Mathematics Commons^™

A Psychometric Investigation Of A Mathematics Placement Test At A Science, Technology, Engineering, And Mathematics (Stem) Gifted Residential High School, Hannah Ruth Anderson

Publications & Research

Educational institutions, at all levels, must justify their use of placement testing and confront questions of their impact on students’ educational outcomes to assure all stakeholders that students are being enrolled in courses appropriate with their ability in order to maximize their chances of success (Linn, 1994; Mattern & Packman, 2009; McFate & Olmsted III, 1999; Norman, Medhanie, Harwell, Anderson, & Post, 2011; Wiggins, 1989). The aims of this research were to (1) provide evidence of Content Validity, (2) provide evidence of Construct Validity and Internal Consistency Reliability, (3) examine the item characteristics and potential bias of the items between …

Energy Stable Numerical Schemes For Ternary Cahn-Hilliard System, Wenbin Chen, Cheng Wang, Shufen Wang, Xiaoming Wang, Steven M. Wise

Mathematics and Statistics Faculty Research & Creative Works

We present and analyze a uniquely solvable and unconditionally energy stable numerical scheme for the ternary Cahn-Hilliard system, with a polynomial pattern nonlinear free energy expansion. One key difficulty is associated with presence of the three mass components, though a total mass constraint reduces this to two components. Another numerical challenge is to ensure the energy stability for the nonlinear energy functional in the mixed product form, which turns out to be non-convex, non-concave in the three-phase space. to overcome this subtle difficulty, we add a few auxiliary terms to make the combined energy functional convex in the three-phase space, …

Why Cutting Trajectories Into Small Pieces Helps To Learn Dynamical Systems Better: A Seemingly Counterintuitive Empirical Result Explained, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In general, the more information we use in machine learning, the more accurate predictions we get. However, recently, it was observed that for prediction of the behavior of dynamical systems, the opposite effect happens: when we replace the original trajectories with shorter pieces -- thus ignoring the information about the system's long-term behavior -- the accuracy of machine learning predictions actually increases. In this paper, we provide an explanation for this seemingly counterintuitive result.

A 3d Image-Guided System To Improve Myocardial Revascularization Decision-Making For Patients With Coronary Artery Disease, Haipeng Tang

Dissertations

OBJECTIVES. Coronary artery disease (CAD) is the most common type of heart disease and kills over 360,000 people a year in the United States. Myocardial revascularization (MR) is a standard interventional treatment for patients with stable CAD. Fluoroscopy angiography is real-time anatomical imaging and routinely used to guide MR by visually estimating the percent stenosis of coronary arteries. However, a lot of patients do not benefit from the anatomical information-guided MR without functional testing. Single-photon emission computed tomography (SPECT) myocardial perfusion imaging (MPI) is a widely used functional testing for CAD evaluation but limits to the absence of anatomical information. …

Why 3d Fragmentation Usually Leads To Cuboids: A Simple Geometric Explanation, Laxman Bokati, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

It has been empirically observed that the average shape of natural fragmentation results -- such as natural rock fragments -- is a distorted cube (known as cuboid). Recently, a complex explanation was provides for this empirical fact. In this paper, we propose a simple geometry-based physical explanation for the ubiquity of cuboid fragments.

Two Runners In The Time Of Social Distancing, Speedboats In The Gulf Of Finland: How To Best Pass?, Julio Urenda, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

If two runners follow the same running path, what is the best trajectory for the faster runner to pass the slower one, taking into account that they should always maintain a prescribed social distance? If a speedboat wants to pass a slower ship following a special canal in the Gulf of Finland, what is the best trajectory? In this paper, we provide answers to both questions.

New Development Of Grid Generation And Image Analysis, Ben Hildebrand

Mathematics Dissertations - Archive

Image segmentation and registration are indispensable tools for the aid in medical diagnoses by experts. The current gold-standard for image segmentation is manual labeling of pixels by experts which is cumbersome and inefficient. In a paper by Zhu et. al. grids are generated through the deformation method for grid generation and differential properties of these grids are used in a deep learning algorithm for image segmentation. In this dissertation, we develop a new method for generating grid images based on the Variational Method. This new grid generation method generates grids based on image pixel intensities which improves upon the deformation …

