Computer Sciences Commons^™

Spiral Unfoldings Of Convex Polyhedra, Joseph O'Rourke

Computer Science: Faculty Publications

The notion of a spiral unfolding of a convex polyhedron, resulting by flattening a special type of Hamiltonian cut-path, is explored. The Platonic and Archimedian solids all have nonoverlapping spiral unfoldings, although among generic polyhedra, overlap is more the rule than the exception. The structure of spiral unfoldings is investigated, primarily by analyzing one particular class, the polyhedra of revolution.

How To Explain The Empirical Success Of Generalized Trigonometric Functions In Processing Discontinuous Signals, Pedro Barragan Olague, Vladik Kreinovich

Departmental Technical Reports (CS)

Trigonometric functions form the basis of Fourier analysis - one of the main signal processing tools. However, while they are very efficient in describing smooth signals, they do not work well for signals that contain discontinuities - such as signals describing phase transitions, earthquakes, etc. It turns out that empirically, one of the most efficient ways of describing and processing such signals is to use a certain generalization of trigonometric functions. In this paper, we provide a theoretical explanation of why this particular generalization is the most empirically efficient one.

How To Make Sure That Everyone Works Towards A Common Goal: Towards Optimal Incentives, Christian Servin, Vladik Kreinovich

Departmental Technical Reports (CS)

No abstract provided.

A Possible Utility-Based Explanation Of Deaton's Paradox (And Habits Of Mind), Hung T. Nguyen, Songsak Sriboonchitta, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

No abstract provided.

How To Compute Von Neumann-Morgenstern Solutions, Martha Osegueda Escobar, Vladik Kreinovich

Departmental Technical Reports (CS)

No abstract provided.

How To Modify Data Processing Algorithms So That They Detect Only Dependencies Which Make Sense To Domain Experts, Geovany Ramirez, Craig Tweedie, Jason Carlsson, Vladik Kreinovich

Departmental Technical Reports (CS)

No abstract provided.

How To Divide A Territory: An Argument In Favor Of Private Property, Mahdokhat Afravi, Vladik Kreinovich

Departmental Technical Reports (CS)

No abstract provided.

The Kumaraswamy Marshal-Olkin Family Of Distributions, Morad Alizadeh, M. H. Tahir, Gauss M. Cordeiro, M. Mansoor, Muhammad Zubair, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

We introduce a new family of continuous distributions called the Kumaraswamy Marshal-Olkin generalized family of distributions. We study some mathematical properties of this family. Its density function is symmetrical, left-skewed, right-skewed and reversed-J shaped, and has constant, increasing, decreasing, upside-down bathtub, bathtub and S-shaped hazard rate. We present some special models and investigate the asymptotics and shapes of the family. We derive a power series for the quantile function and obtain explicit expressions for the moments, generating function, mean deviations, two types of entropies and order statistics. Some useful characterizations of the family are also proposed. The method of maximum …

Students’ Perceptions Of And Responses To Teaching Assistant And Peer Feedback, Kelsey Joy Rodgers, Aladar K. Horvath, Hyunyi Jung, Amanda S. Fry, Heidi A. Diefes-Dux, Monica E. Cardella

Mathematics, Statistics and Computer Science Faculty Research and Publications

Authentic open-ended problems are increasingly appearing in university classrooms at all levels. Formative feedback that leads to learning and improved student work products is a challenge, particularly in large enrollment courses. This is a case study of one first-year engineering student team’s experience with teaching assistant and peer feedback during a series of open-ended mathematical modeling problems called Model-Eliciting Activities. The goal of this study was to gain deep insight into the interactions between students, feedback providers, and written feedback by examining one team’s perceptions of the feedback they received and the changes they made to their solutions based on …

Sequencing Of 15 622 Gene-Bearing Bacs Clarifies The Gene-Dense Regions Of The Barley Genome, María Muñoz-Amatriaín, Stefano Lonardi, Mingcheng Luo, Kavitha Madishetty, Jan T. Svensson, Matthew J. Moscou, Steve Wanamaker, Tao Jiang, Andris Kleinhofs, Gary J. Muehlbauer, Roger P. Wise, Nils Stein, Shane Ma, Edmundo Rodriguez, Dave Kudrna, Prasanna R. Bhat, Shiaoman Chao, Pascal Condamine, Shane Heinen, Josh Resnik, Rod Wing, Heather N. Witt, Matthew Alpert, Marco Beccuti, Serdar Bozdag, Francesca Cordero, Hamid Mirebrahim, Rachid Ounit, Yonghui Wu, Frank You, Jie Zheng, Hana Simková, Jaroslav Dolezel, Jane Grimwood, Jeremy Schmutz, Denisa Duma, Lothar Altschmied, Tom Blake, Phil Bregitzer, Laurel Cooper, Muharrem Dilbirligi, Anders Falk, Leila Feiz, Andreas Graner, Perry Gustafson, Patrick M. Hayes, Peggy Lemaux, Jafar Mammadov, Timothy J. Close

