Applied Mathematics Commons^™

Sentiment Analysis Before And During The Covid-19 Pandemic, Emily Musgrove

Mathematics Summer Fellows

This study examines the change in connotative language use before and during the Covid-19 pandemic. By analyzing news articles from several major US newspapers, we found that there is a statistically significant correlation between the sentiment of the text and the publication period. Specifically, we document a large, systematic, and statistically significant decline in the overall sentiment of articles published in major news outlets. While our results do not directly gauge the sentiment of the population, our findings have important implications regarding the social responsibility of journalists and media outlets especially in times of crisis.

The Commutant Of The Fourier–Plancherel Transform, Brianna Cantrall

Honors Theses

One can see that this matrix is unitary and has eigenvalues {1,−i,−1, I}, each of infinite multiplicity. Throughout the remainder of this thesis, we will convince the reader that the above linear transformation is actually the Fourier transform. We will compute the commutant, as well as its invariant subspaces. The key to do this relies on the Hermite polynomials. Why do we recast the Fourier transform from its well-known and well studied integral form to the matrix form shown above? As we will see, the matrix form allows us to efficiently discover the operator theory of the Fourier transform obfuscated …

Applications Of Machine Learning Algorithms In Materials Science And Bioinformatics, Mohammed Quazi

Mathematics & Statistics ETDs

The piezoelectric response has been a measure of interest in density functional theory (DFT) for micro-electromechanical systems (MEMS) since the inception of MEMS technology. Piezoelectric-based MEMS devices find wide applications in automobiles, mobile phones, healthcare devices, and silicon chips for computers, to name a few. Piezoelectric properties of doped aluminum nitride (AlN) have been under investigation in materials science for piezoelectric thin films because of its wide range of device applicability. In this research using rigorous DFT calculations, high throughput ab-initio simulations for 23 AlN alloys are generated.

This research is the first to report strong enhancements of piezoelectric properties …

Generating A Dataset For Comparing Linear Vs. Non-Linear Prediction Methods In Education Research, Jack Mauro, Elena Martinez, Anna Bargagliotti

Honors Thesis

Machine learning is often used to build predictive models by extracting patterns from large data sets. Such techniques are increasingly being utilized to predict outcomes in the social sciences. One such application is predicting student success. Machine learning can be applied to predicting student acceptance and success in academia. Using these tools for education-related data analysis, may enable the evaluation of programs, resources and curriculum. Currently, research is needed to examine application, admissions, and retention data in order to address equity in college computer science programs. However, most student-level data sets contain sensitive data that cannot be made public. To …

Analyzing Marriage Statistics As Recorded In The Journal Of The American Statistical Association From 1889 To 2012, Annalee Soohoo

CMC Senior Theses

The United States has been tracking American marriage statistics since its founding. According to the United States Census Bureau, “marital status and marital history data help federal agencies understand marriage trends, forecast future needs of programs that have spousal benefits, and measure the effects of policies and programs that focus on the well-being of families, including tax policies and financial assistance programs.”[1] With such a wide scope of applications, it is understandable why marriage statistics are so highly studied and well-documented.

This thesis will analyze American marriage patterns over the past 100 years as documented in the Journal of …

Compare And Contrast Maximum Likelihood Method And Inverse Probability Weighting Method In Missing Data Analysis, Scott Sun

Mathematical Sciences Technical Reports (MSTR)

Data can be lost for different reasons, but sometimes the missingness is a part of the data collection process. Unbiased and efficient estimation of the parameters governing the response mean model requires the missing data to be appropriately addressed. This paper compares and contrasts the Maximum Likelihood and Inverse Probability Weighting estimators in an Outcome-Dependendent Sampling design that deliberately generates incomplete observations. WE demonstrate the comparison through numerical simulations under varied conditions: different coefficient of determination, and whether or not the mean model is misspecified.

Machine Learning With Topological Data Analysis, Ephraim Robert Love

Doctoral Dissertations

Topological Data Analysis (TDA) is a relatively new focus in the fields of statistics and machine learning. Methods of exploiting the geometry of data, such as clustering, have proven theoretically and empirically invaluable. TDA provides a general framework within which to study topological invariants (shapes) of data, which are more robust to noise and can recover information on higher dimensional features than immediately apparent in the data. A common tool for conducting TDA is persistence homology, which measures the significance of these invariants. Persistence homology has prominent realizations in methods of data visualization, statistics and machine learning. Extending ML with …

The Effect Of Initial Conditions On The Weather Research And Forecasting Model, Aaron D. Baker

