Mathematics Commons^™

Challenges In Developing Applications For Aging Populations, Drew Marie Williams, Md O. Gani, Ivor D. Addo, Akm Jahangir Alam Majumder, Chandana Tamma, Mong-Te Wang, Chih-Hung Chang, Sheikh Iqbal Ahamed, Cheng-Chung Chu

Mathematics, Statistics and Computer Science Faculty Research and Publications

Elderly individuals can greatly benefit from the use of computer applications, which can assist in monitoring health conditions, staying in contact with friends and family, and even learning new things. However, developing accessible applications for an elderly user can be a daunting task for developers. Since the advent of the personal computer, the benefits and challenges of developing applications for older adults have been a hot topic of discussion. In this chapter, the authors discuss the various challenges developers who wish to create applications for the elderly computer user face, including age-related impairments, generational differences in computer use, and the …

Collective Estimation Of Multiple Bivariate Density Functions With Application To Angular-Sampling-Based Protein Loop Modeling, Mehdi Maadooliat, Lan Zhou, Seyed Morteza Najibi, Xin Gao, Jianhua Z. Huang

Mathematics, Statistics and Computer Science Faculty Research and Publications

This article develops a method for simultaneous estimation of density functions for a collection of populations of protein backbone angle pairs using a data-driven, shared basis that is constructed by bivariate spline functions defined on a triangulation of the bivariate domain. The circular nature of angular data is taken into account by imposing appropriate smoothness constraints across boundaries of the triangles. Maximum penalized likelihood is used to fit the model and an alternating blockwise Newton-type algorithm is developed for computation. A simulation study shows that the collective estimation approach is statistically more efficient than estimating the densities individually. The proposed …

Almost Perfect Restriction Semigroups, Peter R. Jones

Mathematics, Statistics and Computer Science Faculty Research and Publications

We call a restriction semigroup almost perfect if it is proper and the least congruence that identifies all its projections is perfect. We show that any such semigroup is isomorphic to a ‘W -product’ W(T,Y)W(T,Y), where T is a monoid, Y is a semilattice and there is a homomorphism from T into the inverse semigroup TI_YTIY of isomorphisms between ideals of Y. Conversely, all such W-products are almost perfect. Since we also show that every restriction semigroup has an easily computed cover of this type, the combination yields a ‘McAlister-type’ theorem for all restriction semigroups. …

Two Combinatorial Proofs Of Identities Involving Sums Of Powers Of Binomial Coefficients, John Engbers, Christopher Stocker

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

A Hybrid Segmentation And D-Bar Method For Electrical Impedance Tomography, Sarah J. Hamilton, J. M. Reyes, Samuli Siltanen, X. Zhang

Mathematics, Statistics and Computer Science Faculty Research and Publications

The regularized D-bar method for electrical impedance tomography (EIT) provides a rigorous mathematical approach for solving the full nonlinear inverse problem directly, i.e., without iterations. It is based on a low-pass filtering in the (nonlinear) frequency domain. However, the resulting D-bar reconstructions are inherently smoothed, leading to a loss of edge distinction. In this paper, a novel method that combines a D-bar approach with the edge-preserving nature of total variation (TV) regularization is presented. The method also includes a data-driven contrast adjustment technique guided by the key functions (CGO solutions) of the D-bar method. The new TV-enhanced D-bar …

An Ensemble Model Of Qsar Tools For Regulatory Risk Assessment, Prachi Pradeep, Richard J. Povinelli, Shannon White, Stephen Merrill

Mathematics, Statistics and Computer Science Faculty Research and Publications

Quantitative structure activity relationships (QSARs) are theoretical models that relate a quantitative measure of chemical structure to a physical property or a biological effect. QSAR predictions can be used for chemical risk assessment for protection of human and environmental health, which makes them interesting to regulators, especially in the absence of experimental data. For compatibility with regulatory use, QSAR models should be transparent, reproducible and optimized to minimize the number of false negatives. In silico QSAR tools are gaining wide acceptance as a faster alternative to otherwise time-consuming clinical and animal testing methods. However, different QSAR tools often make conflicting …

Pain Level Detection From Facial Image Captured By Smartphone, Md Kamrul Hasan, Golam Mushih Tanimul Ahsan, Sheikh Iqbal Ahamed, Rechard Love, Reza Salim

Mathematics, Statistics and Computer Science Faculty Research and Publications

Accurate symptom of cancer patient in regular basis is highly concern to the medical service provider for clinical decision making such as adjustment of medication. Since patients have limitations to provide self-reported symptoms, we have investigated how mobile phone application can play the vital role to help the patients in this case. We have used facial images captured by smart phone to detect pain level accurately. In this pain detection process, existing algorithms and infrastructure are used for cancer patients to make cost low and user-friendly. The pain management solution is the first mobile-based study as far as we found …

