Physical Sciences and Mathematics Commons^™

Advanced Mathematical Modeling And Data-Driven Techniques For The Diagnosis Of Diabetes Using Continuous Glucose Monitoring (Cgm) Data, Farah Morsi

Theses

Diabetes mellitus is a major and growing health challenge, particularly in the Middle East and North Africa (MENA) region. Continuous Glucose Monitoring (CGM) provides high-resolution time-series data that capture detailed glucose fluctuations over time. However, conventional CGM summary measures, such as mean glucose, standard deviation, and time-in-range, may not fully describe the nonlinear temporal structure of glucose dynamics.

This thesis investigates nonlinear dynamical approaches for analyzing CGM time series, with a focus on recurrence-based analysis and ordinal-network analysis. Recurrence-based methods, including recurrence quantification analysis (RQA), are used to characterize geometric and temporal patterns in reconstructed phase space, while ordinal networks …

On The Fractional Laplacian Type Operator, Maysam Abdulnaser Zain

Theses

In this thesis, we study analytical structures arising from Dunkl theory and their

applications to harmonic analysis and fractional Laplacian operators. Dunkl operators are differential–difference operators associated with finite reflection groups, providing a natural generalization of the classical Fourier analysis through the introduction of root systems and multiplicity functions. Within this framework, several classical transforms appear as special cases of the (k,a)-generalized Fourier transform. We study the generalized Fourier transform ��ₖ,ₐ, its kernel B_k,a (x,y), and the associated translation operator and convolution structures. Using these tools, we construct the corresponding heat …

Sea-Ice Observation In The Arctic By The Arab Satellite 813, Simulated By The Radiative Transfer Model ‘Sciatran’, Tuqa Mohsin Al Hajri

Theses

The purpose of this research is to explore the spectral behavior of sea ice and to understand how Arctic sea ice surfaces appear when they are observed with a hyperspectral sensor. This is crucial because sea ice changes a lot during the melt season, and different surface types can sometimes look similar to a human eye, but physically they are different. It is thus essential to identify the spectral differences between these surfaces. The main objective of this study is to examine how the spectra of white ice and melt ponds change when their physical and optical properties are varied, …

Control And Entrainment Of Oscillatory Dynamics In An Oncolytic Virus–Tumor Model Under Periodic Therapy Forcing, Aya Salaheddin Shujrawi

Theses

This thesis investigates the dynamics of a tumour–virus interaction model under sinusoidal periodic viral injection, using the three-compartment ordinary differential equation framework of Baabdulla and Hillen (2024). The aim is to characterise how the frequency and amplitude of periodic injection interact with the system's intrinsic oscillatory dynamics, and to identify conditions for stable frequency entrainment. Equilibrium and Hopf bifurcation analysis of the autonomous system yields a supercritical bifurcation at θ_H^auto ≈ 338.45 with intrinsic frequency Ω₀^auto ≈ 0.7552. Introducing a constant baseline injection u₀ = 0.05 raises the threshold to θ_H^forced ≈ 364.85 and shifts …

Analytical And Numerical Methods For Solving Fractional Integro-Differential Equations Using The Modified Operational Matrix Method, Nour Alzoubi

Theses

Fractional calculus has attracted considerable attention in recent years because of its wide applicability to model a variety of linear and nonlinear physical phenomena across different scientific disciplines. In particular, fractional diferential equation systems have proven to be effective in describing processes with memory and hereditary properties. However, the solvability and analysis of such systems strongly depend on the type of fractional operator employed, especially in the presence of nonlocal fractional derivatives with singular kernels, which remain an open and challenging area of research.

The main objective of this thesis is to develop efficient analytical and numerical techniques for solving …

Ai-Powered Student Support And Development Platform, Wadha Rashed Alyammahi

Theses

Over the past few years, academic stress and student mental well-being have become critical concerns in educational settings, significantly affecting academic performance and overall quality of life. Students increasingly rely on digital platforms for academic support; however, many existing solutions lack the ability to adapt to users’ emotional states or provide personalized, context-aware assistance. In response to this challenge, this study presents the design and development of an intelligent, stress-aware conversational support system for students based on advanced natural language processing techniques and large language models.

