Applied Mathematics Commons^™

Exploring The Dynamics Of Romantic Relationships Through The Lens Of Prem Rog, Umang Jain, Dheeraj Sharma, Pranay Goswami, Kuldeep Malik

Journal of Humanistic Mathematics

Romantic relationships are dynamic events that begin, grow, and frequently remain for a long time in a stagnant or fluctuating state until possibly dissipating. Although they are unquestionably the most significant dynamic events in our lives, dynamic systems theory has only recently included them in its formal framework. Without a mathematical model, it would be impossible to analyze and comprehend the dynamics because, in general, love stories are too brief to allow things to stabilize and are affected by the ups and downs of the surrounding community. In this paper, we set up models made up of four ordinary differential …

Sparc Grade 2 Integrated Coding-Math Lessons, Spatial Activities And Robot Coding (Sparc)

Spatial Activities and Robot Coding (SPARC)

SPARC-Math Grade 2 Integrated Coding-Math Lessons with related Utah Core Standards and lessons for Spatial and Programming Language and Geometry.

Estimation Of Net Premium For Flight Delay Insurance Using The Aggregate Loss Model: A Case Study Of Indonesia Otas, Azka Nurul Husna, Yulial Hikmah, Ira Rosianal Hikmah

Jurnal Vokasi Indonesia

Air transportation, as one of the most chosen transportation modes, is frequently susceptible to delays. Flight Delay Insurance offers a vital solution to mitigate the financial losses associated with this risk. Premium pricing is a key factor influencing the decision to purchase this insurance, particularly on Online Travel Agent (OTA) platforms where product offerings are often highly comparable. The aggregate loss method is employed herein to ascertain the net premium (or pure premium) price. The loss severity component (X) is modeled using an empirical distribution, while the loss frequency component (N) is modeled using a Negative Binomial distribution with parameters …

Interactive Effects Of Hyposalinity And Nitrate Loading On Growth, Physiology, And Nitrogen Status Of The Seagrass, Halodule Wrightii, Joseph L. Kowalski, Hudson R. Deyoe, Kirk Cammarata, Kristina P. Vatcheva

School of Earth, Environmental, & Marine Sciences Faculty Publications

The study goal was to examine the interactive physiological effects of two freshwater inflow stressors, nitrate pulses coupled with salinity decrease, on the seagrass Halodule wrightii. A microcosm experiment was designed to approximate an observed freshwater inflow event. Over a 13-day period plants were subjected to three sequential salinity drops (S35→ S23→ S15→ S5) with nitrate-nitrogen added simultaneously at 0, 30 or 60 µM. For comparisons, the Control was no salinity change and no nitrate added denoted by S35/No N. Measurements of H. wrightii shoot production, photosynthesis, respiration, quantum efficiency, %N, C:N ratios and δ¹⁵N …

The Pure Yang Mills Field V2, James Glimm

Department of Applied Mathematics & Statistics Faculty Publications

We construct a pure Yang-Mills field based on a non-Abelian simple gauge group.

Axioms and the mass gap are satisfied.

Distribution Of New Statistics Of Parking Functions And Their Generalizations, Stephan Wagner, Catherine H. Yan, Mei Yin

Mathematics: Faculty Scholarship

In this paper we present new results on the enumeration of parking functions and labeled forests. We introduce new statistics on parking functions, which are then extended to labeled forests via bijective correspondences. We determine the joint distribution of two statistics on parking functions and their counterparts on labeled forests. Our results on labeled forests also serve to explain the mysterious equidistribution between two seemingly unrelated statistics in parking functions recently identified by Stanley and Yin and give an explicit bijection between the two statistics. Extensions of our techniques are discussed, including joint distribution on further refinement of these new …

Qualitative And Numerical Observations Into The Career Trajectories Of Early Career Academics: A Mathematical Model Approach, Oluwatayo M. Ogunmiloro

Tanzania Journal of Science

This study develops and analyzes a mathematical model that describes the interplay among different researcher groups within academia by focusing on how variables such as mentorship, access to funding, and academic peer influence affect the career trajectories of early-career, experienced, redundant, and successful researchers. Using stability theory and relevant theorems of differential equations, this study ensures the existence, uniqueness, positivity, and boundedness of the model's solutions. Additionally, the model’s equilibrium states, are analyzed to determine the local asymptotic stability. Numerical simulations using the Runge-Kutta fourth-order (RK4) method, implemented in Python, are performed to illustrate issues related to career growth within …

