Mathematics Commons^™

Longitudinal Investigation Of The Curricular Effect: An Analysis Of Student Learning Outcomes From The Liecal Project In The United States, Jinfa Cai, Ning Wang, John Moyer, Chuang Wang, Bikai Nie

Mathematics, Statistics and Computer Science Faculty Research and Publications

In this article, we present the results from a longitudinal examination of the impact of a Standards-based or reform mathematics curriculum (called CMP) and traditional mathematics curricula (called non-CMP) on students’ learning of algebra using various outcome measures. Findings include the following: (1) students did not sacrifice basic mathematical skills if they are taught using a Standards-based or reform mathematics curriculum like CMP; (2) African American students experienced greater gain in symbol manipulation when they used a traditional curriculum; (3) the use of either the CMP or a non-CMP curriculum improved the mathematics achievement of all students, including …

A New Approach To Algebraic Coding Theory Through The Applications Of Soft Sets, Florentin Smarandache, Mumtaz Ali

Branch Mathematics and Statistics Faculty and Staff Publications

Algebraic codes play a signifcant role in the minimisation of data corruption which caused by defects such as inference, noise channel, crosstalk, and packet loss. In this paper, we introduce soft codes (soft linear codes) through the application of soft sets which is an approximated collection of codes. We also discuss several types of soft codes such as type-1 soft codes, complete soft codes etc. Further, we construct the soft generator matrix and soft parity check matrix for the soft linear codes. Moreover, we develop two techniques for the decoding of soft codes.

Estimating Statistical Characteristics Under Interval Uncertainty And Constraints: Mean, Variance, Covariance, And Correlation, Ali Jalal-Kamali

Open Access Theses & Dissertations

In many practical situations, we have a sample of objects of a given type. When we measure the values of a certain quantity x for these objects, we get a sequence of values x1, . . . , xn. When the sample is large enough, then the arithmetic mean E of the values xi is a good approximation for the average value of this quantity for all the objects from this class. Other expressions provide a good approximation to statistical characteristics such as variance, covariance, and correlation.

The values xi come from measurements, and measurement is never absolutely accurate.

Often, …

Towards Nominal Formal Languages, Alexander Kurz, Tomoyuki Suzuki, Emilio Tuosto

Engineering Faculty Articles and Research

We introduce formal languages over infinite alphabets where words may contain binders.We define the notions of nominal language, nominal monoid, and nominal regular expressions. Moreover, we extend history-dependent automata (HD-automata) by adding stack, and study the recognisability of nominal languages.

An Investigation Into The Use Of Neural Networks For The Prediction Of The Stock Exchange Of Thailand, Suchira Chaigusin

Theses: Doctorates and Masters

Stock markets are affected by many interrelated factors such as economics and politics at both national and international levels. Predicting stock indices and determining the set of relevant factors for making accurate predictions are complicated tasks. Neural networks are one of the popular approaches used for research on stock market forecast. This study developed neural networks to predict the movement direction of the next trading day of the Stock Exchange of Thailand (SET) index. The SET has yet to be studied extensively and research focused on the SET will contribute to understanding its unique characteristics and will lead to identifying …

A Note On Solid Coloring Of Pure Simplicial Complexes, Joseph O'Rourke

Computer Science: Faculty Publications

We establish a simple generalization of a known result in the plane. The simplices in any pure simplicial complex in R^d may be colored with d+1 colors so that no two simplices that share a (d-1)-facet have the same color. In R² this says that any planar map all of whose faces are triangles may be 3-colored, and in R³ it says that tetrahedra in a collection may be "solid 4-colored" so that no two glued face-to-face receive the same color.

Global Dimension Of Ci: Compete Or Collaborate, Arden L. Bement Jr.

PPRI Digital Library

No abstract provided.

Powerpack: Energy Profiling And Analysis Of High-Performance Systems And Applications, Rong Ge, Xizhou Feng, Shuaiwen Song, Hung-Ching Chang, Dong Li, Kirk W. Cameron

Mathematics, Statistics and Computer Science Faculty Research and Publications

Energy efficiency is a major concern in modern high-performance computing system design. In the past few years, there has been mounting evidence that power usage limits system scale and computing density, and thus, ultimately system performance. However, despite the impact of power and energy on the computer systems community, few studies provide insight to where and how power is consumed on high-performance systems and applications. In previous work, we designed a framework called PowerPack that was the first tool to isolate the power consumption of devices including disks, memory, NICs, and processors in a high-performance cluster and correlate these measurements …

