Mathematics Commons^™

Developing Preservice Teachers’ Mathematical And Pedagogical Knowledge Using An Integrated Approach, Marta Magiera, Leigh A. Van Den Kieboom

Mathematics, Statistics and Computer Science Faculty Research and Publications

This paper describes how an integrated mathematics content and early field-experience course provides opportunities for preservice elementary teachers to develop understanding of mathematics and mathematics teaching. Engaging preservice teachers in solving and discussing mathematical tasks and providing opportunities to implement these tasks with elementary students creates an authentic context for the future teachers to reflect on their own understanding of mathematics, mathematics teaching, and students’ mathematical thinking. Essential elements of the cycle of events in the integrated model of instruction are discussed: preservice students’ acquisition of mathematical concepts in the context of selected tasks in the content course; subsequent posing …

Cnareporter: A Computational Tool For The Generation Of Clinical Reports Of Genomic Alterations, Yuri Kotliarov, Serdar Bozdag, Hangjiong Cheng, Stefan Wuchty, Jean-Claude Zenklusen, Howard A. Fine

Mathematics, Statistics and Computer Science Faculty Research and Publications

Background: Genomic copy number alterations are widely associated with a broad range of human tumors and offer the potential to be used as a diagnostic tool. Especially in the emerging era of personalized medicine medical informatics tools that allow the fast visualization and analysis of genomic alterations of a patient's genomic profile for diagnostic and potential treatment purposes increasingly gain importance. Results: We developed CNAReporter, a software tool that allows users to visualize SNP-specific data obtained from Affymetrix arrays and generate PDF-reports as output. We combined standard algorithms for the analysis of chromosomal alterations, utilizing the widely applied GenePattern framework. …

Character Degrees Of Normally Monomial Maximal Class 5-Groups, Michael Slattery

Mathematics, Statistics and Computer Science Faculty Research and Publications

This paper will impose limits on the possible sets of irreducible character degrees of a normally monomial 5-group of maximal class.

Linearly Ordered Topological Spaces And Weak Domain Representability, Joe Mashburn

Mathematics Faculty Publications

It is well known that domain representable spaces, that is topological spaces that are homeomorphic to the space of maximal elements of some domain, must be Baire. In this paper it is shown that every linearly ordered topological space (LOTS) is homeomorphic to an open dense subset of a weak domain representable space. This means that weak domain representable spaces need not be Baire.

Coarsening In High Order, Discrete, Ill-Posed Diffusion Equations, Catherine Kublik

Mathematics Faculty Publications

We study the discrete version of a family of ill-posed, nonlinear diffusion equations of order 2n. The fourth order (n=2) version of these equations constitutes our main motivation, as it appears prominently in image processing and computer vision literature. It was proposed by You and Kaveh as a model for denoising images while maintaining sharp object boundaries (edges). The second order equation (n=1) corresponds to another famous model from image processing, namely Perona and Malik's anisotropic diffusion, and was studied in earlier papers. The equations studied in this paper are high order analogues of the Perona-Malik equation, and like the …

Gliomapredict: A Clinically Useful Tool For Assigning Glioma Patients To Specific Molecular Subtypes, Aiguo Li, Serdar Bozdag, Yuri Kotliarov, Howard A. Fine

Mathematics, Statistics and Computer Science Faculty Research and Publications

Background: Advances in generating genome-wide gene expression data have accelerated the development of molecular-based tumor classification systems. Tools that allow the translation of such molecular classification schemas from research into clinical applications are still missing in the emerging era of personalized medicine.

Results: We developed GliomaPredict as a computational tool that allows the fast and reliable classification of glioma patients into one of six previously published stratified subtypes based on sets of extensively validated classifiers derived from hundreds of glioma transcriptomic profiles. Our tool utilizes a principle component analysis (PCA)-based approach to generate a visual representation of the analyses, quantifies …

Numerical Solution Of The Five-Moment Ideal Two-Fluid Equations In One Dimension, Marcus Scott

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

Plasmas are frequently treated as a single conducting fluid and modeled using the equations of magnetohydrodynamics. However, this regime works better for low-frequency plasmas. High-frequency plasmas may be modeled using the principles of kinetic theory. For plasmas with frequencies between these two extremes, a two-fluid approach can yield better results. In 2006, Ammar Hakim mathematically modeled a plasma with a set of equations called the five-moment ideal two-fluid equations. An attempt is made reproduce those results. A derivation of this set of equations by taking moments of the Boltzmann equation is presented. Electric and magnetic fields contribute to the source …

Assessment Of Utah Bankruptcies By Census Tracts: A Spatial Statistical Approach, Kenneth Pena

