Statistics and Probability Commons^™

On The Occurrences Of Motifs In Recursive Trees, With Applications To Random Structures, Mohan Gopaladesikan

Open Access Dissertations

In this dissertation we study three problems related to motifs and recursive trees. In the first problem we consider a collection of uncorrelated motifs and their occurrences on the fringe of random recursive trees. We compute the exact mean and variance of the multivariate random vector of the counts of occurrences of the motifs. We further use the Cramér-Wold device and the contraction method to show an asymptotic convergence in distribution to a multivariate normal random variable with this mean and variance. ^ The second problem we study is that of the probability that a collection of motifs (of the …

Exploring The Relationship Between K-8 Prospective Teachers’ Algebraic Thinking Proficiency And The Questions They Pose During Diagnostic Algebraic Thinking Interviews, Leigh A. Van Den Kieboom, Marta T. Magiera, John C. Moyer

Mathematics, Statistics and Computer Science Faculty Research and Publications

In this study, we explored the relationship between prospective teachers’ algebraic thinking and the questions they posed during one-on-one diagnostic interviews that focused on investigating the algebraic thinking of middle school students. To do so, we evaluated prospective teachers’ algebraic thinking proficiency across 125 algebra-based tasks and we analyzed the characteristics of questions they posed during the interviews. We found that prospective teachers with lower algebraic thinking proficiency did not ask any probing questions. Instead, they either posed questions that simply accepted and affirmed student responses or posed questions that guided the students toward an answer without probing student thinking. …

Relatively Congruence-Free Regular Semigroups, Peter R. Jones

Mathematics, Statistics and Computer Science Faculty Research and Publications

Yu, Wang, Wu and Ye call a semigroup S τ -congruence-free, where τ is an equivalence relation on S, if any congruence ρ on S is either disjoint from τ or contains τ . A congruence-free semigroup is then just an ω-congruence-free semigroup, where ω is the universal relation. They determined the completely regular semigroups that are τ -congruence-free with respect to each of the Green’s relations. The goal of this paper is to extend their results to all regular semigroups. Such a semigroup is J –congruence-free if and only if it is either a semilattice or has …

Generalized Exponentiated Moment Exponential Distribution, Zafar Iqbal, Syed Anwer Hasnain, Muhammad Salman, Munir Ahmad, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Moment distributions have a vital role in mathematics and statistics, in particular in probability theory, in the perspective research related to ecology, reliability, biomedical field, econometrics, survey sampling and in life-testing. Hasnain (2013) developed an exponentiated moment exponential (EME) distribution and discussed some of its important properties. In the present work, we propose a generalization of EME distribution which we call it generalized EME (GEME) distribution and develop various properties of the distribution. We also present characterizations of the distribution in terms of conditional expectation as well as based on hazard function of the GEME random variable.

Some Remarks On Recent Characterizations Of Continuous Distributions, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

We would closely look at two recent published papers dealing with characterizations of certain univariate continuous distributions. We shall explain that the main results reported lack important assumptions. These results nevertheless are based on the conditional expectations of monotone functions of the generalized order statistics. We will also mention that similar results have recently been reported without the assumption of monotonicity of the functions of the generalized order statistics.

On Second Order Elliptic Equations And Variational Inequalities With Anisotropic Principal Operators, Vy Khoi Le

Mathematics and Statistics Faculty Research & Creative Works

This paper is about boundary value problems of the form where ƨ is a convex function of ξ.∈ RN rather than a function of the norm|ξ|. The problem is formulated appropriately in an anisotropic Orlicz-Sobolev space associated with ƨ. We study the existence of solutions and some other properties of the above problem and its corresponding variational inequality in such space.

Generalized Least-Squares Regressions Iv: Theory And Classification Using Generalized Means, Nataniel Greene

Publications and Research

The theory of generalized least-squares is reformulated here using the notion of generalized means. The generalized least-squares problem seeks a line which minimizes the average generalized mean of the square deviations in x and y. The notion of a generalized mean is equivalent to the generating function concept of the previous papers but allows for a more robust understanding and has an already existing literature. Generalized means are applied to the task of constructing more examples, simplifying the theory, and further classifying generalized least-squares regressions.

