Mathematics Commons^™

Signal Processing Spreads A Voxel’S Temporal Frequency Task-Activated Peak And Induces Spatial Correlations In Dual-Task Complex-Valued Fmri, Daniel B. Rowe

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

The Transmuted Exponentiated Generalized-G Family Of Distributions, Haitham M. Yousof, Ahmed Z. Afify, Morad Alizadeh, Nadeem Shafique Butt, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

We introduce a new class of continuous distributions called the transmuted exponentiated generalized-G family which extends the exponentiated generalized-G class introduced by Cordeiro et al. (2013). We provide some special models for the new family. Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, generating function, Rényi and Shannon entropies, order statistics and probability weighted moments are derived. The estimation of the model parameters is performed by maximum likelihood. The flexibility of the proposed family is illustrated by means of an applications to real dataset.

Characteristics Of Feedback That Influence Student Confidence And Performance During Mathematical Modeling, Hyunyi Jung, Heidi A. Diefes-Dux, Aladar K. Horvath, Kelsey Joy Rodgers, Monica E. Cardella

Mathematics, Statistics and Computer Science Faculty Research and Publications

This study focuses on characteristics of written feedback that influence students’ performance and confidence in addressing the mathematical complexity embedded in a Model-Eliciting Activity (MEA). MEAs are authentic mathematical modeling problems that facilitate students’ iterative development of solutions in a realistic context. We analyzed 132 first-year engineering students’ confidence levels and mathematical model scores on aMEA(pre and post feedback), along with teaching assistant feedback given to the students. The findings show several examples of affective and cognitive feedback that students reported that they used to revise their models. Students’ performance and confidence in developing mathematical models can be increased when …

Preparing Secondary Mathematics Teachers: Focus On Modeling In Algebra, Hyunyi Jung, Alexia Mintos, Jill Newton

Mathematics, Statistics and Computer Science Faculty Research and Publications

This study addressed the opportunities to learn (OTL) modeling in algebra provided to secondary mathematics pre-service teachers (PSTs). To investigate these OTL, we interviewed five instructors of required mathematics and mathematics education courses that had the potential to include opportunities for PSTs to learn algebra at three universities. We also interviewed a group of three to four PSTs at each of the universities. We coded the interview transcripts using an analytic framework developed based on related literature and policy documents. We report the similarities and differences in perspectives among instructors and PSTs related to modeling at each university, along with …

Predicting Scenarios For Successful Autodissemination Of Pyriproxyfen By Malaria Vectors From Their Resting Sites To Aquatic Habitats; Description And Simulation Analysis Of A Field-Parameterizable Model, Samson Sifael Kiware, George F. Corliss, Stephen Merrill, Dickson W. Lwetoijera, Gregor J. Devine, Silas Majambere, Gerry F. Killeen

Electrical and Computer Engineering Faculty Research and Publications

Background

Large-cage experiments indicate pyriproxifen (PPF) can be transferred from resting sites to aquatic habitats by Anopheles arabiensis - malaria vector mosquitoes to inhibit emergence of their own offspring. PPF coverage is amplified twice: (1) partial coverage of resting sites with PPF contamination results in far higher contamination coverage of adult mosquitoes because they are mobile and use numerous resting sites per gonotrophic cycle, and (2) even greater contamination coverage of aquatic habitats results from accumulation of PPF from multiple oviposition events.

Methods and Findings

Deterministic mathematical models are described that use only field-measurable input parameters and capture the biological …

Characterizations Of Gamma Distribution Via Sub-Independent Random Variables, Gholamhossein Hamedani

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. Inspired by the excellent work of Jin and Lee (2014), we present certain characterizations of gamma distribution based on the concept of sub-independence.

Kumaraswamy-Half-Cauchy Distribution: Characterizations And Related Results, Gholamhossein Hamedani, I. Ghosh

Mathematics, Statistics and Computer Science Faculty Research and Publications

We present various characterizations of a recently introduced distribution (Ghosh 2014), called Kumaraswamy- Half- Cauchy distribution based on: (i) a simple relation between two truncated moments; (ii) truncated moment of certain function of the 1^st order statistic; (iii) truncated moment of certain function of the random variable; (iv) hazard function; (v) distribution of the 1^st order statistic; (vi) via record values. We also provide some remarks on bivariate Gumbel copula distribution whose marginal distributions are Kumaraswamy- Half-Cauchy distributions.

Correction To “Master Regulators, Regulatory Networks, And Pathways Of Glioblastoma Subtypes”, Serdar Bozdag, Aiguo Li, Mehmet Baysan, Howard A. Fine

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

Remarks On Characterizations Of Malinowska And Szynal, Gholamhossein Hamedani, Z. Javanshiri, Mehdi Maadooliat, A. Yazdani

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. An investigator will be vitally interested to know if their model fits the requirements of a particular distribution. To this end, one will depend on the characterizations of this distribution which provide conditions under which the underlying distribution is indeed that particular distribution. In this work, several characterizations of Malinowska and Szynal (2008) for certain general classes of distributions are revisited and simpler proofs of them are presented. These characterizations are …

Quantification Of The Statistical Effects Of Spatiotemporal Processing Of Nontask Fmri Data, M. Muge Karaman, Andrew S. Nencka, Iain P. Bruce, Daniel B. Rowe

