Probability Commons^™

Decoding The Algorithm: The Mathematics Behind Tiktok’S Short-Form Content Success, Ashley N. Lynch

Honors Scholar Theses

Within the realm of social networks, TikTok has become the central hub for short-form video content. The network’s unique ability to capture individual preferences using predictive analytics has greatly contributed to its massive success, allowing the company to optimize its performance and content personalization. In an age where digital media have such a significant influence on society, it is essential that users develop an understanding of how social network algorithms function to make more informed online decisions. Although TikTok’s technological system is primarily undisclosed, the platform certifiably leverages several key mathematical principles within its algorithm to achieve its core goals …

Utilizing Markov Chains To Estimate Allele Progression Through Generations, Ronit Gandhi

Honors Program: Senior Projects (Public)

All populations display patterns in allele frequencies over time. Some alleles cease to exist, while some grow to become the norm. These frequencies can shift or stay constant based on the conditions the population lives in. If in Hardy-Weinberg equilibrium, the allele frequencies stay constant. Most populations, however, have bias from environmental factors, sexual preferences, other organisms, etc. We propose a stochastic Markov chain model to study allele progression across generations. In such a model, the allele frequencies in the next generation depend only on the frequencies in the current one.

We use this model to track a recessive allele …

Teaching A University Course On The Mathematics Of Gambling, Stewart N. Ethier, Fred M. Hoppe

UNLV Gaming Research & Review Journal

Courses on the mathematics of gambling have been offered by a number of colleges and universities, and for a number of reasons. In the past 15 years, at least seven potential textbooks for such a course have been published. In this article we objectively compare these books for their probability content, their gambling content, and their mathematical level, to see which ones might be most suitable, depending on student interests and abilities. This is not a book review (e.g., none of the books is recommended over others) but rather an essay offering advice about which topics to include in a …

Gilmore Girls And Instagram: A Statistical Look At The Popularity Of The Television Show Through The Lens Of An Instagram Page, Brittany Simmons

Student Scholar Symposium Abstracts and Posters

After going on the Warner Brothers Tour in December of 2015, I created a Gilmore Girls Instagram account. This account, which started off as a way for me to create edits of the show and post my photos from the tour turned into something bigger than I ever could have imagined. In just over a year I have over 55,000 followers. I post content including revival news, merchandise, and edits of the show that have been featured in Entertainment Weekly, Bustle, E! News, People Magazine, Yahoo News, & GilmoreNews.

I created a dataset of qualitative and quantitative outcomes from my …

Bootstrapping Vs. Asymptotic Theory In Property And Casualty Loss Reserving, Andrew J. Difronzo Jr.

Honors Projects in Mathematics

One of the key functions of a property and casualty (P&C) insurance company is loss reserving, which calculates how much money the company should retain in order to pay out future claims. Most P&C insurance companies use non-stochastic (non-random) methods to estimate these future liabilities. However, future loss data can also be projected using generalized linear models (GLMs) and stochastic simulation. Two simulation methods that will be the focus of this project are: bootstrapping methodology, which resamples the original loss data (creating pseudo-data in the process) and fits the GLM parameters based on the new data to estimate the sampling …

Choosing Between Parametric And Non-Parametric Tests, Russ Johnson

Journal of Undergraduate Research at Minnesota State University, Mankato

A common question in comparing two sets of measurements is whether to use a parametric testing procedure or a non-parametric procedure. The question is even more important in dealing with smaller samples. Here, using simulation, several parametric and nonparametric tests, such as, t-test, Normal test, Wilcoxon Rank Sum test, van-der Waerden Score test, and Exponential Score test are compared.

Numerical Solutions To The Gross-Pitaevskii Equation For Bose-Einstein Condensates, Luigi Galati

College of Graduate Studies: Theses & Dissertations

In this thesis we compare various potential operators for the two-dimensional (2D) Gross-Pitaevskii equation (GPE) for Bose-Einstein condensates. Both the 2D and the 1D models are scaled to get a three parameter model. Smoothness of initial conditions is considered and choice of method (Split-Step Fourier method with Strang Splitting) is justied. Numerical simulations provide graphical evidence of properties of both focusing and nonfocusing cases.

Determining The Success Of Ncaa Basketball Teams Through Team Characteristics, Raymond Witkos

Honors Projects in Mathematics

Every year much of the nation becomes engulfed in the NCAA basketball postseason tournament more affectionately known as “March Madness.” The tournament has received the name because of the ability for any team to win a single game and advance to the next round. The purpose of this study is to determine whether concrete statistical measures can be used to predict the final outcome of the tournament. The data collected in the study include 13 independent variables ranging from the 2003-2004 season up until the current 2009-2010 season. Different tests were run in an attempt to achieve the most accurate …

Predictive Modeling Of Alumni Donor Behavior, Lauren Prue

Honors Projects in Mathematics

In recent years, college and universities have relied increasingly upon the charitable contributions of its previous graduates; as the costs of tuition rise substantially, development offices are facing the challenge of creating annual fund campaigns that are minimally expensive while providing the maximum potential for return. This study addresses the available constituent database at one University in particular in an effort to identify what criteria are the strongest predictors of donor response at a small, private university located within New England. The analysis utilized predictive modeling and data-mining largely within the software program Rapid Insight to build several models in …

A Coin Flipping Game With Non Transitive Odds, Stacy Jurgens

Honors Capstones

Capstone submitted as a graduation requirement for the BSU Honors Program.