Applied Mathematics Commons^™

Mathematical Modelling And Analysis For The Co-Infection Of Viral And Bacterial Diseases: A Systematic Review Protocol, Timothy Kiprono Yano, Ebenezer Afrifa-Yamoah, Julia Collins, Ute Mueller, Steven Richardson

Research outputs 2022 to 2026

Introduction Breaking the chain of transmission of an infectious disease pathogen is a major public health priority. The challenges of understanding, describing and predicting the transmission dynamics of infections have led to a wide range of mathematical, statistical and biological research problems. Advances in diagnostic laboratory procedures with the ability to test multiple pathogens simultaneously mean that co-infections are increasingly being detected, yet little is known about the impact of co-infections in shaping the course of an infection, infectivity, and pathogen replication rate. This is particularly true of the apparent synergistic effects of viral and bacterial co-infections, which present the …

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 $n=4$.

Modeling Of Light Filamentation For Nonlinear Imaging And Waveguiding, Nicholas Bagley

Mathematics Theses and Dissertations

Ultrashort pulses are capable of extremely high powers; in addition to enabling various applications in defense, sensing, and imaging, they provide a useful arena in which to study nonlinear optical phenomena that are observable only at high intensities. Due to these effects, which can include ionization and thermal blooming, simulation of ultrashort pulse propagation is a complicated multiphysics problem. We provide an overview of techniques used to simulate the propagation of ultrashort pulses in the nonlinear regime, including the formation of light filaments due to the competition of Kerr self-focusing and defocusing (e.g. via plasma generation). We discuss both carrier-resolved …

An Optimization Framework For Data Enrichment: A First Principles Approach To Designing Optimal Smoothers And Splines, Griffin Michael Kearney

Dissertations - ALL

We develop a general framework for state estimation in systems modeled with stochastic dynamics and noisy measurements. Our approach is based on maximum likelihood estimation and employs a variety of techniques from optimization theory including the calculus of variations and discrete optimization to derive optimality conditions for many different types of problems. We make no rigid assumptions on the form of the mapping from measurements to state-estimate or on the distributions of the random processes, making the framework more general than existing techniques such as splines, Kalman smoothing or Gaussian Process Regressions, which are subject to limiting restrictions and modeling …

Safety And Optimality Monitors For Learning-Enabled Systems Using Conformal Prediction, Jackson Cox

McKelvey School of Engineering Graduate Student Theses & Dissertations

The use of machine learning to create data-driven plant models and controllers has led to an increased need for safety and optimality monitors for model-based systems. System plant models are subject to uncertainty due to learning constraints such as unseen data and overfitting or physical constraints such as unknown dynamics and noise. This uncertainty is detrimental to safety-critical systems and must be properly regulated. To curb this uncertainty, we create prediction sets using the guarantees provided by Conformal Prediction. With a user-specified high probability, these prediction sets contain the true plant system states for an entire prediction horizon, which we …

Traveling Waves In Biological Population Models, Ahlam Alzahrani

Theses and Dissertations

In this thesis, we examine the existence of traveling waves in population models. We begin by exploring conditions under which traveling waves exist, even when the migration probability lacks a density function or, if the density function exists, it may be discontinuous. To address this, we impose certain conditions that ensure the monotonicity of the evolution operator, enabling the application of the Monotone Iteration Method. Next, we explore the existence of monotone traveling waves in a general class of integral-difference population models that depend on both the previous state and long-term memory, allowing for the consideration of multiple past states. …

Mathematical Modelling Of Disease Outbreak, Favour Christian, Matthew Molloy

SURE Journal: Science Undergraduate Research Experience Journal

Establishing a model framework for more research necessitates a thorough understanding of the causes, distribution, prevalence, and evolution of infectious illnesses. The main mathematical concept used in this modelling simulation is ordinary differential equations (ODEs). The purpose of this study was to investigate the significance of the many criteria linked to a zombie virus spread. The zombie framework provides an accessible and relatively simple representation of the nature of infectious disease spread, allowing for tractable assumptions and the development of more complex situations.

The models are designed around a zombie outbreak in which the zombie virus is spread through a …

The Mathematical Laws Of Morphology And Biomechanics Through Ontogeny, Wijesooriya Kisal Wijesooriya

The Journal of Purdue Undergraduate Research

No abstract provided.

