Physical Sciences and Mathematics Commons^™

Disjoint And Simultaneously Hypercyclic Pseudo-Shifts, Nurhan Çolakoğlu, Özgür Martin, Rebecca Sanders

Mathematical and Statistical Science Faculty Research and Publications

We characterize disjoint and simultaneously hypercyclic tuples of unilateral pseudo-shift operators on ℓ^p(ℕ) . As a consequence, complementing the results of Bernal and Jung, we give a characterization for simultaneously hypercyclic tuples of unilateral weighted shifts. We also give characterizations for unilateral pseudo-shifts that satisfy the Disjoint and Simultaneous Hypercyclicity Criterions. Contrary to the disjoint hypercyclicity case, tuples of weighted shifts turn out to be simultaneously hypercyclic if and only if they satisfy the Simultaneous Hypercyclicity Criterion.

Functional Singular Spectrum Analysis, Hossein Haghbin, Seyed Morteza Najibi, Rahim Mahmoudvand, Jordan Trinka, Mehdi Maadooliat

Mathematical and Statistical Science Faculty Research and Publications

In this paper, we develop a new extension of the singular spectrum analysis (SSA) called functional SSA to analyze functional time series. The new methodology is constructed by integrating ideas from functional data analysis and univariate SSA. Specifically, we introduce a trajectory operator in the functional world, which is equivalent to the trajectory matrix in the regular SSA. In the regular SSA, one needs to obtain the singular value decomposition (SVD) of the trajectory matrix to decompose a given time series. Since there is no procedure to extract the functional SVD (fSVD) of the trajectory operator, we introduce a computationally …

Characterizations And Reliability Measures Of The Generalized Log Burr Xii Distribution, Fiaz Ahmad Bhatti, Gholamhossein G. Hamedani, Azeem Ali, Sedigheh Mirzaei Salehabadi, Munir Ahmad

Mathematical and Statistical Science Faculty Research and Publications

In this paper, we derive the generalized log Burr XII (GLBXII) distribution [2] from the generalized Burr-Hatke differential equation. We characterize the GLBXII distribution via innovative techniques. We derive various reliability measures (series and parallel). We also authenticate the potentiality of the GLBXII model via economics applications. The applications of characterizations and reliability measures of the GLBXII distribution in different disciplines of science will be profitable for scientists.

Rapid Entry Into Masters In Computing Program For Non-Majors, Gary S. Krenz, Thomas Kaczmarek, John C. Moyer

Mathematical and Statistical Science Faculty Research and Publications

The COSMIC: Change Opportunity - Start Masters in Computing graduate curriculum initiative strives to provide a rapid entry pathway to a professional Master of Science (MS) degree for individuals who do not have an undergraduate degree in computing, but who wish to cross over to a career in the computing field. The goal of our curriculum is to minimize the time students spend preparing for graduate study and maximize experiences relevant for work after graduation. The COSMIC curriculum initiative is similar in concept to other post-baccalaureate conversion programs. However, customization of the COSMIC bridge course and curriculum pathway makes it …

A New Extended Alpha Power Transformed Family Of Distributions: Properties, Characterizations And An Application To A Data Set In The Insurance Sciences, Zubair Ahmad, Eisa Mahmoudi, Gholamhossein Hamedani

Mathematical and Statistical Science Faculty Research and Publications

Heavy tailed distributions are useful for modeling actuarial and financial risk management problems. Actuaries often search for finding distributions that provide the best fit to heavy tailed data sets. In the present work, we introduce a new class of heavy tailed distributions of a special sub-model of the proposed family, called a new extended alpha power transformed Weibull distribution, useful for modeling heavy tailed data sets. Mathematical properties along with certain characterizations of the proposed distribution are presented. Maximum likelihood estimates of the model parameters are obtained. A simulation study is provided to evaluate the performance of the maximum likelihood …

Characterizations Of The Discrete Lindley And Discrete Poisson-Lindley Distributions, Gholamhossein G. Hamedani, Mahrokh Najaf

Mathematical and Statistical Science Faculty Research and Publications

Certain characterizations of the discrete Lindley and discrete Poisson-Lindley distributions, originally introduced by Bakouch, Jazi and Nadarjah (2014) and Sankaran (1970), respectively, are presented. Al-Babtain, Gemeay and Afify (2020) revisited these distributions and provided estimation methods and actuarial measures as well as their applications in medicine. This short note is intended to complete, in some way, Al-Babtain, Gemeay and Afify (2020)’s work. It should be mentioned that the probability mass functions reported in the two papers mentioned above are not correct. In this note, it will be explained why they are not correct.