On Semigroups With Lower Semimodular Lattice Of Subsemigroups, Peter R. Jones

Mathematics, Statistics and Computer Science Faculty Research and Publications

The question of which semigroups have lower semimodular lattice of subsemigroups has been open since the early 1960s, when the corresponding question was answered for modularity and for upper semimodularity. We provide a characterization of such semigroups in the language of principal factors. Since it is easily seen (and has long been known) that semigroups for which Green's relation J is trivial have this property, a description in such terms is natural. In the case of periodic semigroups—a case that turns out to include all eventually regular semigroups—the characterization becomes quite explicit and yields interesting consequences. In the general case, …

An Attempt To Get And Keep Women Involved In Physics, Jim Crumley, Kristen Nairn, Lynn Ziegler

MapCores Faculty Publications

In this talk I will briefly review some of the obstacles to the full participation of women in the STEM disciplines. In order to increase the number of women in physics, computer science, and mathematics we have started a cohort-based program with curricular and scholarship components for women in these majors. I will present the results of our program so far and offer some advice based on our experiences.

Flat Zipper-Unfolding Pairs For Platonic Solids, Joseph O'Rourke

Computer Science: Faculty Publications

We show that four of the five Platonic solids' surfaces may be cut open with a Hamiltonian path along edges and unfolded to a polygonal net each of which can "zipper-refold" to a flat doubly covered parallelogram, forming a rather compact representation of the surface. Thus these regular polyhedra have particular flat "zipper pairs." No such zipper pair exists for a dodecahedron, whose Hamiltonian unfoldings are "zip-rigid." This report is primarily an inventory of the possibilities, and raises more questions than it answers.

Non-Invasive Prenatal Detection Of Trisomy 21 Using Tandem Single Nucleotide Polymorphisms, Sujana Ghanta, Michael Mitchell, Mary Ames, Mats Hidestrand, Pippa Simpson, Mary Goetsch, William Thilly, Craig Struble, Aoy Tomita-Mitchell

Mathematics, Statistics and Computer Science Faculty Research and Publications

Background: Screening tests for Trisomy 21 (T21), also known as Down syndrome, are routinely performed for the majority of pregnant women. However, current tests rely on either evaluating non-specific markers, which lead to false negative and false positive results, or on invasive tests, which while highly accurate, are expensive and carry a risk of fetal loss. We outline a novel, rapid, highly sensitive, and targeted approach to non-invasively detect fetal T21 using maternal plasma DNA.

Methods and Findings: Highly heterozygous tandem Single Nucleotide Polymorphism (SNP) sequences on chromosome 21 were analyzed using High-Fidelity PCR and Cycling Temperature Capillary …

Impact Of Interdisciplinary Undergraduate Research In Mathematics And Biology On The Development Of A New Course Integrating Five Stem Disciplines, Lester Caudill, April L. Hill, Kathy Hoke, Ovidiu Z. Lipan

Department of Math & Statistics Faculty Publications

Funded by innovative programs at the National Science Foundation and the Howard Hughes Medical Institute, University of Richmond faculty in biology, chemistry, mathematics, physics, and computer science teamed up to offer first- and second-year students the opportunity to contribute to vibrant, interdisciplinary research projects. The result was not only good science but also good science that motivated and informed course development. Here, we describe four recent undergraduate research projects involving students and faculty in biology, physics, mathematics, and computer science and how each contributed in significant ways to the conception and implementation of our new Integrated Quantitative Science course, a …

On Circulant And Two-Circulant Weighing Matrices, K. T. Arasu, I. S. Kotsireast, C. Koukouvinos, Jennifer Seberry

Mathematics and Statistics Faculty Publications

We employ theoretical and computational techniques to construct new weighing matrices constructed from two circulants. In particular, we con- struct W (148, 144), W (152, 144), W (156, 144) which are listed as open in the second edition of the Handbook of Combinatorial Designs. We also fill a missing entry in Strassler’s table with answer “YES”, by constructing a circulant weighing matrix of order 142 with weight 100.

