Mathematics Commons^™

Mapping The Stk4/Hippo Signaling Network In Prostate Cancer Cell, Damien Ready, Kader Yagiz, Pooneh Amin, Yuksel Yildiz, Vincent Funari, Serdar Bozdag, Bekir Cinar

Mathematics, Statistics and Computer Science Faculty Research and Publications

Dysregulation of MST1/STK4, a key kinase component of the Hippo-YAP pathway, is linked to the etiology of many cancers with poor prognosis. However, how STK4 restricts the emergence of aggressive cancer remains elusive. Here, we investigated the effects of STK4, primarily localized in the cytoplasm, lipid raft, and nucleus, on cell growth and gene expression in aggressive prostate cancer. We demonstrated that lipid raft and nuclear STK4 had superior suppressive effects on cell growth in vitro and in vivo compared with cytoplasmic STK4. Using RNA sequencing and bioinformatics analysis, we identified several differentially expressed (DE) genes that responded to ectopic …

Nature Of Mathematical Modeling Tasks For Secondary Mathematics Preservice Teachers, Jia He, Eryn Stehr, Hyunyi Jung

Mathematics, Statistics and Computer Science Faculty Research and Publications

This study investigated the nature of written modeling tasks reported by instructors of required courses in five secondary mathematics teacher education programs. These tasks were analyzed based on a framework addressing potential cognitive orientation (simple procedures, complex procedures, and rich tasks) and purpose (epistemological, educational, contextual, and socio-critical modeling) of the tasks. Our analysis suggests that most tasks included questions of more than one cognitive orientation and more than half of the tasks were coded as contextual modeling. We also found that tasks that were coded as contextual modeling offered opportunities for future teachers to engage with questions at all …

Processdriver: A Computational Pipeline To Identify Copy Number Drivers And Associated Disrupted Biological Processes In Cancer, Brittany Baur, Serdar Bozdag

Mathematics, Statistics and Computer Science Faculty Research and Publications

Copy number amplifications and deletions that are recurrent in cancer samples harbor genes that confer a fitness advantage to cancer tumor proliferation and survival. One important challenge in computational biology is to separate the causal (i.e., driver) genes from passenger genes in large, aberrated regions. Many previous studies focus on the genes within the aberration (i.e., cis genes), but do not utilize the genes that are outside of the aberrated region and dysregulated as a result of the aberration (i.e., trans genes). We propose a computational pipeline, called ProcessDriver, that prioritizes candidate drivers by relating cis genes to …

Characterizations Of Kumaraswamy-Laplace, Mcdonald Inverse Weibull And New Generalized Exponential Distributions, Gholamhossein G. Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Nassar (2016) considers an interesting univariate continuous distribution called Kumaraswamy-Laplace which has different forms on two subintervals. He studies certain properties and applications of this distribution. Shahbaz et al. (2016) consider another interesting distribution called McDonald Inverse Weibull distribution. They present some basic properties of their distribution and study the estimations of the parameters as well as discussing its application via an illustrative example. What is lacking in both papers, in our opinion, is the characterizations of these two interesting distributions. the present work is intended to complete, in some way, the works of Nassar and Shahbaz et al. via …

A Short Note On The Paper: "New Characterizations Of The Pareto Distribution", Gholamhossein G. Hamedani, M. Rasekhi

Mathematics, Statistics and Computer Science Faculty Research and Publications

Nofal and El Gebaly (2017), presented certain characterizations of the Pareto distribution based on the conditional expectations of power of the order statistics. In this short note we show that the same results can easily be obtained in terms of the power of the random variable.

Hypothesis Testing For High-Dimensional Problems, Naveen K. Bansal

Mathematics, Statistics and Computer Science Faculty Research and Publications

For high-dimensional hypothesis problems, new approaches have emerged since the publication. The most promising of them uses Bayesian approach. In this chapter, we review some of the past approaches applicable to only law-dimensional hypotheses testing and contrast it with the modern approaches of high-dimensional hypotheses testing. We review some of the new results based on Bayesian decision theory and show how Bayesian approach can be used to accommodate directional hypotheses testing and skewness in the alternatives. A real example of gene expression data is used to demonstrate a Bayesian decision theoretic approach to directional hypotheses testing with skewed alternatives.

