Statistics and Probability Commons^™

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 …

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. …

Cutaneous Malignant Melanoma Incidences Analyzed Worldwide By Sex, Age, And Skin Type Over Personal Ultraviolet-B Dose Shows No Role For Sunburn But Implies One For Vitamin D3, Dianne E. Godar, Madhan Subramanian, Stephen Merrill

Mathematics, Statistics and Computer Science Faculty Research and Publications

Because the incidence of cutaneous malignant melanoma (CMM) was reported to increase with increasing terrestrial UVR (290–400 nm) doses in the US back in 1975 and a recent publication showed no association exists with UVR exposure at all, we set out to fully elucidate the role of UVR in CMM. To achieve this goal, we analyzed the CMM incidences over latitude and estimated the average personal UVR dose in the US and numerous countries (> 50) on 5 continents around the world. Using data from the International Agency for Research on Cancer in 2005, we performed worldwide analysis of CMM …

Untangling The Most Probable Role For Vitamin D3 In Autism, Dianne E. Godar, Stephen J. Merrill

Mathematics, Statistics and Computer Science Faculty Research and Publications

Recent studies indicate an important role for vitamin D₃ in autism spectrum disorder (ASD), although its mechanism is not completely understood. The most puzzling aspect of ASD is that identical twins, who share identical DNA, do not have 100% concordance rates (∼88% for identical and ∼31% for fraternal twins). These findings provide major clues into the etiology: ASD must involve an environmental factor present in the prenatal milieu that both identical twins are not always exposed to because they do not always share it (i.e., placentas). Combined with the exponential increasing rates of ASD around the world, these observations …

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 …

Some Extended Classes Of Distributions: Characterizations And Properties, Gholamhossein G. Hamedani, Gauss M. Cordeiro, M. C.S. Lima, A. D.C. Nascimento

Mathematics, Statistics and Computer Science Faculty Research and Publications

Based on a simple relationship between two truncated moments and certain functions of the th order statistic, we characterize some extended classes of distributions recently proposed in the statistical literature, videlicet Beta-G, Gamma-G, Kumaraswamy-G and McDonald-G. Several properties of these extended classes and some special cases are discussed. We compare these classes in terms of goodness-of-fit criteria using some baseline distributions by means of two real data sets.

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.

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.

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 …

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.

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 …

Local Holomorphic Extension Of Cauchy Riemann Functions, Brijitta Antony

Doctoral Dissertations

"The purpose of this dissertation is to give an analytic disc approach to the CR extension problem. Analytic discs give a very convenient tool for holomorphic extension of CR functions. The type function is introduced and showed how these type functions have direct application to important questions about CR extension. In this dissertation the CR extension theorem is proved for a rigid hypersurface M in C² given by y = (Re ω)^m(Im ω)ⁿ where m and n are non-negative integers. If the type function is identically zero at the origin, then there is no CR extension. …

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 …

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 A. Goetsch, Mats Hidestrand, Pippa Simpson, Andrew N. Pelech, James S. Tweddell, D. Woodrow Benson, John Lough, Michael 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 …

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 …

A Traders Guide To The Predictive Universe- A Model For Predicting Oil Price Targets And Trading On Them, Jimmie Harold Lenz

Doctor of Business Administration Dissertations

At heart every trader loves volatility; this is where return on investment comes from, this is what drives the proverbial “positive alpha.” As a trader, understanding the probabilities related to the volatility of prices is key, however if you could also predict future prices with reliability the world would be your oyster. To this end, I have achieved three goals with this dissertation, to develop a model to predict future short term prices (direction and magnitude), to effectively test this by generating consistent profits utilizing a trading model developed for this purpose, and to write a paper that anyone with …

Projective-Planar Graphs With No K3,4-Minor. Ii., John Maharry, Dan Slilaty

Mathematics and Statistics Faculty Publications

The authors previously published an iterative process to generate a class of projectiveplanar K3,4-free graphs called ‘patch graphs’. They also showed that any simple, almost 4-connected, nonplanar, and projective-planar graph that is K3,4-free is a subgraph of a patch graph. In this paper, we describe a simpler and more natural class of cubic K3,4- free projective-planar graphs which we call M¨obius hyperladders. Furthermore, every simple, almost 4-connected, nonplanar, and projective-planar graph that is K3,4-free is a minor of a M¨obius hyperladder. As applications of these structures we determine the page number of patch graphs and of M¨obius hyperladders.

