Applied Mathematics Commons^™

Conformable Regulator Problems With Fixed Delay, Seth Baur, Joseph E. Smith, Nick Wintz

2025 Student Academic Showcase

In this project, we consider processes guided by a conformable derivative first introduced by Khalil et al in 2014. This time-weighted derivative has many of the same properties as the classical derivative but lacks the semigroup property for the exponential. Here, we study a conformable linear system where the state and control are subject to the same fixed delay. Our process is also subject to wear and tear, represented by a cost functional. Our goal is to find an optimal control that minimizes this cost. This control is propagated by a quasi-Ricatti equation, which itself includes a time delay. Finally, …

Applications For The Conformable Information Filter, Sophia Hungerford, Joseph E. Smith, Nick Wintz

2025 Student Academic Showcase

In this project, we offer application to our previously constructed information filter. The information filter is an algorithm used to estimate the information of a process corrupted in some way. The information filter is mathematically similar to the Kalman filter, widely used in navigation. Unlike the Kalman filter, the information filter propagates backwards in time and is more effective in smoothing. Here, our corrupted system is in terms of conformable derivative introduced by Khalil et al. in 2014. This time-weighted derivative shares many of the same properties as the classical derivative but lacks the usual semigroup property associated with the …

Developing An Unfolding-Incorporated Coarse-Grained Polymer Model For Fibrinogen To Study The Mechanical Behaviour, Vivek Sharma, Poulomi Sadhukhan

Northeast Journal of Complex Systems (NEJCS)

Fibrinogen is a protein found in blood that forms Fibrin polymer network to build a clot during wound healing process when there is a cut in the blood vessel. The fibrin fiber is highly stretchable and shows a complex mechanical properties. The fibrin monomer, Fibrinogen, has a very complex structure which is responsible for its unusual elastic behaviour. In this work, we focus on mechanism of unfolding of D-domain of Fibrinogen, and study its effect in the mechanical behaviour. We develop a coarse-grained (CG) bead-spring model for Fibrinogen which captures the unfolding of folded D-domains along with other necessary structural …

Automating Course Scheduling With Linear Programming And The Python Pulp Framework: First Steps, George K. Thiruvathukal

Computer Science: Faculty Publications and Other Works

This article presents a pragmatic approach to automating course scheduling in an academic setting using linear programming.

We explore how linear optimization via current open-source tools can efficiently handle scheduling constraints such as instructor preferences, teaching loads, course section requirements, and specific time slots. Using Python’s PuLP library and matplotlib for visualization, we built a flexible and accessible scheduling system.

Our research prototype balances course assignments while addressing department-specific needs, demonstrating how linear programming can simplify academic scheduling and improve efficiency.

Although this is a research prototype, our results already demonstrate the ability to generate a correct course schedule that …

Meta-Clustering For Specialized Language Models: Enhancing Contextual Adaptation And Mitigating Hallucinations In Diverse Healthcare Environments, Joshit Mohanty, Vaishali Vaishali, Sandeep Kumar Nayak, Sumit Lahiri

Graduate Student Government Association Research Conference

Large Language Models (LLMs) have significantly advanced conversational AI by enabling dialogic information-seeking and task execution across diverse domains. However, their extensive parameters and broad domain scope lead to “data hallucinations.” These shortcomings are particularly evident in dynamic and diverse environments like India’s healthcare sector, where myriad languages, regional practices, and cultural nuances demand specialized, localized expertise rather than one-size-fits-all generalist models. This paper introduces a meta-clustering framework that integrates Distilled Language Models (DLMs) and Small/Specialized Language Models (SLMs) with meta-learning principles to address these limitations. By drawing on evidence from works such as MedHalu and Med-HALT, the framework seeks …

Using Mathematical Modeling To Study The Dynamics Of Legionnaires’ Disease And Consider Management Options, Mark Z. Wang, Christina J. Edholm, Lihong Zhao

Faculty Articles

Legionnaires' disease (LD) is a largely understudied and underreported pneumonic environmentally transmitted disease caused by the bacteria \textit{Legionella}. It primarily occurs in places with poorly maintained artificial sources of water. There is currently a lack of mathematical models on the dynamics of LD. In this paper, we formulate a novel ordinary differential equation-based susceptible-exposed-infected-recovered (SEIR) model for LD. One issue with LD is the difficulty in its detection, as the majority of countries around the world lack the proper surveillance and diagnosis methods. Thus, there is not much publicly available data or literature on LD. We use parameter estimation for …