Electronic Theses and Dissertations

Modeling our atmosphere and determining forecasts using numerical methods has been a challenge since the early 20th Century. Most models use a complex dynamical system of equations that prove difficult to solve by hand as they are chaotic by nature. When computer systems became more widely adopted and available, approximating the solution of these equations, numerically, became easier as computational power increased. This advancement in computing has caused numerous weather models to be created and implemented across the world. However a challenge of approximating these solutions accurately still exists as each model have varying set of equations and variables to …

Adventures In The "Islands" - Enhancing Student Engagement In Teaching Statistics, Leszek Gawarecki

Mathematics Presentations And Conference Materials

The factors for enhancing student engagement frequently identified are active and problem-based learning as well as real-life experience relevant to students' interests. The importance of using real data in teaching statistics has been repeatedly emphasized and its importance is growing. However, data collection, as part of a student project, faces serious practical problems. It is time-consuming, may require access to equipment, or raise ethical issues.

Fourth Down Decision Making: Challenging The Conservative Nature Of Nfl Coaches, Will Palmquist, Ryan Elmore, Benjamin Williams

DU Undergraduate Research Journal Archive

This thesis analyzes the hypothesis that coaches in the National Football League are often too conservative in their decision making on fourth downs. I used R Studio and NFL play-by-play data to simulate actual football plays and drives according to different fourth down strategies. By measuring expected points per drive over thousands of simulated drives, we are able to evaluate the effectiveness of different fourth down strategies. This research points to a number of conclusions regarding the nature of NFL coaches on fourth downs as well as the complexity of modeling and simulating decision making in a complex sport such …

Applying The Data: Predictive Analytics In Sport, Anthony Teeter, Margo Bergman

Access*: Interdisciplinary Journal of Student Research and Scholarship

The history of wagering predictions and their impact on wide reaching disciplines such as statistics and economics dates to at least the 1700’s, if not before. Predicting the outcomes of sports is a multibillion-dollar business that capitalizes on these tools but is in constant development with the addition of big data analytics methods. Sportsline.com, a popular website for fantasy sports leagues, provides odds predictions in multiple sports, produces proprietary computer models of both winning and losing teams, and provides specific point estimates. To test likely candidates for inclusion in these prediction algorithms, the authors developed a computer model, and test …

The Effect Of Using A Project-Based Learning (Pbl) Approach To Improve Engineering Students' Understanding Of Statistics, Fionnuala Farrell, Michael Carr

Articles

Over the last number of years we have gradually been introducing a project based learning approach to the teaching of engineering mathematics inDublin Institute of Technology. Several projects are now in existence for the teaching of both second-order differential equations and first order differential equations.We intend to incrementally extend this approach acrossmore of the engineering mathematics curriculum. As part of this ongoing process, practical realworld projects in statistics were incorporated into a second year ordinary degree mathematics module. This paper provides an overview of these projects and their implementation. As a means to measure the success of this initiative, we …

Bayesian Hierarchical Meta-Analysis Of Asymptomatic Ebola Seroprevalence, Peter Brody-Moore

CMC Senior Theses

The continued study of asymptomatic Ebolavirus infection is necessary to develop a more complete understanding of Ebola transmission dynamics. This paper conducts a meta-analysis of eight studies that measure seroprevalence (the number of subjects that test positive for anti-Ebolavirus antibodies in their blood) in subjects with household exposure or known case-contact with Ebola, but that have shown no symptoms. In our two random effects Bayesian hierarchical models, we find estimated seroprevalences of 8.76% and 9.72%, significantly higher than the 3.3% found by a previous meta-analysis of these eight studies. We also produce a variation of this meta-analysis where we exclude …

Calculus Of The Impossible: Review Of The Improbability Principle (2014) By David Hand And The Logic Of Miracles (2018) By Lásló Mérő, Samuel L. Tunstall

Numeracy

David J. Hand. 2014. The Improbability Principle: Why Coincidences, Miracles, and Rare Events Happen Every Day (New York, NY: Scientific American/Farrar, Straus and Giroux) 288 pp. ISBN: 978-0374175344.

Lásló Mérő. 2018. The Logic of Miracles: Making Sense of Rare, Really Rare, and Impossibly Rare Events (New Haven, CT: Yale University Press) 288 pp. ISBN: 978-0300224153.

David Hand and Lásló Mérő both grapple with the occurrence of seemingly impossible events in these two popular science books. In this comparative review, I describe the two books, and explain why I prefer Hand's treatment of the impossible.

Mathematics In Contemporary Society - Chapter 12 (Spring 2018), Patrick J. Wallach

Open Educational Resources

Mathematics in Contemporary Society is the textbook that corresponds to MA-321, the course of the same name. The course is designed to provide students with mathematical ideas and methods found in the social sciences, the arts, and in business. Topics will include fundamentals of statistics, scatterplots, graphics in the media, problem solving strategies, dimensional analysis, mathematics in music and art, and mathematical modeling. EXCEL is used to explore real world applications.

