Applied Mathematics Commons^™

(Si14-06) Influence Of Hall Effects On Rotating Mhd Casson Fluid Flow Over A Vertical Plate, Zankhana Mali, Akhil Mittal, Harshad Patel

Applications and Applied Mathematics: An International Journal (AAM)

Studies of Hall effects regarding motion of fluid due to some external forces in MHD transport of reacting Casson fluid with heat generation over an impulsively emerging vertical plate are considered in this work. This theory proposes that because of a sudden rise in temperature and an accompanying surface concentration profile, which shows an elevation with time, the boundary plate has endured rapid expansion. In a rotational environment, this characteristic occurs homogeneously inside a porous uniform material. It applies the Laplace transform method for determining the fundamental equations subject to imposed starting and side conditions. Under isothermal conditions, accurate formulae …

An Agent-Based Model Of Microglia And Neuron Interaction: Implications In Neurodegenerative Disease, Cheyenne Ty, Amanda Case, Emmanuel Mezzulo, Abigail Penland, Kamila Larripa

Spora: A Journal of Biomathematics

Whether immune cells protect or harm the brain is an open question depending on context, and their role is implicated in multiple diseases such as Alzheimer's disease, dementia, and other neurological disorders. Microglia, a specific type of immune cell in the central nervous system, play a key role in homeostasis, and genes associated with an elevated risk of Alzheimer's disease correspond with deficiencies in their behavior. We created an agent-based model that incorporates inflammatory signaling, chemotaxis, and phagocytosis of damaged neurons and allows the exploration of crucial pathways in the maintenance of brain health. We specifically investigated pathways related to …

Discrete Time Risk Processes With Stochastic Premiums And Dividends, Enoch J. Dangbe

Mathematics Dissertations - Archive

Risk processes typically emerge in insurance and finance and are concerned with stochastic representation of uncertainties of real-world events. Main objective amounts to quantifying the chances of both desirable and undesirable events and balancing their mutual impact for the purpose of developing models that in some sense optimize the outcome from the business perspective. Our research is concerned with studying the evolution of the surplus process in which time and assets are integer-valued. Initial capital, random premiums, random claims, dividend payments based on assets’ performance constitute the components of our model. Our findings established recursive formulas for the total expected …

Estimating Per-Infection Cost And Burden For Dengue And Zika As A Function Of Antibody-Dependent Enhancement, Christopher M. Kribs

Mathematics Faculty Publications - Archive

The complex immune interactions produced by the tetravalent dengue vaccine Dengvaxia have foregrounded the important role of antibody-dependent enhancement (ADE) in dengue infection. Some evidence exists that ADE may extend beyond the four dengue serotypes to Zika, a closely related flavivirus transmitted by the same mosquito species as dengue, and may also account for the increased severity of some cases. Estimates of the public health impact of dengue vaccination may then need to include its effects on the transmission of Zika in addition to dengue. This study gathers primary references to build estimates of per-case economic cost and disease burden …

Wave Reflections In A Biophysically Detailed Model Of Cardiac Tissue, Grace Moberg

Honors Theses

Regular heart rhythms are governed by the coordinated spread of action potentials through cardiac tissue. The interaction of an action potential with a tissue heterogeneity may lead to a reflection, where both a retrograde and an anterograde wave propagate off of the initial impulse. Reflections have been experimentally linked to cardiac arrhythmias, but their mechanisms of generation are not well-understood. Mathematically, reflections in phenomenological models of cardiac tissue have been linked to an unstable periodic orbit. These models typically sacrifice detail about the variety of ionic currents and processes involved in action potential propagation in favor of mathematical simplicity. Biophysically …

