Statistics and Probability Commons^™

Flow Anisotropy Due To Thread-Like Nanoparticle Agglomerations In Dilute Ferrofluids, Alexander Cali, Wah-Keat Lee, A. David Trubatch, Philip Yecko

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Improved knowledge of the magnetic field dependent flow properties of nanoparticle-based magnetic fluids is critical to the design of biomedical applications, including drug delivery and cell sorting. To probe the rheology of ferrofluid on a sub-millimeter scale, we examine the paths of 550 μm diameter glass spheres falling due to gravity in dilute ferrofluid, imposing a uniform magnetic field at an angle with respect to the vertical. Visualization of the spheres’ trajectories is achieved using high resolution X-ray phase-contrast imaging, allowing measurement of a terminal velocity while simultaneously revealing the formation of an array of long thread-like accumulations of magnetic …

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 …

Dynamic Child Growth Prediction: A Comparative Methods Approach, Andrada Ivanescu, Ciprian M. Crainiceanu, William Checkley

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

We introduce a class of dynamic regression models designed to predict the future of growth curves based on their historical dynamics. This class of models incorporates both baseline and time-dependent covariates, start with simple regression models and build up to dynamic function-on-function regressions. We compare the performance of the dynamic prediction models in a variety of signal-to-noise scenarios and provide practical solutions for model selection. We conclude that (a) prediction performance increases substantially when using the entire growth history relative to using only the last and first observation; (b) smoothing incorporated using functional regression approaches increases prediction performance; and (c) …

Hemodynamic Characteristics Of Ruptured And Unruptured Multiple Aneurysms At Mirror And Ipsilateral Locations, Ravi Doddasomayajula, Bong Jae Chung, Fernando Mut, Carlos M. Jimenez, Farid Hamzei-Sichani, Christopher M. Putman, Juan R. Cebral

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

BACKGROUND AND PURPOSE: Different hemodynamic patterns have been associated with aneurysm rupture. The objective was to test whether hemodynamic characteristics of the ruptured aneurysm in patients with multiple aneurysms were different from those in unruptured aneurysms in the same patient.

MATERIALS AND METHODS: Twenty-four mirror and 58 ipsilateral multiple aneurysms with 1 ruptured and the others unruptured were studied. Computational fluid dynamics models were created from 3D angiographies. Case-control studies of mirror and ipsilateral aneurysms were performed with paired Wilcoxon tests.

RESULTS: In mirror pairs, the ruptured aneurysm had more oscillatory wall shear stress (P = .007) than the …

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 …

Evaluation Of Some Reliability Characteristics Of A Single Unit System Requiring Two Types Of Supporting Device For Operations, Ibrahim Yusuf, Nura J. Fagge

Applications and Applied Mathematics: An International Journal (AAM)

This study presents the reliability assessment of a single unit connected to two types of external supporting devices for its operation. Each type of external supporting device has two copies I and II on standby. First order differential difference equations method is used to obtain the explicit expression for the steady state availability, busy period due to failure of type I and II supporting devices of repairmen, steady-state availability and profit function. Based on assumed numerical values given to system parameters, graphical illustrations are given to highlight important results. Comparisons are performed to highlight the impact of unit failure and …

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 …

Entropy Production In A Fluid-Solid System Far From Thermodynamic Equilibrium, Bong Jae Chung, Blas Ortega, Ashuwin Vaidya

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Abstract.: The terminal orientation of a rigid body in a moving fluid is an example of a dissipative system, out of thermodynamic equilibrium and therefore a perfect testing ground for the validity of the maximum entropy production principle (MaxEP). Thus far, dynamical equations alone have been employed in studying the equilibrium states in fluid-solid interactions, but these are far too complex and become analytically intractable when inertial effects come into play. At that stage, our only recourse is to rely on numerical techniques which can be computationally expensive. In our past work, we have shown that the MaxEP is a …

Angioarchitectures And Hemodynamic Characteristics Of Posterior Communicating Artery Aneurysms And Their Association With Rupture Status, Bong Jae Chung, Ravi Doddasomayajula, Fernando Mut, Felicitas Detmer, Michael Pritz, Farid Hamzei-Sichani, Waleed Brinjikji, David F. Kallmes, Carlos M. Jimenez, Christopher Putman, Juan Cebral

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

BACKGROUND AND PURPOSE: Intracranial aneurysms originating at the posterior communicating artery are known to have high rupture risk compared with other locations. We tested the hypothesis that different angioarchitectures (ie, branch point configuration) of posterior communicating artery aneurysms are associated with aneurysm hemodynamics, which in turn predisposes aneurysms to rupture.