Privacy Vulnerabilities In The Practices Of Repairing Broken Digital Artifacts In Bangladesh, Syed Ishtiaque Ahmed, Shion Guha, Mohammad Rashidujjaman Rifat, Faysal Hossain Shezan, Nicola Dell

Mathematics, Statistics and Computer Science Faculty Research and Publications

This paper presents a study on the privacy concerns associated with the practice of repairing broken digital objects in Bangladesh. Historically, repair of old or broken technologies has received less attention in ICTD scholarship than design, development, or use. As a result, the potential privacy risks associated with repair practices have remained mostly unaddressed. This paper describes our three-month long ethnographic study that took place at ten major repair sites in Dhaka, Bangladesh. We show a variety of ways in which the privacy of an individual’s personal data may be compromised during the repair process. We also examine people’s perceptions …

Xinupi3: Teaching Multicore Concepts Using Embedded Xinu, Priva Bansal, Rade Latinovich, Tom Lazar, Patrick J. Mcgee, Dennis Brylow

Mathematics, Statistics and Computer Science Faculty Research and Publications

As computer platforms become more advanced, the need to teach advanced computing concepts grows accordingly. This paper addresses one such need by presenting XinuPi3, a port of the lightweight instructional operating system Embedded Xinu to the Raspberry Pi 3. The Raspberry Pi 3 improves upon previous generations of inexpensive, credit card-sized computers by including a quad-core, ARM-based processor, opening the door for educators to demonstrate essential aspects of modern computing like inter-core communication and genuine concurrency.

Embedded Xinu has proven to be an effective teaching tool for demonstrating low-level concepts on single-core platforms, and it is currently used to …

Extremal H-Colorings Of Trees And 2-Connected Graphs, John Engbers, David Galvin

Mathematics, Statistics and Computer Science Faculty Research and Publications

For graphs G and H, an H-coloring of G is an adjacency preserving map from the vertices of G to the vertices of H. H-colorings generalize such notions as independent sets and proper colorings in graphs. There has been much recent research on the extremal question of finding the graph(s) among a fixed family that maximize or minimize the number of H-colorings. In this paper, we prove several results in this area.

First, we find a class of graphs H with the property that for each H∈H, the n-vertex tree that minimizes the number of …

Varieties Of Restriction Semigroups And Varieties Of Categories, Peter R. Jones

Mathematics, Statistics and Computer Science Faculty Research and Publications

The variety of restriction semigroups may be most simply described as that generated from inverse semigroups (S, ·, −1) by forgetting the inverse operation and retaining the two operations x+ = xx−1 and x* = x−1x. The subvariety B of strictrestriction semigroups is that generated by the Brandt semigroups. At the top of its lattice of subvarieties are the two intervals [B2, B2M = B] and [B0, B0M]. Here, B2and B0 are, respectively, generated by the five-element Brandt semigroup and that obtained …

Protein Structure Classification And Loop Modeling Using Multiple Ramachandran Distributions, Seyed Morteza Najibi, Mehdi Maadooliat, Lan Zhou, Jianhua Z. Huang, Xin Gao

Mathematics, Statistics and Computer Science Faculty Research and Publications

Recently, the study of protein structures using angular representations has attracted much attention among structural biologists. The main challenge is how to efficiently model the continuous conformational space of the protein structures based on the differences and similarities between different Ramachandran plots. Despite the presence of statistical methods for modeling angular data of proteins, there is still a substantial need for more sophisticated and faster statistical tools to model the large-scale circular datasets. To address this need, we have developed a nonparametric method for collective estimation of multiple bivariate density functions for a collection of populations of protein backbone angles. …

K-8 Pre-Service Teachers’ Algebraic Thinking: Exploring The Habit Of Mind Building Rules To Represent Functions, Marta T. Magiera, John C. Moyer, Leigh A. Van Den Kieboom

Mathematics, Statistics and Computer Science Faculty Research and Publications

In this study, through the lens of the algebraic habit of mind Building Rules to Represent Functions, we examined 18 pre-service middle school teachers' ability to use algebraic thinking to solve problems. The data revealed that pre-service teachers' ability to use different features of the habit of mind Building Rules to Represent Functions varied across the features. Significant correlations existed between 8 pairs of the features. The ability to justify a rule was the weakest of the seven features and it was correlated with the ability to chunk information. Implications for mathematics teacher education are discussed.

