Mathematics Commons^™

Learning About Modeling In Teacher Preparation Programs, Hyunyi Jung, Eryn Stehr, Jia He, Sharon L. Senk

Hyunyi Jung

This study explores opportunities that secondary mathematics teacher preparation programs provide to learn about modeling in algebra. Forty-eight course instructors and ten focus groups at five universities were interviewed to answer questions related to modeling. With the analysis of the interview transcripts and related course materials, we found few opportunities for PSTs to engage with the full modeling cycle. Examples of opportunities to learn about algebraic modeling and the participants’ perspectives on the opportunities can contribute to the study of modeling and algebra in teacher education.

Using Mixed Effects Modeling To Quantify Difference Between Patient Groups With Diabetic Foot Ulcers, Rachel French

Mahurin Honors College Capstone Experience/Thesis Projects

When diabetes progresses, many patients suffer from chronic foot ulcers. In a study described in Matrix Metalloproteinases and Diabetic Foot Ulcers (Muller et al., 2008), sixteen patients with diabetic foot ulcers were examined throughout a twelve week healing period. During this period, levels of matrix metalloproteinases (MMP-1), their inhibitors (TIMP-1), and the extracellular matrix in a wound area were measured at distinct time intervals for each patient. The ratios of these healing components are vital in determining whether a wound will heal or become chronic and never properly heal. Connecting Local and Global Sensitivities in a Mathematical Model for Wound …

The Most Important Statistics In Football, Jacob Holmen

Essential Studies UNDergraduate Showcase

This research is based on the Five Factors that were devised by Bill Connelly of SBNation. The Five Factors of football include Explosiveness, Efficiency, Field Position, Finishing Drives, and Turnovers. Each factor is composed of associated statistics that when put together make up the most important statistics in football. This research includes the analysis of all 857 FBS (the highest level of NCAA Division I football) games from the 2016 season. Data was analyzed through the use of an Excel spreadsheet. Five different statistics were looked at, each associated with one of the Five Factors. The statistics include Yards per …

Analytics And Baseball's New Generation, John Roche

Essential Studies UNDergraduate Showcase

Major League Baseball has been a catalyst for making decisions in sports and competition from a purely mathematical viewpoint. We have seen teams utilize unique on-field player alignments and roster-building strategies based on statistical observations and applications of math. This project examines the advantages Sabermetrics and analytics present within the sport. Untapped statistical categories that could further the success of teams in the future is also briefly discussed.

Statistical Analysis Of Momentum In Basketball, Mackenzi Stump

Honors Projects

The “hot hand” in sports has been debated for as long as sports have been around. The debate involves whether streaks and slumps in sports are true phenomena or just simply perceptions in the mind of the human viewer. This statistical analysis of momentum in basketball analyzes the distribution of time between scoring events for the BGSU Women’s Basketball team from 2011-2017. We discuss how the distribution of time between scoring events changes with normal game factors such as location of the game, game outcome, and several other factors. If scoring events during a game were always randomly distributed, or …

Farlie-Gumbel-Morgenstern Family: Equivalence Of Uncorrelation And Independence, G. Barmalzan, F. Vali

Applications and Applied Mathematics: An International Journal (AAM)

Considering the characteristics of the bivariate normal distribution, in which uncorrelation of two random variables is equivalent to their independence, it is interesting to verify this problem in other distributions. In other words, whether the multivariate normal distribution is the only distribution in which uncorrelation is equivalent to independence. In this paper, we answer to this question and establish generalized Farlie-Gumbel-Morgenstern (FGM) family is another family of distributions under which uncorrelation is equivalent to independence.

Making Models With Bayes, Pilar Olid

Electronic Theses, Projects, and Dissertations

Bayesian statistics is an important approach to modern statistical analyses. It allows us to use our prior knowledge of the unknown parameters to construct a model for our data set. The foundation of Bayesian analysis is Bayes' Rule, which in its proportional form indicates that the posterior is proportional to the prior times the likelihood. We will demonstrate how we can apply Bayesian statistical techniques to fit a linear regression model and a hierarchical linear regression model to a data set. We will show how to apply different distributions to Bayesian analyses and how the use of a prior affects …

Novel Statistical Models For Quantitative Shape-Gene Association Selection, Xiaotian Dai

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Other research reported that genetic mechanism plays a major role in the development process of biological shapes. The primary goal of this dissertation is to develop novel statistical models to investigate the quantitative relationships between biological shapes and genetic variants. However, these problems can be extremely challenging to traditional statistical models for a number of reasons: 1) the biological phenotypes cannot be effectively represented by single-valued traits, while traditional regression only handles one dependent variable; 2) in real-life genetic data, the number of candidate genes to be investigated is extremely large, and the signal-to-noise ratio of candidate genes is expected …

