Mathematics Commons^™

An Improved Method For Spectroscopic Quality Classification, Elizabeth G. Mayer

Mathematics & Statistics ETDs

Spectral quality classification is a vital step in data cleaning before the

analysis of magnetic resonance spectroscopy (MRS) data can be done. This

analysis compares five methods of quality classification; three of these are

legacy methods, Maudsley et al. (2006), Zhang et al. (2018), and

Bustillo et al. (2020), and two newly created methods that used a random forests

classifier (RFC) to inform their classifications. We found that the random forest

classifier was the most accurate at predicting spectra quality (balanced

accuracy for RF of 88% vs legacy of 70%, 72%, or 72%). A

Random-Forests-Informed Filtering method (RFIFM) for quality …

A Study Of The Efficacy Of Machine Learning For Diagnosing Obstructive Coronary Artery Disease In Non-Diabetic Patients, Demond Larae Handley

Theses and Dissertations

According to the Centers for Disease Control and Prevention, about 18.2 million adults age 20 and older have Coronary Artery Disease in the United States. Early diagnosis is therefore of crucial importance to help prevent debilitating consequences, and principally death for many patients. In this study we use data containing gene expression values from peripheral blood samples in 198 non-diabetic patients, with the goal of developing an age and sex gene expression model for diagnosis of Coronary Artery Disease. We employ machine learning methods to obtain a classification based on genetic information, age and sex. Our implementation uses feed forward …

Pattern Of Health Behavior And Its Association With Self-Rated Health: Evidence From The 2018 Behavioral Risk Factor Surveillance System In The United States, Linh Nguyen, Mamunur Rashid, M. Mazharul Islam

Student Research

Aim: To improve public health services, we need to keep policymakers updated with health-related issues. This study (1) examines the recent pattern of physical activities, smoking, alcohol consumption, and SRH, and (2) investigates the association between the behaviors and SRH status among US citizens.

Method: We extracted data from the latest state-based survey of the 2018 Behavioral Risk Factor Surveillance System (BRFSS), which provides a nationally representative sample of 437,436 American adults. We analyzed the data, mainly employing chi-square tests and logistic regression models.

Results: Physical inactivity and smoking are more common among participants with lower education and household income. …

Italian Sociologists: A Community Of Disconnected Groups, Aliakbar Akbaritabar, Vincent Traag, Alberto Caimo, Flaminio Squazzoni

Articles

Examining coauthorship networks is key to study scientific collaboration patterns and structural characteristics of scientific communities. Here, we studied coauthorship networks of sociologists in Italy, using temporal and multi-level quantitative analysis. By looking at publications indexed in Scopus, we detected research communities among Italian sociologists. We found that Italian sociologists are fractured in many disconnected groups. The giant connected component of the Italian sociology could be split into five main groups with a mixture of three main disciplinary topics: sociology of culture and communication (present in two groups), economic sociology (present in three groups) and general sociology (present in three …

Vanishing Porosity Limit Of The Coupled Stokes-Brinkman System, Mingwen Fei, Dongjuan Niu, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

We investigate the small porosity asymptotic behavior of the coupled Stokes-Brinkman system in the presence of a curved interface between the Stokes region and the Brinkman region. in particular, we derive a set of approximate solutions, validated via rigorous analysis, to the coupled Stokes-Brinkman system. of particular interest is that the approximate solution satisfies a generalized Beavers-Joseph-Saffman-Jones interface condition (1.9) with the constant of proportionality independent of the curvature of the interface.

At The Interface Of Algebra And Statistics, Tai-Danae Bradley

Dissertations, Theses, and Capstone Projects

This thesis takes inspiration from quantum physics to investigate mathematical structure that lies at the interface of algebra and statistics. The starting point is a passage from classical probability theory to quantum probability theory. The quantum version of a probability distribution is a density operator, the quantum version of marginalizing is an operation called the partial trace, and the quantum version of a marginal probability distribution is a reduced density operator. Every joint probability distribution on a finite set can be modeled as a rank one density operator. By applying the partial trace, we obtain reduced density operators whose diagonals …

Analysis Of Gameplay Strategies In Hearthstone: A Data Science Approach, Connor W. Watson

Theses

In recent years, games have been a popular test bed for AI research, and the presence of Collectible Card Games (CCGs) in that space is still increasing. One such CCG for both competitive/casual play and AI research is Hearthstone, a two-player adversarial game where players seeks to implement one of several gameplay strategies to defeat their opponent and decrease all of their Health points to zero. Although some open source simulators exist, some of their methodologies for simulated agents create opponents with a relatively low skill level. Using evolutionary algorithms, this thesis seeks to evolve agents with a higher skill …

A Decision Tree Model To Predict Marginalized Zero-Inflated Poisson Mean, Philip Amewudah

University of New Orleans Theses and Dissertations

No abstract provided.

