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Home / Undergraduate Research Highlights / Mathematics / Computer Sciences
 
Mathematics and Computer Sciences Highlights
Total Listing: 71    (Listed by the order of record adding time, Descending)
( 1 )   Recorded at: 1/13/2010      
Title Normal Quadratics in Ore Extensions, Quantum Planes, and Quantized Weyl Algebras
Journal Acta Applicandae Mathematicae, 2009;108:73-81, Holtz C, Price K.
Description "If q is a nonzero number there are algebras which satisfy (i) yx = qxy and (ii) yx = qxy+1 for the products between variables x and y. In case (i) the algebras are called quantum planes and in case (ii) they are called quantized Weyl algebras. We classified irreducible and prime quadratic polynomials in these algebras."
Faculty Kenneth Price is an associate professor of mathematics.
Student Candis Holtz completed her bachelors degree with an emphasis in secondary education in 2005. She went on to complete a masters degree in mathematics education from UW Oshkosh.
Fund "UW Oshkosh Undergraduate Student and Faculty Collaborative Research Program"
 
( 2 )   Recorded at: 12/16/2009      
Title The Alarm-Off Puzzle
Journal Proceedings of the Midstates Conference for Undergraduate Research in Computer Science and Mathematics, 2008;76-82, Charley S, Hamilton S, Wong R
Description The paper used several versions of a puzzle to demonstrate the power of recursion in problem solving. It also explored the technique of solving difference equations by employing parallel methods used in solving differential equations. The explicit solutions involved some unusual integer value functions with rational coefficients
Faculty Roman Wong is a professor of mathematics
Student Sarah Charley and Shunika Hamilton are currently junior mathematics majors
Fund The research was supported by a 2008 Summer Entrepreneurial Fund for Undergraduate Research from Washington and Jefferson College in Pennsylvania
 
( 3 )   Recorded at: 12/16/2009      
Title Schur aggregation for linear systems and determinants
Journal Theoretical Computer Science, 2008;409:255-268, Pan VY, Grady D, Murphy B, Qian G, Rosholt RE, Ruslanov AD
Description This work proposed a method to achieve high accuracy determinant calculations for large matrices with a high condition number. These matrices, having both very large and very small numbers, are prone to large numerical error. A new pre-conditioning scheme was implemented and tested, and it was found to successfully work and reduce numerical error in computation
Faculty Anatole Ruslanov is an assistant professor of computer science at SUNY Fredonia
Student Devin Grady participated in the research as a senior computer science major at SUNY Fredonia. They collaborated with Victor Pan, distinguished professor in the department of mathematics and computer science at Lehman College, and his team of graduate students Brian Murphy, Guoliang Qian, and Rhys Rosholt. Devin is now in a doctoral program at Rice University working in robotics under Lydia Kavraki
 
( 4 )   Recorded at: 11/24/2009      
Title Self-similar collapse solutions for cylindrical cloud geometries and dynamic equations of state.
Journal Publications of the Astronomical Society of the Pacific, 2009; 121: 485 - 497, Holden L, Hoppins K, Baxter B, Fatuzzo M
Description This work focuses on a fundamental component of the star-formation process - the gravitational collapse of dense molecular cores observed within the large complexes of gas and dust that reside along the plane of our galaxy. Self-similar techniques are employed to model the collapse of cylindrical cores with dynamic equations of state, thereby providing a formalism that allows for the physical processes that govern the gas during the collapse to change. The analysis provides insight into the collapse time and the mass infall rate (an important physical quantity related to the total system luminosity) of filamentary or elongated molecular structures.
Faculty Lisa Holden is an assistant professor of mathematics at Northern Kentucky University. Marco Fatuzzo is an associate professor of physics at Xavier University.
Student Kevin Hoppins, a senior mathematics major at Northern Kentucky University, participated in the research efforts as part of his Honors Capstone Project. Benjamin Baxter, a sophomore mathematics major at Northern Kentucky University, conducted research over the summer and was supported by the Greaves Fund at Northern Kentucky University. Kevin is currently employed and Benjamin is now a junior at NKU.
Fund Marco Fatuzzo was supported by the Hauck Foundation at Xavier University.
 
( 5 )   Recorded at: 11/24/2009      
Title The most general planar transformations that map parabolas into parabolas
Journal Involve, a Journal of Mathematics, 2 (2009), 79-88, Michael Bolt, Timothy Ferdinands, Landon Kavlie
Description Consider the space of vertical parabolas in the plane interpreted generally to include nonvertical lines. It is proved that an injective map from a closed region bounded by one such parabola into the plane that maps vertical parabolas to other vertical parabolas must be the composition of a Laguerre transformation with a non-isotropic dilation. Here, a Laguerre transformation refers to a linear fractional or antilinear fractional transformation of the underlying dual plane.
Faculty Michael Bolt is an associate professor of mathematics.
Student Timothy Ferdinands and Landon Kavlie participated in this research during the summer of 2008. They will both finish their undergraduate degrees during the coming academic year. Both then plan to attend graduate school in mathematics.
Fund The project was funded by an REU supplement to an NSF-RUI grant.
 
