Computer Sciences Commons^™

How To Estimate Resilient Modulus For Unbound Aggregate Materials: A Theoretical Explanation Of An Empirical Formula, Pedro Barragan Olague, Soheil Nazarian, Vladik Kreinovich, Afshin Gholamy

Departmental Technical Reports (CS)

To ensure the quality of pavement, it is important to make sure that the resilient moduli -- that describe the stiffness of all the pavement layers -- exceed a certain threshold. From the mechanical viewpoint, pavement is a non-linear medium. Several empirical formulas have been proposed to describe this non-linearity. In this paper, we describe a theoretical explanation for the most accurate of these empirical formulas.

How To Make A Solution To A Territorial Dispute More Realistic: Taking Into Account Uncertainty, Emotions, And Step-By-Step Approach, Mahdokhat Afravi, Vladik Kreinovich

Departmental Technical Reports (CS)

In many real-life situations, it is necessary to divide a disputed territory between several interested parties. The usual way to perform this division is by using Nash's bargaining solution, i.e., by finding a partition that maximizes the product of the participants' utilities. However, this solution is based on several idealized assumptions: that we know the exact values of all the utilities, that division is performed on a purely rational basis, with no emotions involved, and that the entire decision is made once. In practice, we only know the utilities with some uncertainty, emotions are often involved, and the solution is …

Fuzzy Techniques Provide A Theoretical Explanation For The Heuristic L^P-Regularization Of Signals And Images, Fernando Cervantes, Bryan E. Usevitch, Leobardo Valera, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

One of the main techniques used to de-noise and de-blur signals and images is regularization, which is based on the fact that signals and images are usually smoother than noise. Traditional Tikhonov regularization assumes that signals and images are differentiable, but, as Mandelbrot has shown in his fractal theory, many signals and images are not differentiable. To de-noise and de-blur such images, researchers have designed a heuristic method of l^p-regularization.

l^p-regularization leads to good results, but it is not used as widely as should be, because it lacks a convincing theoretical explanation -- and thus, practitioners are often reluctant to …

Membership Functions Representing A Number Vs. Representing A Set: Proof Of Unique Reconstruction, Hung T. Nguyen, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

In some cases, a membership function m(x) represents an unknown number, but in many other cases, it represents an unknown crisp set. In this case, for each crisp set S, we can estimate the degree m(S) to which this set S is the desired one. A natural question is: once we know the values m(S) corresponding to all possible crisp sets S, can we reconstruct the original membership function? In this paper, we show that the original membership function m(x) can indeed be uniquely reconstructed from the values m(S).

Separation Of Parallel Encoded Complex-Valued Slices (Specs) From A Single Complex-Valued Aliased Coil Image, Daniel B. Rowe, Iain P. Bruce, Andrew S. Nencka, James S. Hyde, Mary C. Kociuba

Mathematics, Statistics and Computer Science Faculty Research and Publications

Purpose

Achieving a reduction in scan time with minimal inter-slice signal leakage is one of the significant obstacles in parallel MR imaging. In fMRI, multiband-imaging techniques accelerate data acquisition by simultaneously magnetizing the spatial frequency spectrum of multiple slices. The SPECS model eliminates the consequential inter-slice signal leakage from the slice unaliasing, while maintaining an optimal reduction in scan time and activation statistics in fMRI studies.

Materials and Methods

When the combined k-space array is inverse Fourier reconstructed, the resulting aliased image is separated into the un-aliased slices through a least squares estimator. Without the additional spatial information from …

Roles Of A Teacher And Researcher During In Situ Professional Development Around The Implementation Of Mathematical Modeling Tasks, Hyunyi Jung, Corey Brady

Mathematics, Statistics and Computer Science Faculty Research and Publications

Partnership with teachers for professional development has been considered beneficial because of the potential of collaborative work in the teacher’s own classroom to be relevant to practice. From this perspective, both teachers and researchers can draw on their own expertise and work as authentic partners. In this study, we address the need for such collaboration and focus on how a teacher and a researcher performed their roles when collaboratively implementing mathematical modeling tasks within a context of in situ professional development. Using multi-tier design-based research, as a framework, a researcher worked in a teacher’s classroom to implement a series of …

Volume 08, Meghan Enzinna, Casey Dawn Gailey, Raven Collins, Chiara Enriquez, Amelia Mcconnell, Alexander Morton, Emma Beckett, Leah G. Parr, Briana Adhikusuma, Taylor Embrey, Rowan Davis, Danielle Sisson, Bianca Cherry, Melissa Cacho, Chloe Woodward, Catherine Rollins, Carson Reeher, Landon Cooper, Haley Vasquez, Marlisha Stewart, Eric Whitehead, Sabrina Walker, James Bates

