Computer Sciences Commons^™

Source Unfoldings Of Convex Polyhedra Via Certain Closed Curves, Jin-Ichi Itoh, Joseph O'Rourke, Costin Vîlcu

Computer Science: Faculty Publications

Abstract. We extend the notion of a source unfolding of a convex polyhedron P to be based on a closed polygonal curve Q in a particular class rather than based on a point. The class requires that Q “lives on a cone” to both sides; it includes simple, closed quasigeodesics. Cutting a particular subset of the cut locus of Q (in P) leads to a non-overlapping unfolding of the polyhedron. This gives a new general method to unfold the surface of any convex polyhedron to a simple, planar polygon

Estimating Correlation Under Interval And Fuzzy Uncertainty: Case Of Hierarchical Estimation, Ali Jalal-Kamali

Departmental Technical Reports (CS)

In many situations, we are interested in finding the correlation ρ between different quantities x and y based on the values x_i and y_i of these quantities measured in different situations i. The correlation is easy to compute when we know the exact sample values x_i and y_i. In practice, the sample values come from measurements or from expert estimates; in both cases, the values are not exact. Sometimes, we know the probabilities of different values of measurement errors, but in many cases, we only know the upper bounds Δ_xi and Δ_yi on …

Semi-Heuristic Target-Based Fuzzy Decision Procedures: Towards A New Interval Justification, Christian Servin, Van-Nam Huynh, Yoshiteru Nakamori

Departmental Technical Reports (CS)

To more adequately describe human decision making, V.-N. Nuynh, Y. Nakamori, and others proposed a special semi-heuristic target-based fuzzy decision procedure. A usual justification for this procedure is based on the selection of the simplest possible membership functions and "and"- and "or"-operations; if we use more complex membership functions and "and"- and "or"-operations, we get different results. Interestingly, in practical applications, the procedure based on the simplest choices most adequately describes human preferences. It is therefore desirable to come up with a justification that explains this empirical fact. Such a justification is proposed in this paper

Modeling Spatial Uncertainties In Geospatial Data Fusion And Mining, Boris Kovalerchuk, Leonid Perlovsky, Michael Kovalerchuk

All Faculty Scholarship for the College of the Sciences

Geospatial data analysis relies on Spatial Data Fusion and Mining (SDFM), which heavily depend on topology and geometry of spatial objects. Capturing and representing geometric characteristics such as orientation, shape, proximity, similarity, and their measurement are of the highest interest in SDFM. Representation of uncertain and dynamically changing topological structure of spatial objects including social and communication networks, roads and waterways under the influence of noise, obstacles, temporary loss of communication, and other factors. is another challenge. Spatial distribution of the dynamic network is a complex and dynamic mixture of its topology and geometry. Historically, separation of topology and geometry …

Challenging Disciplinary Boundaries In The First Year: A New Introductory Integrated Science Course For Stem Majors, Lisa Gentile, Lester Caudill, Mirela Fetea, April L. Hill, Kathy Hoke, Barry Lawson, Ovidiu Z. Lipan, Michael Kerckhove, Carol A. Parish, Krista J. Stenger, Doug Szajda

Department of Math & Statistics Faculty Publications

To help undergraduates make connections among disciplines so they are able to approach, evaluate, and contribute to the solutions of important global problems, our campus has been focused on interdisciplinary research and education opportunities across the science, technology, engineering, and mathematics (STEM) disciplines. This paper describes the mobilization, planning, and implementation of a first-year interdisciplinary course for STEM majors that integrates key concepts found in traditional first-semester biology, chemistry, computer science, mathematics, and physics courses. This team-taught course, Integrated Quantitative Science (IQS), is half of a first-year student’s schedule in both semesters and is composed of a double lecture and …

Human Gene Copy Number Spectra Analysis In Congenital Heart Malformations, Aoy Tomita-Mitchell, Donna K. Mahnke, Craig Struble, Maureen E. Tuffnell, Karl D. Stamm, Mats Hidestrand, Susan Harris, Mary A. Goetsch, Pippa Simpson, David P. Bick, Ulrich Broeckel, Andrew N. Pelech, James S. Tweddell, Michael Mitchell

Mathematics, Statistics and Computer Science Faculty Research and Publications

The clinical significance of copy number variants (CNVs) in congenital heart disease (CHD) continues to be a challenge. Although CNVs including genes can confer disease risk, relationships between gene dosage and phenotype are still being defined. Our goal was to perform a quantitative analysis of CNVs involving 100 well-defined CHD risk genes identified through previously published human association studies in subjects with anatomically defined cardiac malformations. A novel analytical approach permitting CNV gene frequency “spectra” to be computed over prespecified regions to determine phenotype-gene dosage relationships was employed. CNVs in subjects with CHD (n = 945), subphenotyped into 40 …