Impact Of Interdisciplinary Undergraduate Research In Mathematics And Biology On The Development Of A New Course Integrating Five Stem Disciplines, Lester Caudill, April L. Hill, Kathy Hoke, Ovidiu Z. Lipan

Biology Faculty Publications

Funded by innovative programs at the National Science Foundation and the Howard Hughes Medical Institute, University of Richmond faculty in biology, chemistry, mathematics, physics, and computer science teamed up to offer first- and second-year students the opportunity to contribute to vibrant, interdisciplinary research projects. The result was not only good science but also good science that motivated and informed course development. Here, we describe four recent undergraduate research projects involving students and faculty in biology, physics, mathematics, and computer science and how each contributed in significant ways to the conception and implementation of our new Integrated Quantitative Science course, a …

Economic Optimization Of Offshore Wind Farms Using The Geometric Algorithm, Mahidhar Nandigam

Electrical & Computer Engineering Theses & Dissertations

The research project related to this thesis focuses on the optimization of electrical systems for offshore wind farms for a given capacity. The optimal design and planning is a critical issue for developing cost effectively Offshore Wind Farms in energy systems. The Geometric Optimization Algorithms approach has been adopted to develop an optimization program, where the main components of the electrical system of an offshore wind farm and key technical specifications are used as parameters to be optimized for a minimum cost with necessary constraints. The effectiveness of the optimization program can be evaluated with real-time comparison between offshore wind …

Bioinformatics Across The Sciences, Nigel Yarlett

Cornerstone 3 Reports : Interdisciplinary Informatics

No abstract provided.

Quantitative Analysis Of Arterial Spin Labeling Fmri Data Using A General Linear Model, Luis Hernandez-Garcia, Hesamoddin Jahanian, Daniel B. Rowe

Mathematics, Statistics and Computer Science Faculty Research and Publications

Arterial spin labeling techniques can yield quantitative measures of perfusion by fitting a kinetic model to difference images (tagged-control). Because of the noisy nature of the difference images investigators typically average a large number of tagged versus control difference measurements over long periods of time. This averaging requires that the perfusion signal be at a steady state and not at the transitions between active and baseline states in order to quantitatively estimate activation induced perfusion. This can be an impediment for functional magnetic resonance imaging task experiments. In this work, we introduce a general linear model (GLM) that specifies Blood …

A Class Of Models For Uncorrelated Random Variables, Nader Ebrahimi, Gholamhossein Hamedani, Ehsan S. Soofi, Hans Volkmer

Mathematics, Statistics and Computer Science Faculty Research and Publications

We consider the class of multivariate distributions that gives the distribution of the sum of uncorrelated random variables by the product of their marginal distributions. This class is defined by a representation of the assumption of sub-independence, formulated previously in terms of the characteristic function and convolution, as a weaker assumption than independence for derivation of the distribution of the sum of random variables. The new representation is in terms of stochastic equivalence and the class of distributions is referred to as the summable uncorrelated marginals (SUM) distributions. The SUM distributions can be used as models for the joint distribution …

A Methodology For Engineering Collaborative And Ad-Hoc Mobile Applications Using Syd Middleware, Praveen Madiraju, Srilaxmi Malladi, Janaka Balasooriya, Arthi Hariharan, Sushil K. Prasad, Anu Bourgeois

Mathematics, Statistics and Computer Science Faculty Research and Publications

Today’s web applications are more collaborative and utilize standard and ubiquitous Internet protocols. We have earlier developed System on Mobile Devices (SyD) middleware to rapidly develop and deploy collaborative applications over heterogeneous and possibly mobile devices hosting web objects. In this paper, we present the software engineering methodology for developing SyD-enabled web applications and illustrate it through a case study on two representative applications: (i) a calendar of meeting application, which is a collaborative application and (ii) a travel application which is an ad-hoc collaborative application. SyD-enabled web objects allow us to create a collaborative application rapidly with limited coding …

Processing Induced Voxel Correlation In Sense Fmri Via The Ammust Framework, Daniel B. Rowe, Iain P. Bruce

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

Automated Theorem Prover Axiom Management, Ashley T. Holeman, Ewen Denney

STAR Program Research Presentations

Automated Theorem Provers (ATPs), are computer programs that use collections of axioms,which are logical statements assumed to be true, in order to prove conjectures. NASA uses these programs to verify safety and functional requirements in domains like Guidance, Navigation, and Control. There are about 30 axioms on each major topic including the theory of coordinate systems, elementary arithmetic and linear algebra. These axioms have been created over the duration of many projects and combined into a single file. One task is to manage the axioms by arranging them into logical sections, deleting unnecessary ones and rewriting some into a more …

Discrete Groups And The Complex Contact Geometry Of Sl(2, C), Brendan Foreman

Mathematics and Computer Science

We investigate the vertical foliation of the standard complex contact structure on Γ \ Sl(2, C), where Γ is a discrete subgroup. We find that, if Γ is nonelementary, the vertical leaves on Γ \ Sl(2, C) are holomorphic but not regular. However, if Γ is Kleinian, then Γ \ Sl(2, C) contains an open, dense set on which the vertical leaves are regular, complete and biholomorphic to C ∗. If Γ is a uniform lattice, the foliation is nowhere regular, although there are both infinitely many compact and infinitely many nonclosed leaves.

