Computer Sciences Commons^™

Why Zipf's Law: A Symmetry-Based Explanation, Daniel Cervantes, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, we have probability distributions for which, for large values of the corresponding quantity x, the probability density has the form ρ(x) ~ x^−αfor some α > 0. While, in principle, we have laws corresponding to different α, most frequently, we encounter situations -- first described by Zipf for linguistics -- when α is close to 1. The fact that Zipf's has appeared frequently in many different situations seems to indicate that there must be some fundamental reason behind this law. In this paper, we provide a possible explanation.

Supporting Accurate Interpretation Of Self-Administered Medical Test Results For Mobile Health: Assessment Of Design, Demographics, And Health Condition, Jess C. Hohenstein, Eric P.S. Baumer, Lindsay Reynolds, Elizabeth L. Murnane, Dakota O'Dell, Seoho Lee, Shion Guha, Yu Qi, Erin Rieger, Geri K. Gay

Mathematics, Statistics and Computer Science Faculty Research and Publications

Background: Technological advances in personal informatics allow people to track their own health in a variety of ways, representing a dramatic change in individuals’ control of their own wellness. However, research regarding patient interpretation of traditional medical tests highlights the risks in making complex medical data available to a general audience.

Objective: This study aimed to explore how people interpret medical test results, examined in the context of a mobile blood testing system developed to enable self-care and health management.

Methods: In a preliminary investigation and main study, we presented 27 and 303 adults, respectively, with hypothetical results from several …

Italian Folk Multiplication Algorithm Is Indeed Better: It Is More Parallelizable, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Traditionally, many ethnic groups had their own versions of arithmetic algorithms. Nowadays, most of these algorithms are studied mostly as pedagogical curiosities, as an interesting way to make arithmetic more exciting to the kids: by applying to their patriotic feelings -- if they are studying the algorithms traditionally used by their ethic group -- or simply to their sense of curiosity. Somewhat surprisingly, we show that one of these algorithms -- a traditional Italian multiplication algorithm -- is actually in some reasonable sense better than the algorithm that we all normally use -- namely, it is easier to parallelize.

Statistical Analysis Of Network Change, Teresa D. Schmidt, Martin Zwick

Complex Systems Faculty Publications and Presentations

Networks are rarely subjected to hypothesis tests for difference, but when they are inferred from datasets of independent observations statistical testing is feasible. To demonstrate, a healthcare provider network is tested for significant change after an intervention using Medicaid claims data. First, the network is inferred for each time period with (1) partial least squares (PLS) regression and (2) reconstructability analysis (RA). Second, network distance (i.e., change between time periods) is measured as the mean absolute difference in (1) coefficient matrices for PLS and (2) calculated probability distributions for RA. Third, the network distance is compared against a reference distribution …

Summary Of The Special Issue “Neutrosophic Information Theory And Applications” At “Information” Journal, Florentin Smarandache, Jun Ye

Branch Mathematics and Statistics Faculty and Staff Publications

Over a period of seven months (August 2017–February 2018), the Special Issue dedicated to “Neutrosophic Information Theory and Applications” by the “Information” journal (ISSN 2078-2489), located in Basel, Switzerland, was a success. The Guest Editors, Prof. Dr. Florentin Smarandache from the University of New Mexico (USA) and Prof. Dr. Jun Ye from the Shaoxing University (China), were happy to select—helped by a team of neutrosophic reviewers from around the world, and by the “Information” journal editors themselves—and publish twelve important neutrosophic papers, authored by 27 authors and coauthors. There were a variety of neutrosophic topics studied and used by the …

Gradient Estimation For Attractor Networks, Thomas Flynn

Dissertations, Theses, and Capstone Projects

It has been hypothesized that neural network models with cyclic connectivity may be more powerful than their feed-forward counterparts. This thesis investigates this hypothesis in several ways. We study the gradient estimation and optimization procedures for several variants of these networks. We show how the convergence of the gradient estimation procedures are related to the properties of the networks. Then we consider how to tune the relative rates of gradient estimation and parameter adaptation to ensure successful optimization in these models. We also derive new gradient estimators for stochastic models. First, we port the forward sensitivity analysis method to the …