Mathematics, Statistics and Computer Science Faculty Research and Publications

Barley (Hordeum vulgare L.) possesses a large and highly repetitive genome of 5.1 Gb that has hindered the development of a complete sequence. In 2012, the International Barley Sequencing Consortium released a resource integrating whole-genome shotgun sequences with a physical and genetic framework. However, because only 6278 bacterial artificial chromosome (BACs) in the physical map were sequenced, fine structure was limited. To gain access to the gene-containing portion of the barley genome at high resolution, we identified and sequenced 15 622 BACs representing the minimal tiling path of 72 052 physical-mapped gene-bearing BACs. This generated ~1.7 Gb of genomic …

Combining Interval And Probabilistic Uncertainty: What Is Computable?, Vladik Kreinovich, Andrzej Pownuk, Olga Kosheleva

Departmental Technical Reports (CS)

In many practical problems, we need to process measurement results. For example, we need such data processing to predict future values of physical quantities. In these computations, it is important to take into account that measurement results are never absolutely exact, that there is always measurement uncertainty, because of which the measurement results are, in general, somewhat different from the actual (unknown) values of the corresponding quantities. In some cases, all we know about measurement uncertainty is an upper bound; in this case, we have an interval uncertainty, meaning that all we know about the actual value is that is …

Properties Of Catlin’S Reduced Graphs And Supereulerian Graphs, Wei-Guo Chen, Zhi-Hong Chen, Mei Lu

Scholarship and Professional Work - LAS

A graph G is called collapsible if for every even subset R ⊆ V (G), there is a spanning connected subgraph H of G such that R is the set of vertices of odd degree in H. A graph is the reduction of G if it is obtained from G by contracting all the nontrivial collapsible subgraphs. A graph is reduced if it has no nontrivial collapsible subgraphs. In this paper, we first prove a few results on the properties of reduced graphs. As an application, for 3-edge-connected graphs G of order n with d(u) + d(v) ≥ 2(n/p − …

The Kumaraswamy-G Poisson Family Of Distributions, Manoel Wallace A. Ramos, Pedro Rafael D. Marinho, Gauss M. Cordeiro, Ronaldo V. Da Silva, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

For any baseline continuous G distribution, we propose a new generalized family called the Kumaraswamy-G Poisson (denoted with the prefix “Kw-GP”) with three extra positive parameters. Some special distributions in the new family such as the Kw-Weibull Poisson, Kw-gamma Poisson and Kw-beta Poisson distributions are introduced. We derive some mathematical properties of the new family including the ordinary moments, generating function and order statistics. The method of maximum likelihood is used to fit the distributions in the new family. We illustrate its potentiality by means of an application to a real data set.

Concerns About Least Squares Estimation For The Three-Parameter Weibull Distribution: Case Study Of Statistical Software, William V. Harper, Thomas R. James

Mathematics Faculty Scholarship

Least Squares estimation of the 2-parameter Weibull distribution is straightforward; however, there are multiple methods for least squares estimation of the 3-parameter Weibull. The third parameter for the 3-parameter Weibull distribution shifts the origin from 0 to some generally positive value sometimes called the location, threshold, or minimum life. The different methods used by the packages result in fairly major differences in the estimated parameters between the statistical packages. This may have implications for those needing to estimate or apply the results of a 3-parameter Weibull distribution that is used frequently in practice. The results are analyzed in detail based …

Why Linear (And Piecewise Linear) Models Often Successfully Describe Complex Non-Linear Economic And Financial Phenomena: A Fuzzy-Based Explanation, Hung T. Nguyen, Vladik Kreinovich, Olga Kosheleva, Songsak Sriboonchitta

Departmental Technical Reports (CS)

Economic and financial phenomena are highly complex and non-linear. However, surprisingly, in many cases, these phenomena are accurately described by linear models -- or, sometimes, by piecewise linear ones. In this paper, we show that fuzzy techniques can explain the unexpected efficiency of linear and piecewise linear models: namely, we show that a natural fuzzy-based precisiation of imprecise ("fuzzy") expert knowledge often leads to linear and piecewise linear models.