Forecasting Equity Betas Using Option-Implied Moments, Ivan Kolesnikov

CMC Senior Theses

Traditional beta estimates are constructed from historical stock‑and‑market returns and therefore adjust only as fast as realized data accrue. This thesis investigates whether the forward‑looking information embedded in equity‑option prices can enhance beta forecasts. Using near‑end‑of‑day quotes for 236 S&P 500 firms between 2007 and 2024, I extract risk‑neutral variance and skewness, construct five alternative beta estimators (historical, option‑implied, and three hybrids), and evaluate them against realized betas over six‑, twelve‑, and twenty‑four‑month windows. Rolling‑OLS beta remains the most accurate benchmark at short horizons, yet option‑implied moments add economically and statistically significant value when systematic exposure is expected to change …

Novel Generative And Language Model Architectures With Applications, Edison Mucllari

Theses and Dissertations--Mathematics

This dissertation investigates novel architectures to address fundamental challenges in machine learning, particularly focusing on transformer models, recurrent neural networks, GAN and continual learning and their applications in natural language processing and computer vision. We propose the Neumann-Cayley Gated Recurrent Unit (NC-GRU), which leverages a Neumann series-based Scaled Cayley transformation to maintain orthogonal weight matrices, effectively mitigating exploding gradients problems while improving long-term memory retention across prediction tasks. We demonstrate the practical applications of NC-GRU by implementing our proposed architecture into an autoencoder to derive neural molecular fingerprints. Building upon these advancements, we turn our attention to the transformer architecture, …

Weathering And Beyond: Leveraging Mathematical Modeling To Simulate Erosion In Digital Media, Fiona Irving-Beck

Scripps Senior Theses

How might we bring an idea to life from both a mathematical and an artistic perspective? Within Weathering, I use imagery of environmental erosion to explore the differences between physical and digital forms of representation. I created a physical painting of an abandoned copper mine, digitized the work, and then used a mathematical model to digitally “erode” it, which I re-translated into paintings. While the explicit texture present in physical work speaks best to my practice/intent, the mathematical framework that is the basis for my digital work affords a powerful mode of temporal flexibility. Used in conjunction, these two …

Theory And Applications Surrounding Markov Chains, Joseph J. Quisito Jr., Gallean Brown, Elijah Yoder

Capstone Showcase

This capstone project explores the Markov Chain – a mathematical model used to describe systems that transition between states based on probabilities. It begins by introducing the fundamental concepts, including transition matrices, state classifications, and stationary distributions. The paper then applies Markov Chain theory to real-world scenarios, such as simulating Snakes and Ladders games, predicting soccer match outcomes for Manchester United, and generating texts from movie lines. Finally, it discusses key findings, challenges, and potential areas for future research in the field.

Ultrasonic Sensor-Based Sound Synthesis Using Raspberry Pi Pico W, Niraj Jaishwal

Williams Honors College, Honors Research Projects

At the intersection of Human Computer Interaction and digital art, this project transforms simple motion into musical expression. It explores an interactive real-time sound synthesis system using ultrasonic sensors to generate continuous audio. The objective is to design a system that maps physical distances into musical parameters such as pitch and amplitude, which will create a responsive audio environment. Two ultrasonic sensors are used in combination with the Raspberry Pi Pico W microcontroller running CircuitPython and Adafruit Audio Hat for real-time sound output. One sensor controls the pitch of the generated tone, while the other controls volume. This enables expressive …

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 …

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 …

The Faithfulness Of An Extension Of Lawrence-Krammer-Bigelow Representation On The Group Of Conjugating Automorphisms $C_N$ In The Cases $N=3$ And $N=4$, Mohamad Nasser

BAU Journal - Science and Technology

Let $C_n$ be the group of conjugating automorphisms. V. Bardakov defined a representation $\rho$ of $C_n$, which is an extension of Lawrence-Krammer-Bigelow representation of the braid group $B_n$. Bardakov proved that the representation $\rho$ is unfaithful for $n \geq 5$. The cases $n=3,4$ remain open. M. N. Nasser and M. N. Abdulrahim made attempts towards the faithfulness of $\rho$ in the case $n=3$. In this work, we prove that $\rho$ is unfaithful in the both cases $n=3$ and $n=4$.

