Applied Mathematics Commons^™

The Analysis Of Neural Heterogeneity Through Mathematical And Statistical Methods, Kyle Wendling

Theses and Dissertations

Diversity of intrinsic neural attributes and network connections is known to exist in many areas of the brain and is thought to significantly affect neural coding. Recent theoretical and experimental work has argued that in uncoupled networks, coding is most accurate at intermediate levels of heterogeneity. I explore this phenomenon through two distinct approaches: a theoretical mathematical modeling approach and a data-driven statistical modeling approach.

Through the mathematical approach, I examine firing rate heterogeneity in a feedforward network of stochastic neural oscillators utilizing a high-dimensional model. The firing rate heterogeneity stems from two sources: intrinsic (different individual cells) and network …

Personalized Detection Of Anxiety Provoking News Events Using Semantic Network Analysis, Jacquelyn Cheun Phd, Luay Dajani, Quentin B. Thomas

SMU Data Science Review

In the age of hyper-connectivity, 24/7 news cycles, and instant news alerts via social media, mental health researchers don't have a way to automatically detect news content which is associated with triggering anxiety or depression in mental health patients. Using the Associated Press news wire, a semantic network was built with 1,056 news articles containing over 500,000 connections across multiple topics to provide a personalized algorithm which detects problematic news content for a given reader. We make use of Semantic Network Analysis to surface the relationship between news article text and anxiety in readers who struggle with mental health disorders. …

Function Space Tensor Decomposition And Its Application In Sports Analytics, Justin Reising

Electronic Theses and Dissertations

Recent advancements in sports information and technology systems have ushered in a new age of applications of both supervised and unsupervised analytical techniques in the sports domain. These automated systems capture large volumes of data points about competitors during live competition. As a result, multi-relational analyses are gaining popularity in the field of Sports Analytics. We review two case studies of dimensionality reduction with Principal Component Analysis and latent factor analysis with Non-Negative Matrix Factorization applied in sports. Also, we provide a review of a framework for extending these techniques for higher order data structures. The primary scope of this …

The Graphs That Have Antivoltages Using Groups Of Small Order, Vaidy Sivaraman, Dan Slilaty

Mathematics and Statistics Faculty Publications

Given a group Γ of order at most six, we characterize the graphs that have Γ-antivoltages and also determine the list of minor-minimal graphs that have no Γ-antivoltage. Our characterizations yield polynomial-time recognition algorithms for such graphs.

Quantifying Distribution In Carbon Uptake Across A Global Measurement Network Of Terrestrial Ecosystems, John Zobitz, Madeline Oswood

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Extending Statistical Learning For Aneurysm Rupture Assessment To Finnish And Japanese Populations Using Morphology, Hemodynamics, And Patient Characteristics, Felicitas J. Detmer, Sara Hadad, Bong Jae Chung, Fernando Mut, Martin Slawski, Norman Juchler, Vartan Kurtcuoglu, Sven Hirsch, Philippe Bijlenga, Yuya Uchiyama, Soichiro Fujimura, Makoto Yamamoto, Yuichi Murayama, Hiroyuki Takao, Timo Koivisto, Juhana Frösen, Juan R. Cebral

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

OBJECTIVE: Incidental aneurysms pose a challenge for physicians, who need to weigh the rupture risk against the risks associated with treatment and its complications. A statistical model could potentially support such treatment decisions. A recently developed aneurysm rupture probability model performed well in the US data used for model training and in data from two European cohorts for external validation. Because Japanese and Finnish patients are known to have a higher aneurysm rupture risk, the authors' goals in the present study were to evaluate this model using data from Japanese and Finnish patients and to compare it with new models …

Image-Based Modeling Of Blood Flow In Cerebral Aneurysms Treated With Intrasaccular Flow Diverting Devices, Fernando Mut, Bong Jae Chung, Jorge Chudyk, Pedro Lylyk, Ramanathan Kadirvel, David F. Kallmes, Juan R. Cebral