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

There are two questions raised when looking at the spatial pattern of the rate of bankruptcies in Utah: (i) are there similarities between the bankruptcy data in adjacent census tracts and (ii) can local cluster and outliers be identified within the data? Specifically, are there similar rates of bankruptcies in bordering census tracts and are there any localized areas of interest where we find extremely high or extremely low rates of bankruptcies? This study uses spatial statistics to perform tests for spatial autocorrelation to address these two questions. It also looks at commonalities in the clusters and differences in the …

Statistical Analysis Of Wastewater Remediation And Bio-Fuels Production Of Algae, Jay D. Jones

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

The Logan city wastewater treatment system consists of a series of seven large aerated ponds (460 acres) that biologically treats 15 million gallons per day of wastewater from Logan city and six other communities. Tighter regulations of allowed phosphorus levels in the effluent have recently been implemented due to environmental concerns of a downstream reservoir. The Biological Engineering program at Utah State University, the Bio-fuels Center, the Utah Water Research Laboratory (UWRL) and the city of Logan are working together to remediate the wastewater treatment system using microalgae. Algal growth requires the uptake of phosphorus. Thus, phosphorus in the effluent …

A Comparison Of Prediction Methods Of Functional Autoregressive Time Series, Devin Didericksen

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

Functional data analysis (FDA) is a relatively new branch of statistics that has seen a lot of expansion recently. With the advent of computer processing power and more efficient software packages we have entered the beginning stages of applying FDA methodology and techniques to data. Part of this undertaking should include an empirical assessment of the effectiveness of some of the tools of FDA, which are sound on theoretical grounds. In a small way, this project helps advance this objective.

This work begins by introducing FDA, scalar prediction techniques, and the functional autoregressive model of order one - FAR(1). Two …

Assessing The Precision And Accuracy In A Small Sample Of Actical Devices, Peter Sherick

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

Actigraphy is an increasingly popular approach in medicine to assess patient activity levels in a variety of scenarios. The devices are essentially accelerometers encased in a write-watch type assembly. This project sought to determine the device precision and accuracy for the Actical model. In a sample of four Acticals, it was found that intra-device variability was minimal. However, one device was found to be statistically biased in comparison to the other three. This bias could have adverse effects on aggregated or magnitude dependent data analysis. Also, inter-device comparisons may be problematic.

Analysis Of Models For Longitudinal And Clustered Binary Data, Weiming Yang

Mathematics & Statistics Theses & Dissertations

This dissertation deals with modeling and statistical analysis of longitudinal and clustered binary data. Such data consists of observations on a dichotomous response variable generated from multiple time or cluster points, that exhibit either decaying correlation or equi-correlated dependence. The current literature addresses modeling the dependence using an appropriate correlation structure, but ignores the feasible bounds on the correlation parameter imposed by the marginal means.

The first part of this dissertation deals with two multivariate probability models, the first order Markov chain model and the multivariate probit model, that adhere to the feasible bounds on the correlation. For both the …

Analysis Of Transient Growth In Iterative Learning Control Using Pseudospectra, Douglas A. Bristow, John R. Singler

Mechanical and Aerospace Engineering Faculty Research & Creative Works

In this paper we examine the problem of transient growth in Iterative Learning Co ntrol (ILC). Transient growth is generally avoided in design by using robust monotonic convergence (RMC) criteria. However, RMC leads to fundamental performance limitations. We consider the possibility of allowing safe transient growth in ILC algorithms as a means to circumvent these limitations. Here the pseudospectra is used for the first time to study transient growth in ILC. Basic properties of the pseudospectra that are relevant to the ILC problem are presented. Two ILC design problems are considered and examined using pseduospectra. The pseudospectra provides new results …

Development And Implementation Of High-Throughput Snpgenotyping In Barley, Serdar Bozdag, Timothy J. Close, Prasanna R. Bhat, Stefano Lonardi, Yonghui Wu, Nils Rostoks, Luke Ramsay, Arnis Druka, Nils Stein, Jan T. Svensson, Steve Wanamaker, Mikeal L. Roose, Matthew J. Moscou, Shiaoman Chao, Rajeev K. Varshney, Peter Szucs, Kazuhiro Sato, Patrick M. Hayes, David E. Matthews, Andris Kleinhofs, Gary J. Muehlbauer, Joseph Deyoung, David F. Marshall, Kavitha Madishetty, Raymond D. Fenton, Pascal Condamine, Andreas Graner, Robbie Waugh

Mathematics, Statistics and Computer Science Faculty Research and Publications

Background

High density genetic maps of plants have, nearly without exception, made use of marker datasets containing missing or questionable genotype calls derived from a variety of genic and non-genic or anonymous markers, and been presented as a single linear order of genetic loci for each linkage group. The consequences of missing or erroneous data include falsely separated markers, expansion of cM distances and incorrect marker order. These imperfections are amplified in consensus maps and problematic when fine resolution is critical including comparative genome analyses and map-based cloning. Here we provide a new paradigm, a high-density consensus genetic map of …