We also discuss which expert-motivated nonlinear models should be used to get a more accurate description of economic and financial phenomena.

Characterizations Of Levy Distribution Via Sub-Independence Of The Random Variables And Truncated Moments, Gholamhossein G. Hamedani, M. Ahsanullah, Seyed Morteza Najibi

Mathematics, Statistics and Computer Science Faculty Research and Publications

The concept of sub-independence is based on the convolution of the distributions of the random variables. It is much weaker than that of independence, but is shown to be sufficient to yield the conclusions of important theorems and results in probability and statistics. It also provides a measure of dissociation between two random variables which is much stronger than uncorrelatedness. Following Ahsanullah and Nevzorov (2014), we present certain characterizations of Levy distribution based on: (i) the sub-independence of the random variables; (ii) a simple relationship between two truncated moments; (iii) conditional expectation of certain function of the random variable. In …

Missing Photos, Suffering Withdrawal, Or Finding Freedom? How Experiences Of Social Media Non-Use Influence The Likelihood Of Reversion, Eric P.S. Baumer, Shion Guha, Emily Quan, David Mimno, Geri K. Gay

Mathematics, Statistics and Computer Science Faculty Research and Publications

This article examines social media reversion, when a user intentionally ceases using a social media site but then later resumes use of the site. We analyze a convenience sample of survey data from people who volunteered to stay off Facebook for 99 days but, in some cases, returned before that time. We conduct three separate analyses to triangulate on the phenomenon of reversion: simple quantitative predictors of reversion, factor analysis of adjectives used by respondents to describe their experiences of not using Facebook, and statistical topic analysis of free-text responses. Significant factors predicting either increased or decreased likelihood of reversion …

Thyroid Autoimmunity As A Window To Autoimmunity: An Explanation For Sex Differences In The Prevalence Of Thyroid Autoimmunity, Stephen Merrill, Ying Mu

Mathematics, Statistics and Computer Science Faculty Research and Publications

Autoimmune thyroid diseases (AITDs), predominately Graves׳ disease and Hashimoto׳s thyroiditis, comprise the most common autoimmune diseases in humans. Both have the production of anti-thyroid antibody as an important aspect and both are much more prevalent in females, being at least 10 times more common than in males. Using these two clues, a hypothesis for the initiation of thyroid autoimmunity is proposed that helps to make the case that the thyroid is one of the most sensitive sites for autoimmunity and helps account for the prevalence and the observed sex differences in AITDs and associated diseases, such as type 1 diabetes …

Zernike Moments And Genetic Algorithm: Tutorial And Application, Oluleye Babatunde, Leisa Armstrong, Jinsong Leng, Dean Diepeveen

Grain and Other Field Crops Research Articles

Aims/ objectives: To demontrate effectiveness of Zernike Moments for Image Classification. Zernike moment(ZM) is an excellent region-based moment which has attracted the attentions of many image processing researchers since its first application to image analysis. Many papers have been published on several works done on ZM but no single paper ever give a detailed information of how the computation of ZM is done from the time the image is captured to the computation of ZM. This work showed how to effectively apply ZM on RGB images. We have demonstrated the effectiveness of Zernike moment in image classification system. A neuro-genetic …

Dow Theory's Peak-And-Trough Analysis Justified, Chrysostomos Stylios, Vladik Kreinovich

Departmental Technical Reports (CS)

In the analysis of dynamic financial quantities such as stock prices, equity prices, etc., reasonable results are often obtained if we only consider local maxima ("peaks") and local minima ("troughs") and ignore all the other values. The empirical success of this strategy remains a mystery. In this paper, we provide a possible explanation for this success.

Optimal Defensive Strategies In One-Dimensional Risk, Darren B. Glass, Todd W. Neller

Math Faculty Publications

We consider a one-dimensional version of the board game RISK and discuss the problem of how a defending player might choose to distribute his armies along a chain of territories in order to maximize the probability of survival. In particular, we analyze a Markov chain model of this situation and run computer simulations in order to make conjectures as to the optimal strategies. The latter sections of the paper analyze this strategy rigorously and use results on recurrence relations and probability theory in order to prove a related result.