Genomic Analysis Of Immune Response Against Vibrio Cholerae Hemolysin In Caenorhabditis Elegans, Surasri N. Sahu, Jada Lewis, Isha Patel, Serdar Bozdag, Jeong H. Lee, Joseph E. Leclerc, Hediye Nese Cinar

Mathematics, Statistics and Computer Science Faculty Research and Publications

Vibrio cholerae cytolysin (VCC) is among the accessory V. cholerae virulence factors that may contribute to disease pathogenesis in humans. VCC, encoded by hlyA gene, belongs to the most common class of bacterial toxins, known as poreforming toxins (PFTs). V. cholerae infects and kills Caenorhabditis elegans via cholerae toxin independent manner. VCC is required for the lethality, growth retardation and intestinal cell vacuolation during the infection. However, little is known about the host gene expression responses against VCC. To address this question we performed a microarray study in C. elegans exposed to V. cholerae strains with intact and deleted hlyA …

H-Colouring Bipartite Graphs, John Engbers, David Galvin

Mathematics, Statistics and Computer Science Faculty Research and Publications

For graphs G and H, an H-colouring of G (or homomorphism from G to H) is a function from the vertices of G to the vertices of H that preserves adjacency. H-colourings generalize such graph theory notions as proper colourings and independent sets. For a given H, k∈V(H) and G we consider the proportion of vertices of G that get mapped to k in a uniformly chosen H-colouring of G. Our main result concerns this quantity when G is regular and bipartite. We find numbers 0⩽a−(k)⩽a+(k)⩽1 with the property that for all such G, with high probability the proportion is …

Challenging Disciplinary Boundaries In The First Year: A New Introductory Integrated Science Course For Stem Majors, Lisa Gentile, Lester Caudill, Mirela Fetea, April L. Hill, Kathy Hoke, Barry Lawson, Ovidiu Z. Lipan, Michael Kerckhove, Carol A. Parish, Krista J. Stenger, Doug Szajda

Biology Faculty Publications

To help undergraduates make connections among disciplines so they are able to approach, evaluate, and contribute to the solutions of important global problems, our campus has been focused on interdisciplinary research and education opportunities across the science, technology, engineering, and mathematics (STEM) disciplines. This paper describes the mobilization, planning, and implementation of a first-year interdisciplinary course for STEM majors that integrates key concepts found in traditional first-semester biology, chemistry, computer science, mathematics, and physics courses. This team-taught course, Integrated Quantitative Science (IQS), is half of a first-year student’s schedule in both semesters and is composed of a double lecture and …

K-8 Preservice Teachers’ Inductive Reasoning In The Problem-Solving Contexts, Marta Magiera

Mathematics, Statistics and Computer Science Faculty Research and Publications

This paper reports the results from an exploratory study of K-8 pre-service teachers’ inductive reasoning. The analysis of 130 written solutions to seven tasks and 77 reflective journals completed by 20 pre-service teachers lead to descriptions of inductive reasoning processes, i.e. specializing, conjecturing, generalizing, and justifying, in the problem-solving contexts. The uncovered characterizations of the four inductive reasoning processes were further used to describe pathways of successful generalizations. The results highlight the importance of specializing and justifying in constructing powerful generalizations. Implications for teacher education are discussed.

Using Bioinformatics To Efficiently Organize And Analyze Significant Immunogenic Epitope Sequences In Various Stages Of Trypanosoma Cruzi, Karla Singh^, Andrea Wurm, Clemente Aguilar, Alexandre Marques, M-Y Leung*, Igor Almeida*

COURI Symposium Abstracts, Spring 2012

No abstract provided.

Generating Minimal Pair-Wise Covering Test Suites, Luis C. Gutierrez ^, Martine Ceberio *

COURI Symposium Abstracts, Spring 2012

Software is ubiquitous and needs to be reliable. Software testing therefore plays an important role in software development. Proper testing a software system informs about its quality and reliability so as to prevent unexpected behavior during system execution. One of the methods to prevent failures consists in testing a system under different input values, but when all possible input values are tested, an impractical number of test cases might result. In software testing, pair-wise testing is a combinatorial technique which uses combination of pair input values to generate test cases. Using pair-wise testing dramatically reduces the number of test cases, …

Simplicity Is Worse Than Theft: A Constraint-Based Explanation Of A Seemingly Counter-Intuitive Russian Saying, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, simplified models, models that enable us to gauge the quality of different decisions reasonably well, lead to far-from-optimal situations when used in searching for an optimal decision. There is even an appropriate Russian saying: simplicity is worse than theft. In this paper, we provide a mathematical explanation of this phenomenon.

