Mathematics Commons^™

Discrete Grüss Type Inequality On Fractional Calculus, Elvan Akin, Serkan Asliyuce, Ayse Feza Guvenilir, Billur Kaymakcalan

Mathematics and Statistics Faculty Research & Creative Works

We give a discrete Grüss type inequality on fractional calculus.

Models Describing The Sea Level Rise In Key West, Florida, Karm-Ervin Jean

FIU Electronic Theses and Dissertations

Lately, we have been noticing an unusual rise in the sea level near many Floridian cities. By 2060, scientists believe that the sea level in the city of Key West will reach between 22.86 to 60.96 centimeters (Strauss et al. 2012). The consequences of sea level rise are unpleasant by gradually tearing away our beaches and natural resources, destroying our homes and businesses, etc. Definitively, a continual increase of the sea level will affect everyone either directly or indirectly.

In this study, the sea level measurements of four Floridian coastal cities (including Key West) are collected in order to describe …

Gis-Integrated Mathematical Modeling Of Social Phenomena At Macro- And Micro- Levels—A Multivariate Geographically-Weighted Regression Model For Identifying Locations Vulnerable To Hosting Terrorist Safe-Houses: France As Case Study, Elyktra Eisman

FIU Electronic Theses and Dissertations

Adaptability and invisibility are hallmarks of modern terrorism, and keeping pace with its dynamic nature presents a serious challenge for societies throughout the world. Innovations in computer science have incorporated applied mathematics to develop a wide array of predictive models to support the variety of approaches to counterterrorism. Predictive models are usually designed to forecast the location of attacks. Although this may protect individual structures or locations, it does not reduce the threat—it merely changes the target. While predictive models dedicated to events or social relationships receive much attention where the mathematical and social science communities intersect, models dedicated to …

Reversible Peg Solitaire On Graphs, John Engbers, Christopher Stocker

Mathematics, Statistics and Computer Science Faculty Research and Publications

The game of peg solitaire on graphs was introduced by Beeler and Hoilman in 2011. In this game, pegs are initially placed on all but one vertex of a graph G. If xyz forms a path in G and there are pegs on vertices x and y but not z, then a jump places a peg on z and removes the pegs from x and y. A graph is called solvable if, for some configuration of pegs occupying all but one vertex, some sequence of jumps leaves a single peg. We study the game of reversible peg …

From Subcompact To Domain Representable, William Fleissner, Lynne Yengulalp

Mathematics Faculty Publications

No abstract provided.

The Kumaraswamy Marshal-Olkin Family Of Distributions, Morad Alizadeh, M. H. Tahir, Gauss M. Cordeiro, M. Mansoor, Muhammad Zubair, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

We introduce a new family of continuous distributions called the Kumaraswamy Marshal-Olkin generalized family of distributions. We study some mathematical properties of this family. Its density function is symmetrical, left-skewed, right-skewed and reversed-J shaped, and has constant, increasing, decreasing, upside-down bathtub, bathtub and S-shaped hazard rate. We present some special models and investigate the asymptotics and shapes of the family. We derive a power series for the quantile function and obtain explicit expressions for the moments, generating function, mean deviations, two types of entropies and order statistics. Some useful characterizations of the family are also proposed. The method of maximum …

Wright State University Math And Statistics Department History, Joanne Dombrowski, David Miller

Mathematics and Statistics Faculty Publications

No abstract provided.

Sequencing Of 15 622 Gene-Bearing Bacs Clarifies The Gene-Dense Regions Of The Barley Genome, María Muñoz-Amatriaín, Stefano Lonardi, Mingcheng Luo, Kavitha Madishetty, Jan T. Svensson, Matthew J. Moscou, Steve Wanamaker, Tao Jiang, Andris Kleinhofs, Gary J. Muehlbauer, Roger P. Wise, Nils Stein, Shane Ma, Edmundo Rodriguez, Dave Kudrna, Prasanna R. Bhat, Shiaoman Chao, Pascal Condamine, Shane Heinen, Josh Resnik, Rod Wing, Heather N. Witt, Matthew Alpert, Marco Beccuti, Serdar Bozdag, Francesca Cordero, Hamid Mirebrahim, Rachid Ounit, Yonghui Wu, Frank You, Jie Zheng, Hana Simková, Jaroslav Dolezel, Jane Grimwood, Jeremy Schmutz, Denisa Duma, Lothar Altschmied, Tom Blake, Phil Bregitzer, Laurel Cooper, Muharrem Dilbirligi, Anders Falk, Leila Feiz, Andreas Graner, Perry Gustafson, Patrick M. Hayes, Peggy Lemaux, Jafar Mammadov, Timothy J. Close

