Physical Sciences and Mathematics Commons^™

The Product Formula Of Multiple Stochastic Integrals With Respect To The Poisson Space Noise, Yuh-Jia Lee, Hsin-Hung Shih

Journal of Stochastic Analysis

No abstract provided.

American Option Pricing Using Generalised Stochastic Hybrid Systems, Evelyn Buckwar, Sascha Desmettre, Agnes Mallinger, Amira Meddah

Journal of Stochastic Analysis

No abstract provided.

About Fixed Points Of Quantum Channels, Raffaella Carbone

Journal of Stochastic Analysis

No abstract provided.

Induced-Minor-Closed Classes Of Matroids, James Dylan Douthitt

LSU Doctoral Dissertations

A graph is chordal if every cycle of length at least four has a chord. In 1961, Dirac characterized chordal graphs as those graphs that can be built from complete graphs by repeated clique-sums. Generalizing this, we consider the class of simple GF(q)-representable matroids that can be built from projective geometries over GF(q) by repeated generalized parallel connections across projective geometries. We show that this class of matroids is closed under induced minors and characterize the class by its forbidden induced minors, noting that the case when q=2 is distinctive. Additionally, we show that the class of GF(2)-chordal matroids coincides …

Infrared Laser Ablation Of Biomolecules From Formalin-Fixed Tissue, Blessing Chisom Egbejiogu

LSU Doctoral Dissertations

In the research described in this dissertation, a high-precision infrared laser ablation microsampling method was utilized for spatially resolved proteomic and lipidomic analyses of formalin fixed paraffin embedded (FFPE) tissue, a widely used archival sample in biomedical research. Despite its extensive use, FFPE tissue presents challenges for proteomic analysis due to protein cross-linking and modifications introduced during fixation, which can hinder extraction and identification. Developing a streamlined high-resolution method to recover biomolecules from FFPE samples is critical for advancing biomarker discovery, retrospective studies, and multi-omics research. To address these challenges, this study employs an infrared (IR) laser ablation microdissection system …

Ornstein-Uhlenbeck Type Operators Induced By Some Geometric Structures On Complex Domains, Souheyl Jendoubu

Journal of Stochastic Analysis

No abstract provided.

Quantum Extensions Of The Exotic Laplacians And Associated Quantum Heat Semigroups, Luigi Accardi, Un Cig Ji, Kimiaki Saito

Journal of Stochastic Analysis

No abstract provided.

Preface, José Luis Da Silva, Un Cig Ji, Aurel Stan

Journal of Stochastic Analysis

No abstract provided.

Non-Orientable Surfaces Bounded By Knots, Megan K. Fairchild

LSU Doctoral Dissertations

The non-orientable 4-genus of a knot $K$ in $S^{3}$ is defined to be the minimum first Betti number of a non-orientable surface $F$ in $B^{4}$ so that $K$ bounds $F$. We will survey the tools used to compute the non-orientable 4-genus, and use various techniques to calculate this invariant for non-alternating 11 crossing knots, torus knots, and Whitehead doubles. We also will view obstructions to a knot bounding a M\"{o}bius band given by the double branched cover of $S^{3}$ branched over $K$. Additionally, we discuss the problem of the Whitehead double of the Figure 8 knot and survey commonly used …

Weak Solutions Of Spdes In The Space Of Tempered Distributions, Suprio Bhar, Barun Sarkar

Journal of Stochastic Analysis

No abstract provided.

A Family Of Markov Chains, Schur Functions, And Exterior Powers, Philip Feinsilver, John P. Mcsorley

Journal of Stochastic Analysis

No abstract provided.

On An Asset Model Of Merton Type: Long-Term Observations In Financial Time-Series, Shuya Kanagawa, Narn-Rueih Shieh

Journal of Stochastic Analysis

No abstract provided.