( 6 )   Recorded at: 9/23/2009      
Title Self-similar collapse solutions for cylindrical cloud geometries and dynamic equations of state
Journal Publications of the Astronomical Society of the Pacific, 2009;121:485-497, Holden L, Hoppins K, Baxter B, Fatuzzo M
Description This work focuses on a fundamental component of the star-formation process - the gravitational collapse of dense molecular cores observed within the large complexes of gas and dust that reside along the plane of our galaxy. Self-similar techniques are employed to model the collapse of cylindrical cores with dynamic equations of state, thereby providing a formalism that allows for the physical processes that govern the gas during the collapse to change. The analysis provides insight into the collapse time and the mass infall rate (an important physical quantity related to the total system luminosity) of filamentary or elongated molecular structures
Faculty Lisa Holden is an assistant professor of mathematics at Northern Kentucky University. Marco Fatuzzo is an associate professor of physics at Xavier University
Student Kevin Hoppins, a senior mathematics major at Northern Kentucky University, participated in the research efforts as part of his Honors Capstone Project. Benjamin Baxter, a sophomore mathematics major at Northern Kentucky University, conducted research over the summer and was supported by the Greaves Fund at Northern Kentucky University. Kevin is currently employed and Benjamin is now a junior at NKU
Fund Marco Fatuzzo was supported by the Hauck Foundation at Xavier University
 
( 7 )   Recorded at: 9/14/2009      
Title On graphs for which every planar immersion lifts to a knotted spatial embedding
Journal Involve, 2008(1):145-158, DeCelles A, Foisy J, Versace C, Wilson A
Description We call a graph G intrinsically linkable if there is a way to assign over/under information to any planar immersion of G such that the associated spatial embedding contains a pair of nonsplittably linked cycles. We define intrinsically knottable graphs analogously. We show there exist intrinsically linkable graphs that are not intrinsically linked. We also show there are intrinsically knottable that are not intrinsically knotted. In addition, we demonstrate that the property of being intrinsically linkable (knottable) is not preserved by vertex expansion. The project took place during an REU program, summer 2004 at SUNY Potsdam
Faculty
Student Amy DeCelles is a currently graduate student in Mathematics at the University of Minnesota; Chad Versace is currently employed in the private sector, and Alice Wilson is currently teaching mathematics and biology at MassBay Community College.
 
( 8 )   Recorded at: 9/14/2009      
Title Symmetric functions, Pascal matrices, and Stirling matrices
Journal Linear Algebra and Its Applications, 2008;428:1127-1134, Spivey MZ, Zimmer AM
Description We show how to factorize and invert lower-triangular matrices consisting of symmetric polynomials. Since binomial coefficients and Stirling numbers can be represented in terms of symmetric polynomials, these results contain factorizations and inverses of Pascal and Stirling matrices as special cases. This work generalizes that of several other authors on Pascal and Stirling matrices
Faculty Michael Spivey is an associate professor of mathematics and computer science
Student Andrew Zimmer was a junior mathematics and computer science major at the time of the research and did the work for fun, in his spare time. He is currently in a doctoral program in mathematics at the University of Illinois at Urbana-Champaign
Fund The research was not and did not need to be funded
 
( 9 )   Recorded at: 9/11/2009      
Title The numerical solution of the exterior dirichlet problem for the helmholtz’s equation via modified green’s functions approach for the oval of cassini
Journal Far East Jour. Appl. Math, 2009;34:1-20, Warnapala Y, Moragn E
Description In this paper, we used the global Galerkin method to numerically solve the exterior Dirichlet problem for the Helmholtz’s equation for the oval of Cassini in three dimensions based on Jone’s modified integral equation approach. This method was previously used for the sphere, perturbation of the sphere and the ellipsoid with successful results. Theoretical and computational details of the method for small values of k for the oval of Cassini (the Peanut Shape) were found. The convergence results for a finite range of wave numbers were compared with two different coefficient choices for the Modified Integral equation, where we added a series of radiating functions to the true solution
Faculty Yajni Warnapala is the Chair and an Associate Professor of Mathematics
Student Elizabeth Morgan is majoring in mathematics, and is currently applying to graduate schools to pursue a Masters in applied mathematics. She has worked on this research topic since fall of 2007 and is currently writing a senior thesis on the topic. Elizabeth gave a presentation on her research project at the AMS Spring Western Section Meeting in San Francisco
Fund Elizabeth received Provost’s funding from Roger Williams University to present her work at national conferences
 
( 10 )   Recorded at: 9/11/2009      
Title On an optical inertial navigation system - Part I
Journal IEEE Transactions on Automatic Control, 2008;53(8):1850-1863, Iyer R, Meixner J, Buckalew R
Description This paper is the first in a two-part study that introduces a new method for computing the linear velocity and angular velocity of an unmanned air vehicle (UAV) using only the image sequences obtained from image sequences. It shows that it is possible to build a strap-down type inertial navigation system -called an Optical inertial navigation system - using a simple apposition eye, which is a type of compound eye found in insects
Faculty Ram Iyer is an associate professor of mathematics and statistics
Student She is currently in a doctoral program in computional and applied mathematics at the University of Texas at Austin. Richard Buckalew was an undergraduate when he participated in an REU program in Summer 2006. He is now a graduate student at the Ohio University, Athens.
Fund Jessica Meixner, a senior in mathematics, participated in the study in 2006-2008, and she was funded by an REU program in Summer 2006, and by the Honors college from 2006-2008
 
( 11 )   Recorded at: 9/11/2009      
Title Model of a multiple-lens, single-fiber system in a compound eye
Journal International Journal of Applied Electromagnetics and Mechanics, ;28(1-2):73-78, Meixner J, Iyer R
Description In this paper, a Fourier optics model of a compound eye is developed. Model predictions for the acceptance angle are compared against data obtained from an honey-bee eye. It is shown that neighboring facets in a simple apposition eye found in a honey-bee have negligible effect on the image produced by the central facet
Faculty Ram Iyer is an associate professor of mathematics and statistics
Student Jessica Meixner, a senior in mathematics, is currently in a doctoral program in computional and applied mathematics at the University of Texas at Austin
Fund Jessica Meixner was funded by an REU program in Summer 2006, and by the Honors college from 2006-2008
 