Exploring Prospective 1-8 Teachers' Number And Operation Sense In The Context Of Fractions, Marta T. Magiera, Leigh A. Van Den Kieboom

Mathematical and Statistical Science Faculty Research and Publications

This exploratory study examined prospective elementary teachers’ (PSTs’) number and operation sense (NOS) in the context of solving problems with fractions. Drawing on the existing literature, we identified seven skills that characterize fraction-related NOS. We analyzed 230 responses to 23 tasks completed by 10 PSTs for evidence of PSTs’ use of different fraction-related NOS skills. The analysis revealed that PSTs did not use all seven fraction-related NOS skills to the same extent. PSTs’ responses documented their frequent reasoning about the meaning of symbols and formal mathematical language in the context of fractions. To a lesser extent, PSTs’ responses documented their …

Sufficient Dimension Folding In Regression Via Distance Covariance For Matrix‐Valued Predictors, Wenhui Sheng, Qingcong Yuan

Mathematical and Statistical Science Faculty Research and Publications

In modern data, when predictors are matrix/array‐valued, building a reasonable model is much more difficult due to the complicate structure. However, dimension folding that reduces the predictor dimensions while keeps its structure is critical in helping to build a useful model. In this paper, we develop a new sufficient dimension folding method using distance covariance for regression in such a case. The method works efficiently without strict assumptions on the predictors. It is model‐free and nonparametric, but neither smoothing techniques nor selection of tuning parameters is needed. Moreover, it works for both univariate and multivariate response cases. In addition, we …

Cosmic: Us-Based Conversion Master's Degree In Computing, Gary S. Krenz, Thomas Kaczmarek

Mathematical and Statistical Science Faculty Research and Publications

COSMIC is an NSF S-STEM graduate curriculum initiative/conversion program that strives to provide an accelerated pathway to a Master of Science (MS) degree for individuals who do not have an undergraduate degree in computing, but who wish to cross over into the computing field. The structure of our conversion program, the context that motivated it, and insights from conversion students' instructors are presented. Program successes with students from under-represented populations and the limitations that are also experienced are discussed. Our conversion program is based on a highly focused summer bridge course, combined with a customized curriculum pathway that enables people …

The Poisson Topp Leone Generator Of Distributions For Lifetime Data: Theory, Characterizations And Applications, Faton Merovci, Haitham M. Yousof, Gholamhossein Hamedani

Mathematical and Statistical Science Faculty Research and Publications

We study a new family of distributions defined by the minimum of the Poisson random number of independent identically distributed random variables having a Topp Leone-G distribution (see Rezaei et al., (2016)). Some mathematical properties of the new family including ordinary and incomplete moments, quantile and generating functions, mean deviations, order statistics, reliability and entropies are derived. Maximum likelihood estimation of the model parameters is investigated. Some special models of the new family are discussed. An application is carried out on real data set applications sets to show the potentiality of the proposed family.

New Modified Singh-Maddala Distribution: Development, Properties, Characterizations And Applications, Fiaz Ahmad Bhatti, Gholamhossein G. Hamedani, Mustafa Ç. Korkmaz, Munir Ahmad

Mathematical and Statistical Science Faculty Research and Publications

In this paper, a new five-parameter extended Burr XII model called new modified Singh-Maddala (NMSM) is developed from cumulative hazard function of the modified log extended integrated beta hazard (MLEIBH) model. The NMSM density function is left-skewed, right-skewed and symmetrical. The Lambert W function is used to study descriptive measures based on quantile, moments, and moments of order statistics, incomplete moments, inequality measures and residual life function. Different reliability and uncertainty measures are also theoretically established. The NMSM distribution is characterized via different techniques and its parameters are estimated using maximum likelihood method. The simulation studies are performed on the …

On Continuous Images Of Ultra-Arcs, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

Any space homeomorphic to one of the standard subcontinua of the Stone-Čech remainder of the real half-line is called an ultra-arc. Alternatively, an ultra-arc may be viewed as an ultracopower of the real unit interval via a free ultrafilter on a countable set. It is known that any continuum of weight is a continuous image of any ultra-arc; in this paper we address the problem of which continua are continuous images under special maps. Here are some of the results we present.