Incite: The Journal of Undergraduate Scholarship

Introduction from Interim Dean Dr. Jennifer Apperson

Indigenous Peoples and the Modern Era by Meghan Enzinna

"Who Says": How Selena Gomez and the Scene Attempt to Subvert the Popular Standards of Beauty by Casey Dawn Gailey

Art by Raven Collins

Meltdown on Social Media: Amy's Baking Company Meets Kitchen Nightmares by Nathena Haddrill

Art by Chiara Enriquez

Design by Amelia Mcconnell

Worth More Than a Thousand Words: A Visual Rhetorical Discussion of Virtual Reality by Examining "Clouds Over Sidra" by Alexander Morton

Design by Emma Beckett

The Sonata: An Analysis of Piano Sonata No. 14 in C Minor, K. …

Why Lp-Methods In Signal And Image Processing: A Fuzzy-Based Explanation, Fernando Cervantes, Bryan E. Usevitch, Vladik Kreinovich

Departmental Technical Reports (CS)

In signal and image processing, it is often beneficial to use semi-heuristic Lp-methods, i.e., methods that minimize the sum of the p-th powers of the discrepancies. In this paper, we show that a fuzzy-based analysis of the corresponding intuitive idea leads exactly to the Lp-methods.

Limitations Of Realistic Monte-Carlo Techniques, Andrzej Pownuk, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Because of the measurement errors, the result Y = f(X1, ..., Xn) of processing the measurement results X1, ..., Xn is, in general, different from the value y = f(x1, ..., xn) that we would obtain if we knew the exact values x1, ..., xn of all the inputs. In the linearized case, we can use numerical differentiation to estimate the resulting difference Y -- y; however, this requires >n calls to an algorithm computing f, and for complex algorithms and large $n$ this can take too long. In situations when for each input xi, we know the probability distribution …

Skewed Factor Models Using Selection Mechanisms, Hyoung-Moon Kim, Mehdi Maadooliat, Reinaldo B. Arellano-Valle, Marc G. Genton

Mathematics, Statistics and Computer Science Faculty Research and Publications

Traditional factor models explicitly or implicitly assume that the factors follow a multivariate normal distribution; that is, only moments up to order two are involved. However, it may happen in real data problems that the first two moments cannot explain the factors. Based on this motivation, here we devise three new skewed factor models, the skew-normal, the skew-t, and the generalized skew-normal factor models depending on a selection mechanism on the factors. The ECME algorithms are adopted to estimate related parameters for statistical inference. Monte Carlo simulations validate our new models and we demonstrate the need for skewed factor models …

A Feature Selection Algorithm To Compute Gene Centric Methylation From Probe Level Methylation Data, Brittany Baur, Serdar Bozdag

Mathematics, Statistics and Computer Science Faculty Research and Publications

DNA methylation is an important epigenetic event that effects gene expression during development and various diseases such as cancer. Understanding the mechanism of action of DNA methylation is important for downstream analysis. In the Illumina Infinium HumanMethylation 450K array, there are tens of probes associated with each gene. Given methylation intensities of all these probes, it is necessary to compute which of these probes are most representative of the gene centric methylation level. In this study, we developed a feature selection algorithm based on sequential forward selection that utilized different classification methods to compute gene centric DNA methylation using probe …

Spanning Eulerian Subgraphs And Catlin’S Reduced Graphs, Wei-Guo Chen, Zhi-Hong Chen

Scholarship and Professional Work - LAS

A graph G is collapsible if for every even subset R ⊆ V (G), there is a spanning connected subgraph H_R of G whose set of odd degree vertices is R. A graph is reduced if it has no nontrivial collapsible subgraphs. Catlin [4] showed that the existence of spanning Eulerian subgraphs in a graph G can be determined by the reduced graph obtained from G by contracting all the collapsible subgraphs of G. In this paper, we present a result on 3-edge-connected reduced graphs of small orders. Then, we prove that a 3-edge-connected graph G of order n …

Epistemic Considerations On Extensive-Form Games, Cagil Tasdemir

Dissertations, Theses, and Capstone Projects

In this thesis, we study several topics in extensive-form games. First, we consider perfect information games with belief revision with players who are tolerant of each other’s hypothetical errors. We bound the number of hypothetical non-rational moves of a player that will be tolerated by other players without revising the belief on that player’s rationality on future moves, and investigate which games yield the backward induction solution.