( 12 )   Recorded at: 1/6/2009      
Title Closed geodesics on orbifolds of revolution
Journal Houston J Math, 2007;33(4):1011-1025, Borzellino JE, Jordan-Squire CR, Petrics GC, Sullivan DM
Description Using the theory of geodesics on surfaces of revolution, we show that any two-dimensional orbifold of revolution homeomorphic to the two-sphere must contain an infinite number of geometrically distinct closed geodesics. Since any such orbifold of revolution can be regarded as a topological two-sphere with metric singularities, we will have extended Bangert's theorem on the existence of infinitely many closed geodesics on any smooth Riemannian two-sphere. In addition, we give an example of a two-sphere cone-manifold of revolution that possesses a single closed geodesic, thus showing that Bangert's result does not hold in the wider class of closed surfaces with cone manifold structures
Faculty Joseph Borzellino is an associate professor of mathematics
Student Christopher Jordan-Squire of Swarthmore College, Gregory Petrics of Middlebury College, and D. Mark Sullivan of Caltech participated in Cal Poly's 2005 summer NSF REU in operator theory and topology. Christopher and Mark are currently in a doctoral program in mathematics at the University of Washington. Gregory is in a doctoral program in mathematics at Dartmouth College.
Fund The research was partially supported by NSF Grant No. DMS-0353622 and the College of Science and Mathematics at Cal Poly
 
( 13 )   Recorded at: 1/6/2009      
Title On sampling periodic functions
Journal Far East J Math Sci, 2008;29:145-149, Caragiu M, Holodnak J
Description The present research provides a significant pool of examples of sequences not obeying any recurrence relation defined by a continuous iterating function. The sequences considered in the paper are obtained from sampling a periodic function at the integer multiples of a positive number D. It is shown that if D is incommensurate to the period of the function, and if the function has a non-removable discontinuity point, being on the other hand continuous at every translate of that discontinuity point by a non-zero multiple of D, then the sequence of function values obtained from sampling does not satisfy any recurrence relation defined by a continuous function
Faculty Mihai Caragiu is an associate professor of mathematics at Ohio Northern University
Student John Holodnak is a mathematics major currently entering his junior year at Ohio Northern University. Parts of this research were also presented at the 2007 MAA Ohio Spring Meeting and at the 2008 Undergraduate Student Poster Session held in San Diego at the AMS-MAA Joint Meetings
Fund The research was supported by the Getty College of Arts and Sciences at Ohio Northern University
 
( 14 )   Recorded at: 1/6/2009      
Title A lost theorem: definite integrals in asymptotic setting
Journal The American Mathematical Monthly, 2008;115(1):45-56, Cavalcante R, Todorov TT
Description We present a simple yet rigorous theory of integration that is based on two axioms rather than on a construction involving Riemann sums. With several examples we demonstrate how to set up integrals in applications of calculus without using Riemann sums. In our axiomatic approach even the proof of the existence of the definite integral (which does use Riemann sums) becomes slightly more elegant than the conventional one. We also discuss an interesting connection between our approach and the history of calculus. The article is written for readers who teach calculus and its applications. It might be accessible to students under a teacher's supervision and suitable for senior projects on calculus, real analysis, or history of mathematics
Faculty Todor D. Todorov is an assistant professor in Mathematics Department
Student Ray Cavalcante was an undergraduate student at the time this article was written. His work on the article started as a senior project in the Fall of 2005 and was extended in 2006 as an independent study project. Ray Cavalcante is presently employed. He was recently accepted in the graduate program in California State University, San Francisco, starting the Fall of 2008
 
( 15 )   Recorded at: 12/29/2008      
Title Counting fundamental paths in certain Garside semigroups
Journal Journal of Knot Theory and Its Ramifications (JKTR), 2008;17(2)191-211, Cornwell CR, Humphries SP
Description For elements a, b of a monoid, define the word p_k (a,b) = abab? of length k. We find the number of words in a, b which are equal to p_k (a,b)^n in the Artin semigroup < a,b|p_k (a,b) = p_k (b,a) >. This number is related to counting certain paths in the N × N lattice. These Artin groups are examples of two generator Garside groups. We also define other examples of Garside groups G on more than two generators, having fundamental word Delta, and similarly find the number of words equal in G to Delta^n
Faculty Stephen Humphries is a professor in the Mathematics Department at Brigham Young University
Student Christopher Cornwell is now a Ph.D. student in Mathematics Department at Michigan State University. This research started in 2003/2004, when Chris was an undergraduate and completed while he was a graduate (MSc) student at BYU
Fund He was supported by a departmental undergraduate research scholarship
 
( 16 )   Recorded at: 12/29/2008      
Title Classification of nonproduct states with maximum stabilizer dimension
Journal Phys. Rev. A, 2008;77:022309 (5 pages, numbered 022309-1 through 022309-5), Lyons DW, Walck SN, Blanda SA
Description The present study identifies an important class of quantum states from the perspective of quantum entanglement and quantum information technologies. The authors precisely identify the class of nonproduct states with maximum stabilizer dimension under the group of local unitary transformations, and explicitly show the form these states can take. An interesting exceptional set of states appears in the case of four quantum bits
Faculty David Lyons is an associate professor of mathematical sciences. Scott Walck is an associate professor of physics
Student Stephanie Blanda '09, a computer science and mathematics major, participated in the research over summer 2007. Stephanie intends to pursue graduate study in computer science or mathematics
Fund The research was supported by the National Science Foundation through NSF Grant No. PHY-0555506
 