Extracting And Visualizing Data From Mobile And Static Eye Trackers In R And Matlab, Chunyang Li

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Eye tracking is the process of measuring where people are looking at with an eye tracker device. Eye tracking has been used in many scientific fields, such as education, usability research, sports, psychology, and marketing. Eye tracking data are often obtained from a static eye tracker or are manually extracted from a mobile eye tracker. Visualization usually plays an important role in the analysis of eye tracking data. So far, there existed no software package that contains a whole collection of eye tracking data processing and visualization tools. In this dissertation, we review the eye tracking technology, the eye tracking …

Exact Approaches For Bias Detection And Avoidance With Small, Sparse, Or Correlated Categorical Data, Sarah E. Schwartz

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Every day, traditional statistical methodology are used world wide to study a variety of topics and provides insight regarding countless subjects. Each technique is based on a distinct set of assumptions to ensure valid results. Additionally, many statistical approaches rely on large sample behavior and may collapse or degenerate in the presence of small, spare, or correlated data. This dissertation details several advancements to detect these conditions, avoid their consequences, and analyze data in a different way to yield trustworthy results.

One of the most commonly used modeling techniques for outcomes with only two possible categorical values (eg. live/die, pass/fail, …

Which Factors Influence Student Success In Intermediate Algebra, Math 101-102-103?, Linh T. Ward

Mathematics & Statistics ETDs

At The University of New Mexico (UNM), Intermediate Algebra (MATH 120 and MATH 101-102-103) has historically been a so-called “killer course”, with very low pass rates: approximately 40% in Fall 2009 to Spring 2011 and about 50% from Fall 2011 to Spring 2013. Furthermore, many students failed the class multiple times. Since 2013, a computer system called ALEKS has been used to teach the course and, along with some additional interventions, on Albuquerque/Main campus success rates for MATH 101 have increased to roughly 80% and MATH 102 to about 70%. This thesis provides a strategy to identify those 20-30% as-risk …

Convergence Analysis And Error Estimates For A Second Order Accurate Finite Element Method For The Cahn–Hilliard–Navier–Stokes System, Amanda E. Diegel, Cheng Wang, Xiaoming Wang, Steven M. Wise

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we present a novel second order in time mixed finite element scheme for the Cahn–Hilliard–Navier–Stokes equations with matched densities. the scheme combines a standard second order Crank–Nicolson method for the Navier–Stokes equations and a modification to the Crank–Nicolson method for the Cahn–Hilliard equation. in particular, a second order Adams-Bashforth extrapolation and a trapezoidal rule are included to help preserve the energy stability natural to the Cahn–Hilliard equation. We show that our scheme is unconditionally energy stable with respect to a modification of the continuous free energy of the PDE system. Specifically, the discrete phase variable is shown …

Interproximal Distance Analysis Of Stereolithographic Casts Made By Cad-Cam Technology: An In Vitro Study, Melanie Hoffman, Seok-Hwan Cho, Naveen K. Bansal

Mathematics, Statistics and Computer Science Faculty Research and Publications

Statement of problem

The accuracy of interproximal distances of the definitive casts made by computer-aided design and computer-aided manufacturing (CAD-CAM) technology is not yet known.

Purpose

The purpose of this in vitro study was to compare the interproximal distances of stereolithographic casts made by CAD-CAM technology with those of stone casts made by the conventional method.

Material and methods

Dentoform teeth were prepared for a single ceramic crown on the maxillary left central incisor, a 3-unit fixed dental prosthesis (FDP) on the second premolar for a metal-ceramic crown, and a maxillary right first molar for a metal crown. Twenty digital …

Dodrant-Homomorphic Encryption For Cloud Databases Using Table Lookup, Thomas Schwarz

Mathematics, Statistics and Computer Science Faculty Research and Publications

Users of large commercial databases increasingly want to outsource their database operations to a cloud service providers, but guaranteeing the privacy of data in an outsourced database has become the major obstacle to this move. Encrypting all data solves the privacy issue, but makes many operations on the data impossible in the cloud, unless the service provider has the capacity to decrypt data temporarily. Homomorphic encryption would solve this issue, but despite great and on-going progress, it is still far from being operationally feasible. In 2015, we presented what we now call dodrant-homomorphic encryption, a method that encrypts numeric values …

Using Multivariate Statistical Techniques To Aid In A Sports Index Construction, Tiffany Kelly

Mathematics Colloquium Series

Within a quantitative career, you are/will soon be challenged to create an overall value to explain a situational status. For example, socio-economic status, well-being, and in this specific example, happiness among sports fans. This talk seeks to discuss my previous work developed out from student research performed at NSU in its application to my first project for ESPN Sports Analytics, the College Football Fan Happiness Index (http://es.pn/2vmParA) . I will dive into the multivariate statistical techniques of principal component analysis and hierarchal clustering to create this happiness index from a slew of variables.