Characterizations Of Marshall-Olkin Discrete Reduced Modified Weibull Distribution, Gholamhossein G. Hamedani

Mathematical and Statistical Science Faculty Research and Publications

Characterizing a distribution is an important problem in applied sciences, where an investigator is vitally interested to know if their model follows the right distribution. To this end, the investigator relies on conditions under which their model would follow specifically chosen distribution. Certain characterizations of the Marshall-Olkin discrete reduced modified Weibull distribution are presented to complete, in some way, their work.

A New Extension Of Lindley Distribution: Modified Validation Test, Characterizations And Different Methods Of Estimation, Mohamed Ibrahim, Abhimanyu Singh Yadav, Haitham M. Yousof, Hafida Goual, Gholamhossein Hamedani

Mathematical and Statistical Science Faculty Research and Publications

In this paper, a new extension of Lindley distribution has been introduced. Certain characterizations based on truncated moments, hazard and reverse hazard function, conditional expectation of the proposed distribution are presented. Besides, these characterizations, other statistical/mathematical properties of the proposed model are also discussed. The estimation of the parameters is performed through different classical methods of estimation. Bayes estimation is computed under gamma informative prior under the squared error loss function. The performances of all estimation methods are studied via Monte Carlo simulations in mean square error sense. The potential of the proposed model is analyzed through two data sets. …

The Extended Alpha Power Transformed Family Of Distributions: Properties And Applications, Zubair Ahmad, Muhammad Ilyas, Gholamhossein G. Hamedani

Mathematical and Statistical Science Faculty Research and Publications

In this article, a new family of lifetime distributions by adding an additional parameter to the existing distributions is introduced. The new family is called, the extended alpha power transformed family of distributions. For the proposed family, explicit expressions for some mathematical properties along with estimation of parameters through Maximum likelihood Method are discussed. A special sub-model, called the extended alpha power transformed Weibull distribution is considered in detail. The proposed model is very flexible and can be used to model data with increasing, decreasing or bathtub shaped hazard rates. To access the behavior of the model parameters, a small …

Mathematical Modeling Experiences: Narratives From A Preservice Teacher And An Instructor, Sarah Brand, Hyunyi Jung

Mathematical and Statistical Science Faculty Research and Publications

Regardless of the benefits of engaging in mathematical modeling, few preservice teachers (PTs) have experienced mathematical modeling firsthand. This study offers an example of how to make sense of the interaction between the teaching and learning of mathematical modeling by examining a teacher educator’s decision making, her analysis of 36 PTs’ learning, and an in-depth narrative from a PT. Findings show the value of engaging with structurally relevant mathematical modeling tasks and considering social issues via mathematical modeling, resulting in task designs which aim to deepen students’ understanding of society and mathematics.

Characterizations Of Certain Recently Introduced Discrete Distributions, Gholamhossein G. Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Characterizations of certain recently introduced discrete distributions are presented to complete, in some way, the works cited in the References.

Group Presentations As A Site For Collective Modeling Activity, Corey Brady, Hyunyi Jung

Mathematical and Statistical Science Faculty Research and Publications

We approach student presentations of solutions to modeling tasks as occasions for whole-class reflection on the rich conceptual work that small-group teams have done in parallel. Analyzing and interpreting these interactions can offer insights into how a classroom group negotiates a shared sense of what they have learned and what they collectively view as “newsworthy” across groups from their recent (and ongoing) model-building. We describe analytical tools to interpret a classroom’s work during presentations, and we illustrate their use in a single case. This work offers a foothold for design-based research to harness presentations to improve learning, drive instructional decisions, …

Mathematical Modeling And Classroom Discourse: A Case For Modeling-Specific Discussion Strategies, Ashley Dorlack, Hyunyi Jung, Sarah Brand, Samuel Franklin Gailliot

Mathematical and Statistical Science Faculty Research and Publications

No abstract provided.