Where To Build Food Banks: A Machine Learning Approach, Gavin Ruan

The Journal of Purdue Undergraduate Research

Over 44 million Americans currently suffer from food insecurity, of whom 13 million are children. Food insecurity has been shown to cause a wide range of both physical and developmental issues. Across the United States, thousands of food banks and pantries serve as vital sources of food and other forms of aid for food-insecure families. By optimizing food bank locations, food banks and their resources would become more accessible to families who desperately require it. The aim of this paper is to build a machine learning framework that is able to optimize food bank locations and to consider factors such …

Operations On Submodules With The Multiplicative And Quotient Properties, Jiekai Pang

Mathematics & Statistics ETDs

Inspired by the works of Petro, Epstein, Vassilev, and Morre, this thesis aims to study the generalized definitions of the semiprime operation, weakly prime operation, and standard closure operation on rings, that is, the multiplicative operation, weakly multiplicative operation, and standardly multiplicative operation on submodules. Then, we will use Matlis duality to induce the dual notions of these definitions on submodules of Matlis-dualizable Artinian modules. In order to understand the dual notion of the standardly multiplicative operation, that is, the standardly quotient operation, we will classify the operations on the injective hull of residue field of the ring K[[x,y]]/(xy) which …

Theory And Algorithms To Learn, Propagate, And Exploit Uncertainty For Stochastic Optimal Control Of Dynamical Systems, Vignesh Sivaramakrishnan

Electrical and Computer Engineering ETDs

Non-Gaussian uncertainty frequently arises in learning and control problems involving stochastic dynamical systems, particularly in autonomous vehicles, UAVs, satellites, and robotics. In this dissertation, we propose a new framework that leverages characteristic functions that provides a frequency-domain representation of random variables. The dissertation is structured into three key areas. First, we address model-based stochastic optimal control for linear systems with non-Gaussian noise, demonstrating that characteristic functions can be used to enforce chance constraints and control systems toward desired distributions. Second, we explore data-driven stochastic control, utilizing empirical characteristic functions to handle systems with unknown disturbances. In addition, we derive several …

Investigating The Efficacy Of Prompt Engineering Techniques For Research Survey Paper Generation Using Large Language Models, Innocent Obed Awidi

Theses and Dissertations

The recent advancements in large language models (LLMs), such as ChatGPT, offer promising potential for automating academic writing tasks. This study investigates the efficacy of prompt engineering techniques in guiding LLMs to generate high-quality research survey papers, specifically exploring their application in the fields of artificial intelligence (AI) in drug development and large language model customization for classification. Using a mixed-methods approach, this research assessed the impact of prompt engineering on the coherence, relevance, and overall quality of generated content through quantitative and qualitative analyses. Techniques including prompt refinement, contextual prompting, and iterative prompting were systematically applied to enhance the …

Mathematics In Amusement Parks, Kacey Laumann

Honors Projects

This project focuses specifically on the Walt Disney World Park, Magic Kingdom. I started by collecting data through the MyDisneyExperience app. By recording the data, I was then able to create polynomial functions to the fifth the degree. Each attraction received a function which allowed me to predict the wait times for that attraction. Then, by graphing the functions and analyzing the graph using calculus the “best time” and “worst time” to go to the attraction were found. After the analysis the information is used to build a unique schedule for a guest. Then the guest receives this schedule after …

(R2100) Optimality Conditions Of A Topsis Optimization Model And Its Application On Interval-Valued Data, Sudipta Roy, Sandip Chatterjee

Applications and Applied Mathematics: An International Journal (AAM)

The Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) is widely used in the field of multi-criteria decision analysis. Despite its popularity and widespread application, little attention has been given to the mathematical foundation that underlies the TOPSIS algorithm. The existing literature on this subject is far from comprehensive, leaving many aspects of the algorithm unexplored. This paper aims to address this gap in the literature by delving into the optimization problem associated with TOPSIS. Unlike traditional interval analysis theory, which only covers a limited scope, our approach extends to a broader range of scenarios and offers …

(R2111) Effect Of Stenotic-Aneurysmal Arterial Regime On Unsteady Magnetohydrodynamic Non-Newtonian Blood Flow With Heat Radiation, Babatunde A. Joseph, Dada M. Sunday, Bello A.J. Funsho, Akeem B. Disu, Alamu-Awoniran F., Danas James Y.

