Applied Mathematics Commons^™

Non-Stationary Counts With Mixture Distributions, Ziqiang Lin

Legacy Theses & Dissertations (2009 - 2024)

We study a new non--stationary mixture Pengram and thinning model for time series of counts that include the effect of covariate variables on the outcome variable. Properties of the model and performance are discussed. It has a simpler likelihood function than the non--stationary INAR(1) model and therefore MLE estimators for the model's parameters are easier to find. Therefore the model offers an alternative to non--stationary INAR(1).

Concavity In Fractional Calculus, Paul W. Eloe, Jeffrey T. Neugebauer

Mathematics Faculty Publications

No abstract provided.

When Numerical Analysis Crosses Paths With Catalan And Generalized Motzkin Numbers, Paul W. Eloe, Catherine Kublik

Mathematics Faculty Publications

We study a linear doubly indexed sequence that contains the Catalan numbers and relates to a class of generalized Motzkin numbers. We obtain a closed form formula, a generating function and a nonlinear recursion relation for this sequence. We show that a finite difference scheme with compact stencil applied to a nonlinear differential operator acting on the Euclidean distance function is exact, and exploit this exactness to produce the nonlinear recursion relation. In particular, the nonlinear recurrence relation is obtained by using standard error analysis techniques from numerical analysis. This work shows a connection between numerical analysis and number theory, …

A Primer On Noise-Induced Transitions In Applied Dynamical Systems, Eric Forgoston, Richard O. Moore

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Noise plays a fundamental role in a wide variety of physical and biological dynamical systems. It can arise from an external forcing or due to random dynamics internal to the system. It is well established that even weak noise can result in large behavioral changes such as transitions between or escapes from quasi-stable states. These transitions can correspond to critical events such as failures or extinctions that make them essential phenomena to understand and quantify, despite the fact that their occurrence is rare. This article will provide an overview of the theory underlying the dynamics of rare events for stochastic …

A Model To Predict Concentrations And Uncertainty For Mercury Species In Lakes, Ashley Hendricks

Dissertations, Master's Theses and Master's Reports

To increase understanding of mercury cycling, a seasonal mass balance model was developed to predict mercury concentrations in lakes and fish. Results indicate that seasonality in mercury cycling is significant and is important for a northern latitude lake. Models, when validated, have the potential to be used as an alternative to measurements; models are relatively inexpensive and are not as time intensive. Previously published mercury models have neglected to perform a thorough validation. Model validation allows for regulators to be able to make more informed, confident decisions when using models in water quality management. It is critical to quantify uncertainty; …

The Use Of Item Response Theory In Survey Methodology: Application In Seat Belt Data, Mark K. Ledbetter, Norou Diawara, Bryan E. Porter

Mathematics & Statistics Faculty Publications

Problem: Several approaches to analyze survey data have been proposed in the literature. One method that is not popular in survey research methodology is the use of item response theory (IRT). Since accurate methods to make prediction behaviors are based upon observed data, the design model must overcome computation challenges, but also consideration towards calibration and proficiency estimation. The IRT model deems to be offered those latter options. We review that model and apply it to an observational survey data. We then compare the findings with the more popular weighted logistic regression. Method: Apply IRT model to the observed data …

Penalized Mixed-Effects Ordinal Response Models For High-Dimensional Genomic Data In Twins And Families, Amanda E. Gentry

Theses and Dissertations

The Brisbane Longitudinal Twin Study (BLTS) was being conducted in Australia and was funded by the US National Institute on Drug Abuse (NIDA). Adolescent twins were sampled as a part of this study and surveyed about their substance use as part of the Pathways to Cannabis Use, Abuse and Dependence project. The methods developed in this dissertation were designed for the purpose of analyzing a subset of the Pathways data that includes demographics, cannabis use metrics, personality measures, and imputed genotypes (SNPs) for 493 complete twin pairs (986 subjects.) The primary goal was to determine what combination of SNPs and …

Wildfire Emissions In The Context Of Global Change And The Implications For Mercury Pollution, Aditya Kumar