Nonparametric Collective Spectral Density Estimation With An Application To Clustering The Brain Signals, Mehdi Maadooliat, Ying Sun, Tianbo Chen

Mathematics, Statistics and Computer Science Faculty Research and Publications

In this paper, we develop a method for the simultaneous estimation of spectral density functions (SDFs) for a collection of stationary time series that share some common features. Due to the similarities among the SDFs, the log‐SDF can be represented using a common set of basis functions. The basis shared by the collection of the log‐SDFs is estimated as a low‐dimensional manifold of a large space spanned by a prespecified rich basis. A collective estimation approach pools information and borrows strength across the SDFs to achieve better estimation efficiency. Moreover, each estimated spectral density has a concise representation using the …

Smartphone-Based Prenatal Education For Parents With Preterm Birth Risk Factors, U. Olivia Kim, K. Barnekow, Sheikh Iqbal Ahamed, S. Dreier, C. Jones, M. Taylor, Md Kamrul Hasan, M. A. Basir

Mathematics, Statistics and Computer Science Faculty Research and Publications

Objective

To develop an educational mobile application (app) for expectant parents diagnosed with risk factors for premature birth.

Methods

Parent and medical advisory panels delineated the vision for the app. The app helps prepare for preterm birth. For pilot testing, obstetricians offered the app between 18–22 weeks gestational age to English speaking parents with risk factors for preterm birth. After 4 weeks of use, each participant completed a questionnaire. The software tracked topics accessed and duration of use.

Results

For pilot testing, 31 participants were recruited and 28 completed the questionnaire. After app utilization, participants reported heightened awareness of preterm …

Semicontinuity Of Betweenness Functions, Paul Bankston, Aisling Mccluskey, Richard J. Smith

Mathematics, Statistics and Computer Science Faculty Research and Publications

A ternary relational structure〈X,[⋅,⋅,⋅]〉, interpreting a notion of betweenness, gives rise to the family of intervals, with interval [a,b] being defined as the set of elements of X between a and b. Under very reasonable circumstances, X is also equipped with some topological structure, in such a way that each interval is a closed nonempty subset of X. The question then arises as to the continuity behavior—within the hyperspace context—of the betweenness function {x,y}↦[x,y]. We investigate two broad scenarios: the first involves metric spaces and Menger's betweenness interpretation; the second deals with continua and the subcontinuum interpretation.

The Transmuted Geometric-Quadratic Hazard Rate Distribution: Development, Properties, Characterizations And Applications, Fiaz Ahmad Bhatti, Gholamhossein Hamedani, Mustafa Ç. Korkmaz, Munir Ahmad

Mathematics, Statistics and Computer Science Faculty Research and Publications

We propose a five parameter transmuted geometric quadratic hazard rate (TG-QHR) distribution derived from mixture of quadratic hazard rate (QHR), geometric and transmuted distributions via the application of transmuted geometric-G (TG-G) family of Afify et al.(Pak J Statist 32(2), 139-160, 2016). Some of its structural properties are studied. Moments, incomplete moments, inequality measures, residual life functions and some other properties are theoretically taken up. The TG-QHR distribution is characterized via different techniques. Estimates of the parameters for TG-QHR distribution are obtained using maximum likelihood method. The simulation studies are performed on the basis of graphical results to illustrate the performance …

Empirical Bayesian Approach To Testing Multiple Hypotheses With Separate Priors For Left And Right Alternatives, Naveen K. Bansal, Mehdi Maadooliat, Steven J. Schrodi

Mathematics, Statistics and Computer Science Faculty Research and Publications

We consider a multiple hypotheses problem with directional alternatives in a decision theoretic framework. We obtain an empirical Bayes rule subject to a constraint on mixed directional false discovery rate (mdFDR≤α) under the semiparametric setting where the distribution of the test statistic is parametric, but the prior distribution is nonparametric. We proposed separate priors for the left tail and right tail alternatives as it may be required for many applications. The proposed Bayes rule is compared through simulation against rules proposed by Benjamini and Yekutieli and Efron. We illustrate the proposed methodology for two sets of …

Cancerin: A Computational Pipeline To Infer Cancer-Associated Cerna Interaction Networks, Duc Do, Serdar Bozdag