Applications and Applied Mathematics: An International Journal (AAM)

The study aims to investigate the effect of magneto-hydrodynamic on a non-Newtonian unsteady blood flow with internal heat energy in the presence of blood ironic properties characterized by stenosis. The formulated mathematical equations resulted in differential forms and were solved analytically by Differential Transform Method. The obtained solutions were displayed by graphs showing different flow physiognomies like blood velocity, temperature profile, Nusselt number, wall shear stress and stream function.

The results indicated that velocity profile increases as magnetic field, Darcy number and aneurysmal artery rise, while it decreases as heat radiation, Reynold number, and Casson parameter speedup. The temperature profile …

A New Reduced Basis Method For Parabolic Equations Based On Single-Eigenvalue Acceleration, Qijia Zhai, Qingguo Hong, Xiaoping Xie

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we develop a new reduced basis (RB) method, named as Single Eigenvalue Acceleration Method (SEAM), for second order parabolic equations with homogeneous Dirichlet boundary conditions. The high-fidelity numerical method adopts the backward Euler scheme and conforming simplicial finite elements for the temporal and spatial discretizations, respectively. Under the assumption that the time step size is sufficiently small, and time steps are not very large, we show that the singular value distribution of the high-fidelity solution matrix U is close to that of a rank one matrix. We select the eigenfunction associated to the principal eigenvalue of the …

(R2101) Analysis Of Map/Ph/1 Queueing Inventory System With Two Commodity, Working Vacation, (S, S) Replenishment Policy, Essential And Optional Repair, G. Ayyappan, N. Arulmozhi

Applications and Applied Mathematics: An International Journal (AAM)

We examine a queueing inventory model with single server which can offer two types of inventory items: main item (commodity I) and complementary item (commodity II). We assume both commodities have a finite capacity Si, i = 1, 2. Customers reach the system by following the Markovian arrival process (MAP). The service times are considered to be phase-type (PH) distribution. We have considered no customer in the system, even inventory level is positive; the server will start the working vacation, and any customer that arrives during working vacation, the server provides slow service. If an item is not available, the …

(R2108) Global Asymptotic Stability Analysis Of Discrete Time Population Model With Allee Effect Through Lyapunov Function, Govind Jha, Neeraj Kumar, Sarita Jha

Applications and Applied Mathematics: An International Journal (AAM)

This study explores the idea of stability analysis by using Lyapunov functions in discrete time population models; this work focuses on the nth generation. Further, this investigation aims to extend global stability concepts to discrete-time models and considers the influence of the Allee effect on population dynamics. Mathematical formulations and specific modelling approaches are utilized to investigate the behavior of the population system. The results reveal a larger range of stability in comparison to previous findings, emphasizing the effectiveness of the Lyapunov function approach. Specifically highlighted here are the extension of global stability concepts to the nth generation providing insights …

(R2099) Boundedness And Square Integrability In Neutral Differential Equations With Delay And Exponential Stability In Nonlinear Differential Equations Of Third-Order, Fatima Abdellaoui, Mebrouk Rahmane

Applications and Applied Mathematics: An International Journal (AAM)

The Lyapunov second method is an eigenvalue-based technique which consist of finding a Lyapunov function candidate for studying the stability of dynamical systems which is hard to deal with especially in most of nonlinear cases. Studying the stability and some of other qualitative behaviors based on the Lyapunov second method is research topic of actuality because of the wide range of applications of the differential equations. Many authors in the literature have used the second method of Lyapunov in the study of some qualitative behaviors from which the stability, the boundedness and the square integrability of solutions for various kinds …

(R2090) Analysis Of Heat And Mass Transfer In Mhd Boundary Layer Flow Of Chemically Reacting Fluid, Dharati Sheth, Manisha Patel, Dilip Joshi

Applications and Applied Mathematics: An International Journal (AAM)

Analysis of the effects of heat and mass transfer on the chemically responding boundary layer flow of a Casson fluid across a porous stretched sheet in the existence of a crosswise magnetic field is the aim of the existing work. The partial differential equations that control the current flow problems can be converted into similarity equations by applying the right similarity technique. Our goal is to use the DTM-Pade approximation to analytically solve the derived similarity equations. The transformed similarity equations are a group of nonlinear ordinary differential equations for the present flow problem. The analytical approach of the differential …