Applied Mathematics Commons^™

A Study Of Addiction: The Opioid Epidemic, An Analysis At The State And County Level, Jamey Van Dyke

Undergraduate Theses

Addictive diseases such as those stemming from the use of alcohol, cocaine and opioids lead to serious negative consequences at both the individual and societal level. Over the last two decades, there has been a significant increase in opioid prescriptions and addiction. The potential for addiction is related to factors that include genetics, prescriber behavior, user behavior and characteristics, in addition to environmental and systemic determinants. One measure of the seriousness of the opioid epidemic is the number of overdose deaths. In 2017, drug overdoses killed over seventy thousand Americans, and overdose deaths are projected to increase in the future. …

358— Hybridization Of Particle Swam Optimization And Pattern Search Algorithms With Application, Eric Koessler

GREAT Day Posters

We test three methods of hybridizing Particle Swarm Optimization (PSO) and Pattern Search (PS) to improve the global minima, speed, and robustness. All methods let PSO run first followed by PS. The first method lets PSO use a large number of particles for a limited number of iterations. The second method lets PSO run normally until tolerance is reached. The third method lets PSO run normally until the average particle distance from the global best location is within a threshold. Numerical results using non-differentiable test functions reveal that all three methods improve the global minima and robustness versus PSO, while …

483— Effectiveness Of Mmr Vaccination In Orthodox Jewish Neighborhoods, Meenu Mundackal

GREAT Day Posters

Measles is a highly contagious disease, where large outbreaks arise by direct contact between susceptible (unvaccinated) and infectious individuals. Many Orthodox Jewish neighborhoods were affected by measles from 2018-2019. To quantify the vaccination effort on this susceptible population, a retrospective analysis was used to study the NYC and Rockland County populations using a differential equations model. A subsequent model, known as a realistically-structured network model, studied only the NYC population, in relation to typical household size. Vaccination strategies were applied to three cohorts: unvaccinated family members, members with 1 prior MMR dose, and members with 2 prior MMR doses. The …

484— Modeling Social Distancing Methods And Their Effectiveness In Combating The Spread Of Ebola, Rachel Fair

GREAT Day Posters

Ebola Virus Disease (EVD) is a rare but severe disease that is transmitted among humans through direct-contact with, and close proximity to, infected bodily fluids. From 2014-16, West Africa experienced the largest Ebola outbreak ever recorded, infecting over 28,000 people, and killing over 11,000. Although the symptoms of EVD are treatable, the disease can be extremely deadly, with an average of 50% EVD cases resulting in fatality. In areas where healthcare is scarce and vaccinations are not readily available, the practices of social distancing and self-quarantining have been shown to be highly effective in combating the spread of EVD. To …

465— Modeling Vaccine Efficacy For Tuberculosis In A Prison Population, Kaitlyn Mundackal

GREAT Day Posters

Tuberculosis is a highly contagious disease and is particularly problematic in confined communities such as prisons. I simulated how Tuberculosis moves through a prison population and tested how much vaccination effort is needed to control its spread. To explore this, I tested adding ever increasing numbers of randomly placed edges in a network and determined the size of the largest component. Afterwards, I removed edges in the model using two different methods, one illustrating if the edges were removed randomly and the other starting with prisoners that had the most connections, to simulate the effect of vaccination. My results show …

Modeling Fico Score And Loan Amount, Ashleigh Romer

Georgia College Student Research Events

In this research, we use Lending Club data from Kaggle to analyze FICO scores and loan amounts funded using multiple predictors. Lending Club is a US peer-to-peer lending company, headquartered in San Francisco, California. First, we cleaned our big data with 1,048,575 rows and 97 columns and then performed exploratory data analysis. We also used feature engineering and subset selection methods to build a linear model to predict FICO score and amount funded of customers loan requests. Overall, we found that FICO score is best modeled using backward regression which gives an exponential function with the predictors being grade, title, …

A Study Of Cholera Transmission, Urmi Ghosh-Dastidar

Open Educational Resources

A recent cholera outbreak in Haiti brought public attention to this disease. Cholera, a diarrheal disease, is caused by an intestinal bacterium, and if not addressed in a timely manner may become fatal. During the project described here, the students will learn how to solve and address a practical problem such as cholera transmission using various mathematical tools. Students will learn to develop a differential equation model based on practical scenarios, analyze the model using mathematics as well as numerical simulation, and finally describe the results in words that are understandable by the people who are not specialists in this …

The Dual Of The Compressed Shift, M. C. Câmara, William T. Ross

Department of Math & Statistics Faculty Publications

For an inner function u, we discuss the dual operator for the compressed shift P_uS∣_Ku, where K_u is the model space for u. We describe the unitary equivalence/similarity classes for these duals as well as their invariant subspaces.

