Students pursuing a major in the Department of Mathematical, Information & Computer Sciences have the unique opportunity to conduct real-world research alongside expert faculty. This student research involves the methodical formation of a scholarly honors project. The goal of this project and its process is to prepare students for the world of post-baccalaureate scholarship and research.
Work closely with a department faculty mentor to develop a project on a topic of your choosing and culminate research resulting in a presentation of your findings at a conference in spring semester. In preparation of presenting your findings, you will be coached through the various stages of conducting a research project and transforming your work into a scholarly presentation and paper. The Department of Mathematical, Information & Computer Sciences will strongly support you in your research, and you can look forward to working with your faculty mentor throughout the research, editing, and presentation processes with invaluable advice and guidance every step of the way.
2021-22 Student Research
Sentiment Analysis: A Comparison of the Instagram Accounts of PLNU and Other Universities
Alexa Do
Mentor: Dr. Mike Leih
Sentiment analysis is a machine learning, Natural Language Processing technique that associates text with their given emotion. Marketers often use sentiment analysis to gain insights into their customers, especially in discovering areas that they can improve on or should continue doing. Sentiment analysis is often performed on social media platforms so that marketers can modify their content based on the positive sentiments found. Through a collaboration with PLNU’s Marketing Department, sentiment analysis was conducted on the Instagram accounts of PLNU and their competitors. Using the VADER Python library, sentiment scores were created, ranging in numerical values from -1 to +1. These values were then translated as positive, negative, or neutral. By putting the Instagram Posts into categories, the colleges were ranked based on positive sentiment. Each category was then analyzed as to the reasons why a particular college received the top rank. Then sentiment scores were conducted for the universities collectively, demonstrating that Pepperdine received the highest sentiment overall.
Sequential Analysis of the Oncogenetic Proten E7 from High and Low Risk Human Papillomavirus
Camryn Marble and Isabel Garcia
Mentor: Dr. Heidi Woelbern
This study analyzes the impact of hydropathy on high- and low-risk serotypes of Human Papillomavirus (HPV). A review and categorization of HPV serotypes was performed alongside an investigation of epidemiological data. Preliminary hydropathy analysis using the R programming language suggests a correlation between increased hydrophilicity and oncogenic high-risk serotypes.
Anamnesis (short story)
Samuel Cheung
Mentor: Eddie Matthews
“I open my eyes and see the gray interior of my car. Squinting against the brightness, I see the lampposts, stray shopping carts, and evenly spaced diagonal lines of a parking lot. The passenger seat holds my backpack and a few loose sheets of paper with my handwriting scrawled on them. I turn in my seat and see that the backseat has a good number of my clothes haphazardly piled on top of each other.
I inhale and smell the metallic odor of dried blood. Panic shoots through my body as images of last night flood into my mind. I was in a rush to leave. No matter what, I couldn't stay in our apartment. Bella. I left a note on the kitchen table next to the salt and pepper.
I trace my steps backward as the fog of sleep lifts further. I had stared at the warning label on the visor that tells you about seat belts until my eyes ached and then drifted off to sleep. I parked here after driving for hours around town without a destination. I packed without thinking, it was more that I was just trying to get everything in my car. Before that, all that comes is the sight of our bedroom door closing. What happened?” (Full story is on the 3rd floor bulletin board.)
2020-21 Student Research
Finding Renewable Energy Solutions Through GIS
Delaney Hanson
Mentor: Dr. Lori Carter
This project explores Esri's ArcGIS tool and uses its functionality to map out ideal renewable energy locations in specific areas in the United States. Depending on the type of energy source, different factors are considered to draw conclusions about the best places to implement renewable energy power plants. Research into GIS data and renewable energy factors helped guide the search for the datasets that this project required. This paper describes not only the results of ideal locations that were discovered, but also the process of learning and applying the various tools and techniques for the research. The tutorials provided for ArcGIS, demonstrated how the application displays datasets and uses processing tools to manipulate data on a map. The layers that were obtained provided insight to analyze the conditions which would create an ideal site for a solar or wind power plant.
Cloud Based Plasmid Annotation Tool
Leslie Smith
Mentor: Dr. Mike Leih
Plasmid genome analysis is a primary way biologists can study and infer characteristics about antibiotic-resistant bacteria. However, analysis of plasmid genomes has been hindered by inconsistent gene naming, various incomplete databases, and the need for many different tools to identify and analyze plasmid features. We aim to alleviate some of these challenges by providing a single, cloud-based web tool that can link the plasmid genome annotation workflow. With use of the genome analysis tool Prokka, AWS, and RShiny, we are able to provide a web tool for user-friendly plasmid genome upload, annotation, and visualization.