Existence And Nonexistence Of Positive Solutions For Fractional Boundary Value Problems With Lidstone-Inspired Fractional Conditions, Jeffrey Lyons, Jeffrey T. Neugebauer, Aaron G. Wingo

EKU Faculty and Staff Scholarship

This paper investigates the existence and nonexistence of positive solutions for a class of nonlinear Riemann–Liouville fractional boundary value problems of order 𝛼 +2⁢𝑛, where 𝛼 ∈(𝑚 −1,𝑚] with 𝑚 ≥3 and 𝑚,𝑛 ∈ℕ. The conjugate fractional boundary conditions are inspired by Lidstone conditions. The nonlinearity depends on a positive parameter on which we identify constraints that determine the existence or nonexistence of positive solutions. Our method involves constructing Green’s function by convolving the Green functions of a lower-order fractional boundary value problem and a conjugate boundary value problem and using properties of this Green function to apply the Guo–Krasnosel’skii …

Numerical Analysis Of The Seir Model, Abigail R. Beckelhimer

Departmental Honors & Graduate Capstone Projects

Epidemiological models delineate the spread of diseases within a population. In this research project, the Susceptible-Exposed-Infected-Recovered (SEIR) Model was examined numerically for comparison between several methods. Approximations were obtained through Euler’s Method, Taylor’s Method, Runge-Kutta Methods, and Multi-step Methods. Hypothetical situations with parameter alterations were considered in order to better understand the effects the parameters have on the model. The goal of this project was to portray the usefulness of numerical approximations for predicting the behavior of the SEIR model and thus the course of a pandemic.

Learning With Errors Parameter Analysis, Archana Parameswaran

Cybersecurity Undergraduate Research Showcase

We implement a systematic approach for generating, evaluating, and benchmarking Learning with Errors implementations in Sage Math by varying lattice dimensions, moduli, error standard deviations, and multiple error distributions to observe concrete security-efficiency tradeoffs. The security estimator maps parameter sets to concrete security levels and bits, while performance metrics measured computational efficiency and memory requirements. Results indicate that various distribution types do not significantly impact security, though binomial distributions require more computational overhead than discrete gaussian or uniform. Memory requirements increased when modulus q increased from 12289 to 65537. Larger dimensions have an exponentially growing requirement for memory, but this …

Looking Good: The Math Behind Computer Vision*, Corbin Weiss

Campus Research Month

Exploring the mathematical foundations of a Multilayer Perceptron (MLP), a foundational approach to computer vision. Then expanding this understanding to create a visualization of the representation of reality in the MLP.

Unraveling The Impact Of Curricular Complexity On Graduation Time: A Causal Analysis In Higher Education, Ameer Slim

Mathematics & Statistics ETDs

This study examines the causal relationship between program complexity and graduation time at UNM. While program complexity is recognized as a factor influencing student outcomes, its precise impact on graduation timelines remains underexplored. Using comprehensive cohort data, this study employs causal inference methods, including generalized propensity scores, to estimate the effect of complexity on time-to-degree. Findings reveal that higher program complexity extends graduation timelines, even after controlling for demographics and academic preparedness. Socioeconomic factors also play a role. Specifically, programs with more Pell Grant recipients and lower median high school GPAs tend to have lower complexity levels. These results provide …

Unfitted Finite Element Methods For Shape Optimization And Liquid Crystals, Jeremy T. Shahan

LSU Doctoral Dissertations

We present an approach to shape optimization problems that uses an unfitted finite element method (FEM). The domain geometry is represented, and optimized, using a (dis- crete) level set function and we consider objective functionals that are defined over bulk domains. For a discrete objective functional, defined in the unfitted FEM framework, we show that the exact discrete shape derivative essentially matches the shape derivative at the continuous level. In other words, our approach has the benefits of both optimize-then- discretize and discretize-then-optimize approaches.

Specifically, we establish the shape Fréchet differentiability of discrete (unfitted) bulk shape functionals using both the …

Fibonacci Product Cordial Labeling Of Generalized Triangular Snake And Other Graphs, Anthony S. Arial, Soumya Bhoumik

SACAD: Scholarly Activities

A Fibonacci Product Cordial labeling is an assignment of Fibonacci numbers to the vertices of a graph in a way that determines edge labels based on the product of vertex labels, modulo 2. The labeling is valid if the number of edges labeled 0 and 1 differ by at most 1. If a graph allows such a labeling, it is called a Fibonacci Cordial graph. We explore various snake graphs and Helm graphs that can have this type of labeling.