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Modeling the flow dynamics in cerebral aneurysms after the implantation of intrasaccular devices is important for understanding the relationship between flow conditions created immediately posttreatment and the subsequent outcomes. This information, ideally available a priori based on computational modeling prior to implantation, is valuable to identify which aneurysms will occlude immediately and which aneurysms will likely remain patent and would benefit from a different procedure or device. In this report, a methodology for modeling the hemodynamics in intracranial aneurysms treated with intrasaccular flow diverting devices is described. This approach combines an image-guided, virtual device deployment within patient-specific vascular models with …

The Long-Run Effects Of Tropical Cyclones On Infant Mortality, Isabel Miranda

Master's Theses

In the United States alone, each tropical cyclone causes an average of $14.6 billion worth of damages. In addition to the destruction of physical infrastructure, natural disasters also negatively impact human capital formation. These losses are often more difficult to observe, and therefore, are over looked when quantifying the true costs of natural disasters. One particular effect is an increase in infant mortality rates, an important indicator of a country’s general socioeconomic level. This paper utilizes a model created by Anttila-Hughes and Hsiang, that takes advantage of annual variation in tropical cyclones using annual spatial average maximum wind speeds and …

A More Powerful Unconditional Exact Test Of Homogeneity For 2 × C Contingency Table Analysis, Louis Ehwerhemuepha, Heng Sok, Cyril Rakovski

Mathematics, Physics, and Computer Science Faculty Articles and Research

The classical unconditional exact p-value test can be used to compare two multinomial distributions with small samples. This general hypothesis requires parameter estimation under the null which makes the test severely conservative. Similar property has been observed for Fisher's exact test with Barnard and Boschloo providing distinct adjustments that produce more powerful testing approaches. In this study, we develop a novel adjustment for the conservativeness of the unconditional multinomial exact p-value test that produces nominal type I error rate and increased power in comparison to all alternative approaches. We used a large simulation study to empirically estimate the …

Associations Of Hemodynamics, Morphology, And Patient Characteristics With Aneurysm Rupture Stratified By Aneurysm Location, Felicitas J. Detmer, Bong Jae Chung, Carlos Jimenez, Farid Hamzei-Sichani, David Kallmes, Christopher Putman, Juan R. Cebral

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Purpose: The mechanisms of cerebral aneurysm rupture are not fully understood. We analyzed the associations of hemodynamics, morphology, and patient age and gender with aneurysm rupture stratifying by location. Methods: Using image-based models, 20 hemodynamic and 17 morphological parameters were compared in 1931 ruptured and unruptured aneurysms with univariate logistic regression. Rupture rates were compared between males and females as well as younger and older patients and bifurcation versus sidewall aneurysms for different aneurysm locations. Subsequently, associations between hemodynamics and morphology and patient as well as aneurysm characteristics were analyzed for aneurysms at five locations. Results: Compared to unruptured aneurysms, …

Local Hemodynamic Conditions Associated With Focal Changes In The Intracranial Aneurysm Wall, Juan R. Cebral, F. Detmer, Bong Jae Chung, J. Choque-Velasquez, B. Rezai, H. Lehto, R. Tulamo, J. Hernesniemi, M. Niemela, A. Yu, R. Williamson, Khaled Aziz, S. Sakur, S. Amin-Hanjani, F. Charbel, Y. Tobe, A. Robertson, J. Frösen

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

BACKGROUND AND PURPOSE: Aneurysm hemodynamics has been associated with wall histology and inflammation. We investigated associations between local hemodynamics and focal wall changes visible intraoperatively. MATERIALS AND METHODS: Computational fluid dynamics models were constructed from 3D images of 65 aneurysms treated surgically. Aneurysm regions with different visual appearances were identified in intraoperative videos: 1) “atherosclerotic” (yellow), 2) “hyperplastic” (white), 3) “thin” (red), 4) rupture site, and 5) “normal” (similar to parent artery), They were marked on 3D reconstructions. Regional hemodynamics was characterized by the following: wall shear stress, oscillatory shear index, relative residence time, wall shear stress gradient and divergence, …