How to Build a Better Engineer: An Analysis of Integrated CS Ethics Modules
Morgan Wheeler
Mentor: Dr. Lori Carter
Starting in 2019, Point Loma Nazarene University professors Dr. Lori Carter and Dr. Catherine Crockett recognized a need for integration of ethics into computer science (CS) and data science courses, so they have been developing a series of ethics modules to be embedded throughout CS curricula. These modules introduce four ethical frameworks – virtue ethics, analogies, utilitarianism, and deontology - for evaluating ethical dilemmas. Then, in upper-division courses, they are used to discuss relevant social issues pertaining to the topic of the class. Similar approaches to ethics have been made in other fields including medicine and business. Moral psychologists have long argued that practicing language-based reasoning through analyzing ethical dilemmas shapes a more ethical person; however, more recent work has shifted focus from the emphasis on moral reasoning to a development based more on quick emotions and intuitions as the proponents of moral action. To build moral development, those papers recommend having communities that foster moral behavior, learning from moral exemplars, and regularly practicing moral virtues. This paper evaluates the effectiveness of the CS ethics modules by analyzing the current responses from teachers and students, similar approaches to teaching ethics in accounting, and current developments in moral psychology. It is concluded that the modules could benefit by maximizing class discussion time by using pre-class activities, clarifying how the modules should taught, reframing the ethical frameworks in the introductory modules, and creating an additional open-ended module for students in internships.
Building a Cyber Range using Amazon Web Services
Josue Barragan
Mentor: Dr. Maria Zack
2021 Summer Research at PLNU
Analysis and Graphical Representation of Complex Data
Jonathan Hake
Mentor: Dr. Greg Crow
2021 Summer Research at PLNU
2019-20 Student Research
A Study in Securing the Internet of Things
Joey Tuttobene
Mentor: Dr. Mike Leih
Current Internet of Things (IoT) cybersecurity threats were investigated using current literature and direct examination of IoT devices including the 3D printer control software OctoPrint, the autonomous vehicle middleware MOOS-IvP, and a common consumer smart lightbulb. This research found that most IoT devices transmit in plaintext and that software controls alone are insufficient in control systems applications. Recommended best practices for organizations include segregating IoT devices on a network, using non-default credentials, and keeping devices up to date. Manufacturers need to include robust encryption and authentication of messages with their offerings, as well as provide methods to update devices easily and safely. Finally, physical fail-safes can complement imperfect software in IoT control system applications.
Big Data for Savings Groups: A Study and Application of Data Visualization
Maria Bolt
Mentor: Dr. Lori Carter
Big data, despite the inherent challenges it poses, has become more and more influential in recent years due to the ever-growing prominence of digital data as well as the constantly improving data management technologies. It has become a powerful tool for analysis in a wide range of industries and fields, even including applications to international development. However, the ability to gain insight from big data is dependent upon good data visualization. Similarly, the savings group model, an implementation of microfinance in developing countries, has risen in popularity in recent decades. This model has been successful by emphasizing local empowerment, but further advancement in the field is limited by the difficulty of data collection. In this study, it is argued that the application of big data analysis to savings group data could provide the needed support for the continuous improvement of the savings group model. Also, the DreamSave mobile application for savings groups, created by DreamStart Labs, provides a platform from which to begin synthesizing these fields. This research includes a theoretical examination of the aforementioned concepts, as well as a practical data visualization project using data from the DreamSave app. Finally, the study documents the challenges and lessons involved in the realization of the practical project, highlighting how they reflect common issues faced in the data-driven software development industry.
The History of the Cycloid Curve
Natalee Chavez
Mentor: Dr. Maria Zack
During the 17th century prominent mathematicians became fascinated with the cycloid curve. It was their favorite example to use in the development of their new ideas and theorems. They would use it to help them in their new discoveries because the unique properties aligned with the curve. Since it was used by most significant mathematicians of the 17th century, it is important to examine the history of it during this time period. This paper aims to examine mathematicians work with the curve, and similar methods used among mathematicians, and how the cycloid curve aided the development of calculus. In order to answer this question, proofs relating to finding general methods of tangents, areas, arc length to the curve and the brachistochrone problem were examined and analyzed. The methods used by mathematicians will be explained, compared, and contrasted. The relationship to the development of calculus will also be considered and explained. The goal of this paper is to illustrate the importance of the curve and why it must be studied will be demonstrated in this paper.