Mathematics In Contemporary Society - Chapter 13 (Spring 2018), Patrick J. Wallach

Open Educational Resources

Mathematics in Contemporary Society is the textbook that corresponds to MA-321, the course of the same name. The course is designed to provide students with mathematical ideas and methods found in the social sciences, the arts, and in business. Topics will include fundamentals of statistics, scatterplots, graphics in the media, problem solving strategies, dimensional analysis, mathematics in music and art, and mathematical modeling. EXCEL is used to explore real world applications.

Runs Of Identical Outcomes In A Sequence Of Bernoulli Trials, Matthew Riggle

Masters Theses & Specialist Projects

The Bernoulli distribution is a basic, well-studied distribution in probability. In this thesis, we will consider repeated Bernoulli trials in order to study runs of identical outcomes. More formally, for t ∈ N, we let Xt ∼ Bernoulli(p), where p is the probability of success, q = 1 − p is the probability of failure, and all Xt are independent. Then Xt gives the outcome of the tth trial, which is 1 for success or 0 for failure. For n, m ∈ N, we define Tn to be the number of trials needed to first observe n …

Sabermetrics - Statistical Modeling Of Run Creation And Prevention In Baseball, Parker Chernoff

FIU Electronic Theses and Dissertations

The focus of this thesis was to investigate which baseball metrics are most conducive to run creation and prevention. Stepwise regression and Liu estimation were used to formulate two models for the dependent variables and also used for cross validation. Finally, the predicted values were fed into the Pythagorean Expectation formula to predict a team’s most important goal: winning.

Each model fit strongly and collinearity amongst offensive predictors was considered using variance inflation factors. Hits, walks, and home runs allowed, infield putouts, errors, defense-independent earned run average ratio, defensive efficiency ratio, saves, runners left on base, shutouts, and walks per …

Modeling Multimodal Failure Effects Of Complex Systems Using Polyweibull Distribution, Daniel A. Timme

Theses and Dissertations

The Department of Defense (DoD) enlists multiple complex systems across each of their departments. Between the aging systems going through an overhaul and emerging new systems, quality assurance to complete the mission and secure the nation‘s objectives is an absolute necessity. The U.S. Air Force‘s increased interest in Remotely Piloted Aircraft (RPA) and the Space Warfighting domain are current examples of complex systems that must maintain high reliability and sustainability in order to complete missions moving forward. DoD systems continue to grow in complexity with an increasing number of components and parts in more complex arrangements. Bathtub-shaped hazard functions arise …

Essentials Of Structural Equation Modeling, Mustafa Emre Civelek

Zea E-Books Collection

Structural Equation Modeling is a statistical method increasingly used in scientific studies in the fields of Social Sciences. It is currently a preferred analysis method, especially in doctoral dissertations and academic researches. However, since many universities do not include this method in the curriculum of undergraduate and graduate courses, students and scholars try to solve the problems they encounter by using various books and internet resources.

This book aims to guide the researcher who wants to use this method in a way that is free from math expressions. It teaches the steps of a research program using structured equality modeling …

Indicators For Early Assessment Of Palliative Care In Lung Cancer Patients: A Population Study Using Linked Health Data, Maria Kelly, Katie M. O'Brien, Michael Lucey, Kerri Clough-Gorr, Ailish Hannigan

Department of Mathematics Publications

Analysing linked, routinely collected data may be useful to identify characteristics of patients with suspected lung cancer who could benefit from early assessment for palliative care. The aim of this study was to compare characteristics of newly diagnosed lung cancer patients dying within 30 days of diagnosis (short term survivors) with those surviving more than 30 days. To identify indicators for early palliative care assessment we distinguished between characteristics available at diagnosis (age, gender, smoking status, marital status, comorbid disease, admission type, tumour stage and histology) from those available post diagnosis. A second aim was to examine the association between …

A Statistical Study Of Student Success In The Bgsu Honors College, Sarah Hercules

Honors Projects

Higher education has long tried to find the best measures to predict student success. Different colleges often have different guidelines, requiring different criteria to be evaluated. The BGSU Honors College has struggled with retention and recruitment of underrepresented students with their current admission criteria. This analysis studies different measures of student success such as BGSU GPA and number of completed Honors credits for high-achieving BGSU students who enrolled from Fall 2013 through Fall 2016 to find the best predictors of student success through regression analysis. Throughout this paper, the impact of ethnicity, gender, the college of a student’s program, high …

Neural Network Predictions Of A Simulation-Based Statistical And Graph Theoretic Study Of The Board Game Risk, Jacob Munson