Bounding The Convex Hull Relaxation Of The Unit Commitment Problem With The Shapley-Folkman Theorem, Lauren Henderson

All Theses

The Unit Commitment (UC) problem finds an optimal schedule for a set of generators by minimizing the total operation cost subject to demand and operational constraints. The UC problem is often modeled with a mixed-integer linear program (MILP). We employ the Shapley-Folkman Theorem to provide a bound on the size of fractional solutions of its convex hull relaxation. This result is used to obtain a bound on the optimality gap between the MILP and the convex hull relaxation, which is further tightened using several problem-specific properties of UC. We conduct extensive numerical experiments to study the tightness of this threshold, …

Early Ctdna Kinetics As A Dynamic Biomarker Of Cancer Treatment Response, Aaron Li, Emil Lou, Kevin Leder, Jasmine Foo

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Kreig: Examining Affinity Maturation And Antigenic Drift With An Agent-Based Model, Jasmine Af Kreig, Jannatul Ferdous, Ruian Ke, Ruy M. Ribeiro

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Network Analysis Of Progress In Mathematics Research, Anna Singley

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Bodine: Enhancing Netlogo3d Simulations: Computational Efficiency And Online Accessibility Of A Pain Model, Rachael Miller Neilan

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling The Synergistic Interplay Between Malaria Dynamics And Economic Growth, Ruijun Zhao, Hope Enright, Calistus Ngonghala, Olivia Prsoper

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Mathematically Modeling How Trapping Specific Crayfish Life Stages Impacts Removal Efficacy, Relena Pattison, Courtney L. Davis

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Asymptotic Expansion Of A Maier-Saupe Type Potential Near The Nematic-Isotropic Transition Point In Liquid Crystals, Ryan P. Oneill, Giangvuthanh Nguyen, Xiang Xu

OUR Journal: ODU Undergraduate Research Journal

In this paper we study a Maier-Saupe type bulk potential (Maier & Saupe, 1959) in the Landau-de Gennes free energy in the Q-tensor theory modeling nematic liquid crystal configurations. This potential was originally introduced in Katriel et al. (1986), which is considered as a natural enforcement of a physical constraint on the eigenvalues of symmetric, traceless Q-tensors. More specifically, we present a rigorous derivation of the asymptotic expansion of this singular potential near the nematic-isotropic transition point up to the 4-th order.

(Si13-04) System Of Variational Inclusions Involving Cayley Operator And Yosida Approximation Operator With Xor Operations, Mohd Iqbal, Tirth Ram

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we consider and study a new class of system of variational inclusions called a system of variational inclusions involving Cayley operator and Yosida approximation operator with XOR operation. We have shown that our problem is equivalent to a fixed point equation. Based on fixed point formulation, an iterative algorithm is designed to obtain existence and convergence result for our problem.

Human Capital At Home: Evidence From A Randomized Evaluation In The Philippines, Noam Angrist, Sarah Kabay, Dean S. Karlan, Lincoln Lau, Kevin M. Wong

Education Division Scholarship

Children spend most of their time at home in their early years, yet efforts to promote human capital at home in many low- and middle-income settings remain limited. We conduct a randomized controlled trial to evaluate an intervention which encourages parents and caregivers to foster human capital accumulation among their children between ages 3 and 5, with a focus on math and phonics skills. Children gain 0.52 and 0.51 standard deviations relative to the control group on math and phonics tests, respectively (p<0.001). A year later effects persist, but math gains dissipate to 0.15 (p=0.06) and phonics to 0.13 (p=0.12). Effects appear to be mediated largely through instructional support by parents and not other parent investment mechanisms, such as more positive parent-child interactions or additional time spent on education at home beyond the intervention. Our results show that parents can be effective conduits of educational instruction even in low-resource settings.

Large Deviation Theory In Stochastic Processes: Applications To Biological Modeling, Moshe C. Silverstein

Dissertations

This dissertation delves into developing and applying stochastic models to analyze complex biological systems. It leverages Large Deviation Theory (LDT) to gain insights into these systems, focusing on two key examples: neural networks and calcium signaling dynamics. Traditional deterministic methods frequently fail to capture biological processes' randomness and inherent variability. Meanwhile, many stochastic approaches struggle to be mathematically tractable or provide accessible insights. The approach introduced in this study provides rigorous mathematical frameworks to enhance understanding of these stochastic behaviors while remaining tractable and insightful.