Mathematics, Statistics and Computer Science Faculty Research and Publications

Nontask functional magnetic resonance imaging (fMRI) has become one of the most popular noninvasive areas of brain mapping research for neuroscientists. In nontask fMRI, various sources of “noise” corrupt the measured blood oxygenation level-dependent signal. Many studies have aimed to attenuate the noise in reconstructed voxel measurements through spatial and temporal processing operations. While these solutions make the data more “appealing,” many commonly used processing operations induce artificial correlations in the acquired data. As such, it becomes increasingly more difficult to derive the true underlying covariance structure once the data have been processed. As the goal of nontask fMRI studies …

The Antisymmetry Betweenness Axiom And Hausdorff Continua, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

An interpretation of betweenness on a set satisfies the antisymmetry axiom at a point a if it is impossible for each of two distinct points to lie between the other and a. In this paper we study the role of antisymmetry as it applies to the K-interpretation of betweenness in a Hausdorff continuum X, where a point c lies between points a and b exactly when every subcontinuum of X containing both a and b contains c as well.

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.

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 …

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 …

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 …

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 …

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 …

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 . …

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 …

Highly Sensitive Noninvasive Cardiac Transplant Rejection Monitoring Using Targeted Quantification Of Donor-Specific Cell-Free Deoxyribonucleic Acid, Mats Hidestrand, Aoy Tomita-Mitchell, Pip M. Hidestrand, Arnold Oliphant, Mary Goetsch, Karl D. Stamm, Huan-Ling Liang, Chesney Castleberry, D. Woodrow Benson, Gail Stendahl, Pippa Simpson, Stuart Berger, James S. Tweddell, Steven Zangwill, Michael E. Mitchell

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

Micro-Environment Causes Reversible Changes In Dna Methylation And Mrna Expression Profiles In Patient-Derived Glioma Stem Cells, Mehmet Baysan, Kevin Woolard, Serdar Bozdag, Gregory Riddick, Svetlana Kotliarova, Margaret C. Cam, Galina I. Belova, Susie Ahn, Wei Zhang, Hua Song, Jennifer Walling, Holly Stevenson, Paul Meltzer, Howard A. Fine

Mathematics, Statistics and Computer Science Faculty Research and Publications

In vitro and in vivo models are widely used in cancer research. Characterizing the similarities and differences between a patient's tumor and corresponding in vitro and in vivo models is important for understanding the potential clinical relevance of experimental data generated with these models. Towards this aim, we analyzed the genomic aberrations, DNA methylation and transcriptome profiles of five parental tumors and their matched in vitro isolated glioma stem cell (GSC) lines and xenografts generated from these same GSCs using high-resolution platforms. We observed that the methylation and transcriptome profiles of in vitro GSCs were significantly different from their corresponding …

Mcdonald Log-Logistic Distribution With An Application To Breast Cancer Data, M. H. Tahir, Muhammad Mansoor, Muhammad Zubair, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

We introduce a five-parameter continuous model, called the McDonald log-logistic distribution, to extend the two-parameter log-logistic distribution. Some structural properties of this new distribution such as reliability measures and entropies are obtained. The model parameters are estimated by the method of maximum likelihood using L-BFGS-B algorithm. A useful characterization of the distribution is proposed which does not require explicit closed form of the cumulative distribution function and also connects the probability density function with a solution of a first order differential equation. An application of the new model to real data set shows that it can give consistently better fit …

When Semi-Monotone Implies Monotone, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

The basic theme of this talk is the extrinsic description of objects by means of morphisms. One way to do this is to say that all monomorphisms from the object are “special” in some way; the dual of this is to single out epimorphisms to the object.

Quantifying The Statistical Impact Of Grappa In Fcmri Data With A Real-Valued Isomorphism, Iain P. Bruce, Daniel B. Rowe

Mathematics, Statistics and Computer Science Faculty Research and Publications

The interpolation of missing spatial frequencies through the generalized auto-calibrating partially parallel acquisitions (GRAPPA) parallel magnetic resonance imaging (MRI) model implies a correlation is induced between the acquired and reconstructed frequency measurements. As the parallel image reconstruction algorithms in many medical MRI scanners are based on the GRAPPA model, this study aims to quantify the statistical implications that the GRAPPA model has in functional connectivity studies. The linear mathematical framework derived in the work of Rowe , 2007, is adapted to represent the complex-valued GRAPPA image reconstruction operation in terms of a real-valued isomorphism, and a statistical analysis is performed …

A Statistical Fmri Model For Differential T2* Contrast Incorporating T1 And T2* Of Gray Matter, M. Muge Karaman, Iain P. Bruce, Daniel B. Rowe

Mathematics, Statistics and Computer Science Faculty Research and Publications

Relaxation parameter estimation and brain activation detection are two main areas of study in magnetic resonance imaging (MRI) and functional magnetic resonance imaging (fMRI). Relaxation parameters can be used to distinguish voxels containing different types of tissue whereas activation determines voxels that are associated with neuronal activity. In fMRI, the standard practice has been to discard the first scans to avoid magnetic saturation effects. However, these first images have important information on the MR relaxivities for the type of tissue contained in voxels, which could provide pathological tissue discrimination. It is also well-known that the voxels located in gray matter …