Multilevel Asymptotic Parallel-In-Time Techniques For Temporally Oscillatory Pdes, Nicholas Abel

Mathematics & Statistics ETDs

As the clock speeds of individual processors level off and the amount of parallel resources continue to increase rapidly, further exploitation of parallelism is necessary to improve compute times. For time-dependent differential equations, the serial computation of time-stepping presents a bottleneck, but parallel-in-time integration methods offer a way to compute the solution in parallel along the time domain. Parallel-in-time methods have been successful in achieving speedup when computing solutions for parabolic problems; however, for problems with large hyperbolic terms and no strong diffusivity, parallel-in-time methods have traditionally struggled to offer speedup. While work has been done to understand why parallel-in-time …

A Statistical Analysis Of The Unm Facets Design Identity & Beliefs Survey Data, Clarissa A. Sorensen-Unruh

Mathematics & Statistics ETDs

The NSF-funded FACETS (Formation of Accomplished Chemical Engineers for Transforming Society, NSF Award 1623105) grant aims to transform the undergraduate engineering experience in the Department of Chemical and Biological Engineering at the University of New Mexico to address attrition within engineering majors, especially among underserved populations (Brainard & Carlin, 1998). The UNM FACETS Design Identity & Beliefs survey, an assessment tool used as part of the research of the grant, generated the dataset used in this study. I performed several different statistical analyses on the dataset, including confirmatory factor analysis (CFA), principal component analysis (PCA), and cluster analysis. The …

Smoothed Quantiles For Claim Frequency Models, With Applications To Risk Measurement, Ponmalar Suruliraj Ratnam

Theses and Dissertations

Statistical models for the claim severity and claim frequency variables are routinely constructed and utilized by actuaries. Typical applications of such models include identification of optimal deductibles for selected loss elimination ratios, pricing of contract layers, determining credibility factors, risk and economic capital measures, and evaluation of effects of inflation, market trends and other quantities arising in insurance. While the actuarial literature on the severity models is extensive and rapidly growing, that for the claim frequency models lags behind. One of the reasons for such a gap is that various actuarial metrics do not possess ``nice'' statistical properties for the …

Analysis Of Sat And Isat Scores For Madison School District In Rexburg, Idaho, Holly Dawn Palmer

Undergraduate Honors Capstone Projects

Testing is an integral part of measuring education. If used properly SAT scores can be compared across the nation, and statewide tests can compare different school districts to each other if done properly to avoid certain pitfalls (Fetler, 1991). However, if tests do not have a significant impact on a student, their motivation to take the test will be low and test quality cannot be assumed. When the state funds two separate tests for their students but only one has a significant impact on the student, how should the scores for each test be used, and is it okay to …

Fitting Of Lotka-Volterra Model For Coupled Population Growth Data Through Least-Squares Estimation Of Parameters, Jessica Ann Harter

Theses and Dissertations

The population of two types of bacteria found in the Gulf Coast of Florida, V.chagasii and V. harveyi, can be described by the Lotka-Voltera competition model. Using data gathered in experiments conducted by Bury and Pickett (2015), we take a different approach to find parameter estimates using numerical methods in R. In particular, we find a numerical solution to the coupled set of ODEs and minimize the sum of squared errors in order to obtain the optimal parameter estimates that will fit the data best. In order to get a sense of accuracy of these parameter estimates, we use bootstrap …

Novel Inference Methods For Generalized Linear Models Using Shrinkage Priors And Data Augmentation., Arinjita Bhattacharyya

Electronic Theses and Dissertations

Generalized linear models have broad applications in biostatistics and sociology. In a regression setup, the main target is to find a relevant set of predictors out of a large collection of covariates. Sparsity is the assumption that only a few of these covariates in a regression setup have a meaningful correlation with an outcome variate of interest. Sparsity is incorporated by regularizing the irrelevant slopes towards zero without changing the relevant predictors and keeping the resulting inferences intact. Frequentist variable selection and sparsity are addressed by popular techniques like Lasso, Elastic Net. Bayesian penalized regression can tackle the curse of …

The Two Types Of Society: Computationally Revealing Recurrent Social Formations And Their Evolutionary Trajectories, Lux Miranda