06. Sas Program Files For Design And Analysis Of Experiments, Angela Dean, Dan Voss, Danel Draguljic

Design and Analysis of Experiments

SAS program files for use with Design and Analysis of Experiments.

08. R Program Files For Design And Analysis Of Experiments, Angela Dean, Dan Voss, Danel Draguljic

Design and Analysis of Experiments

R program files for use with Design and Analysis of Experiments.

07. Sas Data Files For Design And Analysis Of Experiments, Angela Dean, Dan Voss, Danel Draguljic

Design and Analysis of Experiments

SAS Data files for use with Design and Analysis of Experiments.

Flexibility Of Projective-Planar Embeddings, John Maharry, Neil Robertson, Vaidy Sivaraman, Dan Slilaty

Mathematics and Statistics Faculty Publications

Given two embeddings σ1 and σ2 of a labeled nonplanar graph in the projective plane, we give a collection of maneuvers on projective-planar embeddings that can be used to take σ1 to σ2

Advance Care Planning As A Shared Endeavor: Completion Of Acp Documents In A Multidisciplinary Cancer Program, Melissa A. Clark, Miles Q. Ott, Michelle L. Rogers, Mary C. Politi, Susan C. Miller, Laura Moynihan, Katina Robison, Ashley Stuckey, Don Dizon

Statistical and Data Sciences: Faculty Publications

Objective—We examined the roles of oncology providers in advance care planning (ACP) delivery in the context of a multidisciplinary cancer program.

Methods—Semi-structured interviews were conducted with 200 women with recurrent and/or metastatic breast or gynecologic cancer. Participants were asked to name providers they deemed important in their cancer care and whether they had discussed and/or completed ACP documentation. Evidence of ACP documentation was obtained from chart reviews.

Results—Fifty percent of participants self-reported completing an advance directive (AD) and 48.5% had named a healthcare power of attorney (HPA), 38.5% had completed both, and 39.0% had completed neither document. Among women who …

Alcohol Perceptions And Behavior In A Residential Peer Social Network, Shannon R. Kenney, Miles Q. Ott, Matthew Meisel, Nancy P. Barnett

Statistical and Data Sciences: Faculty Publications

Personalized normative feedback is a recommended component of alcohol interventions targeting college students. However, normative data are commonly collected through campus-based surveys, not through actual participant-referent relationships. In the present investigation, we examined how misperceptions of residence hall peers, both overall using a global question and those designated as important peers using person-specific questions, were related to students’ personal drinking behaviors. Participants were 108 students (88% freshman, 54% White, 51% female) residing in a single campus residence hall. Participants completed an online baseline survey in which they reported their own alcohol use and perceptions of peer alcohol use using both …

Curriculum Guidelines For Undergraduate Programs In Data Science, Richard D. De Veaux, Mahesh Agarwal, Maia Averett, Benjamin Baumer, Andrew Bray, Thomas C. Bressoud, Lance Bryant, Lei Z. Cheng, Amanda Francis, Robert Gould, Albert Y. Kim, Matt Kretchmar, Qin Lu, Ann Moskol, Deborah Nolan, Roberto Pelayo, Sean Raleigh, Ricky J. Sethi, Mutiara Sondjaja, Neelesh Tiruviluamala, Paul X. Uhlig, Talitha M. Washington, Curtis L. Wesley, David White, Ping Ye

Statistical and Data Sciences: Faculty Publications

The Park City Math Institute 2016 Summer Undergraduate Faculty Program met for the purpose of composing guidelines for undergraduate programs in data science. The group consisted of 25 undergraduate faculty from a variety of institutions in the United States, primarily from the disciplines of mathematics, statistics, and computer science. These guidelines are meant to provide some structure for institutions planning for or revising a major in data science.