The main goal of this study is to explore the effectiveness of an LLM-based …

Heat Transfer And Micropolar Characteristic Analysis For Fluid Flow Over A Contracting Permeable Infinite-Length Cylinder: A Fractional Derivative Study, Khalid Al Homran

Theses

This study presents a comprehensive analysis of heat transfer and micropolar fluid characteristics for flow over a contracting permeable infinite-length cylinder using fractional derivative modeling. The micropolar fluid model accounts for microstructure effects that are prevalent in many practical applications, such as polymeric fluids, colloidal suspensions, and biological fluids. The inclusion of fractional derivatives allows the analysis to incorporate memory effects, which provide a more accurate depiction of the physical phenomena compared to classical integer-order models. The governing partial differential equations, representing the momentum, micropolar momentum and energy transport processes, are transformed into a set of nonlinear ordinary differential equations …

Malicious Quic Traffic Detection Using Malicious Quic Traffic Detection Using Malicious Quic Traffic Detection Using Malicious Quic Traffic Detection Using, Choudhary Muhammad Zia

Theses

The enhanced QUIC protocol's encryption capabilities not only encrypt the traffic payload but also encrypt the packet headers that network security tools rely on for packet inspection. This enhanced encryption capability introduces challenges for network operators in monitoring and analyzing network traffic by creating blind spots in firewalls, intrusion detection systems, and deep packet inspection devices. Earlier research has demonstrated that training machine learning classifiers on individual QUIC packets across different classifiers has failed to detect any malicious traffic due to encrypted packet headers.

This thesis demonstrates that shifting to network flow analysis resolves this problem. Rather than analyzing individual …

Towards Efficient Continual Learning: From Memory Optimization To Foundation Models, Zilin Luo

Dissertations and Theses Collection (Open Access)

Continual learning, also termed lifelong learning, enables machine learning models to incrementally acquire new knowledge while mitigating the degradation of previously learned information—a capability essential for adapting to dynamic, real-world data environments. This dissertation investigates the core challenges of continual learning and extends its application to enhancing training efficiency in the era of foundation models. The first part of this dissertation addresses the constraints of few-shot exemplar storage with a novel compression framework. While leveraging class activation maps to downsample non-discriminative pixels, we introduce an adaptive masking model, optimized through bilevel optimization, to store more exemplars efficiently. The second part …

Towards Auto-Evaluation For Large Language Models, Jiahao Ying

Dissertations and Theses Collection (Open Access)

The rapid advancement of large language models (LLMs) has created an urgent need for evaluation methodologies that are timely, scalable, reliable, and informative. Conventional evaluation benchmarks, although essential for measuring model capabilities and guiding model development, are often constructed and maintained through labor-intensive human annotation. As LLMs continue to improve through increases in model scale, training data, and computational resources, static benchmarks may quickly lose discriminative power. Moreover, the growing use of large and diverse training corpora increases the risk of benchmark leakage, which can inflate evaluation results and obscure the true capabilities of models. These challenges call for a …

Fractional Bernstein Polynomial Approximations For Nonlinear Timefractional Partial Differential Equations, Reem Abdul Quzli

Theses

This thesis studies the numerical approximation of nonlinear time-fractional partial differential equations using fractional Bernstein polynomials. The main model considered is the nonlinear time-fractional foam drainage equation, in which the classical time derivative is replaced by the Caputo fractional derivative. This formulation introduces memory effects into the model and allows the present drainage behavior to depend on the previous evolution of the liquid fraction.

The proposed method approximates the solution by a finite expansion of fractional Bernstein basis functions. After substituting this approximation into the governing equation, the residual is expanded in powers of t^�� . The unknown coefficient …

A Hybrid Approach To Phishing Email Detection: Leveraging Machine Learning And Large Language Models, Hessa Shamal Biri

Theses

Phishing attacks have reached a new level of sophistication through the deployment of large language models by attackers. The current AI-generated threats defeat existing detection systems which base their operation on past data. The thesis presents a hybrid system for phishing email detection which combines real email data with synthetic LLM-created samples to enhance traditional machine learning classifiers performance. The study created a hybrid dataset of 20,627 emails by combining 18,631 real messages from the Kaggle Email Classification Dataset with 1,996 synthetic emails. The synthetic emails were generated using four large language models LLaMA-3, Falcon, LLaVA, and Mistral to capture …

Supramolecular Assembly In Short Peptide Systems For Selective Metabolite Recognition And Drug Nanoencapsulation, Maithreyi Ramakrishnan