MATERIALS AND METHODS: A total of 313 posterior communicating artery aneurysms (145 ruptured, 168 unruptured) were studied with image-based computational fluid dynamics. Aneurysms were classified into different angioarchitecture types depending on the location of the aneurysm with respect to parent artery bifurcation. Hemodynamic characteristics were compared between ruptured and unruptured …

Handguns And Hotspots: Spatio- Temporal Models For Gun Violence In Chicago,Il, Shelby Scott

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

A Simulation Of Anthropogenic Columbian Mammoth Extinction, Alex Capaldi

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Spatiotemporal Subspace Feature Tracking By Mining Discriminatory Characteristics, Richard D. Appiah

Doctoral Dissertations

Recent advancements in data collection technologies have made it possible to collect heterogeneous data at complex levels of abstraction, and at an alarming pace and volume. Data mining, and most recently data science seek to discover hidden patterns and insights from these data by employing a variety of knowledge discovery techniques. At the core of these techniques is the selection and use of features, variables or properties upon which the data were acquired to facilitate effective data modeling. Selecting relevant features in data modeling is critical to ensure an overall model accuracy and optimal predictive performance of future effects. The …

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

Olusegun Michael Otunuga

Thermodynamics Of Coherent Structures Near Phase Transitions, Julia M. Meyer, Ivan Christov

The Summer Undergraduate Research Fellowship (SURF) Symposium

Phase transitions within large-scale systems may be modeled by nonlinear stochastic partial differential equations in which system dynamics are captured by appropriate potentials. Coherent structures in these systems evolve randomly through time; thus, statistical behavior of these fields is of greater interest than particular system realizations. The ability to simulate and predict phase transition behavior has many applications, from material behaviors (e.g., crystallographic phase transformations and coherent movement of granular materials) to traffic congestion. Past research focused on deriving solutions to the system probability density function (PDF), which is the ground-state wave function squared. Until recently, the extent to which …

Prediction Of Stress Increase In Unbonded Tendons Using Sparse Principal Component Analysis, Eric Mckinney

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

While internal and external unbonded tendons are widely utilized in concrete structures, the analytic solution for the increase in unbonded tendon stress, Δ���, is challenging due to the lack of bond between strand and concrete. Moreover, most analysis methods do not provide high correlation due to the limited available test data. In this thesis, Principal Component Analysis (PCA), and Sparse Principal Component Analysis (SPCA) are employed on different sets of candidate variables, amongst the material and sectional properties from the database compiled by Maguire et al. [18]. Predictions of Δ��� are made via Principal Component Regression models, and the method …

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, …

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, …

Information Metrics For Predictive Modeling And Machine Learning, Kostantinos Gourgoulias

Doctoral Dissertations

The ever-increasing complexity of the models used in predictive modeling and data science and their use for prediction and inference has made the development of tools for uncertainty quantification and model selection especially important. In this work, we seek to understand the various trade-offs associated with the simulation of stochastic systems. Some trade-offs are computational, e.g., execution time of an algorithm versus accuracy of simulation. Others are analytical: whether or not we are able to find tractable substitutes for quantities of interest, e.g., distributions, ergodic averages, etc. The first two chapters of this thesis deal with the study of the …

Tri-Ponderal Mass Index Vs Body Mass Index In Estimating Body Fat During Adolescence, Courtney M. Peterson, Haiyan Su, Diana Thomas, Moonseong Heo, Amir Golnabi, Angelo Pietrobelli, Steven B. Heymsfield

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Importance Body mass index (BMI) is used to diagnose obesity in adolescents worldwide, despite evidence that weight does not scale with height squared in adolescents. To account for this, health care providers diagnose obesity using BMI percentiles for each age (BMI z scores), but this does not ensure that BMI is accurate in adolescents.

Objective To compare the accuracy of BMI vs other body fat indices of the form body mass divided by heightⁿ in estimating body fat levels in adolescents.

Design, Setting, and Participants Cross-sectional data from the 1999 to 2006 US National Health and Nutrition Examination Survey …

An Investigation Of The Accuracy Of Parallel Analysis For Determining The Number Of Factors In A Factor Analysis, Mandy Matsumoto

Mahurin Honors College Capstone Experience/Thesis Projects

Exploratory factor analysis is an analytic technique used to determine the number of factors in a set of data (usually items on a questionnaire) for which the factor structure has not been previously analyzed. Parallel analysis (PA) is a technique used to determine the number of factors in a factor analysis. There are a number of factors that affect the results of a PA: the choice of the eigenvalue percentile, the strength of the factor loadings, the number of variables, and the sample size of the study. Although PA is the most accurate method to date to determine which factors …

Understanding Angiography-Based Aneurysm Flow Fields Through Comparison With Computational Fluid Dynamics, Juan R. Cebral, F. Mut, Bong Jae Chung, L. Spelle, J. Moret, F. Van Nijnatten, D. Ruijters

