Statistics and Probability Commons^™

Anonpri: A Secure Anonymous Private Authentication Protocol For Rfid Systems, Farzana Rahman, Md. Endadul Hoque, Sheikh Iqbal Ahamed

Mathematics, Statistics and Computer Science Faculty Research and Publications

Privacy preservation in RFID systems is a very important issue in modern day world. Privacy activists have been worried about the invasion of user privacy while using various RFID systems and services. Hence, significant efforts have been made to design RFID systems that preserve users' privacy. Majority of the privacy preserving protocols for RFID systems require the reader to search all tags in the system in order to identify a single RFID tag which not efficient for large scale systems. In order to achieve high-speed authentication in large-scale RFID systems, researchers propose tree-based approaches, in which any pair of tags …

The Battle Against Malaria: A Teachable Moment, Randy K. Schwartz

Journal of Humanistic Mathematics

Malaria has been humanity’s worst public health problem throughout recorded history. Mathematical methods are needed to understand which factors are relevant to the disease and to develop counter-measures against it. This article and the accompanying exercises provide examples of those methods for use in lower- or upper-level courses dealing with probability, statistics, or population modeling. These can be used to illustrate such concepts as correlation, causation, conditional probability, and independence. The article explains how the apparent link between sickle cell trait and resistance to malaria was first verified in Uganda using the chi-squared probability distribution. It goes on to explain …

Incorporating A Spatial Prior Into Nonlinear D-Bar Eit Imaging For Complex Admittivities, Sarah J. Hamilton, Jennifer L. Mueller, Melody Alsaker

Mathematics, Statistics and Computer Science Faculty Research and Publications

Electrical Impedance Tomography (EIT) aims to recover the internal conductivity and permittivity distributions of a body from electrical measurements taken on electrodes on the surface of the body. The reconstruction task is a severely ill-posed nonlinear inverse problem that is highly sensitive to measurement noise and modeling errors. Regularized D-bar methods have shown great promise in producing noise-robust algorithms by employing a low-pass filtering of nonlinear (nonphysical) Fourier transform data specific to the EIT problem. Including prior data with the approximate locations of major organ boundaries in the scattering transform provides a means of extending the radius of the low-pass …

On The Three Dimensional Interaction Between Flexible Fibers And Fluid Flow, Bogdan Nita, Ryan Allaire

Department of Mathematics Faculty Scholarship and Creative Works

In this paper we discuss the deformation of a flexible fiber clamped to a spherical body and immersed in a flow of fluid moving with a speed ranging between 0 and 50 cm/s by means of three dimensional numerical simulation developed in COMSOL . The effects of flow speed and initial configuration angle of the fiber relative to the flow are analyzed. A rigorous analysis of the numerical procedure is performed and our code is benchmarked against well established cases. The flow velocity and pressure are used to compute drag forces upon the fiber. Of particular interest is the behavior …

Quantifying Similarity In Reliability Surfaces Using The Probability Of Agreement, Nathaniel Stevens, C. M. Anderson-Cook

Mathematics

When separate populations exhibit similar reliability as a function of multiple explanatory variables, combining them into a single population is tempting. This can simplify future predictions and reduce uncertainty associated with estimation. However, combining these populations may introduce bias if the underlying relationships are in fact different. The probability of agreement formally and intuitively quantifies the similarity of estimated reliability surfaces across a two-factor input space. An example from the reliability literature demonstrates the utility of the approach when deciding whether to combine two populations or to keep them as distinct. New graphical summaries provide strategies for visualizing the results.

The Pareto-G Extended Weibull Distribution, Oluwaseun Elizabeth Otunuga

Theses, Dissertations and Capstones

In this thesis, the Pareto family of extended Weibull distribution is introduced and discussed extensively. This family consists of the Pareto (Type I) Extended Weibull Distribution or PEW for short, and the Pareto (Type II) Extended Weibull Distribution or otherwise called the Lomax Extended Weibull Distribution or LEW for short. The numbers of the parameters of PEW or LEW depend on the number of parameters for the extended Weibull distribution and type of the Pareto distribution. Some properties of these distributions, such as the hazard rate function, the survival function, moments, skewness, kurtosis, mean deviation and entropies are discussed. The …

Statistical Modeling Of The Default Mode Brain Network Reveals A Segregated Highway Structure, P. E. Stillman, James D. Wilson, M. J. Denny, B. A. Desmarais, Shankar Bhamidi, S. J. Cranmer, Zhong-Lin Lu

Mathematics

We investigate the functional organization of the Default Mode Network (DMN) – an important subnetwork within the brain associated with a wide range of higher-order cognitive functions. While past work has shown the whole-brain network of functional connectivity follows small-world organizational principles, subnetwork structure is less well understood. Current statistical tools, however, are not suited to quantifying the operating characteristics of functional networks as they often require threshold censoring of information and do not allow for inferential testing of the role that local processes play in determining network structure. Here, we develop the correlation Generalized Exponential Random Graph Model (cGERGM) …

The Document Similarity Network: A Novel Technique For Visualizing Relationships In Text Corpora, Dylan Baker

HMC Senior Theses

With the abundance of written information available online, it is useful to be able to automatically synthesize and extract meaningful information from text corpora. We present a unique method for visualizing relationships between documents in a text corpus. By using Latent Dirichlet Allocation to extract topics from the corpus, we create a graph whose nodes represent individual documents and whose edge weights indicate the distance between topic distributions in documents. These edge lengths are then scaled using multidimensional scaling techniques, such that more similar documents are clustered together. Applying this method to several datasets, we demonstrate that these graphs are …

05. Table Of Contents - Design And Analysis Of Experiments, Angela Dean, Dan Voss, Danel Draguljic

Design and Analysis of Experiments

The table of content of Design and Analysis of Experiments.