( 17 )   Recorded at: 2/14/2008      
Title Abundancy "outlaws" of the form /s/(/N/)+/t/)//N/
Journal J Integer Sequences, 2007;10:Article 07.9.6, Stanton W, Holdener J
Description The abundancy index of a positive integer /n/ is defined to be the rational number /I/(/n/) = /s/(/n/)//n/, where /s/ is the sum of divisors function. An abundancy outlaw is a rational number greater than 1 that fails to be in the image of of the map /I/. Abundancy outlaws are important in the study of odd perfect numbers and related questions in number theory. The authors investigated rational numbers of the form (/s/(/N/) + /t/)//N/ and were able to prove that under certain conditions such rationals are abundancy outlaws
Faculty Judy Holdener is an associate professor in the Department of Mathematics
Student William Stanton participated in this research during the summer after his sophomore year; he is currently a senior
Fund The research was supported by the Kenyon College Summer Science Scholars Program
 
( 18 )   Recorded at: 11/19/2007      
Title New type of block design
Journal B I Comb Appl, 2007;50:26-28, Sarvate DG, Beam WA
Description Combinatorial Design Theory includes study of different types of arrangements of elements of a given set which satisfies certain properties. In many of these designs a common thread is to find a collection of subsets where every pair or triple or an n-tuple occurs in the same number of subsets. In this note we define and study designs, called adesigns, where every pair occurs in a different number of subsets of the design. This novel idea caught attention of the Editor-in-Chief of the Bulletin of the Institute of Combinatorics, Professor Ralph Stanton, and he wrote a paper: A note on Sarvate-Beam Triple System, Bulletin of the Institute of Combinatorics and its Application, 2007;50:61-66 and in it named these designs as "Sarvate-Beam Triple Systems".
Faculty Dinesh G. Sarvate is a professor of mathematics
Student William Beam worked on this as a senior; he graduated in May 2007
Fund Department of Mathematics provided Beam partial support to present the paper at the Thirty-Eighth Southeastern International Conference on Combinatorics, Graph Theory and Computing
 
( 19 )   Recorded at: 11/19/2007      
Title Global asymptotic behavior for delay dynamic equations
Journal Nonlinear Anal, 2007;66:1633-1644, Anderson DR, Kenz ZR
Description We found conditions under which solutions of a first-order nonlinear variable-delay dynamic equation go to zero at infinity, for arbitrary time scales that are unbounded above. In an example, we applied our techniques to a logistic dynamic equation on isolated, unbounded time scales. This work unified previous work on delay differential and difference equations, extending the results to delay quantum equations and other general dynamic equations
Faculty Douglas Anderson is an associate professor of mathematics at Concordia College-Moorhead.
Student Zackary Kenz participated in this research in his sophomore year for fun. He is currently a senior, student body president, and doing a summer research project for the Department of Defense
Fund The research was unsupported
 
( 20 )   Recorded at: 11/19/2007      
Title Multidecomposition of ? Km into small cycles and claws
Journal B Inst Comb Appl., 2007;49:32-40, Abueida A, O’Neil T
Description A (G, H)-multidecomposition of ? Km is a partition of the edges of ? Km into copies of G and H with at least one copy of G and at least one copy of H. In this paper, we consider the existence of multidecompositions of ? Km when Gn = K1,n-1 and Hn = Cn for n = 3, 4, and 5
Faculty Atif Abueida is an associate professor of mathematics
Student Theresa O’Neil completed this research as part of independent study project in her senior year in 2005. She later received her MS in Economics from University of North Carolina at Greensboro and is now employed at Bank of America.
Fund The research was not funded externally
 
( 21 )   Recorded at: 11/19/2007      
Title Saari's conjecture for the restricted three-body problem
Journal Celest Mech Dyn Astr., 2007;97:211-223, Roberts GE, Melanson L
Description Saari's conjecture adapted to the restricted three-body problem is proven analytically using BKK theory. Specifically, we show that it is not possible for a solution of the planar, circular, restricted three-body problem to travel along a level curve of the amended potential function unless it is fixed at a critical point (one of the five libration points.) Due to the low dimension of the problem, our proof does not rely on the use of a computer
Faculty Gareth Roberts is an assistant professor of mathematics
Student Lisa Melanson participated in this research the summer after her junior year, continuing on in her senior year in a directed project. She is currently working toward a doctoral degree at Northwestern University in the Engineering Sciences and Applied Mathematics Department
Fund The research was supported by a Fisher Summer Student Research Fellowship through Holy Cross
 
( 22 )   Recorded at: 11/19/2007      
Title q-Dominant and q-recessive matrix solutions for linear quantum systems
Journal Electron J Qual Theor Differ Equat+., 2007;11:1-29, Anderson DR, Moats LM
Description In this study, linear second-order matrix quantum (q-difference) equations were shown to be formally self-adjoint equations with respect to a certain inner product and the associated self-adjoint boundary conditions. A generalized Wronskian was introduced and a Lagrange identity and Abel's formula were established; two reduction-of-order theorems were given. The analysis and characterization of q-dominant and q-recessive solutions at infinity were presented, emphasizing the case when the quantum system is disconjugate
Faculty Douglas Anderson is an associate professor of mathematics
Student Lisa Moats participated in this research in her freshman year for fun. She is currently a sophomore
Fund The research was unsupported
 