Kinematic Spaces And De Vries Algebras: Towards Possible Physical Meaning Of De Vries Algebras, Olga Kosheleva, Francisco Zapata

Departmental Technical Reports (CS)

Traditionally, in physics, space-times are described by (pseudo-)Riemann spaces, i.e., by smooth manifolds with a tensor metric field. However, in several physically interesting situations smoothness is violated: near the Big Bang, at the black holes, and on the microlevel, when we take into account quantum effects. In all these situations, what remains is causality -- an ordering relation. To describe such situations, in the 1960s, geometers H. Busemann and R. Pimenov and physicists E. Kronheimer and R. Penrose developed a theory of kinematic spaces. Originally, kinematic spaces were formulated as topological ordered spaces, but it turned out that kinematic …

Near-Optimal Scheduling And Decision-Making Models For Reactive And Proactive Fault Tolerance Mechanisms, Nichamon Naksinehaboon

Doctoral Dissertations

As High Performance Computing (HPC) systems increase in size to fulfill computational power demand, the chance of failure occurrences dramatically increases, resulting in potentially large amounts of lost computing time. Fault Tolerance (FT) mechanisms aim to mitigate the impact of failure occurrences to the running applications. However, the overhead of FT mechanisms increases proportionally to the HPC systems' size. Therefore, challenges arise in handling the expensive overhead of FT mechanisms while minimizing the large amount of lost computing time due to failure occurrences.

In this dissertation, a near-optimal scheduling model is built to determine when to invoke a hybrid checkpoint …

Teaching Computers To Think: Analysis Of Artificial Intelligence And Connect Four, Kirk Baly, Andrew Freeman, Andrew Jarratt, Kyle Kling, Owen Prough

Symposium on Research and Creative Expression (SORCE)

Connect Four is a classic two person, zero-sum game in which players utilize their wits and gravity to connect four of their own pieces in a horizontal, vertical, or diagonal row while blocking their opponent’s attempt to do the same. We have constructed a simulation of this game which we have used as a base for the implementation and testing of varying Artificial Intelligence (AI) systems. Early strategies worked according to simple strategic methods, while more advanced heuristics employed a Min-Max Tree in tandem with methods to determine how advantageous a certain board would be. This Min-Max Tree goes beyond …

Equitable Labelings Of Caterpillar Graphs, Mark Burek, William Olson, Brock Taulbee

Symposium on Research and Creative Expression (SORCE)

The Graceful Tree Conjecture in graph theory has been open for almost half a century. The conjecture states that the vertices of any tree can be labeled with distinct integers between 0 and the number of edges of the tree in a way that the edges can be uniquely identified by the absolute value of the difference between their vertex labels. One possible approach to prove the conjecture is to prove the more general k-equitable tree conjecture. In a k-equitable labeling we assign integers from the set {0,1,2,…,k-1} to the vertices. Each edge will receive a label that is the …

Mathematical Dispositions And Student Learning: A Metaphorical Analysis, Jinfa Cai, Victoria Robison, John Moyer, Ning Wang, Bikai Nie

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

Combinatorics Using Computational Methods, Derrick Stolee

Department of Mathematics: Dissertations, Theses, and Student Research

Computational combinatorics involves combining pure mathematics, algorithms, and computational resources to solve problems in pure combinatorics. This thesis provides a theoretical framework for combinatorial search, which is then applied to several problems in combinatorics. Some results in space-bounded computational complexity are also presented.

A Common Framework For Restriction Semigroups And Regular *-Semigroups, Peter R. Jones

Mathematics, Statistics and Computer Science Faculty Research and Publications

Left restriction semigroups have appeared at the convergence of several flows of research, including the theories of abstract semigroups, of partial mappings, of closure operations and even in logic. For instance, they model unary semigroups of partial mappings on a set, where the unary operation takes a map to the identity map on its domain. This perspective leads naturally to dual and two-sided versions of the restriction property. From a varietal perspective, these classes of semigroups–more generally, the corresponding classes of Ehresmann semigroups–derive from reducts of inverse semigroups, now taking a to a⁺=aa⁻¹ (or, dually, …

A Cautionary Note On Generalized Linear Models For Covariance Of Unbalanced Longitudinal Data, Jianhua Z. Huang, Min Chen, Mehdi Maadooliat, Mohsen Pourahmadi

Mathematics, Statistics and Computer Science Faculty Research and Publications

Missing data in longitudinal studies can create enormous challenges in data analysis when coupled with the positive-definiteness constraint on a covariance matrix. For complete balanced data, the Cholesky decomposition of a covariance matrix makes it possible to remove the positive-definiteness constraint and use a generalized linear model setup to jointly model the mean and covariance using covariates (Pourahmadi, 2000). However, this approach may not be directly applicable when the longitudinal data are unbalanced, as coherent regression models for the dependence across all times and subjects may not exist. Within the existing generalized linear model framework, we show how to overcome …

