of hydrates, it is proposed to sequester CO₂ in the form of CO₂ hydrate, thereby reducing the amount of greenhouse gases. Hence, hydrates offer a dual solution to two of …

Constraining Giant Planet Occurrence Rates With The Multi-Band Imaging Survey For High-Alpha Planets (Mishaps) Observations Of 47 Tucanae, Alison Crisp

LSU Doctoral Dissertations

Though the confirmed exoplanet population has now reached over 5,500 planets, we still have a plethora of unanswered questions, e.g., regarding their formation mechanisms, true demographics, occurrence rates, and habitability. One remaining question is whether hot Jupiters formed in situ or migrated to their current orbits, so close to their host stars that their periods are 10 days or less. This question can potentially be answered by probing the effects of elemental abundances on hot Jupiter occurrence rates. These rates have been found to correlate with metallicity, but the specific elements responsible for the correlation have largely been unresolved. The …

Synthesis Of Portions Of An Acinetobacter Baumannii Lipooligosaccharide (Los), Brandon Conrad

LSU Doctoral Dissertations

Glycoconjugate vaccines have become an effective strategy for protection against an array of globally persistent diseases resulting from pathogenic bacteria such as Haemophilus influenzae type b (Hib), Neisseria meningitidis, and Salmonella enterica serotype Typhi. Comprised of a carbohydrate (referred to as glycan) covalently inked to a carrier protein, these vaccines can initiate adaptive immunity by inducing B and T cell responses once in the lymphatic system. This is particularly relevant for infants two years of age and younger whose immune systems are not fully developed. A continuously emerging threat in clinical settings, Acinetobacter baumannii is a Gram-negative bacterium …

Quantum Classical Algorithm For Solving The Hubbard Model Via Dynamical Mean-Field Theory, Anshumitra Baul

LSU Doctoral Dissertations

Modeling many-body quantum systems is widely regarded as one of the most promising applications for near-term noisy quantum computers. However, in the near term, system size limitation will remain a severe barrier for applications in materials science or strongly correlated systems. A promising avenue of research is to combine many-body physics with machine learning for the classification of distinct phases. I present a workflow that synergizes quantum computing, many-body theory, and quantum machine learning (QML) for studying strongly correlated systems. In particular, it can capture a putative quantum phase transition of the stereotypical strongly correlated system, the Hubbard model. Following …

Novel Approaches To The Activation Of Chalcogenoglycosides For O-Glycosylation, Tiffany Duong

LSU Doctoral Dissertations

Carbohydrates are integral to various biological processes such as cell signaling, function and regulation. Carbohydrates also play critical roles in various disease and metastatic pathways. This has garnered considerable attention to the field of glycoscience, however, the study of carbohydrate-containing compounds remains a challenge due to the difficulty in obtaining pure samples from natural sources. As a result, the biological evaluation of carbohydrates relies on synthetic chemistry to produce pure compounds in significant quantities. However, the synthesis of carbohydrates present their own challenges owing to the complexity in controlling stereochemistry and regiochemistry. The most significant of these challenges is controlling …

Diving Deeper Into Supercuspidal Representations, Prerna Agarwal

LSU Doctoral Dissertations

In 2013, Reeder and Yu introduced certain low positive depth supercuspidal representations of $p$-adic groups called \textit{epipelagic} representations. These representations generalize the simple supercuspidal representations of Gross and Reeder, which have the lowest possible depth. Epipelagic representations also arise in recent work on the Langlands correspondence; for example, simple supercuspidals appear in the automorphic data corresponding to the Kloosterman $l$-adic sheaf. In this thesis, we take a first step towards the construction of ``\textit{mesopelagic} representation (of Iwahori type)'' which are the higher depth analogues of simple supercuspidal representations. We see that these constructions can be done in a similar way …

Asymptotic Formula For Scattering Problems Related To Thin Metasurfaces, Zachary Jermain

LSU Doctoral Dissertations

The goal of this work is to develop an asymptotic formula for the behavior of a scattered electromagnetic field in the presence of a thin metamaterial known as a metasurface. By using a carefully chosen Green’s function and the single and double layer potentials we analyze the perturbed scattering problem in the presence of the metamaterial and a background scattering problem. By using Lippman-Schwinger type representation formulas for the two fields we develop the asymptotic formula for the perturbed field. From here we prove the asymptotic formula holds up to a specific error term based on the size of the …