( 23 )   Recorded at: 11/6/2007      
Title What's in a name? A study of identifiers
Journal ICPC, 2006;1:3-12, Lawrie D, Morrell C, Feild H, Binkley D
Description Results from a study designed to investigate the impact of program identifier quality on comprehension is presented. The study involved over one hundred programmers ranging from undergraduate students (about 23% of the participants) to those with 40+ years of experience. Each was asked to describe twelve different functions that used one of three different identifier quality levels. The results show that full-word identifiers lead to the best comprehension; however, in many cases, there is no statistical difference between using full words and abbreviations. When considered in the light of limited human short-term memory, the results support the use of well-chosen abbreviations as identifiers with fewer syllables are easier to remember
Faculty Dawn Lawrie is an assistant professor of computer science. Chris Morrell is a professor of mathematical sciences. Dave Binkley is a professor of computer science
Student Henry Feild participated in this research as a Loyola Summer Hauber Fellowship recipient and will be attending the University of Massachusetts Amherst as a first-year graduate student next year
Fund The research was supported through a NSF-RUI grant.
 
( 24 )   Recorded at: 10/31/2007      
Title Quasi-random Structures from elliptic curves
Journal JP J Algebra, Number Theory Appl, 2006;6:561-571, Caragiu M, Johns RA, Gieseler J
Description The distribution properties of the sets obtained by projecting an elliptic curve on the x-axis are investigated. The distribution is proved to be quasi-random. For a certain class of quasi-random walks associated to the projection sets, chi-squared based statistical tests are used to show that from the point of view of the number of returns to the origin they cannot be distinguished from genuine random walks
Faculty Mihai Caragiu and Ronald A. Johns are associate professors of mathematics
Student Justin Gieseler is an undergraduate student majoring in mathematics and computer science. Justin participated in this research during his sophomore year, and presented parts of this research at the Undergraduate Mathematics Day at Dayton, in November 2005, as well as at the 2006 San Antonio Joint AMS-MAA Meetings.
Fund The research was supported by the Getty College of Arts and Sciences at Ohio Northern University
 
( 25 )   Recorded at: 10/31/2007      
Title Kneser’s theorem for upper Banach density
Journal Journal de Theorie des Numbres, 2006;18:323-343, Bihani P, Jin R
Description For a set of non-negative integers with upper Banach density of a, if the upper Banach density of A+A is less than 2a, then it is shown, by using nonstandard analysis, that A+A must have certain structure. This theorem solves one of the inverse problems for upper Banach density. The work demonstrates how a standard problem can be solved using nonstandard methods. The nonstandard analysis uses mathematical logic, which is relatively new to number theorists typically interested in this branch of mathematics
Faculty Renling Jin is an associate professor of mathematics
Student Prerna Bihani graduated in May of 2004 with a BS in mathematics and a minor in philosophy. This work was done over the summer of 2003 and over the 2003-04 academic year as part of a Bachelor’s Essay. Prerna is currently in her third year of graduate school, working towards a PhD at the University of Notre Dame
Fund Funding for the summer research effort was provided by a competitive internal award from College of Charleston’s Summer Undergraduate Research with Faculty program
 
( 26 )   Recorded at: 10/31/2007      
Title Cooling the Macon volunteer clinic
Journal The UMAP J, 2006;27(4):431-447, Denny JK, Trivett CK
Description This paper develops a mathematical model of the air conditioning system at the Macon Volunteer Clinic. Four air conditioning systems control the temperature in the clinic but are poorly arranged and have difficulty regulating the temperature. Using a system of eight differential equations, we model the effects of the outdoor temperature, the air conditioning systems, and people in the clinic. After defining and investigating measures of efficiency and comfort, we use the model to suggest changes to the clinic, which proved effective when implemented
Faculty Jeff Denny is an associate professor of mathematics
Student Carrie K. Trivett participated in this project during the summer after her junior year and is now a mathematics teacher at the Upper School of Mount de Sales Academy in Macon, GA.
Fund This research was supported through a grant from the College of Liberal Arts at Mercer University
 
( 27 )   Recorded at: 2/22/2007      
Title Intelligent virtual companion system for independent living
Journal Proceedings of ‘The International Conference on Artificial Intelligence (ICAI’06), Las Vegas, Nevada, June 26-29, 2006, ©CSREA Press, pp. 439-445, Todd M, Sasi S
Description The main goal of independent living facilities is to maximize the independence and productivity of individuals with disabilities, and their integration and inclusiveness into mainstream society. A component of independent living is an elderly companionship service. In this research, an Intelligent Virtual Companion System for Independent Living (IVCSIL) is designed to add a social companionship aspect to smart home systems. This artificial intelligent system will initiate casual conversation, provide cues for performing daily living tasks, monitoring a subject’s health, and perform secretarial tasks that will enhance autonomy
Faculty Sreela Sasi is associate professor of computer and information science
Student Michael Todd is a senior student in electrical and computer engineering. He will be graduating in December 2006. Michael worked on this project from Spring 2005 through Spring 2006
Fund A Faculty Development Grant from Gannon University was used to meet the expense of the conference
 