The Use Of The Pivot Pairwise Relative Criteria Importance Assessment Method For Determining The Weights Of Criteria, Florentin Smarandache, Dragisa Stanujkic, Edmundas Kazimieras Zavadskas, Darjan Karabasevic, Zenonas Turskis

Branch Mathematics and Statistics Faculty and Staff Publications

The weights of evaluation criteria could have a significant impact on the results obtained by applying multiple criteria decision-making methods. Therefore, the two extensions of the SWARA method that can be used in cases when it is not easy, or even is impossible to reach a consensus on the expected importance of the evaluation criteria are proposed in this paper. The primary objective of the proposed extensions is to provide an understandable and easy-to-use approach to the collecting of respondents’ real attitudes towards the significance of evaluation criteria and to also provide an approach to the checking of the reliability …

Neural Network Predictions Of A Simulation-Based Statistical And Graph Theoretic Study Of The Board Game Risk, Jacob Munson

Murray State Theses and Dissertations

We translate the RISK board into a graph which undergoes updates as the game advances. The dissection of the game into a network model in discrete time is a novel approach to examining RISK. A review of the existing statistical findings of skirmishes in RISK is provided. The graphical changes are accompanied by an examination of the statistical properties of RISK. The game is modeled as a discrete time dynamic network graph, with the various features of the game modeled as properties of the network at a given time. As the network is computationally intensive to implement, results are produced …

Mechanistic Plug-And-Play Models For Understanding The Impact Of Control And Climate On Seasonal Dengue Dynamics In Iquitos, Peru, Nathan Levick

Mathematics & Statistics ETDs

Dengue virus is a mosquito-borne multi-serotype disease whose dynamics are not precisely understood despite half of the world’s human population being at risk of infection. A recent dataset of dengue case reports from an isolated Amazonian city— Iquitos, Peru—provides a unique opportunity to assess dengue dynamics in a simpli- fied setting. Ten years of clinical surveillance data reveal a specific pattern: two novel serotypes, in turn, invaded and exclusively dominated incidence over several seasonal cycles, despite limited intra-annual variation in climate conditions. Together with mechanistic mathematical models, these data can provide an improved understand- ing of the nonlinear interactions between …

An Examination Of The Neural Unreliability Thesis Of Autism, John Butler, Sophie Molholm, Gizely Andrade, John J. Foxe

Articles

An emerging neuropathological theory of Autism, referred to here as “the neural unreliability thesis,” proposes greater variability in moment-to-moment cortical representation of environmental events, such that the system shows general instability in its impulse response function. Leading evidence for this thesis derives from functional neuroimaging, a methodology ill-suited for detailed assessment of sensory transmission dynamics occurring at the millisecond scale. Electrophysiological assessments of this thesis, however, are sparse and unconvincing. We conducted detailed examination of visual and somatosensory evoked activity using high-density electrical mapping in individuals with autism (N = 20) and precisely matched neurotypical controls (N = 20), recording …

Asymptotic Behavior Of Even-Order Damped Differential Equations With P-Laplacian Like Operators And Deviating Arguments, Qingmin Liu, Martin Bohner, Said R. Grace, Tongxing Li

Mathematics and Statistics Faculty Research & Creative Works

We study the asymptotic properties of the solutions of a class of even-order damped differential equations with p-Laplacian like operators, delayed and advanced arguments. We present new theorems that improve and complement related contributions reported in the literature. Several examples are provided to illustrate the practicability, maneuverability, and efficiency of the results obtained. An open problem is proposed.