Physiologic Noise Regression, Motion Regression, And Toast Dynamic Field Correction In Complex-Valued Fmri Time Series, Andrew D. Hahn, Daniel B. Rowe

Mathematics, Statistics and Computer Science Faculty Research and Publications

As more evidence is presented suggesting that the phase, as well as the magnitude, of functional MRI (fMRI) time series may contain important information and that there are theoretical drawbacks to modeling functional response in the magnitude alone, removing noise in the phase is becoming more important. Previous studies have shown that retrospective correction of noise from physiologic sources can remove significant phase variance and that dynamic main magnetic field correction and regression of estimated motion parameters also remove significant phase fluctuations. In this work, we investigate the performance of physiologic noise regression in a framework along with correction for …

Coverings And Matchings In R-Partite Hypergraphs, Douglas S. Altner, J. Paul Brooks

Statistical Sciences and Operations Research Publications

Ryser's conjecture postulates that for r -partite hypergraphs, τ ≤ (r - 1)ν where τ is the covering number of the hypergraph and ν is the matching number. Although this conjecture has been open since the 1960s, researchers have resolved it for special cases such as for intersecting hypergraphs where r ≤ 5. In this article, we prove several results pertaining to matchings and coverings in r -partite intersecting hypergraphs. First, we prove that finding a minimum cardinality vertex cover for an r -partite intersecting hypergraph is NP-hard. Second, we note Ryser's conjecture for intersecting hypergraphs is easily resolved …

On The Hardness Of Counting And Sampling Center Strings, Christina Boucher, Mohamed Omar

All HMC Faculty Publications and Research

Given a set S of n strings, each of length ℓ, and a nonnegative value d, we define a center string as a string of length ` that has Hamming distance at most d from each string in S. The #CLOSEST STRING problem aims to determine the number of center strings for a given set of strings S and input parameters n, ℓ, and d. We show #CLOSEST STRING is impossible to solve exactly or even approximately in polynomial time, and that restricting #CLOSEST STRING so that any one of the parameters n, ℓ, or d is fixed leads to …

Strongly Complete Logics For Coalgebras, Alexander Kurz, Jiří Rosický

Engineering Faculty Articles and Research

Coalgebras for a functor model different types of transition systems in a uniform way. This paper focuses on a uniform account of finitary logics for set-based coalgebras. In particular, a general construction of a logic from an arbitrary set-functor is given and proven to be strongly complete under additional assumptions. We proceed in three parts.

Part I argues that sifted colimit preserving functors are those functors that preserve universal algebraic structure. Our main theorem here states that a functor preserves sifted colimits if and only if it has a finitary presentation by operations and equations. Moreover, the presentation of the …

Using Self Organizing Maps To Analyze Demographics And Swing State Voting In The 2008 U.S. Presidential Election, Paul T. Pearson, Cameron I. Cooper

Faculty Publications

Emergent self-organizing maps (ESOMs) and k-means clustering are used to cluster counties in each of the states of Florida, Pennsylvania, and Ohio by demographic data from the 2010 United States census. The counties in these clusters are then analyzed for how they voted in the 2008 U.S. Presidential election, and political strategies are discussed that target demographically similar geographical regions based on ESOM results. The ESOM and k-means clusterings are compared and found to be dissimilar by the variation of information distance function.

Applications Of Extenics To 2d-Space And 3d-Space, Florentin Smarandache, Victor Vladareanu

Branch Mathematics and Statistics Faculty and Staff Publications

In this article one proposes several numerical examples for applying the extension set to 2D- and 3D-spaces. While rectangular and prism geometrical figures can easily be decomposed from 2D and 3D into 1D linear problems, similarly for the circle and the sphere, it is not possible in general to do the same for other geometrical figures.

Various Characterizations Of Modified Weibull And Log Modified Distributions, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Various characterizations of the well-known modified Weibull and log-modified Weibull distributions are presented. These characterizations are based on a simple relationship between two truncated moments; on the hazard function and on functions of the order statistics.

Generalizing Amdahl’S Law For Power And Energy, Rong Ge, Kirk W. Cameron

Mathematics, Statistics and Computer Science Faculty Research and Publications

Extending Amdahl's law to identify optimal power-performance configurations requires considering the interactive effects of power, performance, and parallel overhead.

Categoricity And Topological Graphs, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

Let X be a topological graph, with arcs joined only at end points. If Y is any locally connected metrizable compactum that is co-elementarily equivalent to X, then Y is homeomorphic to X. In particular, X and Y are homeomorphic if some lattice base for one is elementarily equivalent to some lattice base for the other.