Non-Marginal Decisions: A Novel Bayesian Multiple Testing Procedure, Noirrit Kiran Chandra, Sourabh Bhattacharya

Journal Articles

In this paper, we consider the problem of multiple testing where the hypotheses are dependent. In most of the existing literature, either Bayesian or non-Bayesian, the decision rules mainly focus on the validity of the test procedure rather than actually utilizing the dependency to increase efficiency. Moreover, the decisions regarding different hypotheses are marginal in the sense that they do not depend upon each other directly. However, in realistic situations, the hypotheses are usually dependent, and hence it is desirable that the decisions regarding the dependent hypotheses are taken jointly. In this article, we develop a novel Bayesian multiple testing …

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 …

Mathematically Modeling The Role Of Triglyceride Production On Leptin Resistance, Yu Zhao, Daniel Burkow, Baojun Song

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Diet-induced obesity is becoming more common all over the world, which is increasing the prevalence of obesity-induced chronic diseases such as diabetes, coronary heart disease, cancer, and sleep apnea. Many experimental results show that obesity is often associated with an elevated concentration of plasma leptin and triglycerides. Triglycerides inhibit the passage of leptin across the blood–brain barrier (BBB) to signal the hypothalamus to suppress appetite. However, it is still not clear how triglyceride concentration affects leptin transport across the BBB and energy balance. In this paper, we propose a novel ordinary differential equations model describing the role of leptin in …

Development And Internal Validation Of An Aneurysm Rupture Probability Model Based On Patient Characteristics And Aneurysm Location, Morphology, And Hemodynamics, Felicitas J. Detmer, Bong Jae Chung, Fernando Mut, Martin Slawski, Farid Hamzei-Sichani, Christopher Putman, Carlos Jiménez, Juan R. Cebral

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Purpose: Unruptured cerebral aneurysms pose a dilemma for physicians who need to weigh the risk of a devastating subarachnoid hemorrhage against the risk of surgery or endovascular treatment and their complications when deciding on a treatment strategy. A prediction model could potentially support such treatment decisions. The aim of this study was to develop and internally validate a model for aneurysm rupture based on hemodynamic and geometric parameters, aneurysm location, and patient gender and age. Methods: Cross-sectional data from 1061 patients were used for image-based computational fluid dynamics and shape characterization of 1631 aneurysms for training an aneurysm rupture probability …

Quantitative Appraisal Of Non-Irrigated Cropland In South Dakota, Shelby Riggs

Honors Program: Senior Projects (Public)

This appraisal attempts to remove subjectivity from the appraisal process and replace it with quantitative analysis of known data to generate a fair market value of the subject property. Two methods of appraisal were used, the income approach and the comparable sales approach. For the income approach, I used the average cash rent for the region, the current property taxes for the subject property, and a capitalization rate based on Stokes' (2018) capitalization rate formula to arrive at my income-based valuation. For the comparable sales approach, I utilized Stokes' (2018) research in optimization modeling to estimate a market value for …

Understanding Sexual Violence Against Women, Maria Martinez

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Identification Of Hostile Hemodynamics And Geometries Of Cerebral Aneurysms: A Case-Control Study, Bong Jae Chung, F. Mut, C. M. Putman, F. Hamzei-Sichani, W. Brinjikji, D. Kallmes, C. M. Jimenez, Juan R. Cebral