Topics In Photonic Quantum Technology: Polarization Entanglement Dynamics In Optical Fibers And Low-Light Imaging., Pratik J. Barge

LSU Doctoral Dissertations

Recent advances in quantum photonics promise transformative impacts on computing, communication, sensing, and imaging. This thesis explores two areas in photonic quantum technology: polarization entanglement dynamics in optical fibers and low-light imaging. Optical fibers are the most suitable medium for photonic qubits and long-distance entanglement distribution is a critical requirement to realize quantum technologies. We study the decay of polarization-entanglement of the Bell state photons propagating through imperfect optical fibers with spatially fluctuating refractive index. Furthermore, to extend the distribution distance, we propose the use of dynamical decoupling in the optical fiber using half waveplates and show that significant improvement …

Riesz Particle Markov Chain Monte Carlo Methods, Xiongming Dai

LSU Doctoral Dissertations

Markov chain Monte Carlo (MCMC) methods are simulations that explore complex statistical distributions, while bypassing the cumbersome requirement of a specific analytical expression for the target. This stochastic exploration of an uncertain parameter space comes at the expense of a large number of ``burn-in'' samples, and the computational complexity leads to the curse of dimensionality. Although at the exploration level, some methods have been proposed to accelerate the convergence of the algorithm, such as tempering, Hamiltonian Monte Carlo, Rao-redwellization, and scalable methods for better performance, they cannot avoid the stochastic nature of this exploration. We develop algorithms for the energy …

Advances In Stereoselective Glycosylation: Electron-Withdrawing Groups, Benzyne-Mediated Stereoinversion, And Visible-Light Photochemistry For 1,2-Cis O-Glycosylation, Erik Giovanni Alvarez Valenzuela

LSU Doctoral Dissertations

The symbiotic relationship between humans and their microbiota is essential for health, with imbalances in the complex microbiota ecosystem linked to a variety of disorders ranging from neurodegenerative to gastrointestinal diseases. Bacteria within the human microbiota, comprising over 1000 known species, are densely and diversely coated with oligosaccharides crucial for functions like cell recognition, communication, signaling, adhesion, proliferation, and pathogenic inhibition. However, studying the structure-activity relationships of these sugars which are also secreted by bacteria is challenging due to difficulties in obtaining homogenous samples from natural sources.

Chemical synthesis offers a solution by enabling the production of well-defined oligosaccharides in …

Investigation Of Solvation Structures And Dynamics Of Li-Ion Battery Electrolytes And Amides In Water: An Infrared Spectroscopy, Electrochemical And Computational Study, Ernest O. Nachaki

LSU Doctoral Dissertations

The investigation of solvation structures and dynamics in lithium-ion battery electrolytes and amides in water has significant implications for both fundamental science and practical applications. Understanding the solvation dynamics of lithium electrolytes can lead to the development of safer and more efficient LIBs. The study of hydrogen bond dynamics of N-alkyl substituted amides has important implications for the development of thermos-responsive polymers used in biomedical applications. By understanding how N-alkyl substitutions affect the hydration structure and dynamics of amides, this research can inform the design of polymers with tailored properties for drug delivery, tissue engineering, and other medical applications. This …

Investigations And Characterization Of Loud Transient Noise In Advanced Ligo Detectors, Shania Nichols

LSU Doctoral Dissertations

In the era of gravitational wave (GW) astronomy, the detection of cosmic events such as black hole and neutron star mergers has become routine due to the Advanced LIGO (aLIGO) detectors. However, the sensitivity of these detectors also makes them susceptible to loud transient noise, which can obscure GW signals. This thesis investigates loud transient noise with a Signal-to-Noise Ratio (SNR) greater than 100, focusing particularly on the most extreme transients with SNR exceeding 1000.