Irreversible K-Threshold Number Ck(G) And Saturation Probability P[G] For Corona Product And Double Corona Product Graphs, Eric J. Moon, Soumya Bhoumik, Paul Flesher

SACAD: Scholarly Activities

We discuss the Irreversible k-conversion process for graphs, where a vertex becomes saturated and remains saturated indefinitely if at least k of its neighbors are saturated. We investigate sets S₀, which when initially saturated, lead to complete graph saturation. We are interested in the minimum |S₀| = C_k(G), called the k-threshold number. We consider the construction of the Corona Product Graphs (of C_n and K_p). Additionally, we extend our analysis by defining and exploring Double Corona Product Graphs (of C_n and K_p). Then we incorporate …

Acoustic-Gravity Wave Propagation Based On Solutions To The Generalized Multi-Component Transport Equations, Benedict PiñEyro

Doctoral Dissertations and Master's Theses

Nonlinear atmospheric models have provided important insight into acoustic waves generated by natural and man-made hazards, which may steepen into shocks or N-waves while also dissipating when propagating in the thermosphere. Although models have yielded results that agree with observations of ionospheric perturbations, dynamical models for the diffusive and stratified lower thermosphere often use single gas approximations with height-dependent physical properties that omit the dynamics of the major and minor constituents. Thus, the inter-species diffusion associated with these flows (e.g. variations of mean molecular weight, and specific heat) are not accounted for. This approximation is simpler and less computationally expensive …

Exploring Electrical Impedance Tomography Techniques For Breast Cancer Detection In Three Dimensions, Emily Jean Mader Corcoran

Dissertations (1934 -)

Electrical Impedance Tomography (EIT) is an imaging modality whose reconstruction problem is severely ill-posed; large changes in the interior conductivity can present as small changes in the data. Due to this ill-posedness, reconstructed images generally have low spatial resolution. However, EIT remains a promising area of study for many medical imaging applications, including breast imaging. In this dissertation, a proof of concept study is discussed in Project 1: "Machine Learning for Breast Cancer Detection" wherein machine learning techniques are used to classify breast tumors as malignant or benign from simulated EIT voltage data. Promising results in terms of accuracy and …

Modeling Droplet Levitation Over A Heated Liquid Surface, Jacob E. Davis

Mathematics Theses and Dissertations

Research into the interactions between droplets and liquid surfaces is of importance for a number of practical applications. These applications range from spray cooling techniques in engineering, to infectious disease transmission, to the distribution of aerosolized pharmaceuticals and various challenges in particle transport in multiphase flows. In this study, we focus on the dynamics of a slowly condensing droplet, suspended above an evaporating liquid layer. The key objective of the present study is to formulate comprehensive mathematical models that describe the phenomena of diffusion and heat transfer occurring within this system. Using this, we model the flow around the droplet …

Dual Quaternions For Gravity Recovery Missions, Ryan Kinzie

Doctoral Dissertations and Master's Theses

A dual quaternion-based modeling, state estimation and control approach is introduced as a better alternative to the traditional methods which are currently utilized for gravity recovery missions. The proposed modeling and control approach was verified against and compared to the tangent bundle to Special Euclidean Group 3 through MATLAB simulations. The dual quaternion-based approach shows superior performance over traditional linearized and uncoupled methodologies, in both modeling accuracy of spacecraft translational position, and the ability to control the pose of a test mass relative to its host spacecraft. Utilizing data products from the Gravity Recovery and Climate Experiment Follow-On mission, a …

Stability Analysis In The Twist-Bend Nematic Liquid Crystal Model, Zhenqiang Li

Mathematics & Statistics Theses & Dissertations

The recently discovered twist-bend nematic liquid crystal (LC) phase is characterized by a nanoscale helical modulation of the nematic director n, forming a conical helix along the z-axis at an oblique angle θ. While many models assume a constant cone angle and equal elastic constants K11 = K22 = K33, this dissertation removes both assumptions by considering a fully anisotropic elastic energy with K11 ≠ K22 ≠ K33, and allowing θ to vary spatially. We analyze the stability of this system under frustrated and free boundary conditions using variational methods. …

Predicting Battery Efficiency: A Theoretical Approach, Haiti Schafers

SACAD: Scholarly Activities

The Kansas ElectroRally Races continuously demand faster electric vehicles (EV). When designing a vehicle one of the most important components is the battery. This study was designed to find the following; What is the optimal throttle percentage to run a 36V 20Ah (768Wh) LiFePO4 Rechargeable Battery Pack[1].

The optimal throttle percentage was found with methods detailed in a different section. Based on the performance of the older cars this study choose to focus on 50% and 70%, while obtaining other relevant data to further that inference.