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

BACKGROUND AND PURPOSE: Hostile hemodynamic conditions and geometries are thought to predispose aneurysms for instability and rupture. This study compares stable, unstable, and ruptured aneurysms while controlling for location and patient characteristics. MATERIALS AND METHODS: The hemodynamics and geometries of 165 stable, 65 unstable, and 554 ruptured aneurysms were compared. Hemodynamics was modeled using image-based computational fluid dynamics. Case-control pairs were selected matching aneurysm location, patient age, and sex. Paired Wilcoxon tests were used to compare hemodynamic and geometric variables among different aneurysm groups. The pairing was repeated 100 times, and the combined P values were calculated and adjusted for …

Yelp’S Review Filtering Algorithm, Yao Yao, Ivelin Angelov, Jack Rasmus-Vorrath, Mooyoung Lee, Daniel W. Engels

SMU Data Science Review

In this paper, we present an analysis of features influencing Yelp's proprietary review filtering algorithm. Classifying or misclassifying reviews as recommended or non-recommended affects average ratings, consumer decisions, and ultimately, business revenue. Our analysis involves systematically sampling and scraping Yelp restaurant reviews. Features are extracted from review metadata and engineered from metrics and scores generated using text classifiers and sentiment analysis. The coefficients of a multivariate logistic regression model were interpreted as quantifications of the relative importance of features in classifying reviews as recommended or non-recommended. The model classified review recommendations with an accuracy of 78%. We found that reviews …

Development Of A Statistical Model For Discrimination Of Rupture Status In Posterior Communicating Artery Aneurysms, Felicitas J. Detmer, Bong Jae Chung, Fernando Mut, Michael Pritz, Martin Slawski, Farid Hamzei-Sichani, David Kallmes, Christopher Putman, Carlos Jimenez, Juan R. Cebral

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Background: Intracranial aneurysms at the posterior communicating artery (PCOM) are known to have high rupture rates compared to other locations. We developed and internally validated a statistical model discriminating between ruptured and unruptured PCOM aneurysms based on hemodynamic and geometric parameters, angio-architectures, and patient age with the objective of its future use for aneurysm risk assessment. Methods: A total of 289 PCOM aneurysms in 272 patients modeled with image-based computational fluid dynamics (CFD) were used to construct statistical models using logistic group lasso regression. These models were evaluated with respect to discrimination power and goodness of fit using tenfold nested …

Clustering Mixed Data: An Extension Of The Gower Coefficient With Weighted L2 Distance, Augustine Oppong

Electronic Theses and Dissertations

Sorting out data into partitions is increasing becoming complex as the constituents of data is growing outward everyday. Mixed data comprises continuous, categorical, directional functional and other types of variables. Clustering mixed data is based on special dissimilarities of the variables. Some data types may influence the clustering solution. Assigning appropriate weight to the functional data may improve the performance of the clustering algorithm. In this paper we use the extension of the Gower coefficient with judciously chosen weight for the L2 to cluster mixed data.The benefits of weighting are demonstrated both in in applications to the Buoy data set …

Masked Instability: Within-Sector Financial Risk In The Presence Of Wealth Inequality, Youngna Choi

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

We investigate masked financial instability caused by wealth inequality. When an economic sector is decomposed into two subsectors that possess a severe wealth inequality, the sector in entirety can look financially stable while the two subsectors possess extreme financially instabilities of opposite nature, one from excessive equity, the other from lack thereof. The unstable subsector can result in further financial distress and even trigger a financial crisis. The market instability indicator, an early warning system derived from dynamical systems applied to agent-based models, is used to analyze the subsectoral financial instabilities. Detailed mathematical analysis is provided to explain what financial …

A Practical Guide To Big Data, Ekaterina Smirnova, Andrada Ivanescu, Jiawei Bai, Ciprian M. Crainiceanu

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Big Data is increasingly prevalent in science and data analysis. We provide a short tutorial for adapting to these changes and making the necessary adjustments to the academic culture to keep Biostatistics truly impactful in scientific research.

Physical Applications Of The Geometric Minimum Action Method, George L. Poppe Jr.