Approximating Stationary Statistical Properties, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

It is well-known that physical laws for large chaotic dynamical systems are revealed statistically. Many times these statistical properties of the system must be approximated numerically. the main contribution of this manuscript is to provide simple and natural criterions on numerical methods (temporal and spatial discretization) that are able to capture the stationary statistical properties of the underlying dissipative chaotic dynamical systems asymptotically. the result on temporal approximation is a recent finding of the author, and the result on spatial approximation is a new one. Applications to the infinite Prandtl number model for convection and the barotropic quasi-geostrophic model are …

Using Labeled Data To Evaluate Change Detectors In A Multivariate Streaming Environment, Albert Y. Kim, Caren Marzban, Donald B. Percival, Werner Stuetzle

Statistical and Data Sciences: Faculty Publications

We consider the problem of detecting changes in a multivariate data stream. A change detector is defined by a detection algorithm and an alarm threshold. A detection algorithm maps the stream of input vectors into a univariate detection stream. The detector signals a change when the detection stream exceeds the chosen alarm threshold. We consider two aspects of the problem: (1) setting the alarm threshold and (2) measuring/comparing the performance of detection algorithms. We assume we are given a segment of the stream where changes of interest are marked. We present evidence that, without such marked training data, it might …

Forced Oscillations Of The Korteweg-De Vries Equation On A Bounded Domain And Their Stability, Muhammad Usman, Bingyu Zhang

Mathematics Faculty Publications

It has been observed in laboratory experiments that when nonlinear dispersive waves are forced periodically from one end of undisturbed stretch of the medium of propagation, the signal eventually becomes temporally periodic at each spatial point. The observation has been confirmed mathematically in the context of the damped Kortewg-de Vries (KdV) equation and the damped Benjamin-Bona-Mahony (BBM) equation. In this paper we intend to show the same results hold for the pure KdV equation (without the damping terms) posed on a bounded domain. Consideration is given to the initial-boundary-value problem

uu_xu_xxx 0 < x < 1, t > 0, (*)

It is shown …

Risk Matrix Input Data Biases, Eric D. Smith, William T. Siefert, David Drain

Engineering Management and Systems Engineering Faculty Research & Creative Works

Risk matrices used in industry characterize particular risks in terms of the likelihood of occurrence, and the consequence of the actualized risk. Human cognitive bias research led by Daniel Kahneman and Amos Tversky exposed systematic translations of objective probability and value as judged by human subjects. Applying these translations to the risk matrix allows the formation of statistical hypotheses of risk point placement biases. Industry-generated risk matrix data reveals evidence of biases in the judgment of likelihood and consequence-principally, likelihood centering, a systematic increase in consequence, and a diagonal bias. Statistical analyses are conducted with linear regression, normal distribution fitting, …

The Regular Excluded Minors For Signed-Graphic Matroids, Hongxun Qin, Dan Slilaty, Xiangqian Zhou

Mathematics and Statistics Faculty Publications

We show that the complete list of regular excluded minors for the class of signed-graphic matroids is M*(G₁),...,M*(G₂₉),R₁₅,R₁₆. Here G₁,...,G₂₉ are the vertically 2-connected excluded minors for the class of projective-planar graphs and R₁₅ and R₁₆ are two regular matroids that we will define in the article.

Design And Implementation Of S-Marks: A Secure Middleware For Pervasive Computing Applications, Sheikh Iqbal Ahamed, Haifeng Li, Nilothpal Talukder, Mehrab Monjur, Chowdhury Sharif Hasan

Mathematics, Statistics and Computer Science Faculty Research and Publications

As portable devices have become a part of our everyday life, more people are unknowingly participating in a pervasive computing environment. People engage with not a single device for a specific purpose but many devices interacting with each other in the course of ordinary activity. With such prevalence of pervasive technology, the interaction between portable devices needs to be continuous and imperceptible to device users. Pervasive computing requires a small, scalable and robust network which relies heavily on the middleware to resolve communication and security issues. In this paper, we present the design and implementation of S-MARKS which incorporates device …

The Research On Optimization Of Liner Route Between China To Middle East, Tingyi Chen

World Maritime University Dissertations

No abstract provided.

Research On Value-At-Risk In International Crude Oil Shipping Market, Xiaoyin Cui

World Maritime University Dissertations

No abstract provided.