A stochastic model for a random biological neural network is constructed that addresses the dependencies …

The Feasibility Of Utilizing The Open Dynamic Interaction Network (Odin) App To Assess Rema Data Across 30 Days Among Those Recovering From Alcoholism, Dennis E. Mcchargue, Bilal Khan, Jesscia Phelps, Patrick Duryea, Kimberly A. Tyler, Arthur Andrews, Ellie Reznicek, Lucy Napper, Mohamed Saad, Hsuan-Wee Lee

Department of Psychology: Faculty Publications

About ~4 million people with an alcohol use disorder receive treatment annually, and frequent relapse has produced a rapid revolving door between recovery and use. This paper presents preliminary data from a prospective micro-longitudinal study (30 days) that examines co-evolution of relapse risk processes of people with alcohol use disorders who entered a short-term residential substance use treatment. The primary goal of the current data was to assess the feasibility of using the open dynamic interaction network (ODIN) responsive ecological momentary assessment (rEMA). rEMA collected daily estimates on affect, urges, sober-support engagement, and use. The ODIN app administered twelve questions …

First-Order Algorithms For Convex Smooth Optimization Problems With Homogeneous Linear Constraints, Yidan Guo

All Dissertations

The purpose of this dissertation is to explore the first-order methods that can be used to solve an approximate solution for convex smooth problems with homogeneous linear constraints. It consists of three interconnected research projects.

In the first project, we study the problem of computing the projection of a given vector onto the kernel of a symmetric positive semi-definite matrix. The complexity of an algorithm for computing a numerical solution is evaluated by the total number of matrix-vector multiplications required for computing an approximate solution. Such problems arise commonly in consensus optimization, in which the total number of matrix-vector multiplications …

Optimization Strategies For Political Redistricting, Blake Splitter

All Dissertations

Political redistricting has remained a hot-button issue in the United States for several decades. Every ten years, most states need to redraw their districts to account for changing populations. Sometimes, these district plans can be drawn with the malevolent intention of aiding one political party over another. This dissertation summarizes four distinct methods of drawing these districts using computer algorithms while keeping several objectives in mind. We test these approaches on the case study state of South Carolina, since it provides a sufficiently challenging problem for us to test various algorithms. We find that many of these approaches improve upon …

Efficient First-Order Methods For Some Smooth Nonlinear Optimization Problems, Yunheng Jiang

All Dissertations

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Delta-Shaped Approximation Based Homotopy Analysis Method For Nonlinear Poisson-Type Partial Differential Equations, Cyril Ocloo

Dissertations

This research aims to solve nonlinear Poisson-type partial differential equations (PDEs) by the approach of the homotopy analysis method (HAM) incorporated with approximate particular solutions (APS) using Delta-shaped basis (DSB) approximations.

With the inclusion of the h auxiliary parameters, we tackle nonlinear problems by studying the mathematical characteristics of the h curve. This is to ensure the numerical convergence of the HAM.

In the solution process, we use the homotopy analysis method to convert a nonlinear PDE into linear inhomogeneous PDEs, which are solved using the method of approximate particular solutions with DSB.

A proper value of the h is …

The Role Of Sensing Modalities In Shaping Collective Motion And Group Behavior, Poorendra P. Ramlall

Doctoral Dissertations and Master's Theses

Collective behavior refers to the coordinated movements that emerge from simple interactions between individuals within a group. Traditionally, researchers have modeled these interactions assuming individuals can sense their surroundings in all directions, like having eyes all around their heads. While this is a useful simplification, it does not capture the diverse ways animals actually sense the world. In this thesis, we take inspiration from the natural world, particularly from animals like bats and dolphins that use a combination of hearing and sight to navigate their environments. We explore how combining these sensory cues in a three-dimensional space affects the way …