A Patient-Specific Treatment Model For Graves’ Hyperthyroidism, Balamurugan Pandiyan, Stephen J. Merrill, Flavia Di Bari, Alessandro Antonelli, Salvatore Benvenga

Mathematics, Statistics and Computer Science Faculty Research and Publications

Background: Graves’ is disease an autoimmune disorder of the thyroid gland caused by circulating anti-thyroid receptor antibodies (TRAb) in the serum. TRAb mimics the action of thyroid stimulating hormone (TSH) and stimulates the thyroid hormone receptor (TSHR), which results in hyperthyroidism (overactive thyroid gland) and goiter. Methimazole (MMI) is used for hyperthyroidism treatment for patients with Graves’ disease.

Methods: We have developed a model using a system of ordinary differential equations for hyperthyroidism treatment with MMI. The model has four state variables, namely concentration of MMI (in mg/L), concentration of free thyroxine - FT4 (in pg/mL), and concentration of TRAb …

Regrets, I'Ve Had A Few: When Regretful Experiences Do (And Don't) Compel Users To Leave Facebook, Shion Guha, Eric P.S. Baumer, Geri K. Gay

Mathematics, Statistics and Computer Science Faculty Research and Publications

Previous work has explored regretful experiences on social media. In parallel, scholars have examined how people do not use social media. This paper aims to synthesize these two research areas and asks: Do regretful experiences on social media influence people to (consider) not using social media? How might this influence differ for different sorts of regretful experiences? We adopted a mixed methods approach, combining topic modeling, logistic regressions, and contingency analysis to analyze data from a web survey with a demographically representative sample of US internet users (n=515) focusing on their Facebook use. We found that experiences that arise because …

Advances In Processing, Mining, And Learning Complex Data: From Foundations To Real-World Applications, Jia Wu, Shirui Pan, Chuan Zhou, Gang Li, Wu He, Chengqi Zhang

Information Technology & Decision Sciences Faculty Publications

Processing, mining, and learning complex data refer to an advanced study area of data mining and knowledge discovery concerning the development and analysis of approaches for discovering patterns and learning models from data with a complex structure (e.g., multirelational data, XML data, text data, image data, time series, sequences, graphs, streaming data, and trees) [1–5]. These kinds of data are commonly encountered in many social, economic, scientific, and engineering applications. Complex data pose new challenges for current research in data mining and knowledge discovery as they require new methods for processing, mining, and learning them. Traditional …

Type I General Exponential Class Of Distributions, Gholamhossein G. Hamedani, Haitham M. Yousof, Mahdi Rasekhi, Morad Alizadeh, Seyed Morteza Najibi

Mathematics, Statistics and Computer Science Faculty Research and Publications

We introduce a new family of continuous distributions and study the mathematical properties of the new family. Some useful characterizations based on the ratio of two truncated moments and hazard function are also presented. We estimate the model parameters by the maximum likelihood method and assess its performance based on biases and mean squared errors in a simulation study framework.

Bootcmatch: A Software Package For Bootstrap Amg Based On Graphweighted Matching, Pasqua D'Ambra, Salvatore Filipone, Panayot S. Vassilevski

Mathematics and Statistics Faculty Publications and Presentations

This article has two main objectives: one is to describe some extensions of an adaptive Algebraic Multigrid (AMG) method of the form previously proposed by the first and third authors, and a second one is to present a new software framework, named BootCMatch, which implements all the components needed to build and apply the described adaptive AMG both as a stand-alone solver and as a preconditioner in a Krylov method. The adaptive AMG presented is meant to handle general symmetric and positive definite (SPD) sparse linear systems, without assuming any a priori information of the problem and its origin; the …