Undergraduate Honors Capstone Projects

Comparative social science has a long history of attempts to classify societies and cultures in terms of shared characteristics. However, only recently has it become feasible to conduct quantitative analysis of large historical datasets to mathematically approach the study of social complexity and classify shared societal characteristics. Such methods have the potential to identify recurrent social formations in human societies and contribute to social evolutionary theory. However, in order to achieve this potential, repeated studies are needed to assess the robustness of results to changing methods and data sets. Using an improved derivative of the Seshat: Global History Databank, we …

Demystification Of Graph And Information Entropy, Bryce Frederickson

Undergraduate Honors Capstone Projects

Shannon entropy is an information-theoretic measure of unpredictability in probabilistic models. Recently, it has been used to form a tool, called the von Neumann entropy, to study quantum mechanics and network flows by appealing to algebraic properties of graph matrices. But still, little is known about what the von Neumann entropy says about the combinatorial structure of the graphs themselves. This paper gives a new formulation of the von Neumann entropy that describes it as a rate at which random movement settles down in a graph. At the same time, this new perspective gives rise to a generalization of von …

Universal Vector Neural Machine Translation With Effective Attention, Joshua Yi, Satish Mylapore, Ryan Paul, Robert Slater

SMU Data Science Review

Neural Machine Translation (NMT) leverages one or more trained neural networks for the translation of phrases. Sutskever intro- duced a sequence to sequence based encoder decoder model which be- came the standard for NMT based systems. Attention mechanisms were later introduced to address the issues with the translation of long sen- tences and improving overall accuracy. In this paper, we propose two improvements to the encoder decoder based NMT approach. Most trans- lation models are trained as one model for one translation. We introduce a neutral/universal model representation that can be used to predict more than one language depending on …

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 …

Insights From The Influx Of Prescription Painkillers In Northeast Florida: A Retrospective Analysis, Joseph Free, Michelle Dedeo

Showcase of Osprey Advancements in Research and Scholarship (SOARS)

The opioid epidemic has had, and will have, long-lasting ramifications in the United States. To better understand its impact in the Northeast Florida, this research seeks to identify relationships between hydro- and oxycodone pill concentration at the county and zip code levels and socio-economic factors such as average adjusted gross income and opioid related mortality. This project utilizes time series, regression, and GIS methods to examine local opioid saturation and has led to the development of an interactive Tableau dashboard which allows users to view opioid saturation at various levels of granularity. This analysis is made possible by longitudinal data …

Block Designs, Lucien Poulin, Daniela Genova

Showcase of Osprey Advancements in Research and Scholarship (SOARS)

Block designs are a type of combinatorial structures that can be used to model many different types of problems ranging from experimental design to computer software testing. They can be used to construct schemes that ensure complete optimization and efficiency of the given experiment. We focus mainly on Steiner and Kirkman triple systems, as well as, on different ways for constructing block designs. Well known results in combinatorics such as Fisher’s inequality and Kirkman’s schoolgirl problem are also discussed.

Structure-Activity Relationship Of Novel Diphenyl Ureas Targeting Mycobacterium, Piper Burghduf

Student Scholars Day Posters

In 2017, the World Health Organization reported that 10 million people were infected with tuberculosis, 1.6 million of whom died. Tuberculosis is caused by a bacterium called Mycobacterium tuberculosis, which primarily infects an individual’s lungs. Unfortunately, failure to adhere to the long and arduous drug regimen has contributed to the emergence of antibiotic-resistant strains of M. tuberculosis. Therefore, the need for novel antibiotics is imperative to saving millions of lives. Our lab has recently developed a family of diphenyl ureas that exhibited increased antimicrobial activity toward Mycobacterium. Reported herein is the continuation of our previous research involving the synthesis of …

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 …

Circada: Shiny Apps For Exploration Of Experimental And Synthetic Circadian Time Series With An Educational Emphasis, Lisa Cenek, Liubou Klindziuk, Cindy Lopez, Eleanor Mccartney, Blanca Martin Burgos, Selma Tir, Mary E. Harrington, Tanya L. Leise

Psychology: Faculty Publications

Circadian rhythms are daily oscillations in physiology and behavior that can be assessed by recording body temperature, locomotor activity, or bioluminescent reporters, among other measures. These different types of data can vary greatly in waveform, noise characteristics, typical sampling rate, and length of recording. We developed 2 Shiny apps for exploration of these data, enabling visualization and analysis of circadian parameters such as period and phase. Methods include the discrete wavelet transform, sine fitting, the Lomb-Scargle periodogram, autocorrelation, and maximum entropy spectral analysis, giving a sense of how well each method works on each type of data. The apps also …