Dissertations, Master's Theses and Master's Reports

Wildfires are episodic disturbances that exert a significant influence on the Earth system. They emit substantial amounts of atmospheric pollutants, which can impact atmospheric chemistry/composition and the Earth’s climate at the global and regional scales. This work presents a collection of studies aimed at better estimating wildfire emissions of atmospheric pollutants, quantifying their impacts on remote ecosystems and determining the implications of 2000s-2050s global environmental change (land use/land cover, climate) for wildfire emissions following the Intergovernmental Panel on Climate Change (IPCC) A1B socioeconomic scenario.

A global fire emissions model is developed to compile global wildfire emission inventories for major atmospheric …

Effect Of Neuromodulation Of Short-Term Plasticity On Information Processing In Hippocampal Interneuron Synapses, Elham Bayat Mokhtari

Graduate Student Theses, Dissertations, & Professional Papers

Neurons convey information about the complex dynamic environment in the form of signals. Computational neuroscience provides a theoretical foundation toward enhancing our understanding of nervous system. The aim of this dissertation is to present techniques to study the brain and how it processes information in particular neurons in hippocampus.

We begin with a brief review of the history of neuroscience and biological background of basic neurons. To appreciate the importance of information theory, familiarity with the information theoretic basics is required, these basics are presented in Chapter 2. In Chapter 3, we use information theory to estimate the amount of …

Multiclass Classification Using Support Vector Machines, Duleep Prasanna W. Rathgamage Don

College of Graduate Studies: Theses & Dissertations

In this thesis, we discuss different SVM methods for multiclass classification and introduce the Divide and Conquer Support Vector Machine (DCSVM) algorithm which relies on data sparsity in high dimensional space and performs a smart partitioning of the whole training data set into disjoint subsets that are easily separable. A single prediction performed between two partitions eliminates one or more classes in a single partition, leaving only a reduced number of candidate classes for subsequent steps. The algorithm continues recursively, reducing the number of classes at each step until a final binary decision is made between the last two classes …

On Modeling Quantities For Insurer Solvency Against Catastrophe Under Some Markovian Assumptions, Daniel Jefferson Geiger

Doctoral Dissertations

"Insurance companies sometimes face catastrophic losses, yet they must remain solvent enough to meet the legal obligation of covering all claims. Catastrophes can result in large damages to the policyholders, causing the arrival of numerous claims to insurance companies at once. Furthermore, the severity of an event could impact the time until the next occurrence. An insurer needs certain levels of startup capital to meet all claims, and then must have adequate reserves on a continual basis, even more so when catastrophes occur. This work examines two facets of these matters: for an infinite time horizon, we extend and develop …

Particle Filters For State Estimation Of Confined Aquifers, Graeme Field

UNF Graduate Theses and Dissertations

Mathematical models are used in engineering and the sciences to estimate properties of systems of interest, increasing our understanding of the surrounding world and driving technological innovation. Unfortunately, as the systems of interest grow in complexity, so to do the models necessary to accurately describe them. Analytic solutions for problems with such models are provably intractable, motivating the use of approximate yet still accurate estimation techniques. Particle filtering methods have emerged as a popular tool in the presence of such models, spreading from its origins in signal processing to a diverse set of fields throughout engineering and the sciences including …

Adaptive Methods For Point Cloud And Mesh Processing, Zinat Afrose

Computational Modeling & Simulation Engineering Theses & Dissertations

Point clouds and 3D meshes are widely used in numerous applications ranging from games to virtual reality to autonomous vehicles. This dissertation proposes several approaches for noise removal and calibration of noisy point cloud data and 3D mesh sharpening methods. Order statistic filters have been proven to be very successful in image processing and other domains as well. Different variations of order statistics filters originally proposed for image processing are extended to point cloud filtering in this dissertation. A brand-new adaptive vector median is proposed in this dissertation for removing noise and outliers from noisy point cloud data.

The major …

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 …

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 …

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 …

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 …

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 …

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 …

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, …

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 …