( 28 )   Recorded at: 2/22/2007      
Title The volume principle
Journal Math Mag, 2006;79:251-261, Dickinson WC, Lund K
Description The dual theorems of Menelaus and Ceva are among the most beautiful and useful results in Euclidean geometry. Grunbaum and Shephard, in their article, Ceva, Menelaus and the Area Principle, introduce a simple tool, called the Area Principle, and use it to present deservingly elegant proofs of both Ceva's and Menelaus' Theorems and their generalizations. In this paper, we prove the Volume Principle, which is valid for the Euclidean plane, the hyperbolic plane and the two-dimensional sphere. This tool allows us to extend all the theorems from Grunbaum and Shephard's article, except for those generalizations that require linearity, into these other geometries
Faculty William Dickinson is a professor of mathematics
Student Kristina Lund participated in this research the summer after her junior year and is currently a graduate student in mathematics at the University of Nebraska-Lincoln
Fund The research was supported through a student summer scholars grant from Grand Valley State University
 
( 29 )   Recorded at: 2/21/2007      
Title Linked triangle pairs in a straight edge embedding of K6
Journal The pme J, 2006;213-218, Hughes C, Ludwig LD
Description In 1983, Conway and Gordon showed that any embedding of the complete graph on six vertices, K6, must contain at least one linked triangle pair with a maximum of ten linked pairs. In 2004, a question was posed at a knot theory workshop asking for the total number of linked pairs in any straight-edge of K6. We answered this question by showing that any straight-edge embedding of K6 contains either 1 or 3 linked triangle pairs
Faculty Lewis D. Ludwig is an assistant professor of mathematics and computer science
Student Colleen Hughes participated in this summer research after her sophomore year at Denison and continued the work for her honor’s thesis. She is in her first year of graduate studies at Clemson University
Fund The Howard Hughes Medical Foundation supported this research
 
( 30 )   Recorded at: 2/21/2007      
Title Matching scale-space features in 1D panoramas.
Journal Comput Vis Image Und, 103(3):184-195, Briggs A, Detweiler C, Li Y, Mullen P, Scharstein D
Description The goal of this work is to enable a mobile robot to navigate using 1D panoramic images, i.e., single scanlines spanning 360-degree horizontal views. Invariant features are extracted from the scale-space of such images, and a novel dynamic programming algorithm matches features between different viewpoints. The method can handle arbitrary rotations, missing features, and is robust to changes in lighting conditions and in the presence of some occlusion
Faculty Amy Briggs and Daniel Scharstein are associate professors of computer science
Student Peter Mullen is a researcher based in Seattle. Carrick Detweiler participated in this research during two summers after his sophomore and junior years. He is currently pursuing a PhD in computer science at the Massachusetts Institute of Technology. Yunpeng Li participated in this research during two summers after his junior and senior years. He is currently pursuing a PhD in computer science at Cornell University
Fund The research was supported through NSF-RUI grants
 
( 31 )   Recorded at: 2/21/2007      
Title LDPC codes generated by conics in the classical projective plane
Journal Designs Codes Cryptog, 2006;40(3):343-356, Droms, Sean V., Mellinger, Keith E., and Meyer, C
Description Several classes of Low-Density Parity-Check codes are constructed from various point-line incidence structures in the finite projective plane PG(2,q). The codes are analyzed mathematically and through simulation. Such codes can be used for error-correction on certain memory devices and short range transmissions
Faculty Keith Mellinger is an assistant professor of mathematics
Student Sean Droms and Chris Meyer completed this research after their sophomore and junior years, respectively, during the summer of 2005. Chris Meyer now works at the Naval Surface Warfare Center at Dahlgren. Sean will graduate in May 2007 and aspires to attend graduate school in mathematics next year
Fund The research was funded by the University of Mary Washington's Summer Science Institute
 
( 32 )   Recorded at: 2/21/2007      
Title The greatest prime factor and related sequences
Journal J Algebra Numb Theory Appl, 2006;6:403-409, Caragiu M, Scheckelhoff, L
Description A class of prime sequences, in which each term is the greatest prime factor of a fixed linear function of the previous term, is investigated. Computational evidence is provided, suggesting the conjecture that all such sequences are ultimately periodic. A complete proof of the conjecture is provided in the special case in which the linear polynomial is a translation
Faculty Mihai Caragiu is an associate professor of mathematics
Student Lisa Scheckelhoff is an undergraduate student majoring in mathematics and biology. Lisa Scheckelhoff participated in this research in her senior year and then presented it as part of her senior capstone project in mathematics. Parts of this research were also presented at the 2006 Annual Nebraska Conference for Undergraduate Women in Mathematics and at the 2006 MAA Ohio Spring Meeting
Fund The research was supported by the Getty College of Arts and Sciences at Ohio Northern University
 
( 33 )   Recorded at: 2/21/2007      
Title Application of simulation in computer architecture, Proceedings of the 4th International Conference on Education and Information Systems: Technologies and Applications.
Journal , 2006;1:168-173, Parker BC, Edmondson JR
Description A software teaching tool was created to enhance already existing pedagogy and practice to augment student learning, motivation, and retention of Computer Architecture. The RSC Emulator teaches students through compilation, emulation, and simulation of a virtual RSC (Relatively Simple Computer). Logical groupings of components and the ability to debug component functions down to microcode give students a chance to gain an in-depth understanding of hardware functions by appealing to student needs for visualization and abstraction
Faculty Brenda Parker is an associate professor of computer science
Student James Edmondson is a senior computer science undergraduate.
Fund The research was conducted in Fall of 2005 and Spring of 2006 and supported by an URSCP Grant from the Office of Research and Sponsored Programs at MTSU
 