Nonlinear Least Squares 3-D Geolocation Solutions Using Time Differences Of Arrival, Michael V. Bredemann

Mathematics & Statistics ETDs

This thesis uses a geometric approach to derive and solve nonlinear least squares minimization problems to geolocate a signal source in three dimensions using time differences of arrival at multiple sensor locations. There is no restriction on the maximum number of sensors used. Residual errors reach the numerical limits of machine precision. Symmetric sensor orientations are found that prevent closed form solutions of source locations lying within the null space. Maximum uncertainties in relative sensor positions and time difference of arrivals, required to locate a source within a maximum specified error, are found from these results. Examples illustrate potential requirements …

Modeling The Effects Of Passive Immunity In Birds For The Disease Dynamics Of West Nile Virus, Noelle West, Vinodh K. Chellamuthu

Spora: A Journal of Biomathematics

West Nile Virus (WNV) is a mosquito-borne virus that circulates among birds but also affects humans. Migrating birds carry these viruses from one place to another each year. WNV has spread rapidly across the continental United States resulting in numerous human infections and deaths. Several studies suggest that larval mosquito control measures should be taken as early as possible in a season to control the mosquito population size. Also, adult mosquito control measures are necessary to prevent the transmission of WNV from mosquitoes to birds and humans. To better understand the effective strategy for controlling affected larvae mosquito population, we …

Storage Management Strategy In Mobile Phones For Photo Crowdsensing, En Wang, Zhengdao Qu, Xinyao Liang, Xiangyu Meng, Yongjian Yang, Dawei Li, Weibin Meng

Department of Computer Science Faculty Scholarship and Creative Works

In mobile crowdsensing, some users jointly finish a sensing task through the sensors equipped in their intelligent terminals. In particular, the photo crowdsensing based on Mobile Edge Computing (MEC) collects pictures for some specific targets or events and uploads them to nearby edge servers, which leads to richer data content and more efficient data storage compared with the common mobile crowdsensing; hence, it has attracted an important amount of attention recently. However, the mobile users prefer uploading the photos through Wifi APs (PoIs) rather than cellular networks. Therefore, photos stored in mobile phones are exchanged among users, in order to …

Teaching And Learning Of Fluid Mechanics, Ashwin Vaidya

Department of Mathematics Faculty Scholarship and Creative Works

Fluid mechanics occupies a privileged position in the sciences; it is taught in various science departments including physics, mathematics, environmental sciences and mechanical, chemical and civil engineering, with each highlighting a different aspect or interpretation of the foundation and applications of fluids. Doll’s fluid analogy [5] for this idea is especially relevant to this issue: “Emergence of creativity from complex flow of knowledge—example of Benard convection pattern as an analogy—dissipation or dispersal of knowledge (complex knowledge) results in emergent structures, i.e., creativity which in the context of education should be thought of as a unique way to arrange information so …

Studies Of Oval Tube And Fin Heat Exchangers, Phillip Nielsen

Discovery Day - Prescott

Heating Ventilation and air-conditioning (HVAC) is a system which changes the temperature of the surroundings for the purposes of cooling or heating. This system requires energy to maintain a temperature difference from the outside temperature. This is important since minimized power is one of the requirements for the system to achieve a better efficiency. Optimizing the flow over the evaporator coils is one way to increase the cooling efficiency. This will reduce the power required to have a sustainable system. Optimizing the flow to increase the energy transfer between the fins and the incoming air could result in a greater …

Mitigating Safety Concerns And Profit/Production Losses For Chemical Process Control Systems Under Cyberattacks Via Design/Control Methods, Helen Durand, Matthew Wegener