Characterizations Of A Class Of Distributions By Dual Generalized Order Statistics And Truncated Moments, Filippo Domma, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

The problem of characterizing a distribution is an important problem which has recently attracted the attention of many researchers. Thus, various characterizations have been established in many different directions. The present work deals with the characterizations of a general class of distributions. These characterizations are based on: (i) a simple relationship between two truncated moments, (ii) truncated moment of certain functions of the nth order statistic, (iii) single truncated moment of certain functions of the random variable and (iv) moments of dual generalized order statistics.We like to mention that the characterization (i) which is expressed in terms of the ratio …

Existence Of Disjoint Weakly Mixing Operators That Fail To Satisfy The Disjoint Hypercyclicity Criterion, Rebecca Sanders, Stanislav Shkarin

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

Pharyngeal And Cervical Cancer Incidences Significantly Correlate With Personal Uv Doses Among Whites In The United States, Dianne E. Godar, Rong Tang, Stephen Merrill

Mathematics, Statistics and Computer Science Faculty Research and Publications

Because we found UV-exposed oral tissue cells have reduced DNA repair and apoptotic cell death compared with skin tissue cells, we asked if a correlation existed between personal UV dose and the incidences of oral and pharyngeal cancer in the United States. We analyzed the International Agency for Research on Cancer's incidence data for oral and pharyngeal cancers by race (white and black) and sex using each state's average annual personal UV dose. We refer to our data as ‘white’ rather than ‘Caucasian,’ which is a specific subgroup of whites, and ‘black’ rather than African-American because blacks from other countries …

Towards A Lightweight Approach For Modding Serious Educational Games: Assisting Novice Designers, Jacob Dahleen, Alex Hunsberger, Ryan Weber, Dennis Brylow, C. Shaun Longstreet, Kendra M. L. Cooper

Mathematics, Statistics and Computer Science Faculty Research and Publications

Serious educational games (SEGs) are a growing segment of the education community’s pedagogical toolbox. Effectively creating such games remains challenging, as teachers and industry trainers are content experts; typically they are not game designers with the theoretical knowledge and practical experience needed to create a quality SEG. Here, a lightweight approach to interactively explore and modify existing SEGs is introduced, a toll that can be broadly adopted by educators for pedagogically sound SEGs. Novice game designers can rapidly explore the educational and traditional elements of a game, with a stress on tracking the SEG learning objectives, as well as allowing …

Choosing Between Parametric And Non-Parametric Tests, Russ Johnson

Journal of Undergraduate Research at Minnesota State University, Mankato

A common question in comparing two sets of measurements is whether to use a parametric testing procedure or a non-parametric procedure. The question is even more important in dealing with smaller samples. Here, using simulation, several parametric and nonparametric tests, such as, t-test, Normal test, Wilcoxon Rank Sum test, van-der Waerden Score test, and Exponential Score test are compared.

Spatiotemporal Crime Analysis, James Q. Tay, Abish Malik, Sherry Towers, David Ebert

The Summer Undergraduate Research Fellowship (SURF) Symposium

There has been a rise in the use of visual analytic techniques to create interactive predictive environments in a range of different applications. These tools help the user sift through massive amounts of data, presenting most useful results in a visual context and enabling the person to rapidly form proactive strategies. In this paper, we present one such visual analytic environment that uses historical crime data to predict future occurrences of crimes, both geographically and temporally. Due to the complexity of this analysis, it is necessary to find an appropriate statistical method for correlative analysis of spatiotemporal data, as well …

Light Pollution Research Through Citizen Science, John Kanemoto

STAR Program Research Presentations

Light pollution (LP) can disrupt and/or degrade the health of all living things, as well as, their environments. The goal of my research at the NOAO was to check the accuracy of the citizen science LP reporting systems entitled: Globe at Night (GaN), Dark Sky Meter (DSM), and Loss of the Night (LoN). On the GaN webpage, the darkness of the night sky (DotNS) is reported by selecting a magnitude chart. Each magnitude chart has a different density/number of stars around a specific constellation. The greater number of stars implies a darker night sky. Within the DSM iPhone application, a …

Reduced Major Axis Regression: Teaching Alternatives To Least Squares, William V. Harper

Mathematics Faculty Scholarship

The theoretical underpinnings of standard least squares regression analysis are based on the assumption that the independent variable (often thought of as x) is measured without error as a design variable. The dependent variable (often labeled y) is modeled as having uncertainty or error. Both independent and dependent measurements may have multiple sources of error. Thus the underlying least squares regression assumptions can be violated. Reduced Major Axis (RMA) regression is specifically formulated to handle errors in both the x and y variables. It is an excellent topic to teach students the importance of understanding the assumptions underlying the statistical …

What Is Higher Mathematics? Why Is It So Hard To Interpret? What Can Be Done?, John Tabak

Journal of Interpretation

Courses and seminars in higher mathematics are some of the most challenging assignments faced by academic interpreters. Difficulties interpreting higher mathematics can adversely impact the academic and professional aspirations of deaf mathematics students and professionals. This paper discusses the nature of higher mathematics with the goal of identifying what distinguishes higher mathematics from other subjects; it then reviews the history of attempts to sign/interpret higher mathematics with particular attention to current challenges associated with expressing higher mathematics in sign. The final part of the paper discusses strategies for more effectively expressing higher mathematics in American Sign Language.