A Bivariate Hypothesis Testing Approach For Mapping The Trait-Influential Gene, Garrett Saunders, Matthew D. Meng, John R. Stevens

Mathematics and Statistics Faculty Publications

The linkage disequilibrium (LD) based quantitative trait loci (QTL) model involves two indispensable hypothesis tests: the test of whether or not a QTL exists, and the test of the LD strength between the QTaL and the observed marker. The advantage of this two-test framework is to test whether there is an influential QTL around the observed marker instead of just having a QTL by random chance. There exist unsolved, open statistical questions about the inaccurate asymptotic distributions of the test statistics. We propose a bivariate null kernel (BNK) hypothesis testing method, which characterizes the joint distribution of the two test …

On Congruence Lattices Of Nilsemigroups, Alexander L. Popovich, Peter Jones

Mathematics, Statistics and Computer Science Faculty Research and Publications

We prove that the congruence lattice of a nilsemigroup is modular if and only if the width of the semigroup, as a poset, is at most two, and distributive if and only if its width is one. In the latter case, such semigroups therefore coincide with the nil Δ">Δ Δ -semigroups. It is further shown that if a finitely generated nilsemigroup has modular congruence lattice, then the semigroup is finite.

The Double-Edged Sword: A Mixed Methods Study Of The Interplay Between Bipolar Disorder And Technology Use, Mark Matthews, Elizabeth Murnane, Jaime Snyder, Shion Guha, Pamara Chang, Gavin Doherty, Geri K. Gay

Mathematics, Statistics and Computer Science Faculty Research and Publications

Human behavior is increasingly reflected or acted out through technology. This is of particular salience when it comes to changes in behavior associated with serious mental illnesses including schizophrenia and bipolar disorder. Early detection is crucial for these conditions but presently very challenging to achieve. Potentially, characteristics of these conditions' traits and symptoms, at both idiosyncratic and collective levels, may be detectable through technology use patterns. In bipolar disorder specifically, initial evidence associates changes in mood with changes in technology-mediated communication patterns. However much less is known about how people with bipolar disorder use technology more generally in their lives, …

Time Varying Parameter Estimation Scheme For A Linear Stochastic Differential Equation.Pdf, Michael Otunuga

Olusegun Michael Otunuga

Improving The Accuracy For The Long-Term Hydrologic Impact Assessment (L-Thia) Model, Anqi Zhang, Lawrence Theller, Bernard A. Engel

The Summer Undergraduate Research Fellowship (SURF) Symposium

Urbanization increases runoff by changing land use types from less impervious to impervious covers. Improving the accuracy of a runoff assessment model, the Long-Term Hydrologic Impact Assessment (L-THIA) Model, can help us to better evaluate the potential uses of Low Impact Development (LID) practices aimed at reducing runoff, as well as to identify appropriate runoff and water quality mitigation methods. Several versions of the model have been built over time, and inconsistencies have been introduced between the models. To improve the accuracy and consistency of the model, the equations and parameters (primarily curve numbers in the case of this model) …

Implant Treatment In The Predoctoral Clinic: A Retrospective Database Study Of 1091 Patients, Soni Prasad, Christopher Hambrook, Eric Reigle, Katherine Sherman, Naveen K. Bansal, Arthur F. Hefti

Mathematics, Statistics and Computer Science Faculty Research and Publications

Purpose: This retrospective study was conducted at the Marquette University School of Dentistry to (1) characterize the implant patient population in a predoctoral clinic, (2) describe the implants inserted, and (3) provide information on implant failures.

Materials and Methods: The study cohort included 1091 patients who received 1918 dental implants between 2004 and 2012, and had their implants restored by a crown or a fixed dental prosthesis. Data were collected from patient records, entered in a database, and summarized in tables and figures. Contingency tables were prepared and analyzed by a chi-squared test. The cumulative survival probability of implants was …

Magnetic Control Of Lateral Migration Of Ellipsoidal Microparticles In Microscale Flows, R. Zhou, C. A. Sobecki, J. Zhang, Yanzhi Zhang, Cheng Wang

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

Statistical Computational Topology And Geometry For Understanding Data, Joshua Lee Mike

Doctoral Dissertations

Here we describe three projects involving data analysis which focus on engaging statistics with the geometry and/or topology of the data.