Chemical Engineering and Materials Science Faculty Research Publications

One of the challenges for chemical processes today, from a safety and profit standpoint, is the potential that cyberattacks could be performed on components of process control systems. Safety issues could be catastrophic; however, because the nonlinear systems definition of a cyberattack has similarities to a nonlinear systems definition of faults, many processes have already been instrumented to handle various problematic input conditions. Also challenging is the question of how to design a system that is resilient to attacks attempting to impact the production volumes or profits of a company. In this work, we explore a process/equipment design framework for …

D-Vine Copula Model For Dependent Binary Data, Huihui Lin, N. Rao Chaganty

College of Sciences Posters

High-dimensional dependent binary data are prevalent in a wide range of scientific disciplines. A popular method for analyzing such data is the Multivariate Probit (MP) model. But the MP model sometimes fails even within a feasible range of binary correlations, because the underlying correlation matrix of the latent variables may not be positive definite. In this research, we proposed pair copula models, assuming the dependence between the binary variables is first order autoregressive (AR(1))or equicorrelated structure. Also, when Archimediean copula is used, most paper converted Kendall Tau to corresponding copula parameter, there is no explicit function of Pearson’s correlation coefficient …

Scale-Invariance Ideas Explain The Empirical Soil-Water Characteristic Curve, Edgar Daniel Rodriguez Velasquez, Vladik Kreinovich

Departmental Technical Reports (CS)

The prediction of the road's properties under the influence of water infiltration is important for pavement design and management. Traditionally, this prediction heavily relied on expert estimates. In the last decades, complex empirical formulas have been proposed to capture the expert's intuition in estimating the effect of water infiltration on the stiffness of the pavement's payers. Of special importance is the effect of water intrusion on the pavement's foundation -- known as subgrade soil. In this paper, we show that natural scale-invariance ideas lead to a theoretical explanation for an empirical formula describing the dependence between soil suction and water …

Redesign Of Math 1601 Modeling With Calculus, Dustin Grindstaff

Q2S Enhancing Pedagogy

This is the redesign of the course math 1601 - Modeling with Calculus. It includes a sample syllabus and tentative schedule of topics to be covered. The course must meet the Technological Literacy requirement so I have also included a list of potential GeoGebra activities, as well as, what a sample activity would look like.

H-Discrete Fractional Model Of Tumor Growth And Anticancer Effects Of Mono And Combination Therapies, Kamala Dadashova

Masters Theses & Specialist Projects

In this thesis, we focus on h–discrete and h–discrete fractional representation of a pharmacokinetics-pharmacodynamics (PK-PD) model which describes tumor growth considering time on hNa, where h>0. First, we introduce some definitions, lemmas and theorems on both h–discrete and h–discrete fractional calculus in the preliminary section. In Chapter 3, we work on the PD model with delay by exam ining nabla h–discrete equations and nabla h–discrete fractional equations as well as variation of constants formulas, accordingly. We introduce our model and solve it using theorems we proved in the last section of the indicated chapter. When we do simulation for …

Improved Filtering Of Electron Tomography Edx Data, Kelsey M. Larkin

Senior Theses

Electron microscopy is a very exciting field, which has shown huge developments in the last few decades. There is a continuous development of new methods which feature atomic level resolution. One of these methods is the energy dispersive X-ray (EDX) spectroscopy, which allows the researchers to understand the chemical make-up of the sample. It is particularly exciting that we are able to make EDX tomographic reconstructions and view the 3D structure of a nano-object.

This thesis is focused on developing a new methodology for EDX tomography. In a typical EDX set-up, one detects X-rays from the sample with different energies, …

Preparing For The Future: The Effects Of Financial Literacy On Financial Planning For Young Professionals, Tanay Singh

Senior Theses

Purpose – Many people between the age of 20 and 34 have not considered planning financially for the future in any significant capacity and in doing so, they limit their potential savings. The purpose of this study is to examine what financial expectations are for people in the early stages of their career and determine if improving financial literacy and revealing financial realities helps to produce more accurate or realistic expectations. Ultimately, the goal is to better prepare participants in the study for the working world and increased responsibilities outside of the college/university environment by getting them to start thinking …