Cluster-Based Network Proximities For Arbitrary Nodal Subsets, Kenneth S. Berenhaut, Peter S. Barr, Alyssa M. Kogel, Ryan L. Melvin

Faculty & Staff Scholarship

The concept of a cluster or community in a network context has been of considerable interest in a variety of settings in recent years. In this paper, employing random walks and geodesic distance, we introduce a unified measure of cluster-based proximity between nodes, relative to a given subset of interest. The inherent simplicity and informativeness of the approach could make it of value to researchers in a variety of scientific fields. Applicability is demonstrated via application to clustering for a number of existent data sets (including multipartite networks). We view community detection (i.e. when the full set of network nodes …

Extensions Of The Morse-Hedlund Theorem, Eben Blaisdell

Honors Theses

Bi-infinite words are sequences of characters that are infinite forwards and backwards; for example "...ababababab...". The Morse-Hedlund theorem says that a bi-infinite word f repeats itself, in at most n letters, if and only if the number of distinct subwords of length n is at most n. Using the example, "...ababababab...", there are 2 subwords of length 3, namely "aba" and "bab". Since 2 is less than 3, we must have that "...ababababab..." repeats itself after at most 3 letters. In fact it does repeat itself every two letters. …

Old English Character Recognition Using Neural Networks, Sattajit Sutradhar

College of Graduate Studies: Theses & Dissertations

Character recognition has been capturing the interest of researchers since the beginning of the twentieth century. While the Optical Character Recognition for printed material is very robust and widespread nowadays, the recognition of handwritten materials lags behind. In our digital era more and more historical, handwritten documents are digitized and made available to the general public. However, these digital copies of handwritten materials lack the automatic content recognition feature of their printed materials counterparts. We are proposing a practical, accurate, and computationally efficient method for Old English character recognition from manuscript images. Our method relies on a modern machine learning …

On Comparability Of Bigrassmannian Permutations, John Engbers, Adam Hammett

Mathematics, Statistics and Computer Science Faculty Research and Publications

Let S_n and G_n denote the respective sets of ordinary and bigrassmannian (BG) permutations of order n, and let (G_n,≤) denote the Bruhat ordering permutation poset. We study the restricted poset (B_n,≤), first providing a simple criterion for comparability. This criterion is used to show that that the poset is connected, to enumerate the saturated chains between elements, and to enumerate the number of maximal elements below r fixed elements. It also quickly produces formulas for β(ω) (α(ω), respectively), the number of BG permutations weakly below (weakly above, respectively) a fixed ω ∈ B …

Neutrosophic Operational Research - Vol. 3., Florentin Smarandache, Mohamed Abdel Basset, Victor Chang

Branch Mathematics and Statistics Faculty and Staff Publications

Foreword John R. Edwards This book is an excellent exposition of the use of Data Envelopment Analysis (DEA) to generate data analytic insights to make evidence-based decisions, to improve productivity, and to manage cost-risk and benefitopportunity in public and private sectors. The design and the content of the book make it an up-to-date and timely reference for professionals, academics, students, and employees, in particular those involved in strategic and operational decisionmaking processes to evaluate and prioritize alternatives to boost productivity growth, to optimize the efficiency of resource utilization, and to maximize the effectiveness of outputs and impacts to stakeholders. It …

Fundamentals Of Neutrosophic Logic And Sets And Their Role In Artificial Intelligence (Fundamentos De La Lógica Y Los Conjuntos Neutrosóficos Y Su Papel En La Inteligencia Artificial ), Florentin Smarandache, Maykel Leyva-Vazquez

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophy is a new branch of philosophy which studies the origin, nature and scope of neutralities. This has formed the basis for a series of mathematical theories that generalize the classical and fuzzy theories such as the neutrosophic sets and the neutrosophic logic. In the paper, the fundamental concepts related to neutrosophy and its antecedents are presented. Additionally, fundamental concepts of artificial intelligence will be defined and how neutrosophy has come to strengthen this discipline.