Analyzing The Fractal Dimension Of Various Musical Pieces, Nathan Clark

Industrial Engineering Undergraduate Honors Theses

One of the most common tools for evaluating data is regression. This technique, widely used by industrial engineers, explores linear relationships between predictors and the response. Each observation of the response is a fixed linear combination of the predictors with an added error element. The method is built on the assumption that this error is normally distributed across all observations and has a mean of zero. In some cases, it has been found that the inherent variation is not the result of a random variable, but is instead the result of self-symmetric properties of the observations. For data with these …

Asymptotic Normality Of The Deconvolution Kernel Density Estimators Based On Independent As Well As Strong Mixing Right Censored Data, Wenqing Zhu

Mathematics Dissertations - Archive

We consider estimation of a density when observed lifetime from the convolution model contaminated by additive measurement errors. A kernel type deconvolution density estimator of the unknown distribution based on right censored data is proposed by using the Inverse-Probability-of-Censoring Weighted Average. Further, we discuss the asymptotic normality of the deconvolution kernel density estimators for independent and strong mixing vectors when the error distribution function is either ordinary smooth or supersmooth. Our method is applied to the study conducted by UTSW medical center. The research team at UTSW collected the data of women who underwent cystoscopy fulguration for recurrent urinary tract …

Inverse Problems And Forward Propagation Of Optical Flow, John Montalbo

Mathematics Dissertations - Archive

Optical flow is a concept originally introduced in computer vision that quantifies, and aids in the presentation of, motion (flow field) between two or more images. In essence, it is a solution of an inverse problem recovering a vector field between images through optimization techniques. This work studies the possibility of using optical flow and various techniques of forward propagation of the recovered flow field for a pair of image processing tasks in magnetic resonance imaging (MRI). It is shown that the proposed framework can be efficient in approximating missing image layers, as well as in generation of deliberately modified …

Some Examples Of The Liouville Integrability Of The Banded Toda Flows, Zachary Youmans

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The Toda lattice is a famous integrable system studied by Toda in the 1960s. One can study the Toda lattice using a matrix representation of the system. Previous results have shown that this matrix of dimension n with 1 band and n‚àí1 bands is Liouville integrable. In this paper, we lay the foundation for proving the general case of the Toda lattice, where we consider the matrix representation with dimension n and a partially filled lower triangular part. We call this the banded Toda flow. The main theorem is that the banded Toda flow up to dimension 10 is …

Likelihood Inference For Flexible Cure Rate Models In The Context Of Infectious Diseases With Multiple Exposures, Zachry Joseph Engel

Mathematics Dissertations - Archive

Cure rate models are mostly used to study data arising from cancer clinical trials. Its use in the context of infectious diseases has not been explored well. In 2007, Tournoud and Ecochard rst proposed a mechanistic formulation of cure rate model in the context of infectious diseases with multiple exposures to infection. However, they assumed a simple Poisson distribution to capture the unobserved number of pathogens at each exposure time. In this thesis, we propose a new exible cure rate model to study infectious diseases with discrete multiple exposures to infection. This new model uses the Conway-Maxwell Poisson (COM-Poisson) distribution …

Article The Singular Value Expansion For Arbitrary Bounded Linear Operators, Daniel K. Crane, Mark S. Gockenbach

Michigan Tech Publications, Part 1

The singular value decomposition (SVD) is a basic tool for analyzing matrices. Regarding a general matrix as defining a linear operator and choosing appropriate orthonormal bases for the domain and co-domain allows the operator to be represented as multiplication by a diagonal matrix. It is well known that the SVD extends naturally to a compact linear operator mapping one Hilbert space to another; the resulting representation is known as the singular value expansion (SVE). It is less well known that a general bounded linear operator defined on Hilbert spaces also has a singular value expansion. This SVE allows a simple …

Math Active Learning Lab: Math 103 College Algebra Notebook, Gwennie Byron, Department Of Mathematics, University Of North Dakota

Open Educational Resources

This course notebook has been designed for students of Math 103 (College Algebra) at the University of North Dakota. It has been designed to help you get the most out of the ALEKS resources and your time.

• Topics in the Notebook are organized by weekly learning module.
• Space for notes from ALEKS learning pages, e-book and videos directs you to essential concepts.
• Examples and “You Try It” problems have been carefully chosen to help you focus on these essential concepts.
• Completed Notebook is an invaluable tool when studying for exams.

