Applied Mathematics Commons^™

Majority Decision Using Top-Performing Neural Networks Models For Improved Credit Risk Prediction, Vincent Dey

College of Graduate Studies: Theses & Dissertations

Credit risk prediction remains both a challenging and high-interest problem due to the inherently unbalanced nature of financial datasets and the continuous drive for higher pre- dictive precision. In this work, I build upon previous advancements in credit risk modeling and introduce an ensemble-based Artificial Neural Network (ANN) architecture designed to enhance classification performance. By leveraging a selective ensemble of decision net- works, this approach not only improves prediction accuracy but also mitigates the chal- lenges posed by imbalanced data distributions. While the primary focus is on credit risk prediction, my analysis demonstrates that the proposed model can be effectively …

Applying The Lagrangian Variational Method To Atom Interferometry, Jeffrey W. Heward

College of Graduate Studies: Theses & Dissertations

Atom interferometry in Bose-Einstein condensate systems has emerged as a promising technique for precision metrology. The dynamics of these systems are well-described by the Gross-Pitaevskii equation (GPE), but direct numerical solution of this equation is infeasible for realistic systems. We use the Lagrangian Variational Method (LVM) to approximate solutions of the GPE in 1D and 3D, and we compare the LVM results to the exact solutions. We also present 3D LVM results for a case where numerical solution of the GPE is infeasible.

Towards Understanding Thermal Management In Unsteady Boundary Layer Flow With Ac/Dc Electric Fields, Sara Abdelsalam, M. A. Dagher, Y. A. Elmaboud, A. I. Abdellateef

Basic Science Engineering

Unsteady boundary layer flow induced by alternating current (AC) or direct current (DC) electric field through a porous layer is investigated numerically. The finite difference method based on Crank-Nicolson is applied to solve the nonlinear system. The governing equations are built with fractional shear stress and the Cattaneo heat flux model, and time fractional derivatives are computed using the Caputo fractional derivative. The numerical results are presented to demonstrate the effects of varying parameters on momentum and thermal boundary layer. The results reveal that the time delay in the velocity profile occurs for larger values of both the velocity fractional …

Semi Analytical Solution Ofmhd And Heat Transfer Of Couple Stress Fluid Over A Stretching Sheet With Radiation In Porousmedium, Sara Abdelsalam, M. Khairy, W. Abbas, A.M. Megahed, M.S. Emam

Basic Science Engineering

This comprehensive research examines the dynamics of magnetohydrodynamic (MHD) flow and heat transfer within a couple stress fluid. The investigation specifically focuses on the fluid’s behavior over a vertical stretching sheet embedded within a porous medium, providing valuable insights into the complex interactions between fluid mechanics, thermal transport, and magnetic fields. This study accounts for the significant impact of heat generation and thermal radiation, crucial factors for enhancing heat transfer efficiency in various industrial and technological contexts. The research employs mathematical techniques to simplify complex partial differential equations (PDEs) governing fluid flow and heat transfer. Specifically, suitable similarity transformations are …

A Finite Difference Analysis Of Electroosmotic Flow Of A Two-Layer Jeffrey Fluid In A Vertical Porous Nanochannel, Y. Abdelmaboud, M. A. Elkot, Sara Abdelsalam

Basic Science Engineering

In this paper, we discuss the unsteady two-layer electroosmotic flow (EOF) of the Jeffrey fluid in a vertical porous nanochannel, taking into account the effect of the heat transfer and alternating current (AC) electric fields. In this model, the two layers have different densities and viscosities. The finite difference method is used to solve the governing equations of electrical potential, velocity, and temperature. The results show that the Debye-Hückel parameter is significant in managing electroosmotic flow (EOF) because it affects the electrical double layer (EDL) compression and velocity gradients on the wall. The higher the radiation parameter, the lower the …

Numerical Simulation Via Homotopy Perturbation Approach Of A Dissipative Squeezed Carreau Fluid Flow Due To A Sensor Surface, Sara Abdelsalam, W. Abbas, A.M. Megahed, H. M.H. Sadek, M.S. Emam

Basic Science Engineering

This study rigorously examines the interplay between viscous dissipation, magnetic effects, and thermal radiation on the flow behavior of a non-Newtonian Carreau squeezed fluid passing by a sensor surface within a micro cantilever channel, aiming to deepen our understanding of heat transport processes in complex fluid dynamics scenarios. The primary objective is to elucidate how physical operational parameters influence both the velocity of fluid flow and its temperature distribution, utilizing a comprehensive numerical approach. Employing a combination of mathematical modeling techniques, including similarity transformation, this investigation transforms complex partial differential equations into more manageable ordinary ones, subsequently solving them using …

Modeling The Impacts Of The Current And Projected Temperatures On Spongy Moth Population Dynamics, Adrienne B. Spring