We begin by analyzing the impact of loud transient noise on the binary neutron star (BNS) range of aLIGO detectors across observation runs O2, O3, …

Higher Order Operator Splitting Schemes With Complex Coefficients And Applications, Arun Banjara

LSU Doctoral Dissertations

The goal of this dissertation is to apply the concept of Lie generators for linear semigroups induced by nonlinear flows, originally developed by J. R. Dorroh and J. W. Neuberger in the 1990’s [15], to approximate solutions of initial value problems like

x′(t) = F(x(t)), x(0) = x₀, (1)

where F = (F₁,··· ,F_N), and F_i : R^N ⊃ Ω -> R^N. The method, sometimes referred to as ``Bernard Koopman’s Global Linearization Method,” traces its origins back to the works of Sophus Lie in the 1890’s [30], Gerhard Kowalewski in …

Design Of Long-Distance Entanglement Distribution Protocols For Quantum Networks, Stav Haldar

LSU Doctoral Dissertations

Future quantum technologies such as quantum communication, quantum sensing, and distributed quantum computation, will rely on networks of shared entanglement between spatially separated nodes. Distributing entanglement between these nodes, especially over long distances, currently remains a challenge, due to limitations resulting from the fragility of quantum systems, such as photon losses, non-ideal measurements, and quantum memories with short coherence times. In the absence of full-scale fault-tolerant quantum error correction, which can in principle overcome these limitations, we should understand the extent to which we can circumvent these limitations. In this work, we provide improved protocols and policies for entanglement distribution …

Evaluating Past Progress And Assessing Prediction Breeding Strategies For Sustained Genetic Gains In The Louisiana Sugarcane Variety Development Program, Brayden A. Blanchard

LSU Doctoral Dissertations

The aim of this dissertation is to outline important considerations for the Louisiana Sugarcane Variety Development Program (LSVDP) as it pertains to historical progress, impact, goal setting, and new strategies for continued genetic gains. Industry progress was evaluated with robust regression models to quantify rates of productivity gains. Over the last 50 years, statistically significant productivity gains were identified in sucrose content (45%), cane yield (32.2%), and sugar yield (93%) while pairwise comparisons of decades showed that progress was incremental rather than rapid and sustained once achieved. The decade from 1990-1999 was identified as the only decade with a significant …

Molecular-Level Studies Of Nanopatterned Biomolecules With Atomic Force Microscopy, Ashley R. Walker

LSU Doctoral Dissertations

Atomic force microscopy (AFM) is an analytical technique in which a tipped probe is gently scanned across the surface in a raster pattern to generate digital images of a sample at the nanoscale. The AFM instrument has three general operational modes, which are contact, non-contact and tapping-mode, that can be used to examine materials at the atomic level. Single-molecular details of biological molecules and other soft organic materials can be captured with minimal denaturation in either ambient or liquid environments when using tapping-mode AFM. In tapping-mode, the probe is driven to oscillate vertically while the tip is scanned across the …

Decay Spectroscopy Of 134sb Using X-Array And Saturn, Graeme E. Morgan

LSU Doctoral Dissertations

The ground-state decay of ¹³⁴Sb is reported by the current evaluated nuclear data to be dominated by a 0^-→0⁺ first-forbidden Gamow-Teller transition to the ground state of ¹³⁴Te. In 2013, a recoil-ion time-of-flight (RI-TOF) spectroscopy measurement of ¹³⁴Sb with the Beta-decay Paul Trap (BPT) indicated that the ground-state feeding of ¹³⁴Te is weaker than reported. Simulation work of ¹³⁴Sb ground-state decays replicated the RI-TOF results with the addition of a theorised 5-MeV state that was fed with ~17% of the total β-decay strength. To search for higher energy states and transitions that …

Struggling To Be Positive Problem Solvers – A Study On The Relationship Of Elementary Mathematical Self-Concept, Gender, Learner Identification, And Productive Struggle Trajectories On Constructed Response Questions When Being Taught With A Standardized Curriculum, Kali D. Rogers

LSU Doctoral Dissertations

Mathematical word problems are some of the most difficult problems for students to solve due to their complexity and relationship to real-world situations (Şahin et al., 2014; Verschaffel et al., 2020). With math being known for right-or-wrong answers, these open-ended questions cause much confusion and frustration, specifically for students of various subgroups. In the last several decades, educational teaching expectations have shifted from engaging, self-created learning to robotic and redundant curriculum expectations that induce a ‘teaching to the test’ environment (Shafiyeva, 2021). Mathematics is the powerhouse of where students can experience and succeed with productive struggle learning that teaches the …

Examining The Authenticity Of The 'Ether Model' In Certain O-Glycosylation Reactions, Varad Vinayak Agarkar

LSU Doctoral Dissertations

Acinetobacter baumannii is a gram-negative bacterium species that is responsible for nosocomial infections. It has shown antibiotic resistance and has been designated an urgent threat by the CDC. In Chapter 1, I highlight my efforts in the synthesis of a Kdo building block in the journey towards the construction of an A. baumannii lipooligosaccharide (LOS) core pentasaccharide- a potential candidate for glycoconjugate vaccine against A. baumannii infection. I talk about various optimizations and improvements in the Kdo monosaccharide synthesis and the mechanistic insights I provided about a critical transformation in the synthetic sequence.