The first project involves the development and implementation of kernel density estimation for persistence diagrams. These kernel densities consider neighborhoods for every feature in the center diagram and gives to each feature an independent, orthogonal direction. The creation of kernel densities in this realm yields a (previously unavailable) full characterization of the (random) geometry of a dataspace or data distribution.

In the second project, cohomology is used to guide a search for kidney exchange cycles within a kidney paired …

A Comparison Of Five Statistical Methods For Predicting Stream Temperature Across Stream Networks, Maike F. Holthuijzen

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The health of freshwater aquatic systems, particularly stream networks, is mainly influenced by water temperature, which controls biological processes and influences species distributions and aquatic biodiversity. Thermal regimes of rivers are likely to change in the future, due to climate change and other anthropogenic impacts, and our ability to predict stream temperatures will be critical in understanding distribution shifts of aquatic biota. Spatial statistical network models take into account spatial relationships but have drawbacks, including high computation times and data pre-processing requirements. Machine learning techniques and generalized additive models (GAM) are promising alternatives to the SSN model. Two machine learning …

Dependence Structures In Lévy-Type Markov Processes, Eddie Brendan Tu

Doctoral Dissertations

In this dissertation, we examine the positive and negative dependence of infinitely divisible distributions and Lévy-type Markov processes. Examples of infinitely divisible distributions include Poissonian distributions like compound Poisson and α-stable distributions. Examples of Lévy-type Markov processes include Lévy processes and Feller processes, which include a class of jump-diffusions, certain stochastic differential equations with Lévy noise, and subordinated Markov processes. Other examples of Lévy-type Markov processes are time-inhomogeneous Feller evolution systems (FES), which include additive processes. We will provide a tour of various forms of positive dependence, which include association, positive supermodular association (PSA), positive supermodular dependence (PSD), and positive …

Trace Formulas For Perturbations Of Operators With Hilbert-Schmidt Resolvents, Bishnu Prasad Sedai

Mathematics & Statistics ETDs

In this dissertation, we study Taylor approximations of functions of operators with Hilbert-Schmidt resolvents. We obtain integral representations for traces of the respective Taylor remainders that are analogous to trace formulas obtained in the case of Schatten perturbations in [10, 11, 16].

High Order Hermite And Sobolev Discontinuous Galerkin Methods For Hyperbolic Partial Differential Equations, Adeline Kornelus

Mathematics & Statistics ETDs

Many real-world problems involving dynamics of solid or fluid bodies can be modeled by hyperbolic partial differential equations (PDEs). Up to this point, only solutions to selected PDEs are available. Many PDEs are physically or geometrically complex, resulting in difficulties computing the analytical solutions. In this thesis, we focus on numerical methods for approximating solutions to hyperbolic PDEs. Long-term simulation for the motion of the body described by the PDE requires a method that is not only robust and efficient, but also produces small error because the error will be propagated and accumulated over the course of the simulation. Therefore, …

Merging Peg Solitaire In Graphs, John Engbers, Ryan Weber

Mathematics, Statistics and Computer Science Faculty Research and Publications

Peg solitaire has recently been generalized to graphs. Here, pegs start on all but one of the vertices in a graph. A move takes pegs on adjacent vertices x and y, with y also adjacent to a hole on vertex z, and jumps the peg on x over the peg ony to z, removing the peg on y. The goal of the game is to reduce the number of pegs to one.

We introduce the game merging peg solitaire on graphs, where a move takes pegs on vertices x and z (with a hole on y) and merges them to …

Comparison Of Two Methods In Estimating Standard Error Of Simulated Moments Estimators For Generalized Linear Mixed Models, Danielle K. Duran

Mathematics & Statistics ETDs

We consider standard error of the method of simulated moment (MSM) estimator for generalized linear mixed models (GLMM). Parametric bootstrap (PB) has been used to estimate the covariance matrix, in which we use the estimates to generate the simulated moments. To avoid the bias introduced by estimating the parameters and to deal with the correlated observations, (Lu, 2012) proposed a multi-stage block nonparametric bootstrap to estimate the standard errors. In this research, we compare PB and nonparametric bootstrap methods (NPB) in estimating the standard errors of MSM estimators for GLMM. Simulation results show that when the group size is large, …

A Perspective On The Challenges And Issues In Developing Biomarkers For Human Allergic Risk Assessments, Ying Mu, Dianne E. Godar, Stephen Merrill

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.