Theses and Dissertations

The spongy moth (Lymantria dispar) is an invasive forest pest that has caused significant ecological damage across the United States. Its invasion front is shaped by a number of factors, including temperature in both the northern and southern regions. With ongoing climate change, areas that were previously uninhabitable may become increasingly favorable for moth population establishment and expansion, while other areas may experience thermal stress limiting persistence. This study develops a temperature-driven population model to analyze how temperature affects the spongy moth population dynamics along the invasion front. This model incorporates temperature effects on fecundity, stage-specific survival rates, …

Investigating The Temperature Effects On Aedes Aegypti And Dengue Virus In Central Argentina: Perspectives From Mathematical Modeling, Morgan H. Jackson

Theses and Dissertations

Dengue virus (DENV) causes over 390 million infections and around 40,000 deaths worldwide each year. DENV is primarily transmitted by the mosquito Aedes aegypti, and both the life cycle of these mosquitoes and DENV transmission are significantly impacted by temperature. In the temperate region of Central Argentina, where dengue outbreaks first began in 2009, outbreaks only occur following new introductions of DENV from other regions. Due to the relationships between temperature and DENV and temperature and Ae. aegypti, the risk of an outbreak changes throughout the year. Here, we develop and analyze mathematical models for both mosquito population dynamics and …

Swarming Segregation: Leveraging Swarm Intelligence And Regionalization As Instruments For School District Desegregation, Jeffrey Wooten

Theses and Dissertations

Even after Brown led to the South briefly having the most diverse schools in the nation, schools throughout the Northeast have remained the most segregated in the nation for decades. While federal jurisprudence has made compelling desegregation pursuant to the Equal Protection Clause more challenging, New Jersey has a particularly favorable landscape to address severe segregation. With a highly diverse, densely populated public enrollment, favorable state constitutional precedent, and a history of successfully compelling desegregation, New Jersey is fertile ground exploring regional desegregation. Scholars, judges, and even plaintiffs in ongoing litigation (Latino Action Network v. N.J.) have called for New …

Bayesian Networks For Safety-Critical Systems, Joseph Mietkiewicz

Theses

This thesis addresses a operational challenge in modern industrial operations: the increasing complexity of systems and the consequent cognitive burden on operators. As industrial technologies advance, the human-computer interface has become the primary conduit for information flow, playing a pivotal role in operational decision-making. However, the proliferation of data often leads to information overload, potentially compromising rather than enhancing operator performance. This research explores an approach to this pressing issue through the application of Bayesian networks as decision support systems in safety- critical scenarios. Our study employs a multi-faceted approach, combining theoretical modeling with empirical testing. Through collaboration with industry …

Universality Of Complex Valued Neural Networks, Sauvik Mondal

Graduate Research Theses & Dissertations

Neural networks have become central to modern natural science. One of the key components of these networks is the choice of a suitable activation function. In this manuscript, we explore the selection of an optimal activation function in the context of complex-valued neural networks. We aim to characterize the activation functions $\sigma\colon \mathbb{C} \rightarrow \mathbb{C}$, where each neuron performs the operation $\mathbb{C}^N \rightarrow \mathbb{C}$, defined as: $z \mapsto \sigma(b + w^Tz)$. First, we briefly discuss the real-valued counterpart, including the importance of function approximation and the renowned universal approximation theorem. Subsequently, we examine various criteria for complex activation functions that …

Long Term Dynamics Of A Stage Structured Population Model With Nonlocal Dispersal, Md Yasin

Graduate Research Theses & Dissertations

This thesis is based on the 2023 paper “Dynamics of Classical Solutions of a Two-Stage Structured Population Model with Nonlocal Dispersal.” We study the long-term behavior of a population with two life stages, juvenile and adult, moving across space using nonlocal dispersal mechanism. The main goal is to understand the conditions under which the species survives or goes extinct on the long run. This is determined by a key value called the principal spectrum point, λp.

First, using results from the literature on existence of solutions for general initial value problems on Banach spaces, we establish that for any given …

Facial Reduction Of Semidefinite Relaxations Of Binary Quadratic Problems, Ian Sugrue

Graduate Research Theses & Dissertations

A standard technique for bounding a combinatorial optimization problem is to form a semidefinite relaxation of the problem by "lifting" the problem into a higher dimensional space of symmetric matrices. For some combinatorial problems such as maximum k-cluster, the resulting semidefinite relaxation is not strictly feasible. In the context of the maximum k-cluster problem, we present an equivalent, strictly feasible semidefinite relaxation by way of the dimensionality reduction technique known as facial reduction. We provide a recipe to form this semidefinite relaxation directly, bypassing the lifting and facial reduction steps entirely. We then present our work on generalizing this result, …

Eulerian Smoke Simulation With Multiple Fields, Diyang Zhang

Dartmouth College Master’s Theses

Fluid simulation is a cornerstone of computer graphics, enabling the realistic depiction of dynamic phenomena such as smoke, fire, and other gaseous behaviours. This thesis focuses on advancing Eulerian smoke simulation techniques, with a particular emphasis on grid-based simulations that capture intricate vortical structures and fine visual details.