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

BACKGROUND AND PURPOSE: Hemodynamics is thought to be an important factor for aneurysm progression and rupture. Our aim was to evaluate whether flow fields reconstructed from dynamic angiography data can be used to realistically represent the main flow structures in intracranial aneurysms. MATERIALS AND METHODS: DSA-based flow reconstructions, obtained during interventional treatment, were compared qualitatively with flow fields obtained from patient-specific computational fluid dynamics models and quantitatively with projections of the computational fluid dynamics fields (by computing a directional similarity of the vector fields) in 15 cerebral aneurysms. RESULTS: The average similarity between the DSA and the projected computational fluid …

Uncovering Functional Relationships In Leukemia, Reginald Mcgee

Biology and Medicine Through Mathematics Conference

No abstract provided.

On The Analysis Of The Sir Epidemic Model For Small Networks: An Application In Hospital Settings, Martin Lopez-Garcia

Biology and Medicine Through Mathematics Conference

No abstract provided.

Optimal Experimental Design To Characterize A Wave Source Using Dosimeter Measurements, Renee L. Gooding

Mathematics & Statistics ETDs

When modeling physical phenomena we want to solve the inverse problem by estimating the parameters that characterize the source model that we are interested in. In this thesis, we focus on the optimal placement of a finite number of individual sensors, called dosimeters, in two and three dimensions with a time dependent Gaussian wave source. Using a computational model along with experimental data, we design an iterative process to determine the optimal placement of an additional sensor such that the noise in the measurements has a minimal effect on the parameter estimation. First, we estimate the parameters that characterize the …

Deterministic And Probabilistic Methods For Seismic Source Inversion, Juan Pablo Madrigal Cianci

Mathematics & Statistics ETDs

The national Earthquake Information Center (NEIC) reports an occurrence of about 13,000 earthquakes every year, spanning different values on the Richter scale from very mild (2) to "giant earthquakes'' (8 and above). Being able to study these earthquakes provides useful information for a wide range of applications in geophysics. In the present work we study the characteristics of an earthquake by performing seismic source inversion; a mathematical problem that, given some recorded data, produces a set of parameters that when used as input in a mathematical model for the earthquake generates synthetic data that closely resembles the measured data. There …

Cancer Modeling: From Optimal Cell Renewal To Immunotherapy, Cesar L. Alvarado

Mathematics & Statistics ETDs

Cancer is a disease caused by mutations in normal cells. According to the National Cancer Institute, in 2016, an estimated 1.6 million people were diagnosed and approximately 0.5 million people died from the disease in the United States. There are many factors that shape cancer at the cellular and organismal level, including genetic, immunological, and environmental components. In this thesis, we show how mathematical modeling can be used to provide insight into some of the key mechanisms underlying cancer dynamics. First, we use mathematical modeling to investigate optimal homeostatic cell renewal in tissues such as the small intestine with an …

Modeling Trait Evolutionary Processes With More Than One Gene, Huan Jiang

Mathematics & Statistics ETDs

Phylogenetic comparative methods have been used to test evolutionary signals through trait evolutionary processes. Traditionally, biologists use one phylogenetic tree as a tool to handle dependent data for the traits of interest and hence utilize one gene only. However, it is more informative if the evolutionary processes of a trait are presented by phylogenetic trees reconstructed by the DNA alignments from more than one gene. In this work, we explain and develop two methods involving modeling the trait evolutionary processes: (a) two gene trees via the Brownian motion (BM) model; and (b) two gene trees via the Ornstein-Uhlenbeck (OU) model. …

Comparing Methods Of Measuring Chaos In The Symbolic Dynamics Of Strange Attractors, James J. Scully

Georgia State Undergraduate Research Conference

No abstract provided.

Hemodynamic Differences Between Unstable And Stable Unruptured Aneurysms Independent Of Size And Location: A Pilot Study, Waleed Brinjikji, Bong Jae Chung, Carlos Jimenez, Christopher Putman, David F. Kallmes, Juan R. Cebral

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Background While clinical and angiographic risk factors for intracranial aneurysm instability are well established, it is reasonable to postulate that intra-aneurysmal hemodynamics also have a role in aneurysm instability. Objective To identify hemodynamic characteristics that differ between radiologically unstable and stable unruptured intracranial aneurysms. Materials and methods 12 pairs of unruptured intracranial aneurysms with a 3D rotational angiographic set of images and followed up longitudinally without treatment were studied. Each pair consisted of one stable aneurysm (no change on serial imaging) and one unstable aneurysm (demonstrated growth of at least 1 mm diameter or ruptured during follow-up) of matching size …