Bounds For The Number Of Independent And Dominating Sets In Trees, Daniel K. Arabia

Theses, Dissertations and Culminating Projects

In this work, we investigate bounds on the number of independent sets in a graph and its complement, along with the corresponding question for number of dominating sets. Nordhaus and Gaddum gave bounds on χ(G)+χ(G) and χ(G) χ(G), where G is any graph on n vertices and χ(G) is the chromatic number of G. Nordhaus-Gaddum- type inequalities have been studied for many other graph invariants. In this work, we concentrate on i(G), the number of independent sets in G, and ∂(G), the number of dominating sets in G. We focus our attention on Nordhaus-Gaddum-type inequalities over trees on a fixed …

A Community Of Learning In An Elementary School Mathematics Classroom, Megan Louise Roeder

Theses, Dissertations and Culminating Projects

The goal of this study was to investigate opportunities for cultivating a community of learning in an elementary school mathematics classroom using four guiding principles for productive disciplinary engagement. A community of learning involves teachers and students participating equally in negotiating, sharing, and producing knowledge as co-learners, coteachers, and co-collaborators in the classroom. Characteristics of a community of learning align with effective teaching and learning practices described by national governing bodies and researchers in the field of mathematics education. The essence of a community of learning is beneficial in an elementary mathematics classroom because it invokes deep learning about disciplinary …

The Role Of Covariational Reasoning In Pre-Service Teachers’ Meanings For Quadratic And Exponential Relationships, Madhavi Vishnubhotla

Theses, Dissertations and Culminating Projects

Researchers have indicated that students have difficulties recognizing quadratic and exponential change and do not maintain productive meanings for these relationships. Other researchers have documented that students are capable of developing productive meanings for mathematical ideas via covariational reasoning. This dissertation reports the results of an investigation into ways in which preservice teachers can leverage covariational reasoning to develop meanings for quadratic and exponential relationships. I collected data by engaging two preservice teachers in semi-structured clinical interviews and a semester long teaching experiment. My analyses reveal that whereas in the pre-interviews, the participants did not have meanings that supported differentiating …

Optimizing L1 Loss Regularizer And Its Application To Eeg Inverse Problem, Kiran Kumar Mainali

Mathematics Dissertations - Archive

Sparse reconstruction occurs frequently in science and engineering and real-world applications, including statistics, finance, imaging, biological system, compressed sensing, and, today more than ever, machine learning and data science in general. Mathematically, they are often modeled as l1-minimization problems. There are a number of existing numerical methods that can efficiently solve such l1-minimization problems, such as Alternating Direction Methods of Multipliers (ADMM), Fast Iterative Shrinkage Thresholding Algorithm (FISTA), and Homotopy algorithm. In this dissertation, we will introduce a special type of l1-minimization problem called the Sylvester Least Absolute Shrinkage and Selection Operator (SLASSO) problem. In theory, an SLASSO problem can …

Mathematical Modeling Of Scavengers And Zebras On The African Savanna With Disease Dynamics, Crystal Dawn Mackey

Mathematics Dissertations - Archive

The purpose of this dissertation is to use mathematical models to see how anthrax in the zebra population in Etosha National Park (ENP) interacts with scavenger populations and disease dynamics. First, we study if scavengers can save zebras from anthrax. Then we introduce a disease in the jackal population to see if anthrax in zebras can help propagate rabies in jackals. Finally, the last two models we develop describe the interaction between competing scavengers: jackals and vultures, with exploitative and interference competition. ENP is home to many different animals such as lions, jackals, hyenas, zebras, elephants, etc. Each year grazing …

Optimal Bandwidth Selection For Deconvoluted Kernel Density Estimation Using Bootstrap Method, Souad Sosa

Mathematics Dissertations - Archive

To estimate an unknown density when observed measurements are from the convolution model contaminated by additive measurement errors, Stefanski and Carroll (1990) proposed using Fourier inversion on the product of Fourier transform of a kernel function and the characteristic function of the error variable. One important element in constructing such a density estimator is the bandwidth. The goal of this research is to establish an optimal bandwidth so that the mean integrated squared error of the estimator is minimized. The bootstrap method is used to accomplish this goal. The simulation results show that the estimated optimal bandwidths provide adequate estimation …