Using Machine Learning to Analyze Athletic Mechanics During Movement
Jacob Bell
Mentor: Dr. Ryan Botts
2020 Summer Research at PLNU
Stitching Together a Decade of Survey Data
Sean Lovullo
Mentor: Dr. Greg Crow
2020 Summer Research at PLNU
Applications of Abstract Algebra to Cryptography
Anthony Marciel
Mentor: Dr. Jesus Jimenez
2020 Summer Research at PLNU
Integrating AWS Cloud Technologies into a Special Topics Course
Jasmine Yabut
Mentor: Dr. Mike Leih
2020 Summer Research at PLNU
2018-19 Student Research
Mentor: Jesús Jiménez
We study a homomorphic encryption scheme, which allows operations to be performed on data while it is encrypted. This scheme is implemented using polynomial rings in SageMath. The construction of irreducible polynomials in a given field is considered. Isomorphisms between two fields are found, and the method is evaluated.
Mentor: Catherine Crockett
A knot is a closed curve in space that does not intersect itself. A double (triple) crossing is where two (three) strands of the knot meet. A specific family of knots, namely torus knots, is studied. The relationship between the number of double crossings and triple crossings is investigated for certain torus knots.
Computational Analysis of the Relationships Between Antibiotic Resistance and Plasmid Backbone Genes
Mentor: Ryan Botts
Plasmid-encoded antibiotic resistance is a growing public health threat. Understanding relationships between antibiotic resistance genes (ARGs) and plasmid backbone structure would provide insight into how bacterial plasmids acquire such genes. This computational analysis characterizes plasmids by determining insertion patterns of ARGs most frequently associated with given plasmid backbones.
Mentor: Mike Mooring and Ryan Botts
Based on a camera trap survey in the Talamanca Cordillera of Costa Rica, we determined that Neotropical mammalian predators differed in their prey selection method: some species selected the most abundant prey, others preferred certain species regardless of abundance, and some used a combination of both methods.
Do you know what you just agreed to?
2017-18 Student Research
RSA Encryption Using Polynomial Rings
Michelle Freed
Mentor: Jesus Jimenez
This project explores the mathematics underlying the Rivest–Shamir–Adleman (RSA) encryption algorithm. RSA encrypts messages using modular arithmetic over the ring of integers. We extend the algorithm by using modular operations over the ring of polynomials over a finite field. We give examples using a field with two elements.
Error Correcting Code
Ashleigh Meyers
Mentor: Jesus Jimenez
To combat data corruption that occurs in transmission, error correcting code (ECC) protects the integrity of a message by detecting and correcting errors. This is done by transforming the message into a matrix that operations can be performed on to check if an error was made and determine what the original message was.
An Interactive Tool for the Study of Plasmid Backbone Gene Labels
Zac Lindsey
Mentor: Ryan Botts
The problem of inconsistent product names within the NCBI Nucleotide database must be quantified in order to prevent further hindrance of study. We created a tool that assists in identifying and quantifying backbone gene annotation inconsistencies and provides a way to help fix the problem.
Study of Knot Theory
Moyra Dyer
Mentor: Catherine Crockett
Research performed at PLNU
Homomorphic Encryption
Bryan Tapley
Mentor: Jesus Jimenez
Research performed at PLNU
Setting up a game for a study on human perception of violence in video games
Steven Dols and Chris Richey
Mentor: Benjamin Mood
Research performed at PLNU
Fake Co-Visitation Attacks on Social Media
Amanda Timmons
Mentor: Benjamin Mood
Research performed at PLNU
Instructional and Pedagogical uses of Amazon Web Services 2018
Joey Tuttobene
Mentor: Mike Leih
Research performed at PLNU
Mobile App Creation for iPhone
Gabe Garcia
Mentor: Lori Carter
Research Performed at PLNU
2016-17 Student Research
How Frequently are ISCR Elements Recombining to Produce Novel Antibiotic-Resistant Bacteria?
Rachel Platz
Advisor: Dr. Ryan Botts
Antibiotic-resistant bacteria pose a risk to public health. The CDC reported two million cases of antibiotic-resistant infection per year in the United States and twenty-three thousand led to death. Bacteria acquire antibiotic resistance genes, ARGs, through recombination and different mobile genetic elements. In recent studies, ISCR elements have been recognized as a powerful ARGs capture and movement system. It is important to understand how these elements are evolving; specifically, how frequently they are recombining and capturing ARGs to move and create bacteria with novel combinations of antibiotic resistance. We analyzed the evolutionary history of ISCR elements and the genes they frequently carry to determine if recombination of the elements is slower than evolution of individual genes.
