Shadowable Diffeomorphisms With Dominated Splitting, Naoya Sumi

Journal of Stochastic Analysis

We study the shadowability for diffeomorphisms with dominated

splitting. In this paper we show that if a diffeomorphism f has a periodic

saddle q whose unstable manifold is compatible with dominated splitting in

some sense and if f is shadowable, then any other periodic point p has a large

local stable set. Our result does not require the hyperbolicity of p.

On A Remark Of De Gennes Concerning Three-Dimensional Polyelectrolytes, Shiquan Li, Carl Mueller

Journal of Stochastic Analysis

This work is inspired by a remark of de Gennes [3] about polyelectrolytes, which are charged polymers. A common model for a polymer is a self-avoiding or self-repelling random walk or Brownian motion. For polyelectrolytes, the repelling potential is the Coulomb potential arising from pairs of charged particles. We show that in the continuous case of a Brownian motion in three dimensions, the spread of the polymer, in particular the radius of gyration of a polyelectrolyte of length T grows linearly with T, up to logarithmic corrections.

On The Existence, Uniqueness And Stability Of Solutions Of Sdes With State-Dependent Variable Exponent, Mustafa Avci

Journal of Stochastic Analysis

We study a time-inhomogeneous nonlinear SDE with drift and diffusion governed by state-dependent variable exponents. This framework generalizes models like the geometric Brownian motion (GBM) and the constant elasticity of variance (CEV), offering flexibility to capture complex dynamics while posing analytical challenges. Using a fixed-point approach, we prove existence and uniqueness, analyze higher-order moments, derive asymptotic estimates, and assess stability. Finally, we illustrate an application where Poisson’s equation admits a probabilistic representation via a timehomogeneous nonlinear SDE with state-dependent variable exponents.

Companion Matrices Associated To Stochastic Matrices, Andreas Boukas, Philip Feinsilver

Journal of Stochastic Analysis

Starting with a stochastic matrix, we study the behavior of powers of an associated companion matrix, which has the same characteristic polynomial as the original matrix. In general the companion matrix will have negative entries while maintaining rowsums equal to 1. We will find the growth rate even if the Ces`aro limit of the sums of the companion matrix diverge. Surprisingly, in the irreducible aperiodic case the powers of the companion matrix will converge even though the norm of the matrix exceeds 1 and it has possibly negative entries.

Z+-Valued Additive Processes In Law With Nonnegative Increments, Nadjib Bouzar

Journal of Stochastic Analysis

The goal of this article is to study in depth the subclass of Z+- valued additive processes in law with nonnegative increments. We establish key distributional properties of these processes and obtain some existence results under a variety of conditions. We show that they form a subclass of the family of inhomogeneous Markov chains with spatial homogeneity. We extend the notion of factoring introduced by Sato (2004, [9]) for Rd-valued additive processes in law to their Z+-valued counterparts with nonnegative increments. We give a sufficient condition for the existence of a factoring for these processes. Lastly, we obtain their representation …

Correlative In Situ Nonlinear Optical Characteriztion Of Plasmonic Colloidal Nanoparticle Growth Dynamics, Stena C. Peterson

LSU Doctoral Dissertations

Colloidal noble metal nanoparticles are of extreme interest as nanomaterials and for the wide variety of their possible applications in nanomedicine. The unique linear and nonlinear optical processes associated with these nanomaterials can be studied using a variety of spectroscopic techniques including extinction, second harmonic generation (SHG), and two-photon fluorescence (TPF) spectroscopy. In order to better understand and optimize these nanomaterials for their desired applications, it is important to investigate the growth and photophysical dynamics associated with gold nanoparticles, silver-gold core-shell (Ag-Au CS) nanoparticles, and gold-silver-gold core-shell-shell (Au-Ag-Au CSS) nanoparticles in addition to how their size, surface morphology, composition. and …

Extreme Geomagnetic Storm Effects On Earth's Radiation Belts Observed By Calet On The International Space Station, Anthony W. Ficklin