Mathematics, Statistics and Computer Science Faculty Research and Publications

Barley (Hordeum vulgare L.) possesses a large and highly repetitive genome of 5.1 Gb that has hindered the development of a complete sequence. In 2012, the International Barley Sequencing Consortium released a resource integrating whole-genome shotgun sequences with a physical and genetic framework. However, because only 6278 bacterial artificial chromosome (BACs) in the physical map were sequenced, fine structure was limited. To gain access to the gene-containing portion of the barley genome at high resolution, we identified and sequenced 15 622 BACs representing the minimal tiling path of 72 052 physical-mapped gene-bearing BACs. This generated ~1.7 Gb of genomic …

Students’ Perceptions Of And Responses To Teaching Assistant And Peer Feedback, Kelsey Joy Rodgers, Aladar K. Horvath, Hyunyi Jung, Amanda S. Fry, Heidi A. Diefes-Dux, Monica E. Cardella

Mathematics, Statistics and Computer Science Faculty Research and Publications

Authentic open-ended problems are increasingly appearing in university classrooms at all levels. Formative feedback that leads to learning and improved student work products is a challenge, particularly in large enrollment courses. This is a case study of one first-year engineering student team’s experience with teaching assistant and peer feedback during a series of open-ended mathematical modeling problems called Model-Eliciting Activities. The goal of this study was to gain deep insight into the interactions between students, feedback providers, and written feedback by examining one team’s perceptions of the feedback they received and the changes they made to their solutions based on …

The Kumaraswamy-G Poisson Family Of Distributions, Manoel Wallace A. Ramos, Pedro Rafael D. Marinho, Gauss M. Cordeiro, Ronaldo V. Da Silva, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

For any baseline continuous G distribution, we propose a new generalized family called the Kumaraswamy-G Poisson (denoted with the prefix “Kw-GP”) with three extra positive parameters. Some special distributions in the new family such as the Kw-Weibull Poisson, Kw-gamma Poisson and Kw-beta Poisson distributions are introduced. We derive some mathematical properties of the new family including the ordinary moments, generating function and order statistics. The method of maximum likelihood is used to fit the distributions in the new family. We illustrate its potentiality by means of an application to a real data set.

Concerns About Least Squares Estimation For The Three-Parameter Weibull Distribution: Case Study Of Statistical Software, William V. Harper, Thomas R. James

Mathematics Faculty Scholarship

Least Squares estimation of the 2-parameter Weibull distribution is straightforward; however, there are multiple methods for least squares estimation of the 3-parameter Weibull. The third parameter for the 3-parameter Weibull distribution shifts the origin from 0 to some generally positive value sometimes called the location, threshold, or minimum life. The different methods used by the packages result in fairly major differences in the estimated parameters between the statistical packages. This may have implications for those needing to estimate or apply the results of a 3-parameter Weibull distribution that is used frequently in practice. The results are analyzed in detail based …

Long-Time Dynamics Of 2d Double-Diffusive Convection: Analysis And/Of Numerics, Florentina Tone, Xiaoming Wang, Djoko Wirosoetisno

Mathematics and Statistics Faculty Research & Creative Works

We consider a two-dimensional model of double-diffusive convection and its time discretisation using a second-order scheme (based on backward differentiation formula for the time derivative) which treats the non-linear term explicitly. Uniform bounds on the solutions of both the continuous and discrete models are derived (under a timestep restriction for the discrete model), proving the existence of attractors and invariant measures supported on them. as a consequence, the convergence of the attractors and longtime statistical properties of the discrete model to those of the continuous one in the limit of vanishing timestep can be obtained following established methods.