Murray State Theses and Dissertations

We translate the RISK board into a graph which undergoes updates as the game advances. The dissection of the game into a network model in discrete time is a novel approach to examining RISK. A review of the existing statistical findings of skirmishes in RISK is provided. The graphical changes are accompanied by an examination of the statistical properties of RISK. The game is modeled as a discrete time dynamic network graph, with the various features of the game modeled as properties of the network at a given time. As the network is computationally intensive to implement, results are produced …

A Traders Guide To The Predictive Universe- A Model For Predicting Oil Price Targets And Trading On Them, Jimmie Harold Lenz

Doctor of Business Administration Dissertations

At heart every trader loves volatility; this is where return on investment comes from, this is what drives the proverbial “positive alpha.” As a trader, understanding the probabilities related to the volatility of prices is key, however if you could also predict future prices with reliability the world would be your oyster. To this end, I have achieved three goals with this dissertation, to develop a model to predict future short term prices (direction and magnitude), to effectively test this by generating consistent profits utilizing a trading model developed for this purpose, and to write a paper that anyone with …

Modeling Fantasy Football Quarterbacks, Kyle Zeberlein, Myles Wallin

Celebration of Learning

Fantasy football is a way to score NFL players based off of their statistics in particular categories. We have created formulas for modeling every quarterback’s fantasy football points per game in the 2015-2016 season. Our model is partitioned into four sub-models depending on the length of the quarterback’s career in the NFL. We have developed a weighted model based on previous years’ performance of the quarterback, of the defense, and of the quarterback against the defense using data from the NFL. We compare our projections for the season against Yahoo’s projections for the season.

Statistics In League Of Legends: Analyzing Runes For Last-Hitting, Brian M. Hook

Mathematics: Student Scholarship & Creative Works

While other sports have statisticians to evaluate players and their stats, in electronic sports there is a need for statisticians to evaluate different parts of the game. League of Legends is the most popular of ESports and is the focus of this discussion. The mechanic of focus here is runes which give boosts to the players stats in-game like being able to do extra damage. We will be finding the effectiveness of these runes by looking at gold efficiency, help with last hitting, and extra damage dealt through the use of Python.

Secondary Mathematics Teachers’ Attitudes And Beliefs Toward Statistics: Developing An Initial Profile, Christina M. Zumbrun

Dissertations

Over the last several decades, mathematics education researchers have given increased attention to students’ and teachers’ attitudes and beliefs toward mathematics and statistics, but no work has been done that examines practicing secondary mathematics teachers’ (SMTs’) attitudes and beliefs towards statistics in light of the GAISE framework and the Common Core State Standards for Mathematics (CCSSM). This study begins to address this gap in the research by creating the Teacher Attitude and Beliefs toward Statistics Survey (TABSS), a synthesis of items taken from the Survey of Attitudes Toward Statistics (Schau, 2003), the Statistics Course Attitude Scale and newly developed items …

Building A Predictive Model For Baseball Games, Jordan Robertson Tait

All Graduate Theses, Dissertations, and Other Capstone Projects

In this paper, we will discuss a method of building a predictive model for Major League Baseball Games. We detail the reasoning for pursuing the proposed predictive model in terms of social popularity and the complexity of analyzing individual variables. We apply a coarse-grain outlook inspired by Simon Dedeos' work on Human Social Systems, in particular the open source website Wikipedia [2] by attempting to quantify the influence of winning and losing streaks instead of analyzing individual performance variables. We will discuss initial findings of data collected from the LA Dodgers and Colorado Rockies and apply further statistical analysis to …

Adaptive Randomization Designs, Jenna Colavincenzo

Statistics

Adaptive design methodologies use prior information to develop a clinical trial design. The goal of an adaptive design is to maintain the integrity and validity of the study while giving the researcher flexibility in identifying the optimal treatment. An example of an adaptive design can be seen in a basic pharmaceutical trial. There are three phases of the overall trial to compare treatments and experimenters use the information from the previous phase to make changes to the subsequent phase before it begins.

Adaptive design methods have been in practice since the 1970s, but have become increasingly complex ever since. One …

Constructing Phylogenetic Trees Using Maximum Likelihood, Anna Cho

Scripps Senior Theses

Maximum likelihood methods are used to estimate the phylogenetic trees for a set of species. The probabilities of DNA base substitutions are modeled by continuous-time Markov chains. We use these probabilities to estimate which DNA bases would produce the data that we observe. The topology of the tree is also determined using base substitution probabilities and conditional likelihoods. Felsenstein [2] introduced this method of finding an estimate for the maximum likelihood phylogenetic tree. We will explore this method in detail in this paper.