On The Mixtures Of Weibull And Pareto (Iv) Distribution: An Alternative To Pareto Distribution, I. Ghosh, Gholamhossein G. Hamedani, Naveen K. Bansal, Mehdi Maadooliat

Mathematics, Statistics and Computer Science Faculty Research and Publications

Finite mixture models have provided a reasonable tool to model various types of observed phenomena, specially those which are random in nature. In this article, a finite mixture of Weibull and Pareto (IV) distribution is considered and studied. Some structural properties of the resulting model are discussed including estimation of the model parameters via expectation maximization (EM) algorithm. A real-life data application exhibits the fact that in certain situations, this mixture model might be a better alternative than the rival popular models.

On Characterizations Of Mcllog, Ellogw, Pthl And K-Ge Distributions, Gholamhossein G. Hamedani, Nadeem Shafique Butt

Mathematics, Statistics and Computer Science Faculty Research and Publications

Huang S. and Oluyede (2016), Oluyede et al. (2016), Krishnarani (2016) and Rather and Rather (2017) consider the "McDonald Log-Logistic", the "Exponentiated Log-Logistic Weibull", the "Power Transformation Half-Logistic" and "k-Generalized Exponential" distributions, respectively, and study certain properties and applications of these distributions. The present short note is intended to complete, in some way, the above mentioned works via establishing certain characterizations of these distributions in different directions.

Characterizations And Infinite Divisibility Of Certain Recently Introduced Distributions Iii, Gholamhossein G. Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Certain characterizations of recently proposed univariate continuous distributions are presented in different directions. This work may be a source of preventing reinventing and duplicating the existing distributions and calling them newly proposed distributions.

A Bayesian Variable Selection Approach Yields Improved Detection Of Brain Activation From Complex-Valued Fmri, Cheng-Han Yu, Raquel Prado, Hernando Ombao, Daniel B. Rowe

Mathematics, Statistics and Computer Science Faculty Research and Publications

Voxel functional magnetic resonance imaging (fMRI) time courses are complex-valued signals giving rise to magnitude and phase data. Nevertheless, most studies use only the magnitude signals and thus discard half of the data that could potentially contain important information. Methods that make use of complex-valued fMRI (CV-fMRI) data have been shown to lead to superior power in detecting active voxels when compared to magnitude-only methods, particularly for small signal-to-noise ratios (SNRs). We present a new Bayesian variable selection approach for detecting brain activation at the voxel level from CV-fMRI data. We develop models with complex-valued spike-and-slab priors on the activation …

Analysis Of High Performance Scientific Programming Workflows, Withana Kankanamalage Umayanganie Klaassen

Open Access Theses & Dissertations

Substantial time is spent on building, optimizing and maintaining large-scale software that is run on supercomputers. However, little has been done to utilize overall resources efficiently when it comes to including expensive human resources. The community is beginning to acknowledge that optimizing the hardware performance such as speed and memory bottlenecks contributes less to the overall productivity than does the development lifecycle of high-performance scientific applications. Researchers are beginning to look at overall scientific workflows for high performance computing. Scientific programming productivity is measured by time and effort required to develop, configure, and maintain a simulation experiment and its constituent …

The Rsa Cryptosystem, Rodrigo Iglesias

Williams Honors College, Honors Research Projects

This paper intends to present an overview of the RSA cryptosystem. Cryptosystems are mathematical algorithms that disguise information so that only the people for whom the information is intended can read it. The invention of the RSA cryptosystem in 1977 was a significant event in the history of cryptosystems. We will describe in detail how the RSA cryptosystem works and then illustrate the process with a realistic example using fictional characters. In addition, we will discuss how cryptosystems worked prior to the invention of RSA and the advantage of using RSA over any of the previous cryptosystems. This will help …

Meeting Real World Demands Of The Global Economy: An Employer's Perspective, Doreen Mcgunagle, Laura Zizka