Improvements On Segment Based Contours Method For Dna Microarray Image Segmentation, Yang Li

Doctoral Dissertations

DNA microarray is an efficient biotechnology tool for scientists to measure the expression levels of large numbers of genes, simultaneously. To obtain the gene expression, microarray image analysis needs to be conducted. Microarray image segmentation is a fundamental step in the microarray analysis process. Segmentation gives the intensities of each probe spot in the array image, and those intensities are used to calculate the gene expression in subsequent analysis procedures. Therefore, more accurate and efficient microarray image segmentation methods are being pursued all the time.

In this dissertation, we are making efforts to obtain more accurate image segmentation results. We …

Better Physical Activity Classification Using Smartphone Acceleration Sensor, Muhammad Arif, Mohsin Bilal, Ahmed Kattan, Sheikh Iqbal Ahamed

Mathematics, Statistics and Computer Science Faculty Research and Publications

Obesity is becoming one of the serious problems for the health of worldwide population. Social interactions on mobile phones and computers via internet through social e-networks are one of the major causes of lack of physical activities. For the health specialist, it is important to track the record of physical activities of the obese or overweight patients to supervise weight loss control. In this study, acceleration sensor present in the smartphone is used to monitor the physical activity of the user. Physical activities including Walking, Jogging, Sitting, Standing, Walking upstairs and Walking downstairs are classified. Time domain features are extracted …

Stochastic Modeling And Analysis Of Energy Commodity Spot Price Processes, Olusegun Michael Otunuga

USF Tampa Graduate Theses and Dissertations

Supply and demand in the World oil market are balanced through responses to price movement with considerable complexity in the evolution of underlying supply-demand

expectation process. In order to be able to understand the price balancing process, it is important to know the economic forces and the behavior of energy commodity spot price processes. The relationship between the different energy sources and its utility together with uncertainty also play a role in many important energy issues.

The qualitative and quantitative behavior of energy commodities in which the trend in price of one commodity coincides with the trend in price of …

Extreme Self-Adjoint Extensions Of A Semibounded Q-Difference Operator, Miron B. Bekker, Martin Bohner, Hristo Voulov

Mathematics and Statistics Faculty Research & Creative Works

For a certain q-difference operator introduced and studied in a series of articles by the same authors, we investigate its extreme self-adjoint extensions, i.e., the so-called Friedrichs and Kreǐn extensions. We show that for the interval of parameters under consideration, the Friedrichs extension and the Kreǐn extension are distinct and give values of the parameter in the von Neumann formulas that correspond to those extensions and describe their resolvent operators. A crucial role in our investigation plays the fact that both the Friedrichs and the Kreǐn extensions are scale invariant. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

The Inferred Cardiogenic Gene Regulatory Network In The Mammalian Heart, Jason Bazil, Karl D. Stamm, Xing Li, Raghuram Thiagarajan, Timonthy J. Nelson, Aoy Tomita-Mitchell, Daniel A. Beard

Mathematics, Statistics and Computer Science Faculty Research and Publications

Cardiac development is a complex, multiscale process encompassing cell fate adoption, differentiation and morphogenesis. To elucidate pathways underlying this process, a recently developed algorithm to reverse engineer gene regulatory networks was applied to time-course microarray data obtained from the developing mouse heart. Approximately 200 genes of interest were input into the algorithm to generate putative network topologies that are capable of explaining the experimental data via model simulation. To cull specious network interactions, thousands of putative networks are merged and filtered to generate scale-free, hierarchical networks that are statistically significant and biologically relevant. The networks are validated with known gene …

A New Adjustment Of Laplace Transform For Fractional Bloch Equation In Nmr Flow, Sunil Kumar, Devendra Kumar, U. S. Mahabaleshwar

Applications and Applied Mathematics: An International Journal (AAM)

This work purpose suggest a new analytical technique called the fractional homotopy analysis transform method (FHATM) for solving time fractional Bloch NMR (nuclear magnetic resonance) flow equations, which are a set of macroscopic equations that are used for modeling nuclear magnetization as a function of time. The true beauty of this article is the coupling of the homotopy analysis method and the Laplace transform method for systems of fractional differential equations. The solutions obtained by the proposed method indicate that the approach is easy to implement and computationally very attractive.