Dissertations, Theses, and Capstone Projects

Short peptides can form adaptive supramolecular assemblies, and understanding how minimal sequences organize around neurometabolites or hydrophobic cancer drugs enables the rational design of functional materials. This thesis combines molecular dynamics with experimental validation to establish design rules linking peptide sequence to emergent structure and function. Chapter 1 outlines the molecular determinants governing peptide assembly. Chapter 2 reviews computational workflows that reveal sequence-dependent conformations and supramolecular organization. Chapter 3 applies these principles to Dynamic Peptide Libraries which identify tetrapeptides that selectively interact with neurometabolites. Chapter 4 extends the same interaction-driven framework to design tryptophan-rich pentapeptides that co-assemble with kinase inhibitors …

Whitney Extension Problem For Fractional Sobolev Spaces And Besov Spaces, Han Li

Dissertations, Theses, and Capstone Projects

In the dissertation, we go through the development of the Whitney extension problem and prove a type of results for the Whitney extension problem for homogeneous fractional Sobolev spaces and homogeneous Besov spaces.

This dissertation consists of four chapters:

Chapter 1: We recall the history of the Whitney extension problem and talk about some early works which have been done for the Whitney extension problem. We also mention our new results.

Chapter 2: We introduce some basic notations, definitions and preliminary results.

Chapter 3: We show the existence of a bounded linear extension operator for homogeneous fractional Sobolev space L …

Radiotheranostics For Gynecological Pathologies, Joni Sebastiano

Dissertations, Theses, and Capstone Projects

Molecular imaging, specifically positron emission tomography (PET), is vital for detecting disease and understanding its biological makeup. The exploitation of radiolabeled antibodies for PET imaging has proven to be indispensable to the field of molecular imaging over the last several decades. The development of radioimmunoconjugates for use in immunoPET has not only allowed for the sensitive, specific, and high-resolution detection of disease, but has also enabled a deeper understanding of the disease biology, ultimately guiding more personalized therapeutic strategies. Most typically, this technology is harnessed for the diagnosis and treatment of cancer, however more recently, the field has explored the …

Quiver Of Affine Monoid Of A Vector Space Over Finite Field, James Junie Chen Cleary

Dissertations, Theses, and Capstone Projects

In this paper, we study the quiver of the complex monoid algebra CAFF(n, q). There are n + 1 maximal subgroups of AFF(n, q), each isomorphic to AGL(k, q) for some 0 ≤ k ≤ n. Every irreducible representation of CAFF(n, q) arises from a character of CAGL(k, q) for a suitable k. Thus, we study two different approaches to classifying the characters of CAGL(k, q). Next, we compute the full quiver Q(CAFF(n, q)). Finally, we show that this quiver is a disjoint union of straight-line paths and that its basic algebra has radical square zero. Hence, it has finite …

Mediating Energy And Charge Transfer Dynamics Of Lead Halide Perovskite Nanocrystals Via Surface Chemical Approaches, Aaron S. Malinoski

Dissertations, Theses, and Capstone Projects

Energy and charge transfer are the fundamental mechanisms by which semiconductor nanocrystals interact with their external environment and underpin all light-conversion related applications. Lead halide perovskite nanocrystals (PNCs) are a relatively new class of semiconductor nanocrystals that possess a unique and dynamic surface chemical environment. Investigations into the influence of these surface chemical conditions on the electronic coupling between surface-bound molecular acceptors and the perovskite nanocrystals, and how the surface chemistry can be manipulated, in turn controlling the charge and energy transfer mechanisms, is the focus of this dissertation. Through ligand-shell engineering using commercially available, inexpensive small molecules, the surface …

Scaling Limits Of Critical Observables Through The High Dimensional Incipient Infinite Cluster, Pranav Chinmay

Dissertations, Theses, and Capstone Projects

We give a general construction of the incipient infinite cluster in high dimensional percolation, and use it as a decoupling tool to rigorize geometric heuristics for analyzing the asymptotics of observables at criticality. Examples include demonstrating the limiting distribution of the chemical distance and full-strength asymptotics for k-point functions, which constitute foundational inputs for scaling limit results associated to critical clusters.