( 34 )   Recorded at: 12/8/2006      
Title Infinite family of approximations of the Digamma function
Journal J Math Comp Modelling, 2006; 43(11-12):1329-1336, Muqattash I, Yahdi M
Description The aim of the work was to find “good” approximations to the Digamma function ?. We construct an infinite family of “basic” functions covering the Digamma function. These functions are shown to approximate ? locally and asymptotically. Local and global bounding error functions are found and new inequalities for the Digamma functions are introduced
Faculty Mohammed Yahdi is assistant professor of mathematics at Ursinus College
Student Isa Muqattash participated in this research the summer after his junior year,; he graduated from Ursinus College in 2005 and is currently on a graduate school fellowship and teaching assistantship at Columbia University
Fund funded through the Ursinus College Summer Fellows program
 
( 35 )   Recorded at: 12/8/2006      
Title Toward a practical data privacy scheme for a distributed implementation of the Smith-Waterman genome sequence comparison algorithm
Journal Proc 2006 ISOC Ntwk Distrib Sys Sec Symp, 13:253-265, Szajda D, Pohl M, Owen J, Lawson B
Description This paper introduces a strategy for enhancing data privacy in some distributed volunteer computations, providing an important first step toward a general data privacy solution for these computations. The strategy is used to provide enhanced data privacy for the Smith-Waterman local nucleotide sequence comparison algorithm. Our modified Smith-Waterman algorithm provides reasonable performance, identifying most, and in many cases all, sequence pairs that exhibit statistically significant similarity according to the unmodified algorithm, with reasonable levels of false positives. Moreover the modified algorithm achieves a net decrease in execution time, with no increase in memory requirements. Most importantly, our scheme represents an important first step toward providing data privacy for a practical and important real-world algorithm
Faculty Douglas Szajda is an associate professor of Computer Science; Jason Owen is an assistant professor of Mathematics; Barry Lawson is an assistant professor of Computer Science.
Student Michael Pohl was a junior while completing this work. He will continue his study at the University of Richmond over the next year.
Fund This work was partially supported by a grant from the National Science Foundation.
 
( 36 )   Recorded at: 12/8/2006      
Title On decompositions of the KdV 2-soliton
Journal J Nonlinear Sci, 2006;16:179-200, Benes N, Kasman A, Young K
Description The soliton is an important concept in mathematics, physics and engineering because it is a nonlinear wave which exhibits particle-like properties. This paper, in particular, investigates the interaction of two solitons of the KdV equation that was originally written to describe surface waves of water on a canal. If one does not look closely, it may appear that the two "humps" of water simply pass right through each other. However, as is well known, a closer investigation reveals a nonlinear interaction that manifests itself in the form of a "phase shift". Original results in this paper include a demonstration of non-synchronicity in the asymptotic behavior of incoming and outgoing solitons, as well as novel decompositions of the solution that reveal the nature of the collision
Faculty Alex Kasman is an associate professor of mathematics at the College of Charleston
Student Nick Benes worked on this project as part of his graduate studies in mathematics at the College of Charleston. Kevin Young worked on this project as an undergraduate during the Summer of 2004, between his junior and senior years. Young is now a graduate student at the University of California at Berkeley and Benes is continuing with his graduate education at the College of Charleston
Fund The project was supported solely by the Department of Mathematics at the College of Charleston
 
( 37 )   Recorded at: 7/19/2006      
Title Irreducible polynomials and full elasticity in rings of integer-valued polynomials
Journal Journal of Algebra, 2005(293):595–610, Chapman ST, McClain BA
Description Let D be a unique factorization domain and S an infinite subset of D. If f(X) is an element in the ring of integer-valued polynomials over S with respect to D (denoted Int(S, D)), then we characterize the irreducible elements of Int(S, D) in terms of the fixed-divisor of f(X). The characterization allows us to show that every nonzero rational number n/m is the leading coefficient of infinitely many irreducible polynomials in the ring Int(Z) = Int(Z, Z). Further use of the characterization leads to an analysis of the particular factorization properties of such integer-valued polynomial rings. In the case where D = Z, we are able to show that every rational number greater than 1 serves as the elasticity of some polynomial in Int(S, Z) (i.e., Int(S, Z) is fully elastic)
Faculty Scott Chapman is a professor of mathematics
Student Barbara McClain is employed by the National Security Agency. Part of this work is contained in her Senior Honors Thesis at Trinity University.
 
( 38 )   Recorded at: 7/19/2006      
Title p-adic interpolation of the Fibonacci sequence via hypergeometric functions
Journal The Fibonacci Quarterly, 2005(43.3):213-226, Bihani P, Sheppard WP, Young PT
Description Several authors have considered the problem of extending the Fibonacci sequence to arbitrary real or complex subscripts. In this paper we consider the extent to which the Fibonacci and Lucas sequences can be extended to arbitrary p-adic subscripts in a continuous way. In the process we determine several new expressions, both p-adic and real, for the Fibonacci sequence in terms of hypergeometric functions and combinatorial sums
Faculty Paul Thomas Young is professor of mathematics
Student The work was done as a summer project in 2002, when Prerna Bihani was a sophomore and Wendy Sheppard was a graduate student at College of Charleston. Prerna received her Bachelor of Science degree in mathematics in 2004 and is now a graduate student in mathematics at the University of Notre Dame. Wendy received her Master of Science degree in mathematics in 2004 and is currently a visiting lecturer in the mathematics department at the College of Charleston.
 