A Probabilistic Modeling Analysis Of The Longitudinal Immune Response To Infection And Vaccination Across Demographic Groups And Pulmonary Symptoms, James O'Hanlon, Kaitlyn Sullivan, Lyndsey M. Muehling, Glenda Canderan, Jie Sun, Judith A. Woodfolk, Jeffrey M. Wilson, Rayanne A. Luke

Spora: A Journal of Biomathematics

Antibody and cytokine kinetics describe the dynamic response to immune events such as infection and vaccination. These dynamics are not fully understood, and mathematical characterization may help explain variability across demographic groups and pulmonary symptoms post-acute infection. We fit time-dependent probability models to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) data to obtain distributions of longitudinal antibody response and cytokine values. To assess differences between groups, an overlap metric is applied to the modeled response curves. Our antibody models suggest significant differences between male and female populations and demonstrate deficient antibody responses of less-healthy groups such as smokers. Our cytokine …

Optimal Intervention Strategies In Age-Structured Sirvd Model: Epidemiological And Economic Analysis Of Covid-19 In Korea, Joon Chun, Melisa Hendrata

Spora: A Journal of Biomathematics

This study employed an age-structured Susceptible-Infected-Recovered-Vaccinated-Deceased (SIRVD) model to design optimal COVID‑19 intervention strategies by integrating epidemiological dynamics with economic costs. Using empirical data from South Korea, we estimated transmission parameters and analyzed quarantine-based non-pharmaceutical interventions (NPIs) alongside targeted vaccination scenarios. Our results indicated that a stronger form of mild NPI (upper range of Level I), when combined with targeted vaccination that prioritized seniors, achieved substantial reductions in infection peaks and overall economic burden. These findings underscore the effectiveness of age-specific strategies in epidemic management and offer critical insights for policymakers seeking balanced, resource-efficient approaches.

Inhomogeneous Branching Random Walks: Incorporating Genealogy And Density Effects, Lauren Ajax, Beatrice Durham, Pratima Hebbar, Cade Johnston, Jiayi Zhang

Spora: A Journal of Biomathematics

We introduce a novel framework using inhomogeneous branching random walks (BRWs) to model biological processes, specifically by introducing genealogy-dependence in branching rates and displacement distributions to model bacterial colony growth. Current stochastic models often either assume independent and identical behavior of individual agents or incorporate only spatiotemporal inhomogeneity, ignoring the effect of genealogy-based inhomogeneity on the long-time behavior of these processes. Such asymptotics are of independent mathematical interest and are crucial in understanding the emergence of patterns. We propose several inhomogeneous BRW models in 2D space where displacement distributions and branching rates vary with time, space, and genealogy. A combined …

On The Existence And Asymptotic Stability Of Lord-Shulman System With Microtemperature, Marwa Boudeliou, Brahim Kilani, Abdelhak Djebabla, Hamed Abderrahmane Bouraoui

BAU Journal - Science and Technology

In this article, we consider the Lord-Shulman porous-elastic system with dissipation due to microtemperature effects. First, we show that the system is exponentially stable provided that the new stability number X=0. Otherwise, we prove the lack of exponential stability under the assumption X≠0. Furthermore, in the last case, we show that the solution decays polynomially.

Toward Conditions For Consensus Of Noisy Bounded-Confidence Models, Madeline Reeve

HMC Senior Theses

Models of opinion dynamics aim to describe the spread of opinions over time in a social network. However, many canonical models are deterministic and thus may fail to capture uncertainty present in social interactions. This work investigates the effect of adding noise into bounded-confidence models, a class of opinion dynamics models where agents are more likely to be influenced by opinions close to their own. In particular, we propose a noisy modification of the Deffuant–Weisbuch bounded-confidence model. We prove that in this model all agents eventually adopt the same opinion—that is, our model converges to consensus. In doing so, we …

Eigenvalue Bound Preservation: Numerical Experiments On The 2d Q-Tensor Flow, Marcel C. Deguzman

Knowledge and Creativity Expo

We study the evolution of nematic liquid crystals in two dimensions using the Q-tensor model, a continuum framework that describes the orientational order of rod-like molecules via symmetric, traceless matrices. Focusing on the Landau-de Gennes energy and its associated gradient flow, we consider a reduced two-dimensional formulation in which the Q-tensor is fully described by two scalar functions. This reduction simplifies the system to a nonlinear, coupled PDE for the scalars, while preserving essential physical features. A key question is whether the eigenvalues of the Q-tensor remain within the physically admissible range under this flow. Building on a theoretical result …