Characterizations Of Levy Distribution Via Sub-Independence Of The Random Variables And Truncated Moments, Gholamhossein G. Hamedani, M. Ahsanullah, Seyed Morteza Najibi

Mathematics, Statistics and Computer Science Faculty Research and Publications

The concept of sub-independence is based on the convolution of the distributions of the random variables. It is much weaker than that of independence, but is shown to be sufficient to yield the conclusions of important theorems and results in probability and statistics. It also provides a measure of dissociation between two random variables which is much stronger than uncorrelatedness. Following Ahsanullah and Nevzorov (2014), we present certain characterizations of Levy distribution based on: (i) the sub-independence of the random variables; (ii) a simple relationship between two truncated moments; (iii) conditional expectation of certain function of the random variable. In …

Missing Photos, Suffering Withdrawal, Or Finding Freedom? How Experiences Of Social Media Non-Use Influence The Likelihood Of Reversion, Eric P.S. Baumer, Shion Guha, Emily Quan, David Mimno, Geri K. Gay

Mathematics, Statistics and Computer Science Faculty Research and Publications

This article examines social media reversion, when a user intentionally ceases using a social media site but then later resumes use of the site. We analyze a convenience sample of survey data from people who volunteered to stay off Facebook for 99 days but, in some cases, returned before that time. We conduct three separate analyses to triangulate on the phenomenon of reversion: simple quantitative predictors of reversion, factor analysis of adjectives used by respondents to describe their experiences of not using Facebook, and statistical topic analysis of free-text responses. Significant factors predicting either increased or decreased likelihood of reversion …

Thyroid Autoimmunity As A Window To Autoimmunity: An Explanation For Sex Differences In The Prevalence Of Thyroid Autoimmunity, Stephen Merrill, Ying Mu

Mathematics, Statistics and Computer Science Faculty Research and Publications

Autoimmune thyroid diseases (AITDs), predominately Graves׳ disease and Hashimoto׳s thyroiditis, comprise the most common autoimmune diseases in humans. Both have the production of anti-thyroid antibody as an important aspect and both are much more prevalent in females, being at least 10 times more common than in males. Using these two clues, a hypothesis for the initiation of thyroid autoimmunity is proposed that helps to make the case that the thyroid is one of the most sensitive sites for autoimmunity and helps account for the prevalence and the observed sex differences in AITDs and associated diseases, such as type 1 diabetes …

Free Split Bands, Francis Pastijn, Justin Albert

Mathematics, Statistics and Computer Science Faculty Research and Publications

We solve the word problem for the free objects in the variety consisting of bands with a semilattice transversal. It follows that every free band can be embedded into a band with a semilattice transversal.

Extremal H-Colorings Of Graphs With Fixed Minimum Degree, John Engbers

Mathematics, Statistics and Computer Science Faculty Research and Publications

For graphs G and H, a homomorphism from G to H, or H-coloring of G, is a map from the vertices of G to the vertices of H that preserves adjacency. When H is composed of an edge with one looped endvertex, an H-coloring of G corresponds to an independent set in G. Galvin showed that, for sufficiently large n, the complete bipartite graph Κ is the n-vertex graph with minimum degree δ that has the largest number of independent sets. In this article, we begin the project of generalizing this result …

Incorporating Relaxivities To More Accurately Reconstruct Mr Images, Muge Karaman, Iain P. Bruce, Daniel B. Rowe

Mathematics, Statistics and Computer Science Faculty Research and Publications

Purpose

To develop a mathematical model that incorporates the magnetic resonance relaxivities into the image reconstruction process in a single step.