A Formal Context Specific Trust Model (Ftm) For Multimedia And Ubiquitous Computing Environment, Sheikh Iqbal Ahamed, Munirul M. Haque, Nilothpal Talukder

Mathematics, Statistics and Computer Science Faculty Research and Publications

In order to ensure secure sharing of resources in an ad-hoc network of handheld devices in a multimedia and ubiquitous computing environment, mutual collaboration is essential. However, the limitations, such as poor storage and computational capability of these multimedia and ubiquitous devices stand as the bottleneck for effective sharing of resources. As a result of this drawback, the adversaries are obtaining access to the new doors for security breaches. Mutual Trust is the weapon used to combat security violations by restricting malicious devices from participating in any interaction in such an open and dynamic environment. In this paper, we present …

Noise Assumptions In Complex-Valued Sense Mr Image Reconstruction, Daniel B. Rowe, Iain P. Bruce

Mathematics, Statistics and Computer Science Faculty Research and Publications

In fMRI, brain images are not measured instantaneously and a volume of images can take two seconds to acquire at a low 64x64 resolution. Significant effort has been put forth on many fronts to decrease image acquisition time including parallel imaging. In parallel imaging, sub-sampled spatial frequency points are measured in parallel and combined to form a single image. Measurement time is decreased at the expense of increased image reconstruction difficulty and time. One significant parallel imaging technique known as SENSE utilizes a complex-valued regression coefficient estimation process with transposes replaced by conjugate transposes. However, in SENSE the noise structure …

Acm/Springer Mobile Networks And Applications (Monet) Special Issue On “Advanced Mobile Applications And Intelligent Multimedia Systems For Ubi-Com”, Jong Hyuk Park, Shu-Ching Chen, Mieso Denko, Sheikh Iqbal Ahamed

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

Dnagents: Genetically Engineered Intelligent Mobile Agents, Jeremy Otho Kackley

Dissertations

Mobile agents are a useful paradigm for network coding providing many advantages and disadvantages. Unfortunately, widespread adoption of mobile agents has been hampered by the disadvantages, which could be said to outweigh the advantages. There is a variety of ongoing work to address these issues, and this is discussed. Ultimately, genetic algorithms are selected as the most interesting potential avenue. Genetic algorithms have many potential benefits for mobile agents. The primary benefit is the potential for agents to become even more adaptive to situational changes in the environment and/or emergent security risks. There are secondary benefits such as the natural …

On Folding A Polygon To A Polyhedron, Joseph O'Rourke

Computer Science: Faculty Publications

We show that the open problem presented in "Geometric Folding Algorithms: Linkages, Origami, Polyhedra" [DO07] is solved by a theorem of Burago and Zalgaller [BZ96] from more than a decade earlier.

Fastmedusa: A Parallelized Tool To Infer Gene Regulatory Networks, Serdar Bozdag, Aiguo Li, Stefan Wuchty, Howard A. Fine

Mathematics, Statistics and Computer Science Faculty Research and Publications

Motivation: In order to construct gene regulatory networks of higher organisms from gene expression and promoter sequence data efficiently, we developed FastMEDUSA. In this parallelized version of the regulatory network-modeling tool MEDUSA, expression and sequence data are shared among a user-defined number of processors on a single multi-core machine or cluster. Our results show that FastMEDUSA allows a more efficient utilization of computational resources. While the determination of a regulatory network of brain tumor in Homo sapiens takes 12 days with MEDUSA, FastMEDUSA obtained the same results in 6 h by utilizing 100 processors. Availability: Source code and documentation of …

On Flat Polyhedra Deriving From Alexandrov's Theorem, Joseph O'Rourke

Computer Science: Faculty Publications

We show that there is a straightforward algorithm to determine if the polyhedron guaranteed to exist by Alexandrov's gluing theorem is a degenerate flat polyhedron, and to reconstruct it from the gluing instructions. The algorithm runs in O(n³) time for polygons whose gluings are specified by n labels.