LSU Doctoral Dissertations

This dissertation examines changes in Earth's energetic-particle environment using measurements from the Calorimetric Electron Telescope (CALET) on the International Space Station. Although CALET was designed primarily for high-energy cosmic-ray and gamma-ray observations, its count rates provide nearly continuous measurements of particles of ~1 MeV and above. The analysis uses the CHDX, CHDY, and IMC4X channels, which have approximate electron thresholds of $>\!1.5$, $\!>3.4$, and $\!>8.2$~MeV and proton thresholds of $>\!17$, $\!>37$, and $\!>52$~MeV, respectively. Because these measurements do not identify particle species, the observations are interpreted using their geographic and geomagnetic distributions, the relative …

Long-Term Effects Of Harvesting Disturbance And Site Preparation On Soil Properties And Tree Growth In A Loblolly Pine (Pinus Taeda) Forest, Kyle M. Caccamesi

LSU Master's Theses

Productivity decline between rotations has long been a concern in intensively managed forest plantations. Research done over the last century has provided greater clarity on why this phenomenon occurs. The objective of this research was to observe long-term soil and tree growth characteristics that are likely to be influenced by operational harvesting activities. The experiment was conducted in Washington Parish, Louisiana on a site dominated by Ruston soil series, a well-drained, fine loamy, siliceous and thermic typic Paleudult. A randomized complete block design with 2 x 2 x 2 factorial treatments was used. The treatment factors were harvesting method, fertilization, …

The Study Of Hydrophobic Biomolecules With Matrix Assisted Laser Desorption Ionization Mass Spectrometry And Atomic Force Microscopy, Brandy L. Perkins

LSU Doctoral Dissertations

Abstract

Matrix assisted laser desorption ionization (MALDI) mass spectrometry (MS) can be used to obtain localization and chemical information of hydrophobic biomolecules on tissue samples.  A technique has been developed to modify a standard MALDI matrix that improves the selectivity for hydrophobic biomolecules on the tissue sample. The modification involves the use of a Group of Uniform Materials Based on Organic Salts (GUMBOS). GUMBOS are ionic liquids (IL) that are bulky organic ions with a counter ion that can be changed for tuning.  They are more stable than traditional matrices under vacuum.  Unlike traditional IL’s, the GUMBOS melting point ranges …

A Data-Driven Framework For Mitigating Breast Cancer Overdiagnosis: From Estimation To Risk-Adjusted Computer-Aided Diagnosis, William M. Brown Jr.

LSU Doctoral Dissertations

In Computer-Aided Diagnosis (CAD) of cancer, standard cost metrics (false-positives and false-negatives) fundamentally fail to account for overdiagnosis. Overdiagnosis is a critical scenario where a disease is correctly detected (true-positive) but is biologically indolent and would never have caused the patient harm or symptoms. While widely recognized in the medical community as a major healthcare crisis driving stressful and invasive overtreatment, overdiagnosis remains severely under-researched within computer science and engineering. This dissertation addresses this interdisciplinary gap by defining the three key computational challenges of overdiagnosis: (i) accurate estimation, (ii) harm quantification, and (iii) algorithmic mitigation. To overcome the estimation challenge, …

Scattered Light Noise At Ligo Livingston Observatory Induced By Microseismic Ground Motion, Debasmita Nandi

LSU Doctoral Dissertations

Gravitational waves are “ripples” in the fabric of spacetime and create a minuscule change in the distance between two points. After publishing his theory of general relativity in 1915, Albert Einstein predicted the existence of gravitational waves as a consequence of the theory. Almost 100 years after the theoretical prediction, gravitational waves were detected for the first time in 2015 by the Advanced LIGO detectors in Livingston, Louisiana, and Hanford, Washington. Gravitational waves have a very small amplitude, making it very challenging to detect them. Different types of noise sources either of instrumental or environmental origin can reduce the astrophysical …

Cooperative Evolution For Discovering Scalable Spiking Neural Network Architectures, Catherine C. Rodriquez

LSU Master's Theses

SNNs are a foundational model in neuromorphic computing, where efficient architectures must be discovered for a wide range of applications. Evolutionary methods, such as EONS, offer a flexible approach to this search but become increasingly difficult to scale as task complexity grows due to the rapidly expanding combined topology–parameter search space and associated memory demands. To address this challenge, we propose a co-evolutionary ensemble framework in which a population of candidate SNNs is evolved with fitness defined by each network’s marginal contribution to group performance. Grounded in cooperative game theory and difference evaluation functions from multiagent systems, this formulation provides …