The Relationship Between Mathematics and Military Education Based on the Eighteenth-Century French Text, Nouveau Cours De Mathématiques, À L'Usage, Bernard Forest de Bélidor
Elizabeth Kenyon
Advisor: Dr. Maria Zack
This paper investigates the relationship between mathematics and military tactics in the eighteenth century. Surely armies and militiamen needed some sort of instruction in order to have an understanding of defense and military tactics. The process of education is the focus of this study. By translating various sections of Bernard Forest De Bélidor's text, Nouveau Cours De Mathématiques, À L'Usage written in 1725, it is possible to demonstrate the manner in which mathematical concepts were used to instruct militaries. Upon translating four "applications," two concentrated on geometry and the other two focused on trigonometry, the relationship between mathematics and military strategies can be demonstrated. This paper analyzes a few of the "applications" individually to better gain an understanding of how militaries could use mathematical information. These applications serve as illustrations as to how to employ the methods learned from earlier sections in the text. The primary idea is that with a strong mathematical foundation, soldiers would be better equipped in battle and would be better able to construct various military structures.
Spiritual Formation in Student-Athletes
Hayley Richardson
Advisors: Dr. Greg Crow & Dr. Maria Zack
The research conducted in this project statistically analyzes the spiritual formation and practices of students at Point Loma Nazarene University. Specifically, it looks at the differences between the student-athletes and the non-student-athletes at Point Loma as it pertains to their spiritual formation and practices. From this research, it was determined that student-athletes have about the same or worse spiritual formation and practices then their non-athlete counterparts. As a result of this study, the Point Loma Athletic Department can see areas in which it can seek to design experiences and practices that enhance the spiritual formation of its students-athletes.
2015–16 Student Research
Data Analysis on PLNU Students
Kathleen Wilson
Advisors: Dr. Greg Crow and Dr. Maria Zack
This project explores PLNU student behavior. From surveys taken by students throughout their time at PLNU, it can be seen whether this time has had a positive or negative impact on the development of things such as personality and spirituality.
Assessing Methods for Analyzing MacTel
Joseph Conrad, Jonathan Paul, and Annie Thwing
Advisors: Dr. Ryan Botts and Dr. Lori Carter
This project produces realistic data analogous to Macular Telangiectasia, which can be used to assess signal analysis tools. One of these tools is the Wavelet Transform, a tool for signal analysis and compression in identifying and establishing the significance of the contributing factors of genetic diseases.
2014–15 Student Research
Analysis of a Neural Network-Based Public Key Protocol
Aaron McKinstry
Advisor: Dr. Jesus Jimenez
Kanter et al. (2002) proposed a key exchange protocol that uses the convergence of interacting neural networks. A variant of the protocol was analyzed by Shamir et al. (2002). In this paper, the variant protocol is analyzed. A theory of non-updating steps is proposed as an explanation for a dimensional phenomenon exhibited by the protocol, and then falsified by simulation. The protocol is then mathematically analyzed as a Markov chain; convergence follows from its properties, and it is proved the neural networks do not always converge.
2013-14 Student Research
Statistical Analysis on Chapel Attendance
Amy Hinds
Advisors: Dr. Greg Crow and Dr. Maria Zack
The research conducted in this project statistically analyzes the trends in PLNU's chapel attendance; it looks at how likely a student is to attend chapel based on certain attributes and characteristics. The aim of this study is to better understand the composition of PLNU's chapel congregation and predict future patterns of chapel attendance.
Elliptic Curve Cryptography
Ethan Wade
Advisor: Dr. Jesus Jimenez
Plane curves of the form Ax^3+Bx^2 y+Cxy^2+Dy^3+Ex^2+Fxy+Gy^2+Hx+ly+j=0 are called elliptic curves. These curves have been studied for hundreds of years and have cropped up in many areas such as physics, factoring, and cryptography. It is the latter this paper focuses on. Currently, the National Security Agency (NSA) and the Central Security Service (CSS) strongly advocate for the use of elliptic curve cryptography (ECC) due to its remarkable efficiency when it comes to an equal level of security of other methods such as RSA and Diffie-Hellman (DH), which are widely in place as of the writing of this paper. With that in mind, this paper sets out to explore the mathematics and methods behind ECC.
Plasmid Identification Using Gene Clusters
Kristen Petersen
Advisor: Dr. Ryan Botts
Plasmid mediated antibiotic resistance has made treating bacterial infections difficult and costly. Machine learning is used to identify common gene patterns within individual plasmids, as well as across multiple plasmids. Common survival strategies can be used to indicate where the plasmid is likely to be found.