Beta Burr Xii Or Five Parameter Beta Lomax Distribution: Remarks And Characterizations, Z. Javanshiri, Mehdi Maadooliat

Mathematics, Statistics and Computer Science Faculty Research and Publications

The distributions taken up in two recently published papers are compared and certain characterizations of them are presented. These characterizations are based on: (i) a simple relationship between two truncated moments; (ii) truncated moments of certain functions of the nth order statistic; (iii) truncated moments of certain functions of the random variable.

Regularized Multivariate Regression Models With Skew-T Error Distributions, Lianfu Chen, Mohsen Pourahmadi, Mehdi Maadooliat

Mathematics, Statistics and Computer Science Faculty Research and Publications

We consider regularization of the parameters in multivariate linear regression models with the errors having a multivariate skew-t distribution. An iterative penalized likelihood procedure is proposed for constructing sparse estimators of both the regression coefficient and inverse scale matrices simultaneously. The sparsity is introduced through penalizing the negative log-likelihood by adding L₁-penalties on the entries of the two matrices. Taking advantage of the hierarchical representation of skew-t distributions, and using the expectation conditional maximization (ECM) algorithm, we reduce the problem to penalized normal likelihood and develop a procedure to minimize the ensuing objective function. Using a …

Counting Independent Sets Of A Fixed Size In Graphs With Given Minimum Degree, John Engbers, David Galvin

Mathematics, Statistics and Computer Science Faculty Research and Publications

Galvin showed that for all fixed δ and sufficiently large n, the n-vertex graph with minimum degree δ that admits the most independent sets is the complete bipartite graph . He conjectured that except perhaps for some small values of t, the same graph yields the maximum count of independent sets of size t for each possible t. Evidence for this conjecture was recently provided by Alexander, Cutler, and Mink, who showed that for all triples with , no n-vertex bipartite graph with minimum degree δ admits more independent sets of size t than . …

Ranking World Class Chess Players Using Only Results From Head-To-Head Games, Sterling Swygert

Senior Theses

This honors thesis explores a method of ranking the world’s top ten chess grand- masters using only the outcomes of games containing only players in that very set. This method allows for players in a single era to be quickly ranked via algorithmic and numerical means, including very specific information, from a statistical stand- point. Furthermore, unlike the rating systems that are commonly used, the Elo and the Glicko systems, this method is Classicist in its statistical approach, rather than Bayesian. Finally, this ranking method also differs from others as it limits the infor- mation to games between the individuals …

Surface Reconstruction Using Differential Invariant Signatures, Sophors Khut

Mathematics, Statistics, and Computer Science Honors Projects

This thesis addresses the problem of reassembling a broken surface. Three di- mensional curve matching is used to determine shared edges of broken pieces. In practice, these pieces may have different orientation and position in space, so edges cannot be directly compared. Instead, a differential invariant signature is used to make the comparison. A similarity score between edge signatures determines if two pieces share an edge. The Procrustes algorithm is applied to find the translations and rotations that best fit shared edges. The method is implemented in Matlab, and tested on a broken spherical surface.

Hurdle Models And Age Effects In The Major League Baseball Draft, Justin Sims

Mathematics, Statistics, and Computer Science Honors Projects

Major League Baseball (MLB) franchises expend an abundance of resources on scouting in preparation for the June Amateur Draft. In addition to the classic "tools" assessed, another factor considered is age: younger players may get selected over older players of equal ability because of anticipated development, whereas college players may get selected over high school players due to a shortened latency before reaching the majors. Additionally, Little League rules in effect until 2006 operated on an August 1-July 31 year, meaning that, in their youth, players born on August 1 were the eldest relative to their cohort. We examine the …

Parallel Design Patterns And Program Performance, Yu Zhao

Mathematics, Statistics, and Computer Science Honors Projects

With the rapid advancement of parallel and distributed computing (PDC), three types of hardware and their corresponding software (hardware-software pairs) are becoming more and more popular: Distributed Memory Systems with the Message Passing Interface (MPI) library, Shared Memory Systems with the OpenMP library and Co-processor Systems with a general purpose parallel computing library. Alongside the development of both hardware and software aspects of PDC, the process of designing parallel programs has also improved significantly over the years. A consequence of this is that researchers have been able to describe many parallel design patterns, which are recurring solutions to well-known problems …

Oscillation Theorems For Fourth-Order Half-Linear Delay Dynamic Equations With Damping, Ravi P. Agarwal, Martin Bohner, Tongxing Li, Chenghui Zhang

Mathematics and Statistics Faculty Research & Creative Works

This article is concerned with oscillatory behavior of a class of fourth-order half-linear delay dynamic equations with damping on a time scale. Some new oscillation criteria are established. © 2013 Springer Basel.