Statistical Evaluation Of A New Orleans Historic Rainfall Dataset (1840–1893), Arielle C. Filostrat

LSU Master's Theses

This study evaluates the climatic credibility of a newly identified historical rainfall dataset for New Orleans, Louisiana, spanning 1840–1893. The New Orleans Historical Dataset (NOHD) is compared to a modern observational record from the Audubon rain gauge (1893–2024) to determine whether nineteenth-century rainfall observations are consistent with known precipitation behavior in the region. Establishing the reliability of early records is critical for extending climatological baselines and improving understanding of long-term rainfall variability.

Historical rainfall observations were first evaluated through archival review using the New Orleans Medical and Surgical Journal and other nineteenth-century meteorological records to verify notable rainfall events. Daily …

A Stochastic Maximum Principle For Singular Mean-Field Regime-Switching Optimal Control, Maalvladedon Ganet Some, Edward Korveh

Journal of Stochastic Analysis

In this paper, we investigate a mean-field singular stochastic optimal control problem for systems governed by mean-field regime-switching singular stochastic differential equations. The state process is assumed to depend on both a regular and a singular control, and the coefficient associated with the singular component is allowed to be regime dependent. We derive both necessary and sufficient singular stochastic maximum principles. Because the regular control domain is not assumed to be convex, we employ the spike variation technique and obtain the necessary maximum principle by introducing a second-order adjoint process. As an application, we use the main theoretical results to …

Generalized Delayed Black–Scholes Formula, Bi Gole Hubert Le, Auguste Aman

Journal of Stochastic Analysis

The aim of this paper is to derive an explicit pricing formula for European options when the underlying asset follows a linear generalized delay differential equation in two distinct financial markets. The pricing methodology is based on the construction of an equivalent martingale measure using Girsanov’s theorem. Our models preserve both the no-arbitrage condition and market completeness. As such, this work extends the framework previously developed by Arriojas et al. in [16], providing a broader class of delay-based option pricing models.

Robust Optimal Consumption, Investment And Reinsurance For Recursive Preferences, Elizabeth Dadzie, Wilfried Kuissi Kamdem, Marcel Ndengo

Journal of Stochastic Analysis

This paper investigates a robust optimal consumption, investment, and reinsurance problem for an insurer with Epstein-Zin recursive preferences operating under model uncertainty. The insurer’s surplus follows the diffusion approximation of the Cramér-Lundberg model, and the insurer can purchase proportional reinsurance. Model ambiguity is characterised by a class of equivalent probability measures, and the insurer, being ambiguity-averse, aims to maximise utility under the worst-case scenario. By solving the associated coupled forward-backward stochastic differential equation (FBSDE), we derive closed-form solutions for the optimal strategies and the value function. Our analysis reveals how ambiguity aversion, risk aversion, and the elasticity of intertemporal substitution …

An Itô Integral For A Two-Sided Lévy Process, Raluca Balan, Jaime Garza

Journal of Stochastic Analysis

In this article, we construct an Itô integral with respect to a two-sided finite-variance Lévy process {L(x)}x∈R, without a Gaussian component. Using Rosenthal inequality for discrete-time martingales, we give an estimate for the p-th moment of this integral, for any even integer p ≥ 2. Then, using Poisson-Malliavin calculus, we show that the Itô integral is an extension of the Hitsuda-Skorokhod integral with respect to the compensated Poisson random measure associated to the Lévy process.

Supersymmetric Quantum Fields Via Quantum Probability, Radhakrishnan Balu

Journal of Stochastic Analysis

The super version of imprimitivity theorem is available now to describe global supersymmetry of systems using the representations of super Lie groups (SLG). This result uses the equivalence between super Harish- Chandra pairs and super Lie groups, at the categorical level, and is applicable to super Poincaré group and generalizes a smooth SI to super context. We apply the result to build supersymmetric quantum fields. Towards this end, we set up a super Fock space of a disjoint union of super Hilbert spaces which is equivalent to super tensoring of boson (even) part symmetrically and that of fermion (odd) part …

Convergence To Fractional Brownian Motion For Weighted Random Sums In Besov Space, Ibrahima Mendy

Journal of Stochastic Analysis

We consider infinite sums of weighted i.i.d. random variables, with finite variance and arbitrary distribution, and we derives conditions for the weak convergence in Besov space of normalized sums to fractional Brownian motion (fBm).