Computational Insights Into Nucleosome Dynamics In Epigenetics Using Molecular Dynamics Simulations, Rutika Patel

Dissertations, Theses, and Capstone Projects

Nucleosome core particles (NCP) are the building blocks that form a highly organized and compact chromatin structure. Nucleosomes package DNA in the nucleus of eukaryotic cells. The NCP consists of about 147 base pairs of DNA wrapped around the histone octamer, with 1.65 superhelical turns in a left-handed manner. The histone octamer is composed of two copies of H3, H4, H2A, and H2B. Together with histone H1 and linker DNA, they further assemble into a higher-order chromatin structure. The nucleosome complex is stabilized by electrostatic interactions between positively charged histone residues and the negatively charged DNA backbone. To effectively access …

Algorithmic Problems In Automorphic Orbits Of Free Groups, Siobhan B. O'Connor

Dissertations, Theses, and Capstone Projects

One of the fundamental problems in the field of combinatorial group theory is telling when two group presentations represent isomorphic groups. Since applying a free group automorphism to the set of relators of a presentation gives an isomorphic group, we want to be able to quickly decide when looking at a relator whether a given word can be sent to it via an automorphism. We give a hands-on introduction to the automorphisms of free groups using patterns of colored beads. We show that you can make this decision correctly in constant time on average by looking for "orbit-blocking" words that …

Electromagnetic Counterparts To Active Galactic Nucleus Disk-Embedded Binary Black Hole Mergers, Emily Mcpike

Dissertations, Theses, and Capstone Projects

The accretion disks of active galactic nuclei (AGN) are promising environments for producing binary black hole (BBH) mergers, which have been detected via gravitational waves (GW) with LIGO-Virgo-KAGRA (LVK). BBH mergers embedded in AGN disks are unique among GW formation channels in their generic ability to produce electromagnetic (EM) counterparts, via interactions between the merger remnant and the surrounding disk gas (though these are not always observable). While such mergers represent valuable multi-messenger sources, the lack of predictive statistical models in existing literature currently limits our ability to select possible EM counterparts with GW detections in archival data and in …

Parkinson’S Disease Phenotype Stratification Using Multiple Correspondence Analysis, Kelly Astudillo

Dissertations, Theses, and Capstone Projects

Parkinson’s disease (PD) is the second most common neurodegenerative disorder, with over 12 million people projected to be affected by 2040 (Dorsey et al., 2018). Deep phenotyping and stratification can provide useful information regarding PD pathogenesis and can aid in the  development of disease modifying therapies that aim to delay the progression or prevent the onset of neurodegeneration (Blandini et al., 2019; Smith & Schapira, 2022). Utilizing multivariate methods such as multiple correspondence analysis (MCA) permits for the simultaneous analysis of distinct data modalities. To the best of our knowledge, MCA has not been previously used to explore phenotype patterns …

Variational Methods For Semilinear Pdes With Dirac Singularities, Samuel J. Magill

Dissertations, Theses, and Capstone Projects

This dissertation utilizes a variational framework for semilinear elliptic equations in two dimensions with Dirac measure data. The central objects of study are equations of the form −ΔU = f(U) + Σ_j=1^N α_jδ_pj on bounded Lipschitz domains Ω ⊂ ℝ² with homogeneous Dirichlet boundary condition, and on a flat torus 𝕋², where α_j is positive for the Dirichlet setting and α_j is negative on the torus. Solutions are obtained by minimizing the restriction of an energy functional to an order interval determined by explicit sub- and supersolutions; the Euler–Lagrange equation is recovered …

A Predictive Coding Account Of Spatial Working Memory Following Prophylactic Levetiracetam Administration Prior To Traumatic Brain Injury, Omeima Mutwali

Dissertations, Theses, and Capstone Projects

Traumatic brain injury (TBI) symptom prevention and remediation is an important area of research that would benefit vulnerable groups, including active-duty and veteran soldiers. These patients can sustain penetrative forces in fields of combat or in training, which result in focal lesions that trigger inflammatory and degenerative processes in the brain. Both primary and secondary injuries are associated with changes to cognition, behavior and affective state. This disease poses increased risk of epileptogenesis, as well. Given these outcomes, prior research has evaluated levetiracetam (LEV) as a prophylactic treatment for seizures, cognitive deficits and negative emotionality. LEV acts as a presynaptic …