Dissertations, Theses, and Capstone Projects

This thesis extends the landscape of rare events problems solved on stochastic systems by means of the \textit{geometric minimum action method} (gMAM). These include partial differential equations (PDEs) such as the real Ginzburg-Landau equation (RGLE), the linear Schroedinger equation, along with various forms of the nonlinear Schroedinger equation (NLSE) including an application towards an ultra-short pulse mode-locked laser system (MLL).

Additionally we develop analytical tools that can be used alongside numerics to validate those solutions. This includes the use of instanton methods in deriving state transitions for the linear Schroedinger equation and the cubic diffusive NLSE.

These analytical solutions are …

Using Random Forests To Describe Equity In Higher Education: A Critical Quantitative Analysis Of Utah’S Postsecondary Pipelines, Tyler Mcdaniel

Butler Journal of Undergraduate Research

The following work examines the Random Forest (RF) algorithm as a tool for predicting student outcomes and interrogating the equity of postsecondary education pipelines. The RF model, created using longitudinal data of 41,303 students from Utah's 2008 high school graduation cohort, is compared to logistic and linear models, which are commonly used to predict college access and success. Substantially, this work finds High School GPA to be the best predictor of postsecondary GPA, whereas commonly used ACT and AP test scores are not nearly as important. Each model identified several demographic disparities in higher education access, most significantly the effects …

Score Test And Likelihood Ratio Test For Zero-Inflated Binomial Distribution And Geometric Distribution, Xiaogang Dai

Masters Theses & Specialist Projects

The main purpose of this thesis is to compare the performance of the score test and the likelihood ratio test by computing type I errors and type II errors when the tests are applied to the geometric distribution and inflated binomial distribution. We first derive test statistics of the score test and the likelihood ratio test for both distributions. We then use the software package R to perform a simulation to study the behavior of the two tests. We derive the R codes to calculate the two types of error for each distribution. We create lots of samples to approximate …

Pricing Asian Options: Volatility Forecasting As A Source Of Downside Risk, Adam T. Diehl

Undergraduate Economic Review

Asian options are a class of derivative securities whose payoffs average movements in the underlying asset as a means of hedging exposure to unexpected market behavior. We find that despite their volatility smoothing properties, the price of an Asian option is sensitive to the choice of volatility model employed to price them from market data. We estimate the errors induced by two common schemes of forecasting volatility and their potential impact upon trading.

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 …

Predicting The Next Us President By Simulating The Electoral College, Boyan Kostadinov

Publications and Research

We develop a simulation model for predicting the outcome of the US Presidential election based on simulating the distribution of the Electoral College. The simulation model has two parts: (a) estimating the probabilities for a given candidate to win each state and DC, based on state polls, and (b) estimating the probability that a given candidate will win at least 270 electoral votes, and thus win the White House. All simulations are coded using the high-level, open-source programming language R. One of the goals of this paper is to promote computational thinking in any STEM field by illustrating how probabilistic …

Modeling Mayfly Nymph Length Distribution And Population Dynamics Across A Gradient Of Stream Temperatures And Stream Types, Jeremy Anthony, Jennifer Baccam, Imanuel Bier, Emily Gregg, Leif Halverson, Ryan Mulcahy, Emmanuel Okanla, Samira A. Osman, Adam R. Pancoast, Kevin C. Schultz, Alex Sushko, Jennifer Vorarath, Yia Vue, Austin Wagner, Emily Gaenzle Schilling, John M. Zobitz

Spora: A Journal of Biomathematics

We analyze a process-based temperature model for the length distribution and population over time of mayfly nymphs. Model parameters are estimated using a Markov Chain Monte Carlo parameter estimation method utilizing length distribution data at five different stream sites. Two different models (a standard exponential model and a modified Weibull model) of mayfly mortality are evaluated, where in both cases mayfly length growth is a function of stream temperature. Based on model-data comparisons to the modeled length distribution and the Bayesian Information Criterion, we found that approaches that length distribution data can reliably estimate 2–3 model parameters. Future model development …