An Efficient And Long-Time Accurate Third-Order Algorithm For The Stokes–Darcy System, Wenbin Chen, Max Gunzburger, Dong Sun, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

A third order in time numerical IMEX-type algorithm for the Stokes–Darcy system for flows in fluid saturated karst aquifers is proposed and analyzed. a novel third-order Adams–Moulton scheme is used for the discretization of the dissipative term whereas a third-order explicit Adams–Bashforth scheme is used for the time discretization of the interface term that couples the Stokes and Darcy components. the scheme is efficient in the sense that one needs to solve, at each time step, decoupled Stokes and Darcy problems. Therefore, legacy Stokes and Darcy solvers can be applied in parallel. the scheme is also unconditionally stable and, with …

Birth Mass Is The Key To Understanding The Negative Correlation Between Lifespan And Body Size In Dogs, Rong Fan, Gayla R. Olbricht, Xavior Baker, Chen Hou

Mathematics and Statistics Faculty Research & Creative Works

Larger dog breeds live shorter than the smaller ones, opposite of the mass-lifespan relationship observed across mammalian species. Here we use data from 90 dog breeds and a theoretical model based on the first principles of energy conservation and life history tradeoffs to explain the negative correlation between longevity and body size in dogs. We found that the birth/adult mass ratio of dogs scales negatively with adult size, which is different than the weak interspecific scaling in mammals. Using the model, we show that this ratio, as an index of energy required for growth, is the key to understanding why …

The Decay Of Disease Association With Declining Linkage Disequilibrium: A Fine Mapping Theorem, Mehdi Maadooliat, Naveen K. Bansal, Jibal Upadhya, Manzur R. Farazi, Xiang Li, Max M. He, Scott J. Hebbring, Zhan Ye, Steven J. Schrodi

Mathematics, Statistics and Computer Science Faculty Research and Publications

Several important and fundamental aspects of disease genetics models have yet to be described. One such property is the relationship of disease association statistics at a marker site closely linked to a disease causing site. A complete description of this two-locus system is of particular importance to experimental efforts to fine map association signals for complex diseases. Here, we present a simple relationship between disease association statistics and the decline of linkage disequilibrium from a causal site. Specifically, the ratio of Chi-square disease association statistics at a marker site and causal site is equivalent to the standard measure of pairwise …

Impact Of Myh6 Variants In Hypoplastic Left Heart Syndrome, Aoy Tomita-Mitchell, Karl D. Stamm, Donna K. Mahnke, Min-Su Kim, Pip M. Hidestrand, Huan-Ling Liang, Mary Goetsch, Pippa Simpson, Andrew N. Pelech, James S. Tweddell, D. Woodrow Benson, John Lough, Michael E. Mitchell

Mathematics, Statistics and Computer Science Faculty Research and Publications

Hypoplastic left heart syndrome (HLHS) is a clinically and anatomically severe form of congenital heart disease (CHD). Although prior studies suggest that HLHS has a complex genetic inheritance, its etiology remains largely unknown. The goal of this study was to characterize a risk gene in HLHS and its effect on HLHS etiology and outcome. We performed next-generation sequencing on a multigenerational family with a high prevalence of CHD/HLHS, identifying a rare variant in the α-myosin heavy chain (MYH6) gene. A case-control study of 190 unrelated HLHS subjects was then performed and compared with the 1000 Genomes Project. Damaging …

A Note On The Howson Property In Inverse Semigroups, Peter R. Jones

Mathematics, Statistics and Computer Science Faculty Research and Publications

An algebra has the Howson property if the intersection of any two finitely generated subalgebras is again finitely generated. A simple necessary and sufficient condition is given for the Howson property to hold on an inverse semigroup with finitely many idempotents. In addition, it is shown that any monogenic inverse semigroup has the Howson property.

Integration Over Curves And Surfaces Defined By The Closest Point Mapping, Catherine Kublik, Richard Tsai

Mathematics Faculty Publications

We propose a new formulation for integrating over smooth curves and surfaces that are described by their closest point mappings. Our method is designed for curves and surfaces that are not defined by any explicit parameterization and is intended to be used in combination with level set techniques. However, contrary to the common practice with level set methods, the volume integrals derived from our formulation coincide exactly with the surface or line integrals that one wishes to compute. We study various aspects of this formulation and provide a geometric interpretation of this formulation in terms of the singular values of …