Second, we consider players who have no way of assigning probabilities to various possible outcomes, and define players as conservative, moderate and aggressive depending on the way they choose, and show that all …

Generalized Transmuted Family Of Distributions: Properties And Applications, Morad Alizadeh, Faton Merovci, Gholamhossein G. Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

We introduce and study general mathematical properties of a new generator of continuous distributions with two extra parameters called the Generalized Transmuted Family of Distributions. We investigate the shapes and present some special models. The new density function can be expressed as a linear combination of exponentiated densities in terms of the same baseline distribution. We obtain explicit expressions for the ordinary and incomplete moments and generating function, Bonferroni and Lorenz curves, asymptotic distribution of the extreme values, Shannon and R´enyi entropies and order statistics, which hold for any baseline model. Further, we introduce a bivariate extension of the new …

Adjoint Fuzzy Partition And Generalized Sampling Theorem, Irina Perfilieva, Michal Holčapek, Vladik Kreinovich

Departmental Technical Reports (CS)

A new notion of adjoint fuzzy partition is introduced and the reconstruction of a function from its F-transform components is analyzed. An analogy with the Nyquist-Shannon-Kotelnikov sampling theorem is discussed.

Robustness As A Criterion For Selecting A Probability Distribution Under Uncertainty, Songsak Sriboonchitta, Hung T. Nguyen, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

Often, we only have partial knowledge about a probability distribution, and we would like to select a single probability distribution $\rho(x)$ out of all probability distributions which are consistent with the available knowledge. One way to make this selection is to take into account that usually, the values $x$ of the corresponding quantity are also known only with some accuracy. It is therefore desirable to select a distribution which is the most robust -- in the sense the x-inaccuracy leads to the smallest possible inaccuracy in the resulting probabilities. In this paper, we describe the corresponding most robust probability distributions, …

Why Dependence Of Productivity On Group Size Is Log-Normal, Francisco Zapata, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Empirical analysis shows that, on average, the productivity of a group log-normally depends on its size. The current explanations for this empirical fact are based on reasonably complex assumptions about the human behavior. In this paper, we show that the same conclusion can be made in effect, from first principles, without making these complex assumptions.

Line-Of-Sight Pursuit And Evasion Games On Polytopes In R^N, John Phillpot

HMC Senior Theses

We study single-pursuer, line-of-sight Pursuit and Evasion games in polytopes in $\mathbb{R}^n$. We develop winning Pursuer strategies for simple classes of polytopes (monotone prisms) in Rⁿ, using proven algorithms for polygons as inspiration and as subroutines. More generally, we show that any Pursuer-win polytope can be extended to a new Pursuer-win polytope in more dimensions. We also show that some more general classes of polytopes (monotone products) do not admit a deterministic winning Pursuer strategy. Though we provide bounds on which polytopes are Pursuer-win, these bounds are not tight. Closing the gap between those polytopes known to be …

Voting Aggregation Leads To (Interval) Median, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

When we have several results of measuring or estimating the same quantities, it is desirable to aggregate them into a single estimate for the desired quantities. A natural requirement is that if the majority of estimates has some property, then the aggregate estimate should have the same property. It turns out that it is not possible to require this forall possible properties -- but we can require it for bounds, i.e., for properties that the value of the quantity is in between given bounds a and b. In this paper, we prove that if we restrict the …

Why Superellipsoids: A Probability-Based Explanation, Pedro Barragan Olague, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, it turns out that the set of possible values of the deviation vector is (approximately) a super-ellipsoid. In this paper, we provide a theoretical explanation for this empirical fact -- an explanation based on the natural notion of scale-invariance.

Automated Conjecturing Approach For Benzenoids, David Muncy

Theses and Dissertations

Benzenoids are graphs representing the carbon structure of molecules, defined by a closed path in the hexagonal lattice. These compounds are of interest to chemists studying existing and potential carbon structures. The goal of this study is to conjecture and prove relations between graph theoretic properties among benzenoids. First, we generate conjectures on upper bounds for the domination number in benzenoids using invariant-defined functions. This work is an extension of the ideas to be presented in a forthcoming paper. Next, we generate conjectures using property-defined functions. As the title indicates, the conjectures we prove are not thought of on our …

Geometric Deformations Of Sodalite Frameworks, Ciprian Borcea, Ileana Streinu

Computer Science: Faculty Publications

In mathematical crystallography and computational materials science, it is important to infer flexibility properties of framework materials from their geometric representation. We study combinatorial, geometric and kinematic properties for frameworks modeled on sodalite.