Temporal Scales Of Sediment Accumulation, Mass Wasting, And Stratigraphy Across The Mississippi River Delta Front, Jeffrey E. Duxbury

LSU Doctoral Dissertations

The Mississippi River Delta Front (MRDF) is a subaqueous apron of rapidly deposited, weakly

consolidated sediment extending from the subaerial portions of the Mississippi River’s Birdsfoot Delta, historically known for sediment transport via mass wasting. To better understand the spatial and temporal dynamics of processes influencing the MRDF, 29 cores ranging from 5.8 to 8.71 meters in length were collected from the South Pass (SP) and Southwest Passes (SWP). These cores targeted specific depositional environments, including the undisturbed topset apron, medial mudflow gully, mudflow lobe, and prodelta. The cores were analyzed along their full lengths for gamma density, grain size, …

Thermal Noise Measurement Below The Standard Quantum Limit, Ronald Pagano

LSU Doctoral Dissertations

Quantum mechanics places sensitivity restrictions on physical measurements. These limitations manifest themselves in interferometric force and displacement measurements as uncertainty both in the photon number measured at a photodetector (shot noise), and in the quantum radiation pressure applied to the interferometer (quantum back action noise manifested as quantum radiation pressure noise). The balance between shot noise and quantum radiation pressure noise imposes the Standard Quantum Limit (SQL). A large body of work has been dedicated to measuring these quantum effects and mitigating them. Owing to the inherently small scale at which quantum effects are visible, classical effects must be subverted …

Studying The Low-Lying Structure Of 9b Via The 10b(3he,A)9b Reaction, Rachel M. Shaffer

LSU Doctoral Dissertations

The unstable nature of ⁹B makes it a challenging isotope to study. The first-excited state of ⁹B has been particularly difficult to characterize. Since the first experimental observation of this state in 1955, many experimental and theoretical nuclear structure studies have sought to classify it, but with large discrepancies in the energy and width values from these results, the properties of the state remain inconclusive.

An experiment using the ¹⁰B(³He,α)⁹B reaction was performed at the John D. Fox Superconducting Linear Accelerator Laboratory at Florida State University in an effort to populate and characterize …

Baryon Number Violation Search, Tyler D. Stokes

LSU Doctoral Dissertations

Understanding the fundamental forces and symmetries of nature has long been a central goal of particle physics. While the Standard Model (SM) provides a successful framework, it does not guarantee the conservation of baryon number B or lepton number L, thus motivating searches for their violation. Proton decay, a fundamental process violating B, has been at the forefront of experimental searches for decades.

The discovery of the weak neutral current in 1973 unified the electromagnetic and weak forces and inspired the creation of Grand Unified Theories (GUTs) that also unify the strong force. In 1974, the first-ever GUT, …

Malliavin Calculus On The Clifford Algebra, Takayoshi Watanabe

Journal of Stochastic Analysis

No abstract provided.

Modelling Uncertain Volatility Using Quantum Stochastic Calculus: Unitary Vs Non-Unitary Time Evolution, Will Hicks

Journal of Stochastic Analysis

No abstract provided.

Synthesis And Characterization Of Bimetallic Plasmonic Nanoparticles Using Linear And Nonlinear Spectroscopy, Daniel Babayode

LSU Doctoral Dissertations

Recent exploration in the field of nanomaterials has led to the investigation of noble metal nanoparticles for various nanomedical applications. The spectroscopy of these nanoparticles is studied using both linear and nonlinear optical processes such as second harmonic generation (SHG), two-photon fluorescence (TPF), and extinction spectroscopy. Details pertaining to the growth dynamics of silver-gold core-shell (Ag@Au CS) nanoparticles (NPs) and gold-silver-gold core-shell-shell (Au@Ag@Au CSS) nanoparticles (NPs) are currently being investigated in order to obtain better control and optimization of the nanoparticle size and surface morphology. Transmission electron microscopy (TEM) images show that the nanoparticles have tunable core and shell sizes …

The Math Mind Measures: A User Guide, H. Colleen Sinclair, Stacey R. Terrio, Youn Kyoung Kim

Reports

The development of the Math Mind Measures survey originated from a research-practitioner partnership (RPP) project funded by The Gates Foundation (namely the R+D Partnership for Math Equity). As a part of the project, our team wanted to understand what contributes to math motivation in students. Unfortunately, when looking for instruments to assess motivation we could find little consensus on which motivational factor(s) mattered most and how to measure them.