2012-13 Student Research
Applications of Image Processing to Automate Tumor Image Quantifications
Caylor Booth
Advisor: Dr. Ryan Botts
This project developed a Java-based computer program that automates tumor image analysis through objective classification of pixels. The project then examined other image processing methods, like filtering and edge detection, to determine if they would expedite this analysis.
On the Alexander Polynomial and Related Invariants
Joy Chieh-Jung Chen
Advisor: Dr. Catherine Crockett
A key problem in the study of knot theory involves distinguishing which knots are equivalent and which are not. To differentiate knots, their invariants, or characteristics, are compared. One such invariant is the Alexander Polynomial; its properties and relationships to other invariants, particularly the unknotting number, are explored.
An Analysis of the Effects of PLNU's Enrollment Cap on Student Values
Kassandra Ham
Advisors: Dr. Maria Zack and Dr. Greg Crow
In 1999, PLNU reached its city-imposed enrollment cap. As a result, it became more selective in admitting students to the undergraduate program. By compiling and analyzing data from surveys distributed to incoming freshman and graduating seniors at PLNU since 1993, it is possible to examine the effects of the enrollment cap on the values of students and see how they align with PLNU's core values.
The History and Mathematics of Perspective Devices
Olivia Heunis
Advisor: Dr. Maria Zack
Perspective is a method, governed by the physical laws of optics, which creates the illusion of a three-dimensional space on a two-dimensional surface. The development of perspective in art owes much of its progress to various perspective devices, that is, mechanized contraptions used by artists to understand and reproduce images with adherence to the laws of optics. This project aims to trace the development of perspective devices through the inspection of several key examples, and thoroughly examine the mathematics by which they function.
Simulation-Based Application of Artificial Intelligence to General Game Playing
Sean Lewis
Advisor: Dr. Jeff McKinstry
The goal behind General Game Playing (GGP) is to develop an intelligent agent that will automatically learn how to play different games at the expert level without any human intervention. Many intelligent GGP programs have used game-tree search, but this may not be the best approach. Throughout this project, the Monte Carlo/Upper Confidence bounds applied to Trees (UCT) simulation-based approach is implemented, which may be the better decision-making algorithm.
John Wallis and Quadratures
Catherine Quimby
Advisor: Dr. Maria Zack
This project examines the influence of John Wallis' work in finding the quadrature of the circle and the development of the cycloid curve by mathematicians over time. It then looks at how the two topics fit together and lead to the development of integral calculus.
2011-12 Student Research
An Analysis of Trends in Chapel Attendance Patterns
Chanell Anderson and Lauren Waggoner
Advisors: Dr. Greg Crow and Dr. Maria Zack
Chapel is an integral part of nearly every student’s time at PLNU. Every Monday, Wednesday, and Friday provides a time for the student body to gather together as a whole along with faculty and staff to participate in Christ-centered community. Prior to fall 2011, students enrolled in 12 or more units and all residential students with freshman or sophomore standing were required to attend 36 chapels each semester and students with junior or senior standing were required to attend 28. In fall 2008, the student-led service Time Out was offered to students as another opportunity to receive chapel credit during the week. Through spring 2009, students could receive a maximum of three chapel credits per week, meaning Time Out could count as an alternate third chapel credit for a given week. This policy changed in fall 2009, however, and in a given week students could earn up to four chapel credits if they were to attend each chapel service and Time Out. Because of flexibility in acquiring chapel credits, it can be valuable from a chapel programming perspective to understand the makeup of the congregation at different points of the semester. This project explores the last five years of chapel attendance, from fall 2006 to spring 2011, to better understand trends in attendance patterns, identify any emerging trends related to student demographics in the congregation throughout each semester, and determine if there are any correlations between the chapel speaker and who is in attendance. This will build off the research project completed by Marilee Rickett, a 2010 PLNU graduate, who began analysis work on chapel attendance from 2006 to 2009.
Image Compression Using Tensor Decomposition
Nathaniel McClatchey
Advisors: Dr. Ryan Botts and Dr. Jesus Jimenez
This paper describes multidimensional image compression using canonical polyadic tensor decomposition. It suggests methods for decomposing two- and higher-dimensional tensors, then describes how the result may be used for compression. Finally, the results of this technique are compared with the results of other popular image compression techniques.
The Calculus of Variations
Tyler Levasseur
Advisors: Dr. Ryan Botts and Dr. Jesus Jimenez
The purpose of this paper is to explain the fundamental techniques of the calculus of variations. This includes explaining the details of the derivations of the Euler-Lagrange equation and the Beltrami identity, and their applications to the brachistochrone problem.