Solving Set Cover With Pairs Problem Using Quantum Annealing, Yudong Cao, Shuxian Jiang, Debbie Perouli, Sabre Kais

Mathematics, Statistics and Computer Science Faculty Research and Publications

Here we consider using quantum annealing to solve Set Cover with Pairs (SCP), an NP-hard combinatorial optimization problem that plays an important role in networking, computational biology, and biochemistry. We show an explicit construction of Ising Hamiltonians whose ground states encode the solution of SCP instances. We numerically simulate the time-dependent Schrödinger equation in order to test the performance of quantum annealing for random instances and compare with that of simulated annealing. We also discuss explicit embedding strategies for realizing our Hamiltonian construction on the D-wave type restricted Ising Hamiltonian based on Chimera graphs. Our embedding on the Chimera graph …

A Generalized Gamma-Weibull Distribution: Model, Properties And Applications, R. S. Meshkat, H. Torabi, Gholamhossein G. Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

We prepare a new method to generate family of distributions. Then, a family of univariate distributions generated by the Gamma random variable is defined. The generalized gamma-Weibull (GGW) distribution is studied as a special case of this family. Certain mathematical properties of moments are provided. To estimate the model parameters, the maximum likelihood estimators and the asymptotic distribution of the estimators are discussed. Certain characterizations of GGW distribution are presented. Finally, the usefulness of the new distribution, as well as its effectiveness in comparison with other distributions, are shown via an application of a real data set.

Learning About Modeling In Teacher Preparation Programs, Hyunyi Jung, Eryn Stehr, Jia He, Sharon L. Senk

Mathematics, Statistics and Computer Science Faculty Research and Publications

This study explores opportunities that secondary mathematics teacher preparation programs provide to learn about modeling in algebra. Forty-eight course instructors and ten focus groups at five universities were interviewed to answer questions related to modeling. With the analysis of the interview transcripts and related course materials, we found few opportunities for PSTs to engage with the full modeling cycle. Examples of opportunities to learn about algebraic modeling and the participants’ perspectives on the opportunities can contribute to the study of modeling and algebra in teacher education.

Remarks On A Paper Of Ahmad, Ahmad And Ahmed, Gholamhossein G. Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Ahmad et al. (2015) consider a Transmuted Kumaraswamy distribution and study certain properties of their distribution. In the title of their paper they mention characterization of this distribution, but no characterization are presented in their paper. In the present short note, we establish certain characterizations of the Transmuted Kumaraswamy distribution in three directions.

The Transmuted Weibull-Pareto Distribution, Ahmed Z. Afify, Haitham M. Yousof, Nadeem Shafique Butt, Gholamhossein G. Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

A new generalization of the Weibull-Pareto distribution called the transmuted Weibull-Pareto distribution is proposed and studied. Various mathematical properties of this distribution including ordinary and incomplete moments, quantile and generating functions, Bonferroni and Lorenz curves and order statistics are derived. The method of maximum likelihood is used for estimating the model parameters. The flexibility of the new lifetime model is illustrated by means of an application to a real data set.

Worldwide Cutaneous Malignant Melanoma Incidences Analyzed By Sex, Age, And Skin Type Over Time (1955–2007): Is Hpv Infection Of Androgenic Hair Follicular Melanocytes A Risk Factor For Developing Melanoma Exclusively In People Of European-Ancestry?, Stephen Merrill, Madhan Subramanian, Dianne E. Godar

Mathematics, Statistics and Computer Science Faculty Research and Publications

The cutaneous malignant melanoma (CMM) incidence has been increasing in an exponential manner in certain populations around the world for over 7 decades. To help illuminate the etiology, we performed worldwide temporal (1955–2007) CMM incidence analysis by sex, age (0–14, 15–29, 30–49, 50–69, 70–85+), and skin type on 6 continents using data from the International Agency for Research on Cancer. We observe an exponential increase in the CMM incidence over time and an increase of about 2 orders of magnitude between age groups 0–14 and 15–29 exclusively in European-ancestry populations around the world independent of skin type (I–III or III–IV). …

Maximal Class P-Groups With Large Character Degree Gaps, Michael Slattery

Mathematics, Statistics and Computer Science Faculty Research and Publications

In Mann (More on normally monomial p-groups, 2015), he proves some bounds on the size of gaps between character degrees of maximal class p-groups. In this note we construct a family of examples that shows that one of these bounds is sharp.

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 …

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 …

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 …

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 …

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.

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 …

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 …

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.

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 …

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.

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 …

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 …

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 …