Pricing Variance Swaps Using Extended Heston Model, Semere Gebresilasie, Mulue Gebreslasie, Indranil Sengupta

Journal of Stochastic Analysis

Abstract. In this study, we introduce a variance swap for the underlying asset utilizing the Heston model, incorporating a long-term variance that is treated as a stochastic function of time. We develop a closed-form solution for the variance swap under this framework, where the log returns are driven by a compound Poisson process. Our analysis of historical data reveals that long-term variance is not constant; instead, it fluctuates over time, reflecting market dynamics more accurately. By integrating this time-varying long-term variance into the model, we achieve an improvement in prediction performance of approximately 60%. Furthermore, we perform model calibration using …

Movement Ecology And Population Dynamics Of Box-Nesting Black-Bellied Whistling-Ducks (Dendrocygna Autumnalis) In Louisiana, Katie E. Miranda

LSU Master's Theses

Understanding demographic and behavioral processes underlying population dynamics is essential for effective wildlife management, especially for species subject to harvest pressure or experiencing population shifts. Black-bellied Whistling-Ducks (Dendrocygna autumnalis) are currently undergoing a notable northward range expansion and are increasing in abundance across the southeastern United States, raising management concerns for both ecological and economic reasons. As a result, there is growing public support for a special Black-bellied Whistling-Duck-specific harvest season, yet little research has been conducted on this species, particularly within newly-established populations. To address this gap, I conducted this study with the goal of evaluating seasonal …

The Case For Ice Rises At Ross Bank Since The Middle Miocene, William Weber

LSU Master's Theses

Many tens of ice rises exist at the marine margins of the Antarctic Ice Sheet. Isle-type ice rises in particular are those where an ice shelf is pinned to an underlying submarine bank. Recent and ongoing studies show that Ross Bank, on the middle continental shelf of central Ross Sea, was the former site of an important Ross Ice Shelf ice rise during the advance and retreat of the West Antarctic Ice Sheet (WAIS) in the last glacial cycle. Ross Bank is a broad and anomalously shallow water platform whose crest rises to 170 m water depth. Despite their importance …

Unraveling The Nanoscopic Characteristics Of The Heterogeneous Deep Eutectic Solvent Formed By Lauric Acid And N-Methylacetamide: An Experimental And Computational Approach, Laura X. Sepulveda

LSU Doctoral Dissertations

Deep eutectic solvents (DESs) are attractive systems for extraction and separation of compounds. One example of this is the DES formed by the combination of lauric acid (LA) and N-methylacetamide (NMA), system that has been shown to efficiently separate oil/water mixtures through gel formation between LA and oil molecules. Structural characterization of this system using small-angle X-ray scattering (SAXS) and vibrational spectroscopy revealed the existence of nanometer-scale LA domains embedded in a continuous polar NMA phase, where LA and NMA interact through hydrogen bonding. These LA domains are responsible for the separation efficiency of linear organic molecules. However, this DES …

Evaluating Soil Health And Crop Yield In Louisiana Agricultural Systems: Impacts Of Best Management Practices And Prediction Models, Hector J. Mendoza Lagos

LSU Doctoral Dissertations

The adoption of conservation management practices is critical for improving soil health, enhancing nutrient use efficiency, and sustaining crop productivity in row crop systems in Louisiana. This study evaluated the role of conservation agronomic practices, soil biochemical indicators, and machine learning predictive models to improve soil nutrient dynamics, soil health indicators, microbial communities (MC), and crop productivity on a corn (Zea mays L.) research plot scale and in a commercial forty-hectare cotton (Gassypium hirsutum L.)-corn-soybean (Glycine max L.) rotation system in northeast Louisiana. The objectives of the study were to evaluate soil nutrient dynamics and MCs under …

Commissioning And Validation Of An Electron Treatment Planning System: Following Mppg.5.B Guidelines, Hailey N. Reaux

LSU Master's Theses

Purpose: The purpose of this work was to commission and validate the electron treatment planning system ElectronRT (eRT) (.decimal, Sanford, FL) for clinical use following the recommendations outlined in the American Association of Physicists in Medicine (AAPM) Medical Physics Practice Guideline (MPPG) 5.b (2022). The system’s ability to accurately calculate electron dose distributions was evaluated under normal and oblique beam incidence, varying field sizes and source-to-surface distances (SSDs), and irregular surface geometries.