Materials and methods

In magnetic resonance imaging, the complex-valued measurements of the acquired signal at each point in frequency space are expressed as a Fourier transformation of the proton spin density weighted by Fourier encoding anomalies: T₂^⁎, T₁, and a phase determined by magnetic field inhomogeneity (∆B) according to the MR signal equation. Such anomalies alter the expected symmetry and the signal strength of the k-space observations, resulting in images distorted …

The Minimal Zn-Symmetric Graphs That Are Not Zn-Spherical, Lowell Abrams, Dan Slilaty

Mathematics and Statistics Faculty Publications

Given a graph G equipped with faithful and fixed-point-free Γ-action (Γ a finite group) we define an orbit minor H of G to be a minor of G for which the deletion and contraction sets are closed under the Γ-action. The orbit minor H inherits a Γ-symmetry from G, and when the contraction set is acyclic the action inherited by H remains faithful and fixed-point free. When G embeds in the sphere and the Γ-action on G extends to a Γ-action on the entire sphere, we say that G is Γ-spherical. In this paper we determine for every odd value …

Boundary Problems For One And Two Dimensional Random Walks, Miky Wright

Masters Theses & Specialist Projects

This thesis provides a study of various boundary problems for one and two dimensional random walks. We first consider a one-dimensional random walk that starts at integer-valued height k > 0, with a lower boundary being the x-axis, and on each step moving downward with probability q being greater than or equal to the probability of going upward p. We derive the variance and the standard deviation of the number of steps T needed for the height to reach 0 from k, by first deriving the moment generating function of T. We then study two types of two-dimensional random walks with …

Mathematical Modeling Of Trending Topics On Twitter, Jonathan S. Skaza

Honors Projects in Mathematics

Created in 2006, Twitter is an online social networking service in which users share and read 140-character messages called Tweets. The site has approximately 288 million monthly active users who produce about 500 million Tweets per day. This study applies dynamical and statistical modeling strategies to quantify the spread of information on Twitter. Parameter estimates for the rates of infection and recovery are obtained using Bayesian Markov Chain Monte Carlo (MCMC) methods. The methodological strategy employed is an extension of techniques traditionally used in an epidemiological and biomedical context (particularly in the spread of infectious disease). This study, which addresses …

An Assessment Of The Performances Of Several Univariate Tests Of Normality, James Olusegun Adefisoye

FIU Electronic Theses and Dissertations

The importance of checking the normality assumption in most statistical procedures especially parametric tests cannot be over emphasized as the validity of the inferences drawn from such procedures usually depend on the validity of this assumption. Numerous methods have been proposed by different authors over the years, some popular and frequently used, others, not so much. This study addresses the performance of eighteen of the available tests for different sample sizes, significance levels, and for a number of symmetric and asymmetric distributions by conducting a Monte-Carlo simulation. The results showed that considerable power is not achieved for symmetric distributions when …

Integrating Data Transformation In Principal Components Analysis, Mehdi Maadooliat, Jianhua Z. Huang, Jianhua Hu

Mathematics, Statistics and Computer Science Faculty Research and Publications

Principal component analysis (PCA) is a popular dimension-reduction method to reduce the complexity and obtain the informative aspects of high-dimensional datasets. When the data distribution is skewed, data transformation is commonly used prior to applying PCA. Such transformation is usually obtained from previous studies, prior knowledge, or trial-and-error. In this work, we develop a model-based method that integrates data transformation in PCA and finds an appropriate data transformation using the maximum profile likelihood. Extensions of the method to handle functional data and missing values are also developed. Several numerical algorithms are provided for efficient computation. The proposed method is illustrated …

Analysing Student Work Involving Geometric Concepts, Hyunyi Jung

Mathematics, Statistics and Computer Science Faculty Research and Publications

Hyunyi Jung reflects on why students struggle to understand trigonometry.