Journal of Aviation/Aerospace Education & Research

Educational programs prepare students theoretically for the workplace, but many programs are still lacking in the real-world skills that the workplace requires. This is especially evident in Science, Technology, Engineering, and Math (STEM) education where today’s graduates hold a fundamental role in advancing science, medicine, sustainability, national security, and the economy, yet the programs to prepare them are falling short of employer expectations. At present, there is a lack of information on the necessary skills for workplace success that is specific to Airline, Aerospace, Defense (A&D) and related Industries’ STEM graduates. This paper attempts to fill this gap by offering …

Linear Algebra Applications In 3d Computer Graphics, Albert A. Antero, Chris Choung, Chris Goff

Math 365 Class Projects

Linear Transformations, Homogenous Coordinates, World Matrix, Project Matrices, Normalized Device Coordinates, View Matrix

Logic -> Proof -> Rest, Maxwell Taylor

Senior Independent Study Theses

REST is a common architecture for networked applications. Applications that adhere to the REST constraints enjoy significant scaling advantages over other architectures. But REST is not a panacea for the task of building correct software. Algebraic models of computation, particularly CSP, prove useful to describe the composition of applications using REST. CSP enables us to describe and verify the behavior of RESTful systems. The descriptions of each component can be used independently to verify that a system behaves as expected. This thesis demonstrates and develops CSP methodology to verify the behavior of RESTful applications.

Sports Analytics With Computer Vision, Colby T. Jeffries

Senior Independent Study Theses

Computer vision in sports analytics is a relatively new development. With multi-million dollar systems like STATS’s SportVu, professional basketball teams are able to collect extremely fine-detailed data better than ever before. This concept can be scaled down to provide similar statistics collection to college and high school basketball teams. Here we investigate the creation of such a system using open-source technologies and less expensive hardware. In addition, using a similar technology, we examine basketball free throws to see whether a shooter’s form has a specific relationship to a shot’s outcome. A system that learns this relationship could be used to …

International Students’ Expectations Of Information Literacy Instruction, Nicole Johnston, Meggan Houlihan, Jodi Neindorf

Research outputs 2014 to 2021

This paper presents the findings of a case study that investigated international university students’ expectations and experiences of information literacy across two countries. The results from this case study provide insights that can be utilized by librarians working with international students, to plan and develop their information literacy instruction classes and programs. Armed with an awareness of what international students’ expectations and experiences with information literacy programs are, librarians can develop more meaningful instruction that better meets the information needs of international students. Moving beyond the pilot survey, the researchers aim to improve the survey instrument and collaborate with librarians …

Statistical Analysis Of Momentum In Basketball, Mackenzi Stump

Honors Projects

The “hot hand” in sports has been debated for as long as sports have been around. The debate involves whether streaks and slumps in sports are true phenomena or just simply perceptions in the mind of the human viewer. This statistical analysis of momentum in basketball analyzes the distribution of time between scoring events for the BGSU Women’s Basketball team from 2011-2017. We discuss how the distribution of time between scoring events changes with normal game factors such as location of the game, game outcome, and several other factors. If scoring events during a game were always randomly distributed, or …

Why Rectified Linear Neurons Are Efficient: Symmetry-Based, Complexity-Based, And Fuzzy-Based Explanations, Olac Fuentes, Justin Parra, Elizabeth Y. Anthony, Vladik Kreinovich

Departmental Technical Reports (CS)

Traditionally, neural networks used a sigmoid activation function. Recently, it turned out that piecewise linear activation functions are much more efficient -- especially in deep learning applications. However, so far, there have been no convincing theoretical explanation for this empirical efficiency. In this paper, we show that, by using different uncertainty techniques, we can come up with several explanations for the efficiency of piecewise linear neural networks. The existence of several different explanations makes us even more confident in our results -- and thus, in the efficiency of piecewise linear activation functions.