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 …

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 …

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 …

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 …

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 …

Machine Learning Based Models For Simulation And Analysis Of Bulk Earth Melt System, Abin Shakya

LSU Doctoral Dissertations

Understanding the segregation of bulk Earth melt systems into metallic (core) and silicate (mantle) phases under high-pressure and high-temperature conditions is central to modeling Earth’s interior, yet relevant experimental and computational studies remain limited. This work develops a machine learning–based simulation pipeline that iteratively couples first-principles (quantum mechanical) calculations with neural network training to generate high-fidelity force fields. Using major-element Fe–Mg–Si–O melt systems, with and without H and N, as testbeds, we demonstrate that this framework enables large-scale molecular dynamics simulations at near first-principles accuracy. We further introduce a sequence of phase identification methods, progressing from statistical binning of elemental …

Extremal Connectivity In Graphs And Matroids, Yiwei Ge

LSU Doctoral Dissertations

Connectivity is a central theme in both graph theory and matroid theory. This dissertation investigates extremal connectivity in graphs and matroids, with emphasis on unavoidable structures and minimal connectivity phenomena.

Chapter 2 introduces cycle-contraction minors of graphs and investigates their structural properties. We establish a connection between cc-minors and induced subgraphs via graph duality. The main result gives an unavoidable-families characterization for cc-minors of sufficiently large loopless $2$-connected graphs.

Chapter 3 studies super-minimally $3$-connected graphs, namely $3$-connected graphs that have no proper $3$-connected subgraphs. We establish extremal bounds on structural parameters of these graphs, including the minimum number of degree-$3$ …

Circuits And Enumeration Problems For Matroids, Christine H. Cho

LSU Doctoral Dissertations

This dissertation is a collection of work concerning the structure and enumeration of circuits and other distinguished sets in a matroid. The Tutte polynomial, recognized as the universal deletion-contraction invariant in matroid and graph theory, is a natural starting point when considering enumeration problems for matroids. The main result in Chapter 2 generalizes a theorem of Dean Lucas concerning the Tutte polynomial and its behavior under rank-preserving weak maps. This generalization provides an avenue for comparing the numbers of circuits, bases, rank-k flats, and hyperplanes of a matroid containing an element given two distinct, yet related, elements.

Chapter 3 addresses …

Curriculum For A Two Semester Calculus Course Specializing In Life Science And Data Science, Patrick Mcclain

LSU Master's Theses

Traditionally, introductory calculus has been designed for engineering and physics students, often leaving students majoring in data science or life sciences with a curriculum that lacks professional relevance and is overly reliant on problems that focus on computational fluency. This thesis proposes a two-semester sequence, called MATH 153X and MATH 154X, specifically tailored for the Louisiana State University (LSU) Dual Enrollment program and university-level data science and life sciences majors. By integrating modern computational tools—such as symbolic calculators and artificial intelligence (AI) tools—the proposed curriculum shifts the pedagogical focus from procedural symbolic manipulation toward conceptual literacy.

Through a series …

Effect Of Light Elements On The Melting Behavior Of Liquid Iron Alloys Under Earth’S Inner Core Boundary Conditions, Olaniyi Anisere

LSU Master's Theses

The temperature at Earth’s inner core boundary (ICB) is set by the melting temperature of the iron-rich outer core at core pressures, yet this remains uncertain because melting depends strongly on composition and pressure. Light elements are required to explain the core’s density deficit, but the identity, abundance, and combined influence of these elements on melting under ICB conditions are still debated. This thesis quantifies how candidate light elements modify the melting behavior of iron alloys at ICB-relevant pressures and uses these composition-dependent melting relations to constrain ICB temperature.

Melting relations were determined using molecular dynamics simulations in VASP accelerated …

Marine Vehicle Dynamics Using Koopman Operator Theory With Hybrid Observables, Mikhalib A L Green

LSU Master's Theses

Accurate modeling of marine vehicle dynamics remains challenging due to strong nonlinear hydrodynamic effects, environmental disturbances, and sensitivity to configuration changes, particularly for small-scale platforms. Classical physics-based models require extensive parameter identification and often exhibit degraded performance outside narrow operating regimes, while purely data-driven approaches may lack structure or impose high computational cost. This thesis presents a data-driven Koopman operator framework with hybrid observables for modeling the dynamics of unmanned marine vehicles. The proposed approach combines structured monomial observables with a learned neural network embedding to construct a lifted state representation in which the nonlinear vehicle dynamics are approximated by …

Large-Scale File Fragment Classification Via Multi-View Learning, Samuel Hildebrand

LSU Master's Theses

File reassembly is one of the most fundamental tasks in digital forensics, enabling recovery of data from potentially damaged storage media even when file system metadata is unavailable. This thesis reviews more than two decades of work in the realm of file carving, with a particular focus on fragmented file carving, which remains a focus of research, and file fragment classification, a principal component of fragmented file carving. This thesis serves a literature review of both file carving and fragmented file carving, surveys the massive amounts of data needed for the task of fragment classification and the datasets that serve …

From Network Packets To Physical Consequences: Network-Level Spoofing And Loss Of Visibility In Industrial Control Systems, Lillian B. Beck

LSU Master's Theses

Industrial Control Systems (ICS) are the foundation of critical infrastructure as they provide resources like clean water, electricity, and natural gas to support our everyday functions. Given their essential role in modern society, the failure or compromise of ICS systems can lead to significant negative consequences and public safety impacts. Understanding how these systems can be targeted and exploited by malicious actors is necessary to improve their security and resilience.

This research examines how an attacker could manipulate a real-world ICS network by targeting a fully functional Natural Gas (NG) Compressor Station Platform that emulates real operations. This research led …

Recovery And Validation Of Fragmented Rar Files Through The Scalpel3 Application, Thomas L. Landaiche Iii

LSU Master's Theses

A core component of filesystems includes an address table or other means of tracking metadata on where a given file resides within a disk image. This is crucial for regular operation of a computer, or disk analysis in digital forensics. When filesystem information is missing or corrupted, locating saved files on a disk becomes challenging. Whether the disk was accidentally wiped or intentionally tampered with, data still present on the disk, even while untracked, can possibly be recovered beyond what the filesystem registers. File carving in digital forensics is important for these scenarios when data recovery is necessary but address …

Forbidden Induced Restrictions And Unavoidable Minors In Matroids, Matthew P. Mizell

LSU Doctoral Dissertations

Targets are matroids that arise from a nested sequence of flats in a projective geometry. This class of matroids was introduced by Nelson and Nomoto, who found the forbidden induced restrictions for binary targets. In this dissertation, their result is generalized to targets arising from projective geometries over $GF(q)$. In addition, targets arising from nested sequences of affine flats are introduced and the forbidden induced restrictions for these affine targets are determined.

In 1963, Halin and Jung proved that every simple graph with minimum degree at least four has $K_5$ or $K_{2,2,2}$ as a minor. Mills and Turner proved an …