Mathematics, Statistics and Computer Science Faculty Research and Publications

MicroRNAs (miRNAs) inhibit expression of target genes by binding to their RNA transcripts. It has been recently shown that RNA transcripts targeted by the same miRNA could “compete” for the miRNA molecules and thereby indirectly regulate each other. Experimental evidence has suggested that the aberration of such miRNA-mediated interaction between RNAs—called competing endogenous RNA (ceRNA) interaction—can play important roles in tumorigenesis. Given the difficulty of deciphering context-specific miRNA binding, and the existence of various gene regulatory factors such as DNA methylation and copy number alteration, inferring context-specific ceRNA interactions accurately is a computationally challenging task. Here we propose a computational …

Reality Versus Grant Application Research “Plans”, Linda Burhansstipanov, Linda U. Krebs, Daniel Petereit, Mark Dignan, Sheikh Iqbal Ahamed, Michele Sargent, Krisin Cina, Kimberly Crawford, Doris Thibeault, Simone Bordeaux, Shalini Kanekar, Golam Mushih Tanimul Ahsan, Drew Williams, Ivor D. Addo

Mathematics, Statistics and Computer Science Faculty Research and Publications

This article describes the implementation of the American Indian mHealth Smoking Dependence Study focusing on the differences between what was written in the grant application compared to what happened in reality. The study was designed to evaluate a multicomponent intervention involving 256 participants randomly assigned to one of 15 groups. Participants received either a minimal or an intense level of four intervention components: (1) nicotine replacement therapy, (2) precessation counseling, (3) cessation counseling, and (4) mHealth text messaging. The project team met via biweekly webinars as well as one to two in-person meetings per year throughout the study. The project …

A Note On Sum, Difference, Product And Ratio Of Kumaraswamy Random Variables, Avishek Mallick, Indranil Ghosh, Gholamhossein G. Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Explicit expressions for the densities of S = X₁ + X₂ , D = X₁ − X₂ , P = X₁X₂ and R= X₁/X₂ are derived when X₁ and X₂ are independent or sub-independent Kumaraswamy random variables. The expressions appear to involve the incomplete gamma functions. Some possible real life scenarios are mentioned in which such quantities might be of interest.

Combinatorial Proofs Of Identities Of Alzer And Prodinger And Some Generalizations, John Engbers, Christopher Stocker

Mathematics, Statistics and Computer Science Faculty Research and Publications

We provide combinatorial proofs of identities published by Alzer and Prodinger. These identities include that for integers b, n, and r with b ≥ 1 and n − 1 ≥ r ≥ 0 we have

and for integers b, n, and r with b ≥ 0 and n − 1 ≥ r ≥ 0 we have

Our combinatorial proofs generalize squares to sth powers, and involve generalized Eulerian numbers and generalized Delannoy numbers.

Dynamic Statistical Models For Pyroclastic Density Current Generation At Soufrière Hills Volcano, Robert L. Wolpert, Elaine T. Spiller, Eliza S. Calder

Mathematics, Statistics and Computer Science Faculty Research and Publications

To mitigate volcanic hazards from pyroclastic density currents, volcanologists generate hazard maps that provide long-term forecasts of areas of potential impact. Several recent efforts in the field develop new statistical methods for application of flow models to generate fully probabilistic hazard maps that both account for, and quantify, uncertainty. However, a limitation to the use of most statistical hazard models, and a key source of uncertainty within them, is the time-averaged nature of the datasets by which the volcanic activity is statistically characterized. Where the level, or directionality, of volcanic activity frequently changes, e.g., during protracted eruptive episodes, or at …

Impacts Of Simultaneous Multislice Acquisition On Sensitivity And Specificity In Fmri, Benjamin B. Risk, Mary C. Kociuba, Daniel B. Rowe

Mathematics, Statistics and Computer Science Faculty Research and Publications

Simultaneous multislice (SMS) imaging can be used to decrease the time between acquisition of fMRI volumes, which can increase sensitivity by facilitating the removal of higher-frequency artifacts and boosting effective sample size. The technique requires an additional processing step in which the slices are separated, or unaliased, to recover the whole brain volume. However, this may result in signal “leakage” between aliased locations, i.e., slice “leakage,” and lead to spurious activation (decreased specificity). SMS can also lead to noise amplification, which can reduce the benefits of decreased repetition time. In this study, we evaluate the original slice-GRAPPA (no leak block) …