Estimation Of Heterogeneous Panels With Structural Breaks, Badi Baltagi

Center for Policy Research

This paper extends Pesaran's (2006) work on common correlated effects (CCE) estimators for large heterogeneous panels with a general multifactor error structure by allowing for unknown common structural breaks. Structural breaks due to new policy implementation or major technological shocks, are more likely to occur over a longer time span. Consequently, ignoring structural breaks may lead to inconsistent estimation and invalid inference. We propose a general framework that includes heterogeneous panel data models and structural break models as special cases. The least squares method proposed by Bai (1997a, 2010) is applied to estimate the common change points, and the consistency …

Generalized Least-Squares Regressions V: Multiple Variables, Nataniel Greene

Publications and Research

The multivariate theory of generalized least-squares is formulated here using the notion of generalized means. The multivariate generalized least-squares problem seeks an m dimensional hyperplane which minimizes the average generalized mean of the square deviations between the data and the hyperplane in m + 1 variables. The numerical examples presented suggest that a multivariate generalized least-squares method can be preferable to ordinary least-squares especially in situations where the data are ill- conditioned.

Identifying Locations Of Active Corrosion Growth From Successive In-Line Inspections, Tom Bubenik, William V. Harper, Pam Moreno, Steven Polasik

Mathematics Faculty Scholarship

The integrated approach covered by this paper identifies corrosion activity using a combination of statistics, inspection-signal comparisons, and engineering analyses. The approach relies on an understanding of ILI and the mechanisms that cause corrosion and its growth. Pipeline operators can use the approach to calculate remaining lives, prioritize repairs and mitigation, and extend reassessment intervals. This process is collectively known as statistically-active corrosion.

Activin-A And Bmp4 Levels Modulate Cell Type Specification During Chir-Induced Cardiomyogenesis, Min-Su Kim, Audrey Horst, Steven Blinka, Karl D. Stamm, Donna K. Mahnke, James Schuman, Rebekah Gundry, Aoy Tomita-Mitchell, John Lough

Mathematics, Statistics and Computer Science Faculty Research and Publications

The use of human pluripotent cell progeny for cardiac disease modeling, drug testing and therapeutics requires the ability to efficiently induce pluripotent cells into the cardiomyogenic lineage. Although direct activation of the Activin-A and/or Bmp pathways with growth factors yields context-dependent success, recent studies have shown that induction of Wnt signaling using low molecular weight molecules such as CHIR, which in turn induces the Activin-A and Bmp pathways, is widely effective. To further enhance the reproducibility of CHIR-induced cardiomyogenesis, and to ultimately promote myocyte maturation, we are using exogenous growth factors to optimize cardiomyogenic signaling downstream of CHIR induction. As …

E-Esas: Evolution Of A Participatory Design-Based Solution For Breast Cancer (Bc) Patients In Rural Bangladesh, Mohammad Munirul Haque, Ferdaus Kawsar, Mohammad Adibuzzaman, Md Miftah Uddin, Sheikh Iqbal Ahamed, Richard Love, Ragib Hasan, Rumana Dowla, Tahmina Ferdousy, Reza Salim

Mathematics, Statistics and Computer Science Faculty Research and Publications

Healthcare facility is scarce for rural women in the developing world. The situation is worse for patients who are suffering from diseases that require long-term feedback-oriented monitoring such as breast cancer. Lack of motivation to go to the health centers on patients’ side due to sociocultural barriers, financial restrictions and transportation hazards results in inadequate data for proper assessment. Fortunately, mobile phones have penetrated the masses even in rural communities of the developing countries. In this scenario, a mobile phone-based remote symptom monitoring system (RSMS) with inspirational videos can serve the purpose of both patients and doctors. Here, we present …

A Novel Scoring Based Distributed Protein Docking Application To Improve Enrichment, Prachi Pradeep, Craig Struble, Terrence Neumann, Daniel S. Sem, Stephen Merrill

Mathematics, Statistics and Computer Science Faculty Research and Publications

Molecular docking is a computational technique which predicts the binding energy and the preferred binding mode of a ligand to a protein target. Virtual screening is a tool which uses docking to investigate large chemical libraries to identify ligands that bind favorably to a protein target. We have developed a novel scoring based distributed protein docking application to improve enrichment in virtual screening. The application addresses the issue of time and cost of screening in contrast to conventional systematic parallel virtual screening methods in two ways. Firstly, it automates the process of creating and launching multiple independent dockings on a …