Mathematics Commons^™

Enots Wolley Variations And Related Sequences, Nathan Myles Nichols

Master's Theses (2009 -)

The Enots Wolley sequence is a lexicographically earliest sequence (LES) that is closely related to the Yellowstone sequence. It is an open conjecture by N. J. Sloane that every number with at least two distinct prime factors appears as a term of the Enots Wolley sequence. In this thesis, this conjecture is proved for a variation of the Enots Wolley sequence that operates on the binary representation of a positive integer rather than the prime factorization. The methods used are then applied to prove some new properties of the prime factorization Enots Wolley sequence.

Transcriptional Profile Of Cohesin Complex Mutations In The Background Of Npm1 And Runx1-Runx1t1 Aml, Jacob Tiegs

Master's Theses (2009 -)

Acute Myeloid Leukemia is a cancer of the blood, characterized by a heterogenous mixture of disease causing mutations. Mutations of the cohesin complex is a group of such mutations and occur alongside several other driving mutations in the development of Acute Myeloid Leukemia. This thesis specifically focuses on cohesin complex mutations in the context of concurrence with NPM1 mutation and the Core Binding Factor (CBF) mutation RUNX1-RUNX1T1 in three distinct components. The first two components involved Differential Expression Analysis (DEA) to identify significantly differentiated genes in each model, followed by Gene Set Enrichment Analysis (GSEA) to identify Gene Ontology (GO) …

Graph Neural Networks For Inverse Problems With Flexible Meshes, William Herzberg

Dissertations (1934 -)

This thesis addresses the electrical impedance tomography (EIT) image reconstruction problem where samples may have irregular discretizations and presents two, new, learned reconstruction algorithms which leverage a graph framework. These new frameworks consider the irregular, non-uniform data as a graph thus allowing graph neural networks to be applied directly to the data defined over irregular meshes. Currently in imaging, convolutional neural networks are used most frequently in learned methods because they are spatially invariant and have the ability to leverage localized information. In addition, many images are represented by rows and columns of uniformly sized pixels which can easily be …

The Role Of Self-Tutorial In Introductory Physics Student Performance On Test Of Understanding Of Vectors, Katherine Finegan

Master's Theses (2009 -)

A single-interaction self-guided lesson was designed to teach basic vector concepts to introductory physics students. The self-guided lesson was tested for efficacy by comparing pre-test and post-test subscores on a Test of Understanding of Vectors (TUV) and comparing subscore differences to students in the same physics courses who had not taken the self-guided lesson. Analysis showed no significant differences in subscore differences between students taking the self-guided lesson and those in comparable control groups, indicating that more robust interventions are needed and/or further work must be done on the self-guided lesson to improve student vector understanding.

Temporal Sentiment Mapping System For Time-Synchronized Data, Jiachen Ma

Dissertations (1934 -)

Temporal sentiment labels are used in various multimedia studies. They are useful for numerous classification and detection tasks such as video tagging, segmentation, and labeling. However, generating a large-scale sentiment dataset through manual labeling is usually expensive and challenging. Some recent studies explored the possibility of using online Time-Sync Comments (TSCs) as the primary source of their sentiment maps. Although the approach has positive results, existing TSCs datasets are limited in scale and content categories. Guidelines for generating such data within a constrained budget are yet to be developed and discussed. This dissertation tries to address the above issues by …

All Pairs Routing Path Enumeration Using Latin Multiplication And Julia, Haochen Sun

Dissertations (1934 -)

Enumerating all routing paths among Autonomous Systems (ASes) at an Internet-scale is an intractable problem. The Border Gateway Protocol (BGP) is the standard exterior gateway protocol through which ASes exchange reachability information. Building an efficient path enumeration tool for a given network is an essential step toward estimating the resiliency of the network to cyber security attacks, such as routing origin and path hijacking. In our work, we use the matrix Latin multiplication method to compute all possible paths among all pairs of nodes. We parallelize this computation through the domain decomposition for matrix multiplication and implement our solution in …

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.

Enacting Systemic Change: The Evolving Landscape Of Computer Science Education In The State Of Wisconsin, Heather Bort

Dissertations (1934 -)

Over the last decade, the Systems Lab at Marquette University has undertaken a grand challenge to positively impact learners and educators in the state of Wisconsin with computer science education innovation. We have moved through a progression in maturity around recognizing the need for and implementing a propagation plan to achieve this desired outcome. This work showcases several novel innovations with increasing overall effectiveness in creating a more diverse community of computer science educators and learners in the state. We demonstrate a pattern of increased engagement, sustainable change, and measurable impact, that has resulted in a more accessible and inclusive …

Sepsis Monitoring Using Contextually-Tailored Online Change Point Detection And Beyond, Nazmus Sakib

Dissertations (1934 -)

Considering morbidity, mortality, and annual treatment costs, the dramatic rise in the incidence of sepsis and septic shock among intensive care unit (ICU) admissions in US hospitals is an increasing concern. The recent excruciating statistics regarding sepsis mortality, the average length of hospital stay, and annual treatment costs made sepsis treatment and research a critical domain in medical informatics. The aims of this dissertation center around four research questions. First, we discuss how we can investigate the prevalence and underlying relation of the sepsis diagnosis criteria (qSOFA and SIRS) and its implications in Medical Informatics and predictive analytics. Second, we …

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 …

Functional Singular Spectrum Analysis: Nonparametric Decomposition And Forecasting Approaches For Functional Time Series, Jordan Christopher Trinka

Dissertations (1934 -)

In this dissertation, we develop nonparametric decomposition methods and the subsequent forecasting techniques for functional, time-dependent data known as functional time series (FTS). We use ideas from functional data analysis (FDA) and singular spectrum analysis (SSA) to introduce the nonparametric decomposition method known as functional SSA (FSSA) and its associated forecasting techniques. We also extend these developed methodologies into multivariate FSSA (MFSSA) over different dimensional domains and its subsequent forecasting routines so that we may perform nonparametric decomposition and prediction of multivariate FTS (MFTS). The FSSA algorithm may be viewed as a signal extraction technique and we find that the …

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 …

Using Machine Learning Tools To Predict The Severity Of Osteoarthritis Based On Knee X-Ray Data, Yaorong Xiao

Master's Theses (2009 -)

Knee osteoarthritis(OA) is a very general joint disease that disturb many people especially people over 60. The severity of pain caused by knee OA is the most important portent to disable. Until now, the bad impact of osteoarthritis on health care and public health systems is still increasing.In this paper, we will build a machine learning model to detect the edge of the knee based on the X-ray image and predict the severity of OA. We use a clustering algorithm and machine learning tools to predict the severity of OA in knee X-ray images. The data is coming from …

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.

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, …

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 …

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.

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.

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.

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 …