We propose several detail-preserving frameworks that incorporate various scalar and vector fields within the simulation pipeline, including velocity, impulse, and Lamb vectors, along with their decompositions and transformed representations. By mathematically analyzing the properties of impulse, we derive its scalar fields decomposition (ImpSFD), which introduces an alternative numerical interpretation, and Vortex-Particles in …

Horizontal Infiltration Of Water Through Porous Snow As A Gravity Current, Anthony Cheng

Dartmouth College Master’s Theses

On the surface of the Greenland ice sheet or around the margins of the Antarctic ice shelf, water infiltrates porous ice. It is important to understand this infiltration process since water populating the pore space of ice directly impacts the density, porosity, and wetness of ice. These properties influence the mechanics and tensile strength of ice, as greater amounts of infiltration result in faster or more widespread deformation events, which may lead to adverse climatic effects such as sea level rise and ocean current disruption. While studies have considered the thermodynamics and fluid mechanics of water vertically percolating through snow …

Essays On Technological Change And Scientific Research, Max Mayca

Electronic Theses & Dissertations (2024 - present)

The primary objective of economic science has long been to understand and promote growth, as it contributes to a more prosperous civilization and improves individual well-being. The core drivers of growth—capital accumulation, human capital development, and technological progress—are well-established. While capital deepening enables scaling of production, and human capital enhances labor productivity, technological and scientific advancements remain the most critical, as they continually redefine the efficiency frontier. Given this centrality, it is essential to understand how technological progress affects labor markets, how research resources should be allocated, and how technology relates to human capital formation.

The first part of this …

Modelling The Formation Of Unslanted Holographic Gratings In Hybrid Photopolymer Media, Jack Lyons, Dana Mackey, Izabela Naydenova

Articles

The theoretical modelling of holographic recording in photopolymers has been an important tool in their optimisation. More complex, hybrid organic/inorganic photopolymers have been developed in pursuit of materials with higher sensitivity, low shrinkage, high dynamic range and environmental stability. Recent attempts to augment the existing models for the redistribution of inorganic nanoparticles in holographic recording were successful but there is still a knowledge gap in regards to modelling optical losses, mutual cross-diffusion, the formation of slanted holographic gratings and polymerization induced shrinkage in hybrid photopolymer media. This paper will describe a novel approach to modelling the formation of unslanted holographic …

Geometric Modeling, Reconstruction And Evaluation Of Maize Leaf Morphology In 3d, Zhaocheng Xiang

Dissertations and Doctoral Documents, University of Nebraska-Lincoln, 2023–

Maize is a vital crop for global food security, yet quantitative characterization of its three-dimensional (3D) morphology remains a major challenge due to the geometric complexity of curved leaf structures and occlusions during data collection. This work presents an integrated framework for the digital reconstruction, parametric modeling, and functional analysis of maize leaf morphology and canopy architecture, advancing the precision and interpretability of phenotyping and modeling in smart agriculture.

First, we propose a descriptive and parametric model that represents maize leaves through three fundamental components: midrib, cross-section, and blade contour. Each is described by geometric curves and controlled by biologically …

Dynamics Of Prey-Prey Mutualism With Varying Carrying Capacity And Herd Behavior In The Presence Of Predator, Felix Dela Djokoto

UNF Graduate Theses and Dissertations

This study investigates the dynamics of mutualistic relationships between two prey species in the presence of a predator, by taking into account herding in one species along with the influence of carrying capacities between two prey species. These mutualistic dynamics are presented by constructing two mathematical models, namely an indirect and direct mutualism model. As the strength of the symbiotic relationship increases the indirect model goes through transcritical bifurcation to Hopf bifurcation whereas in the direct mutualism model goes through saddle-node bifurcation to Hopf bifurcation.

Analysis Of Bin Packing Variants, Kyle T. Ambrose

UNF Graduate Theses and Dissertations

The Bin Packing problem is a classic and widely studied optimization problem that arises naturally in applications like manufacturing, logistics, and memory allocation, where space and resource constraints are critical. In this thesis, we first demonstrate the NP-completeness of Bin Packing via a reduction from Three-Dimensional Matching, establishing its foundational complexity. We then survey core heuristics for the one-dimensional case and extend our analysis to two and three-dimensional variants, including both offline and online strategies. Special attention is given to stochastic bin packing, where item sizes are modeled as random variables drawn from distributions such as uniform, truncated normal, and …