A Permutation Test And Spatial Cross-Validation Approach To Assess Models Of Interspecific Competition Between Trees, David Allen, Albert Y. Kim

Statistical and Data Sciences: Faculty Publications

Measuring species-specific competitive interactions is key to understanding plant communities. Repeat censused large forest dynamics plots offer an ideal setting to measure these interactions by estimating the species-specific competitive effect on neighboring tree growth. Estimating these interaction values can be difficult, however, because the number of them grows with the square of the number of species. Furthermore, confidence in the estimates can be overestimated if any spatial structure of model errors is not considered. Here we measured these interactions in a forest dynamics plot in a transitional oak-hickory forest. We analytically fit Bayesian linear regression models of annual tree radial …

Describing Quasi-Graphic Matroids, Nathan Bowler, Daryl Funk, Dan Slilaty

Mathematics and Statistics Faculty Publications

The class of quasi-graphic matroids recently introduced by Geelen, Gerards, and Whittle generalises each of the classes of frame matroids and liftedgraphic matroids introduced earlier by Zaslavsky. For each biased graph (G, B) Zaslavsky defined a unique lift matroid L(G, B) and a unique frame matroid F(G, B), each on ground set E(G). We show that in general there may be many quasi-graphic matroids on E(G) and describe them all: for each graph G and partition (B, L, F) of its cycles such that B satisfies the theta property and each cycle in L meets each cycle in F, there …

Sufficient Dimension Folding In Regression Via Distance Covariance For Matrix‐Valued Predictors, Wenhui Sheng, Qingcong Yuan

Mathematical and Statistical Science Faculty Research and Publications

In modern data, when predictors are matrix/array‐valued, building a reasonable model is much more difficult due to the complicate structure. However, dimension folding that reduces the predictor dimensions while keeps its structure is critical in helping to build a useful model. In this paper, we develop a new sufficient dimension folding method using distance covariance for regression in such a case. The method works efficiently without strict assumptions on the predictors. It is model‐free and nonparametric, but neither smoothing techniques nor selection of tuning parameters is needed. Moreover, it works for both univariate and multivariate response cases. In addition, we …

Art, Artfulness, Or Artifice?: A Review Of The Art Of Statistics: How To Learn From Data, By David Spiegelhalter, Jason Makansi

Numeracy

David Spiegelhalter. 2019. The Art of Statistics: How to Learn From Data. (London: The Penguin Group). 444 pp. ISBN 978-1541618510

The author successfully eases the reader away from the rigor of statistical methods and calculations and into the realm of statistical thinking. Despite an engaging style and attention-grabbing examples, the reader of The Art of Statistics will need more than a casual grounding in statistics to get what Spiegelhalter, I believe, intends from his book. It should be viewed as a companion to a more rigorous textbook on statistical methods but not necessarily a book that makes statistics any …

Analytic Threads - Annual Newsletters 2014-2020, Messiah University

Educator Scholarship & Departmental Newsletters

Faculty and student updates. Analytic Threads is the annual newsletter of the Department of Computing, Mathematics and Physics at Messiah University. It is sent annually to alumni and is also available electronically at the website messiah.edu/cmp

Cosmic: Us-Based Conversion Master's Degree In Computing, Gary S. Krenz, Thomas Kaczmarek

Mathematical and Statistical Science Faculty Research and Publications

COSMIC is an NSF S-STEM graduate curriculum initiative/conversion program that strives to provide an accelerated pathway to a Master of Science (MS) degree for individuals who do not have an undergraduate degree in computing, but who wish to cross over into the computing field. The structure of our conversion program, the context that motivated it, and insights from conversion students' instructors are presented. Program successes with students from under-represented populations and the limitations that are also experienced are discussed. Our conversion program is based on a highly focused summer bridge course, combined with a customized curriculum pathway that enables people …

Markov Chain Epidemic Models And Parameter Estimation, Oluwatobiloba Ige

Theses, Dissertations and Capstones

Over the years, various parts of the world have experienced disease outbreaks. Mathematical models are used to describe these outbreaks. We study the transmission of disease in simple cases of disease outbreaks by using compartmental models with Markov chains. First, we explore the formulation of compartmental SIS (Susceptible-Infectious-Susceptible) and SIR (Susceptible-Infectious-Recovered) disease models. These models are the basic building blocks of other compartmental disease models. Second, we build SIS and SIR disease models using both discrete and continuous time Markov chains. In discrete time models, transmission occurs at fixed time steps, and in continuous time models, transmission may occur at …