Development Of Scoring Rubrics And Pre-Service Teachers Ability To Validate Mathematical Proofs, Timothy J. Middleton

Mathematics & Statistics ETDs

The basic aim of this exploratory research study was to determine if a specific instructional strategy, that of developing scoring rubrics within a collaborative classroom setting, could be used to improve pre-service teachers facility with proofs. During the study, which occurred in a course for secondary mathematics teachers, the primary focus was on creating and implementing a scoring rubric, rather than on direct instruction about proofs. In general, the study had very mixed results. Statistically, the quantitative data indicated no significant improvement occurred in participants' ability to validate proofs. However, the qualitative results and the considerable improvement by some participants …

A Comparison Of Balanced Truncation Methods For Closed Loop Systems, John R. Singler, Belinda A. Batten

Mathematics and Statistics Faculty Research & Creative Works

Real-time control of a physical system necessitates controllers that are low order. In this paper, we compare two balanced truncation methods as a means of designing low order compensators for partial differential equation (PDE) systems. The first method is the application of balanced truncation to the compensator dynamics, rather than the state dynamics, as was done in cite{Skelton:1984}. The second method, LQG balanced truncation, applies the balancing technique to the Riccati operators obtained from a specific LQG design. We discuss snapshot-based algorithms for constructing the reduced order compensators and present numerical results for a two dimensional convection diffusion PDE system.

On Generalized Hurwitz-Lerch Zeta Distributions, Mridula Garg, Kumkum Jain, S. L. Kalla

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we introduce a function which is an extension to the general Hurwitz-Lerch Zeta function. Having defined the incomplete generalized beta type-2 and incomplete generalized gamma functions, some differentiation formulae are established for these incomplete functions. We have introduced two new statistical distributions, termed as generalized Hurwitz-Lerch Zeta beta type-2 distribution and generalized Hurwitz-Lerch Zeta gamma distribution and then derived the expressions for the moments, distribution function, the survivor function, the hazard rate function and the mean residue life function for these distributions. Graphs for both these distributions are given, which reflect the role of shape and scale …

Bilinear Immersed Finite Elements For Interface Problems, Xiaoming He

Mathematics and Statistics Faculty Research & Creative Works

In this dissertation we discuss bilinear immersed finite elements (IFE) for solving interface problems. The related research works can be categorized into three aspects: (1) the construction of the bilinear immersed finite element spaces; (2) numerical methods based on these IFE spaces for solving interface problems; and (3) the corresponding error analysis. All of these together form a solid foundation for the bilinear IFEs.

The research on immersed finite elements is motivated by many real world applications, in which a simulation domain is often formed by several materials separated from each other by curves or surfaces while a mesh independent …

A Snapshot Algorithm For Linear Feedback Flow Control Design, Benjamin T. Dickinson, Belinda A. Batten, John R. Singler

Mathematics and Statistics Faculty Research & Creative Works

The control of fluid flows has many applications. For micro air vehicles, integrated flow control designs could enhance flight stability by mitigating the effect of destabilizing air flows in their low Reynolds number regimes. However, computing model based feedback control designs can be challenging due to high dimensional discretized flow models. In this work, we investigate the use of a snapshot algorithm proposed in Ref. 1 to approximate the feedback gain operator for a linear incompressible unsteady flow problem on a bounded domain. The main component of the algorithm is obtaining solution snapshots of certain linear flow problems. Numerical results …

Creating Multi Objective Value Functions From Non-Independent Values, Christopher D. Richards

Theses and Dissertations

Decisions are made every day and by everyone. As these decisions become more important, involve higher costs and affect a broader group of stakeholders it becomes essential to establish a more rigorous strategy than simply intuition or "going with your gut". In the past several decades, the concept of Value Focused Thinking (VFT) has gained much acclaim in assisting Decision Makers (DMs) in this very effort. By identifying and organizing what a DM values VFT is able to decompose the original problem and create a mathematical model to score and rank alternatives to be chosen. But what if the decision …

A Proper Orthogonal Decomposition Approach To Approximate Balanced Truncation Of Infinite Dimensional Linear Systems, John R. Singler, Belinda A. Batten

Mathematics and Statistics Faculty Research & Creative Works

We extend a method for approximate balanced reduced order model derivation for finite dimensional linear systems developed by Rowley (Int. J. Bifur. Chaos Appl. Sci. Eng. 15(3) (2005), pp. 997-1013) to infinite dimensional systems. The algorithm is related to standard balanced truncation, but includes aspects of the proper orthogonal decomposition in its computational approach. The method can be also applied to nonlinear systems. Numerical results are presented for a convection diffusion system.

A Berry-Esseen Theorem For Sample Quantiles Under Weak Dependence, S. N. Lahiri, Shuxia Sun

Mathematics and Statistics Faculty Publications

This paper proves a Berry-Esseen theorem for sample quantiles of strongly-mixing random variables under a polynomial mixing rate. The rate of normal approximation is shown to be O(n^-1/2) as n -> infinity, where n denotes the sample size. This result is in sharp contrast to the case of the sample mean of strongly-mixing random variables where the rate O(n^-1/2) is not known even under an exponential strong mixing rate. The main result of the paper has applications in finance and econometrics as financial time series important data often are heavy-tailed and quantile …