Methods: The eRT beam model was configured using commissioning data from an Elekta Infinity linear accelerator at Mary Bird Perkins Cancer Center (MBPCC). Validation measurements were performed for …

Distributed File Carving, Brad J. Baudin

LSU Master's Theses

File carving is a fundamental technique in the digital forensics community, enabling analysts to recover deleted files from disk images without relying on filesystem metadata; however, as storage capacities continue to increase, modern file carving tools face significant scalability challenges, with carving time growing substantially alongside disk image size, particularly in the presence of file fragmentation. Fragmentation, a common behavior in modern filesystems, distributes file data across non-contiguous disk blocks to maximize space utilization, and in large disk images this distribution can span wide logical distances, increasing the search space and reducing carving efficiency, causing traditional approaches to struggle within …

Momentum Space Algorithm For Electronic Structure Of Double-Incommensurate Trilayer Graphene, Kenneth Silver Beard

LSU Doctoral Dissertations

Numerical algorithms for computing the electronic structure of incommensurate 2D-materials using ab initio models are critical for predicting material properties and guiding experiments. For bilayers, momentum space and continuum models have been introduced to approximate observables of ab initio tight-binding models using a momentum description, despite the lack of periodicity in the tight-binding model required for Bloch theory. A similar structure has been introduced for double-incommensurate trilayers using a continuum model, where the three lattices are mutually incommensurate. However, this description leads to a four-dimensional lattice space, and numerical convergence of the density of states has been observed to be …

Greedy Algorithms And Matroids, Kiri M. Strack

LSU Master's Theses

In a connected graph with weights on the edges, a minimum-weight spanning tree can be obtained by repeatedly choosing minimum-weight edges while avoiding choosing the edge set of any cycle. This algorithm is known as Kruskal’s Algorithm, although it was first introduced by Boruvka in 1926. Prim introduced an alternative algorithm in which, at each step, the chosen set of edges forms a connected graph. Both of these algorithms make locally optimal choices that eventually yield a global optimum. This thesis considers how these algorithms can be extended to matroids. In particular, it is shown that matroids are exactly the …

Automated Analysis Of Radiation Oncology Incident Reports Using Large Language Models, Nathan A. Dobranski

LSU Master's Theses

Patient safety incident reporting in radiation oncology requires expert analysis that is time-intensive and subject to variability. This thesis presents the development and technical validation of a locally deployed large language model (LLM) system for automated incident report analysis across multiple cancer centers. The system was designed for automated summarization and taxonomy assignment of Radiation Oncology Incident Learning System (RO-ILS) reports, operating entirely on local infrastructure to preserve patient privacy. A two-round, multi-rater evaluation methodology was employed, incorporating 600 total expert evaluations from two academic cancer centers. Round 1 established baseline performance using Mistral 7B and Mixtral 8x7B models with …

Recent Wetland Elevation Dynamics In Coastal Louisiana, Usa, Elizabeth Harris

LSU Master's Theses

Coastal marshes globally are increasingly vulnerable to accelerating relative sea-level rise (RSLR), which threatens their capacity to maintain elevation through feedbacks among sediment supply, vegetation productivity, hydrology, and soil processes. Although many marshes can persist under moderate rates of sea-level rise through vertical accretion and belowground biomass production, this resilience is strongly constrained by sediment availability and subsurface processes such as autocompaction and organic matter decomposition. High accretion is often assumed to confer marsh resilience; however, subsurface processes, particularly autocompaction driven by surface loading, can substantially offset elevation gains. Coastal Louisiana experiences among the highest rates of RSLR worldwide due …