Long forms: Consequently, we integrated and strengthened existing measures – where available – of 10 different motivational variables, developing a pool of 138 items. We call this collection of items the …

Physics-Informed Heterogeneous Spatiotemporal Graph Neural Network For Reservoir Simulation, Ahmed A.M.A. Abdullah

LSU Master's Theses

Reservoir simulation is the state-of-the-art method for predicting the flow of petroleum reservoir fluids in porous media. It provides an accurate and unbiased prediction of the performance of petroleum reservoirs under different operating conditions. Despite its advantages, reservoir simulation is computationally expensive; with typical full-field simulation models running for several hours. This limitation is worsened when simulating reservoirs with several equations for each cell, such as multiphysics or compositional reservoir simulation. The goal of this research is to provide a fast and accurate spatiotemporal machine-learning model that incorporates discretized governing mass balance equations for training. To achieve this, we propose …

Nanofabrication Of Tetraphenyl Porphyrin Surface Assemblies Linked With Tin Tetrachloride: A Scanning Probe Microscopy Investigation, Quynh Do

LSU Doctoral Dissertations

Scanning probe microscopy (SPM) and colloidal lithography methods were used to study the covalent coupling of porphyrins to surfaces. In this dissertation, experimental methods for SPM operation, techniques, and applications are described. Measurement of tip-sample interactions between a sharp tip and surface is translated into digital image data maps with x-, y-, and z-data. Colloidal lithography can be used to fabricate test platforms for AFM studies. The periodicity and arrangement of the designed nanostructures is determined by the size of the colloidal particles used for surface masks. Data processing is required to obtain images and topography information from raw AFM …

Understanding Mechanisms For Coastal Marsh Sustainability In A Changing Climate, Ashley R. Booth

LSU Doctoral Dissertations

In the Chenier Plain of Louisiana and Texas, coastal marshes are subject to high rates of relative sea level rise (RSLR), restricted sedimentation, and declining elevation attributed to subsidence and decades of intensive management. These marshes were created via mineral sedimentation but now largely accrete via organic matter accumulation. This organic matter accumulation (OMA) – or the balance between plant productivity and decomposition – is essential for maintaining elevation and thus long-term sustainability. However, management for elevation is complicated by a poor understanding of how abiotic factors like flooding and salinity impact processes driving OMA and elevation. To better understand …

Vision-Language Integration For Enhanced Locomotion Mode Prediction, Ehsan Ahmadi

LSU Master's Theses

Wearable exoskeletons offer significant potential in enhancing human mobility in industrial environments. However, their adaptability to dynamic, task-intensive settings presents challenges, especially in accurately predicting locomotion modes such as ladder climbing, stair navigation, low-space movement, and obstacle navigation. This research proposes a multimodal framework that integrates visual data and speech commands to improve locomotion mode prediction in unpredictable environments. Multimodal data was collected using smart glasses, capturing both the user’s perspective (field-of-view, FOV) and voice during locomotion tasks. State-of-the-art models—CLIP, ImageBind, and GPT-4o—process these visual and linguistic inputs to predict locomotion activities. The models were evaluated in zero-shot and fine-tuned …

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 …

Improving Rice Yield Using Sensor Based Nitrogen Application And Best Management Practices (Bmps) In Rice-Soybean And Rice-Crawfish Rotational Systems, Charles Darnall

LSU Master's Theses

Sustainable rice farming requires effective nutrient management and conservation practices to maintain high yields and minimize environmental impact. Implementing best management practices (BMPs) promotes lower fertilizer application rates, increased N use efficiency, improves soil health, and water quality. Demonstration fields established in two different rotational cropping systems (rice-soybean and rice-crawfish) in Kaplan, LA in 2023. In each rotation system, the benefits of BMPs (sensor based mid-season N management and cover cropping) compared to farmer’s practice (FP) were evaluated using yield, yield components, soil and water quality as metrics. The rice-soybean fields in 2023 and 2024 were both planted with PVL03 …

Cp Decomposition Initialization Schemes For Speeding-Up Of Convolutional Neural Networks, Mollee M. Swift

LSU Master's Theses

While machine learning and convolutional neural networks (CNNs) are making strides, a persistent effort remains to optimize classification techniques and target redundancies from a large number of parameters naturally present in CNNs. While CNNs have become more accessible across machine learning, the aim is to make their use optimal for central processing unit (CPU) schemes with varying degrees of computational power. Tensor decomposition methods, specifically canonical polyadic (CP) decomposition, look to reduce parameters by compressing specific layers in a CNN. However, they have certain inconsistencies, and their full potential remains untouched as decomposition research is endless, with many facets one …

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, …