1d Crust-Magnetosphere Coupling Model For Magnetars, Kennedy M. Jeter

Dissertations, Theses, and Capstone Projects

Magnetars are the most extremely magnetized objects in the universe. Their strong magnetic fields generate high-energy magnetic flares with instantaneous luminosity that can outshine their host galaxy. Previous works have explored how Hall drift in the crust affects the dynamics of magnetic field lines in the magnetosphere. This work investigates how a change in the magnetosphere, such as a flare or an outburst, can excite Hall evolution in the crust. We investigate how the twisting and untwisting of magnetic field lines in a magnetar’s magnetosphere launches Hall waves through its crust using a one-dimensional numerical model. We use the Dedalus …

Considering Numerical Relativity For Upgrades In Mcfacts Merger Dynamics, Shawn K. Ray

Dissertations, Theses, and Capstone Projects

Binary black hole mergers (BBH), some likely originating from active galactic nuclei (AGN), are observed by ground-based detectors such as LIGO-Virgo-KAGRA (LVK) and will be detected by future space-based detectors such as the Laser Interferometer Space Antenna (LISA) and the Laser Interferometer Lunar Antenna (LILA). The dynamics of AGN may be responsible for a significant fraction of BBH mergers soon to be observed by LISA and LILA, yet the dynamics of BBH mergers within AGN disks remains ambiguous despite their appearance in gravitational wave observations. Monte carlo For AGN Channel Testing and Simulation (McFACTS) is an open-source software used to …

Inductive Biases In Field-Level Cosmological Inference From Galaxy Catalogs, James O'Connor Baldwin

Dissertations, Theses, and Capstone Projects

We perform field-level likelihood-free inference of the matter density parameter Ωm from simulated galaxy catalogs using machine learning models with differing inductive biases. Using features extracted from hydrodynamic simulations in the CAMELS suite, we investigate how both observable choice and model architecture govern the extraction of cosmological information. We consider galaxy positions and line-of-sight peculiar velocities, both separately and in combination, and compare permutation-invariant Deep Sets, implemented with either standard multilayer perceptrons (MLPs) or Kolmogorov–Arnold Networks (KANs), to graph neural networks (GNNs) implemented with MLPs, which explicitly encode spatial relations. We evaluate inference performance under both in-distribution and out-of-distribution (OOD) …

Identifying Textual Predictors Of Early Termination In Clinical Trials In Medicine: An Explainable Machine-Learning Study, Rohan Ramnarain

Dissertations, Theses, and Capstone Projects

About one in five clinical trials in medicine ends early, wasting valuable resources and reducing the evidence available for developing life-saving medical treatments. This project uses a method called Trial2Vec, which is a self-supervised machine-learning method that converts clinical trial documents into dense numerical representations that capture their key design and clinical characteristics, to turn each proposed clinical trial’s written protocol into a compact numerical profile (a process referred to as embedding). These profiles are then paired with a predictive machine learning models to identify the words and phrases in the trial documents that can signal a higher risk of …

Identifying Helium Emission-Line Stars With The Condor Array Telescope, Julia Stewart

Dissertations, Theses, and Capstone Projects

Helium emission-line stars, including cataclysmic variables (CVs), AM Canum Venaticorum (AM CVn) binaries, symbiotic stars, and X-ray binaries, are tracers of compact object binary populations in the Milky Way, and may be viable progenitor systems of Type Ia supernovae. Their space densities are not well constrained - just over 100 AM CVn stars are known out of a Galactic population that may be closer to 100,000. Identifying such systems in large numbers requires wide-field, narrow-band photometric surveys capable of detecting faint emission-line sources across significant sky areas.

In this thesis, I present a narrow-band photometric search for helium emission-line stars …

Reexamining The Croton Aqueduct: A Ward-Level Microhistorical Analysis Of Infrastructure And Cholera Mortality In 1849 New York City, Alexandria R. Toothman

Dissertations, Theses, and Capstone Projects

This work reexamines the Croton Aqueduct’s role in public health by shifting analysis from the citywide level to the ward level, revealing that infrastructure expansion did not produce uniform benefits across New York City. When the Croton Aqueduct opened in 1842, it was celebrated as an achievement that would deliver pure water and eliminate disease. However, only seven years after its opening, in 1849, cholera returned with greater force in the Sixth Ward. This work shows that the uneven distribution of Croton infrastructure corresponded with uneven cholera mortality rates, challenging narratives that present Croton as a singular triumph of urban …