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.

Managing The Spread Of Alfalfa Stem Nematodes (Ditylenchus Dipsaci): The Relationship Between Crop Rotation Periods And Pest Re-Emergence, S. Jordan, Claudia Nischwitz, R. Ramirez, Luis F. Gordillo

Mathematics and Statistics Faculty Publications

Alfalfa is a critical cash/rotation crop in the western region of the United States, where it is common to find crops affected by the alfalfa stem nematode (Ditylenchus dipsaci). Understanding the spread dynamics associated with this pest would allow growers to design better management programs and farming practices. This understanding is of particular importance given that there are no nematicides available against alfalfa stem nematodes and control strategies largely rely on crop rotation to non-host crops or by planting resistant varieties of alfalfa. In this paper we present a basic host-parasite model that describes the spread of the …

Effects Of Cell Cycle Noise On Excitable Gene Circuits, Alan Veliz-Cuba, Chinmaya Gupta, Matthew R. Bennett, Krešimir Josić, William Ott

Mathematics Faculty Publications

We assess the impact of cell cycle noise on gene circuit dynamics. For bistable genetic switches and excitable circuits, we find that transitions between metastable states most likely occur just after cell division and that this concentration effect intensifies in the presence of transcriptional delay. We explain this concentration effect with a three-states stochastic model. For genetic oscillators, we quantify the temporal correlations between daughter cells induced by cell division. Temporal correlations must be captured properly in order to accurately quantify noise sources within gene networks.

Convolutions And Green’S Functions For Two Families Of Boundary Value Problems For Fractional Differential Equations, Paul W. Eloe, Jeffrey T. Neugebauer

Mathematics Faculty Publications

We consider families of two-point boundary value problems for fractional differential equations where the fractional derivative is assumed to be the Riemann-Liouville fractional derivative. The problems considered are such that appropriate differential operators commute and the problems can be constructed as nested boundary value problems for lower order fractional differential equations. Green's functions are then constructed as convolutions of lower order Green's functions. Comparison theorems are known for the Green's functions for the lower order problems and so, we obtain analogous comparison theorems for the two families of higher order equations considered here. We also pose a related open question …

Generalized Least-Powers Regressions I: Bivariate Regressions, Nataniel Greene

Publications and Research

The bivariate theory of generalized least-squares is extended here to least-powers. The bivariate generalized least-powers problem of order p seeks a line which minimizes the average generalized mean of the absolute pth power deviations between the data and the line. Least-squares regressions utilize second order moments of the data to construct the regression line whereas least-powers regressions use moments of order p to construct the line. The focus is on even values of p, since this case admits analytic solution methods for the regression coefficients. A numerical example shows generalized least-powers methods performing comparably to generalized least-squares methods, …

A Browser-Based Ide For The Muzecs Platform, Omokolade Hunpatin, Casey O'Hare, Ryan Thomas, Dennis Brylow

Mathematics, Statistics and Computer Science Faculty Research and Publications

We report on a scalable, portable, and secure visual development environment for programming embedded Arduino platforms with Chromebooks in a successful secondary school computer science curriculum. Our web-based environment is part of the larger MUzECS project, an inexpensive replacement module for the Exploring Computer Science (ECS) course being widely deployed in United States high schools. Students use MUzECS to gain a deeper understanding of computing, through a set of blocks which provide appropriate abstractions for working with low-level hardware.

MUzECS improves upon the existing curriculum module by reducing the hardware cost by an order of magnitude, while still preserving the …