04. Chapters - Design And Analysis Of Experiments, Angela Dean, Dan Voss, Danel Draguljic

Design and Analysis of Experiments

A list of the chapters from Design and Analysis of Experiments.

02. Preface Of Design And Analysis Of Experiments - 2nd Edition, Angela Dean, Dan Voss, Danel Draguljic

Design and Analysis of Experiments

Preface of the second edition of Design and Analysis of Experiments.

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

Design and Analysis of Experiments

R Data files for Design and Analysis of Experiments.

Influences Of Probability Instruction On Undergraduates' Understanding Of Counting Processes, Kayla Blyman

Theses and Dissertations--Education Sciences

Historically, students in an introductory finite mathematics course at a major university in the mid-south have struggled the most with the counting and probability unit, leading instructors to question if there was a better way to help students master the material. The purpose of this study was to begin to understand connections that undergraduate finite mathematics students are making between counting and probability. By examining student performance in counting and probability, this study provides insights that inform future instruction in courses that include counting and probability. Consequently, this study lays the groundwork for future inquiries in the field of undergraduate …

Bounding And Stabilizing Realizations Of Biased Graphs With A Fixed Group, Nancy Ann Neudauer, Dan Slilaty

Mathematics and Statistics Faculty Publications

Given a group Γ and a biased graph (G, B), we define a what is meant by a Γ-realization of (G, B) and a notion of equivalence of Γ-realizations. We prove that for a finite group Γ and t ≥ 3, that there are numbers n(Γ) and n(Γ, t) such that the number of Γ-realizations of a vertically 3-connected biased graph is at most n(Γ) and that the number of Γ-realizations of a nonseparable biased graph without a (2Ct , ∅)-minor is at most n(Γ, t). Other results pertaining to contrabalanced biased graphs are presented as well as an analogue …

Chain Transitive Homeomorphisms On A Space: All Or None, Ethan Akin, Juho Rautio

Mathematics and Statistics Faculty Research & Creative Works

Extending earlier work, we consider when a compact metric space can be realized as the omega limit set of a discrete time dynamical system. This is equivalent to asking when the space admits a chain transitive homeomorphism. We approach this problem in terms of various conditions on the connected components of the space. We also construct spaces where all homeomorphisms are chain transitive.

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 …

Cutaneous Malignant Melanoma Incidences Analyzed Worldwide By Skin Type Over Advancing Age Of Males And Females: Evidence Estrogen And Androgenic Hair Are Risk Factors, Dianne E. Godar, Madhan Subramanian, Stephen Merrill

Mathematics, Statistics and Computer Science Faculty Research and Publications

We previously analyzed cutaneous malignant melanoma (CMM) incidences worldwide by sex, age, and Fitzpatrick skin type over time (1955-2007) and found only European-ancestry populations have exponential increasing incidences and about a 2-log increase in the risk between the youngest age groups (0-14 and 15-29 yr). We proposed the increasing incidence over time may be from the spread of Human Papilloma Virus (HPV) found in CMM biopsies, and that the 2-log incidence increase between the youngest age groups might be from developing androgenic hair. The increasing incidence with age may be from white hairs transmitting UV radiation to follicular melanocytes. Here …

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

A Comprehensive Analysis Of Team Streakiness In Major League Baseball: 1962-2016, Paul H. Kvam, Zezhong Chen

Department of Math & Statistics Faculty Publications

A baseball team would be considered “streaky” if its record exhibits an unusually high number of consecutive wins or losses, compared to what might be expected if the team’s performance does not really depend on whether or not they won their previous game. If an average team in Major League Baseball (i.e., with a record of 81-81) is not streaky, we assume its win probability would be stable at around 50% for most games, outside of peculiar details of day-to-day outcomes, such as whether the game is home or away, who is the starting pitcher, and so on.

In this …

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 …

All Sites But Skin Cancer Incidences Analyzed Worldwide By Sex, Age, And Skin Type Over Time (1955-2007), Advancing Age, And Uvb Dose Reveals Important Carcinogenic Drivers, Dianne E. Godar, Rossen Gurov, Stephen Merrill

Mathematics, Statistics and Computer Science Faculty Research and Publications

Because we observed increasing incidences over time, advancing age, higher estrogen levels, decreasing UVB (290-315 nm) doses, or lower vitamin D₃, and Human Papillomavirus hiding in immune-privileged sites of hair follicles play roles in melanoma, we wondered if the majority of cancers might have similar carcinogenic drivers. To investigate this possibility, we performed worldwide analysis of all sites but skin cancer over time (1955-2007), advancing age, and UVB doses for males and females with all skin types and ages (0-85+) and in five age groups using IARC data. To investigate Human Papillomavirus’s role, we analyzed the incidences of …

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 …

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 …