Extremal H-Colorings Of Graphs With Fixed Minimum Degree, John Engbers

Mathematics, Statistics and Computer Science Faculty Research and Publications

For graphs G and H, a homomorphism from G to H, or H-coloring of G, is a map from the vertices of G to the vertices of H that preserves adjacency. When H is composed of an edge with one looped endvertex, an H-coloring of G corresponds to an independent set in G. Galvin showed that, for sufficiently large n, the complete bipartite graph Κ is the n-vertex graph with minimum degree δ that has the largest number of independent sets. In this article, we begin the project of generalizing this result …

Free Split Bands, Francis Pastijn, Justin Albert

Mathematics, Statistics and Computer Science Faculty Research and Publications

We solve the word problem for the free objects in the variety consisting of bands with a semilattice transversal. It follows that every free band can be embedded into a band with a semilattice transversal.

Designing For Mistrust, Eric Gossett

ACMS Conference Proceedings 2015

The 2014 ACM North Central Region programming contest contained a problem about a group of v bandits who want to use multiple locks to seal their treasure and distribute keys in such a way that no group of less than m bandits can open all the locks. The problem asks for an algorithm that will determine the number of locks needed for any set of parameters (v, m). I will present an analytic solution that produces a minimum number of locks, a recurrence relation solution, and a constructive algorithm that can print out a table showing the …

The Mathematics Of Evolution, Steven R. Lay

ACMS Conference Proceedings 2015

Like many universities, Lee University has a non-major’s course for liberal arts students. The course typically includes a potpourri of topics: logical thinking, scientific notation, linear functions, estimation, and probability. At Lee, we have found a way to conclude the course that applies these varied topics to an issue designed to engage student interest and promote critical thinking. We have developed a series of three lessons on “The Mathematics of Evolution.” The first lesson is on radiometric dating. The second lesson is on the origin and progression of life. And the third lesson deals with the nature of the DNA …

A Triune Philosophy Of Mathematics, Dusty Wilson

ACMS Conference Proceedings 2015

What is mathematics and is it discovered or invented? The Humanist, Platonist, and Foundationalist each provide answers. But are the options within the philosophy of mathematics so limited? Rather than viewing and describing mathematics in a mutually exclusive manner, each of these approaches includes components of truth from a greater triune philosophy of mathematics. This talk will introduce this inclusive triune paradigm through which to explore fundamental questions about mathematics.

Software Engineering I: Teaching Challenges, Paul C. Grabow

ACMS Conference Proceedings 2015

The term software engineering can be traced to the late 1960s in response to large-scale, software development problems. Since then it has evolved as a discipline, both within industry and the academy. There have been distinct educational successes: “Standard practice” has matured (and found its way into more textbooks),the ACM and IEEE Computer Society have published curriculum guidelines, computer science programs commonly offer at least one software engineering course, and software engineering degrees (undergraduate or graduate) are more common. However, software engineering still presents a challenge. The term itself has become contorted by companies (and society in general); software has …

Mystery Of The Infinite: Developing A Mathematically Based Summer Scholars Program, Christopher Micklewright

ACMS Conference Proceedings 2015

For the past two years, the Templeton Honors College, at Eastern University, has been conducting a Summer Scholars Program for high school students. The program, which has offered courses in a variety of topics, brings students to campus for an intensive residential program, coupled with pre-program and post-program work, for which students can earn college credit. In summer 2014, I helped to develop a mathematically based course, to include rigorous study of discrete mathematics, as well as a variety of lectures and extracurricular activities integrating faith and philosophy with mathematics. In this presentation, I will give an overview of the …

The Best Religious Calendar, Andrew Simoson

ACMS Conference Proceedings 2015

Many religions have deep roots in the rhythms of the moon. And ever since at least the fifth century BC man has known that the moon repeats itself every n = 19 years. Is this integer valuen the best of all choices?Easter follows such a calendar. We briefly show that 19 is second best. And then we run time backwards, and give a rationale as to why a certain species of cicada has a life cycle of 17 years. The answer involves the moon, the Farey series, and Kepler’s laws of motion.

Math, God And Politics—A Fight Over Geometry In 19th Century Italy, Donna Pierce

ACMS Conference Proceedings 2015

In 1839 a polemic, reminiscent of the Renaissance public challenges over mathematical problems, was issued by the leader of the synthetic school of geometry, Vincent Flauti, to the analytical school, headed by Fortunato Padula. Three geometric problems were proposed, all carefully chosen to guarantee a victory for the synthetic school. The judges were from the Royal Academy of Sciences, men also favorable to the synthetic method. Why then did the analytics take up this challenge, and who were the real victors? This was not just a fight over the ‘correct’ way to do geometry, it was a fight over politics, …