Multi-Type Display Calculus For Dynamic Epistemic Logic, Sabine Frittella, Giuseppe Greco, Alexander Kurz, Alessandra Palmigiano, Vlasta Sikimić

Engineering Faculty Articles and Research

In the present paper, we introduce a multi-type display calculus for dynamic epistemic logic, which we refer to as Dynamic Calculus. The displayapproach is suitable to modularly chart the space of dynamic epistemic logics on weaker-than-classical propositional base. The presence of types endows the language of the Dynamic Calculus with additional expressivity, allows for a smooth proof-theoretic treatment, and paves the way towards a general methodology for the design of proof systems for the generality of dynamic logics, and certainly beyond dynamic epistemic logic. We prove that the Dynamic Calculus adequately captures Baltag-Moss-Solecki’s dynamic epistemic logic, and enjoys Belnap-style cut …

On Six-Parameter Fréchet Distribution: Properties And Applications, Haitham M. Yousof, Ahmed Z. Afify, Abd El Hadi N. Ebraheim, Gholamhossein G. Hamedani, Nadeem Shafique Butt

Mathematics, Statistics and Computer Science Faculty Research and Publications

This paper introduces a new generalization of the transmuted Marshall-Olkin Fréchet distribution of Afify et al. (2015), using Kumaraswamy generalized family. The new model is referred to as Kumaraswamy transmuted Marshall-Olkin Fréchet distribution. This model contains sixty two sub-models as special cases such as the Kumaraswamy transmuted Fréchet, Kumaraswamy transmuted Marshall-Olkin, generalized inverse Weibull and Kumaraswamy Gumbel type II distributions, among others. Various mathematical properties of the proposed distribution including closed forms for ordinary and incomplete moments, quantile and generating functions and Rényi and η-entropies are derived. The unknown parameters of the new distribution are estimated using the maximum …

Certain Characterizations Of Recently Introduced Distributions, Gholamhossein G. Hamedani, Seyed Morteza Najibi

Mathematics, Statistics and Computer Science Faculty Research and Publications

Various characterizations of twenty two recently introduced distributions are presented. These characterizations are based on: (I) ration of two truncated moments; (ii) the hazard function and (iii) conditional expectations.

A New Weibull-G Family Of Distributions, M. H. Tahir, Muhammad Zubair, M. Mansoor, Gauss M. Cordeiro, Morad Alizadeh, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Statistical analysis of lifetime data is an important topic in reliability engineering, biomedical and social sciences and others. We introduce a new generator based on the Weibull random variable called the new Weibull-G family. We study some of its mathematical properties. Its density function can be symmetrical, left-skewed, right-skewed, bathtub and reversed-J shaped, and has increasing, decreasing, bathtub, upside-down bathtub, J, reversed-J and S shaped hazard rates. Some special models are presented. We obtain explicit expressions for the ordinary and incomplete moments, quantile and generating functions, Renyi entropy, order statistics and reliability. Three useful characterizations based on truncated moments are …

Worldwide Cutaneous Malignant Melanoma Incidences Analyzed By Sex, Age, And Skin Type Over Time (1955–2007): Is Hpv Infection Of Androgenic Hair Follicular Melanocytes A Risk Factor For Developing Melanoma Exclusively In People Of European-Ancestry?, Stephen Merrill, Madhan Subramanian, Dianne E. Godar

Mathematics, Statistics and Computer Science Faculty Research and Publications

The cutaneous malignant melanoma (CMM) incidence has been increasing in an exponential manner in certain populations around the world for over 7 decades. To help illuminate the etiology, we performed worldwide temporal (1955–2007) CMM incidence analysis by sex, age (0–14, 15–29, 30–49, 50–69, 70–85+), and skin type on 6 continents using data from the International Agency for Research on Cancer. We observe an exponential increase in the CMM incidence over time and an increase of about 2 orders of magnitude between age groups 0–14 and 15–29 exclusively in European-ancestry populations around the world independent of skin type (I–III or III–IV). …

Algorithmic Foundations Of Heuristic Search Using Higher-Order Polygon Inequalities, Newton Henry Campbell Jr.

CCAC Theses and Dissertations

The shortest path problem in graphs is both a classic combinatorial optimization problem and a practical problem that admits many applications. Techniques for preprocessing a graph are useful for reducing shortest path query times. This dissertation studies the foundations of a class of algorithms that use preprocessed landmark information and the triangle inequality to guide A* search in graphs. A new heuristic is presented for solving shortest path queries that enables the use of higher order polygon inequalities. We demonstrate this capability by leveraging distance information from two landmarks when visiting a vertex as opposed to the common single landmark …

Tabulating Pseudoprimes And Tabulating Liars, Andrew Shallue

Scholarship

This paper explores the asymptotic complexity of two problems related to the Miller-Rabin-Selfridge primality test. The first problem is to tabulate strong pseudoprimes to a single fixed base $a$. It is now proven that tabulating up to $x$ requires $O(x)$ arithmetic operations and $O(x\log{x})$ bits of space. The second problem is to find all strong liars and witnesses, given a fixed odd composite $n$. This appears to be unstudied, and a randomized algorithm is presented that requires an expected $O((\log{n})^2 + |S(n)|)$ operations (here $S(n)$ is the set of strong liars). Although interesting in their own right, a notable application …

To The Memory Of R. Freivalds, Efim Kinber

School of Computer Science & Engineering Faculty Publications

The paper contains author’s memories of his mentor and teacher R. M. Freivalds.