Chemical O-glycosylation is a significant research …

Multiphoton Quantum Sensing, Fatemeh Mostafavikhatam

LSU Doctoral Dissertations

While the fundamental principles of light-matter interaction are well-understood and drive countless technologies, the world of multiphoton processes remains a fascinating puzzle, holding the potential to drastically alter our understanding of how light interacts with matter at its most basic level [1–4]. This rich interplay of light and matter unveils novel phenomena that can be harnessed for sensing with exceptional precision, as exemplified by multiphoton quantum sensing. This thesis delves into the applications of multiphoton quantum protocols, particularly in imaging, communication, and plasmonic sensing, to surpass classical limitations and achieve enhanced sensitivity. We explore the potential of multiphoton quantum processes, …

Molybdenum Alkylidyne Complexes With Phenoxide Ligands For Alkyne Metathesis, Marvin L. Stewart Jr

LSU Doctoral Dissertations

Abstract

Alkyne metathesis is a powerful synthetic tool, which provides easy access to complex organic molecules in a single-step. It is a dynamic covalent reaction that scrambles alkynes, carbon-carbon triple bonds (C≡C). Molybdenum- or tungsten-alkylidyne (Mo≡C, W≡C) complexes are typically used as catalyst to cleave and reform alkyne bonds. Our goal has been to gain a deeper understanding of the intrinsic differences between functional ligands by the development of novel phenoxide ligands.

In chapter 2 we explore the detailed synthesis of novel phenoxide podand ligands in an effort to identify their mo-alkylidyne complexes. We were able to synthesize a variety …

Benthic Community Response To The Impacts Of Proposed Sediment Diversions In Louisiana Estuaries, Jillian C. Tupitza

LSU Doctoral Dissertations

Sediment diversions designed to mitigate land loss in coastal Louisiana will likely cause ecosystem-wide shifts. The first diversion, planned for Barataria Bay, will divert fresh water and sediment from the Mississippi River into the surrounding wetlands to help them keep pace with high rates of relative sea-level rise (RSLR). Estuarine benthic communities were used in this study as tools to characterize ecological patterns in the context of anticipated salinity changes. I reviewed relevant literature, conducted a two-year survey of Barataria Bay benthos, executed a reciprocal transplant experiment to describe changes that might occur in both community composition and trophic dynamics, …

The Lowest Discriminant Ideal Of Cayley-Hamilton Hopf Algebras, Zhongkai Mi

LSU Doctoral Dissertations

Discriminant ideals are defined for an algebra R with central subalgebra C and trace tr : R → C. They are indexed by positive integers and more general than discriminants. Usually R is required to be a finite module over C. Unlike the abundace of work on discriminants, there is hardly any literature on discriminant ideals. The levels of discriminant ideals relate to the sums of squares of dimensions of irreducible modules over maximal ideals of C containing these discriminant ideals. We study the lowest level when R is a Cayley-Hamilton Hopf algebra, i.e. C is also a Hopf subalgebra, …

All-Optical Probes Of Particle-Like Charge Migration Dynamics, Kyle A. Hamer

LSU Doctoral Dissertations

Particle-like charge migration (CM) is the coherent, back-and-forth motion of a positively-charged electron hole along the backbone of a molecule following a sudden ionization. CM in small molecules generally occurs on an Angstrom (10^-10 m) spatial scale and an attosecond (10^-18 s) timescale. I use time-dependent density-functional theory (TDDFT) to simulate CM modes in organic molecules, and to explore all-optical probes of this attosecond electron dynamics using high-harmonic spectroscopy (HHS). By leveraging my results from previous studies of two-center interferences in carbon dichalcogens, in which I separated the harmonic signal into contributions from individual Kohn-Sham orbitals, I first …