Asymptotic Profiles And Disease Prevalence At The Steady State For An Sis Patch Model, Daozhou Gao, Xin Li

Mathematics and Statistics Faculty Publications

Infected individuals often display mobility patterns that differ significantly from those of healthy individuals-traveling less frequently, covering shorter distances, visiting fewer destinations, and altering their timing and modes of movement. In this paper, to explore the influence of changes in travel frequency and destination on the spatial spread of infectious diseases, we propose a susceptible-infectious-susceptible patch model in which susceptible and infected populations have different dispersal rates and connectivity matrices. We first establish the threshold dynamics in terms of the basic reproduction number R-0 and show the existence and uniqueness of endemic equilibrium (EE) when R-0>1. Then we examine …

Comparative Machine Learning Models For Disease Risk Prediction, Mercy Mawusi Agbley

Theses, Dissertations and Capstones

Accurate prediction of disease outcomes is crucial for improving clinical decision-making and enabling early intervention. This study compares the performance of various statistical and machine learning models for clinical risk prediction using two healthcare datasets: diabetic retinopathy and heart disease. The models assessed include Logistic Regression, LASSO, k-Nearest Neighbors (KNN), Support Vector Machines (SVM), Neural Networks, Random Forests, Gradient Boosting Machines (GBM), and a stacked ensemble model. Prior to modeling, datasets were split into train and test sets. Standardization was applied to numeric features whilst categorical features were one-hot encoded. These transformations were later applied to the test set. Principal …

Detecting And Repairing Conflicting Constraints In Co-Trained Physics-Informed Neural Networks For Composite Curing Processes, Cooper J. Evans

Dissertations, Master's Theses and Master's Reports

Composite materials have become a critical component of modern manufacturing, especially in the automotive and aerospace industries. The curing process for these composites has been modeled using a variety of partial differential equations representing the heat transfer and composite curing kinetics. Optimizing the applied temperature profile is critical for maximizing the efficiency and capacity of composite part manufacturers. Constraints must be placed on the inputs and outputs of the model, including but not limited to, the applied temperature profile, part temperature, and final degree of cure. Conflicting sets of constraints are easy to unknowingly impose due to the highly coupled …

Memory Effects In Many-Body Systems, Jeffrey Beckstrand

Master's Projects

This thesis investigates memory effects in many-body systems through the MoriZwanzig Formalism for projected dynamics of a Hamiltonian System which yields the Generalized Langevin Equation (GLE). The GLE is a stochastic differential equation (SDE) that studies the dynamics of observables under the effects of many other observables in the system. Although satisfying, the GLE has a term called the Memory Kernel that encodes the past of the system and introduces a computational challenge by introducing a non-Markovian property to the equation. The kernel is often approximated by introducing a delta function, which simplifies the computation, but at the loss of …

Mathematicly Rigorous Quantum General Relativity, I: Pure, James Glimm

Department of Applied Mathematics & Statistics Faculty Publications

A pure quantum general relativity field is one lacking in matter. Such a field has a Lorentzian space-time geometry. A renormalized perturbation expansion, truncated to all finite orders, establishes  the existence of pure quantum general relativity with full mathematical rigor

Type Ii Diabetes Treatment Comparison Via Compartment Modeling, Abigail M. Collins

Theses and Dissertations

Type II diabetes mellitus affects one in ten adults worldwide, yet the effects of treatment type and adherence level on developing complications and quality of life have not been well characterized at the population level, and mathematical modeling offers a structured way to examine these dynamics. This thesis adapts the Boutayeb et al. (2004) model to incorporate dynamic treatment types and levels of adherence, producing nine scenarios in which complication development rate and complication recovery rate differed, to compare peak complications and quality of life across treatment and adherence conditions. Using a system of ordinary differential equations and compartment modeling, …

Modeling French Language Preservation: An Optimal Control Problem, Charlotte Blasi

Scripps Senior Theses

The French language is one of the most globally spoken languages, with over 300 million speakers and designated the official language of 29 nations. French continues to prosper as a result of its titular nations' imperialist history that emphasized linguistic diffusion as well as the support of international organizations dedicated to promoting both the language and the culture of French-speaking nations. In this thesis, we explore the nuanced history of French-speaking countries and one institution dedicated  to promoting the French language, the OIF. We further examine the media mechanism of the OIF and construct a system of Ordinary Differential Equations …