( 39 )   Recorded at: 7/19/2006      
Title Tight bounds on plurality
Journal Information Processing Letters, 2005(96):93-95, Srivastava N, Taylor AD
Description We consider the problem of efficiently finding a ball of a plurality color within a finite set of colored balls. The corresponding question for a majority color has been studied in depth. We show here that n-1-choose-two comparisons are necessary in the worst case, and we give an algorithm that never uses more than this many comparisons
Faculty Alan D. Taylor is the Marie Louise Bailey Professor of Mathematics
Student Nikhil Srivastava was an undergraduate at Union College when this was written as a part of his senior thesis. He graduated in June, 2005 and is now doing Ph.D. work in computer science at Yale University
 
( 40 )   Recorded at: 7/19/2006      
Title Statistical methods in the journal
Journal The New England Journal of Medicine, 2005(353):1977-1979, Horton NJ, Switzer SS
Description This article surveys recent issues of "The New England Journal of Medicine" for the use of statistical methods. Prior work by Emerson and Colditz (1979, 1989) had shown a growth in the use of statistics in this widely read medical journal. We found a continued trend toward increased use of newer and more sophisticated statistical methods not normally covered in an introductory statistics course. This growth has important implications in medical and statistical education
Faculty Nicholas Horton is an assistant professor of Mathematics at Smith College
Student Suzanne Switzer participated in this research the summer after her junior year and anticipates graduating in May 2006
Fund The research was funded by the Howard Hughes Medical Institute
 
( 41 )   Recorded at: 1/6/2006      
Title When Thue-Morse meets Koch
Journal Fractals: Complex Geometry, Patterns, and Scaling in Nature and Societ, 2005, 13, 191-206, Jun Ma, Judy Holdener. (Kenyon College).
Description Using turtle geometry and polygon maps, the Thue-Morse sequence is realized as a limit of polygonal curves in the plane. This sequence of curves converges to the Koch Snowflake in the Hausdorff metric. The Thue-Morse sequence is then generalized to obtain other sequences that encode curves converging to the Koch Snowflake.
Faculty Judy Holdener is an associate professor of mathematics at Kenyon College.
Student Jun Ma participated in this research during the summer of 2004 following his junior year at Kenyon College. He continued the work throughout the following fall and was funded through Kenyon's Summer Science Scholar program. Jun received Kenyon's Tomsich Science Award (a research award typically awarded to faculty) for this work. He is currently working towards his Ph.D. in Statistics at Duke University.
 
( 42 )   Recorded at: 1/6/2006      
Title The Cover Pebbling Number of Graphs
Journal Discrete Mathematics, 2005, 296, 15-23, Betsy Crull, Tammy Cundiff, Paul Feltman, Glenn H. Hurlbert, Lara Pudwell, Zsuzsanna Szaniszlo, Zsolt Tuza (Valparaiso University).
Description A pebbling move on a vertex-edge graph consists of taking two pebbles off of one vertex and placing another pebble on an adjacent vertex. The cover pebbling number of the graph is the minimum number of pebbles such that however the pebbles are initially placed on the vertices of the graph we can eventually, after a series of pebbling move, put a pebble on every vertex of the graph simultaneously.
Faculty Zsuzsanna Szaniszlo is an associate professor at Valparaiso University, Glenn H. Hurlbert is a professor at Arizona State University, Zsolt Tuza is a research professor at the Computer and Automation Institute of the Hungarian Academy of Sciences.
Student The other four authors were working as an undergraduate research group at Valparaiso University. During the time of the project Betsy Crull and Paul Feltman were freshmen and are now juniors, Tammy Cundiff was a senior, she is now employed in industry, and Lara Pudwell was a senior, she is now in the Ph.D. program of the mathematics department at Rutgers University.
 
( 43 )   Recorded at: 1/6/2006      
Title SUITEDasher – A Multilingual Keyboard and Mouse Interface for Motor-Impaired Users
Journal Proceedings of 11th International Conference on Human-Computer Interaction (HCI 2005), Las Vegas, NV, 2005, 7, CD-ROM (10 pages), David Lyle, Bill Manaris. (College of Charleston).
Description A speech user interface for motor-impaired users was designed and prototyped. Design objectives included improved usability relative to an earlier system, multilingual support, and platform independence. To achieve these objectives, SUITEDasher presents a minimal graphical user interface, incorporates a trigram-based probabilistic model, and loads appropriate syntactic, lexical, and (potentially) phonetic models dynamically at run time. Usability tests indicate that SUITEDasher is 30% more efficient than its predecessor.
Faculty Bill Manaris is an associate professor of computer science at the College of Charleston in South Carolina, USA.
Student David Lyle participated in this research the summer after his junior year and then continued it as a senior project. He is currently employed in industry.
Fund The research was supported through a College of Charleston SURF grant.
 
( 44 )   Recorded at: 9/29/2005      
Title Use of R as a Toolbox for Mathematical Statistics Exploration
Journal The American Statistician, , 2004, 58(4), 343-357, N. J. Horton, E. R. Brown, L. Qian (Smith College).
Description The R language, a freely available environment for statistical computing and graphics is widely used in many fields. This expert-friendly system has a powerful command language and programming environment, combined with an active user community. In this paper, we discuss how R is ideal as a platform to support experimentation in mathematical statistics, both at the undergraduate and graduate levels. Using a series of case studies and activities, we describe how R can be utilized in a mathematical statistics course as a toolbox for experimentation. These activities, often requiring only a few dozen lines of code, offer the student the opportunity to explore statistical concepts and experiment, while providing an introduction to the framework and idioms available in this rich environment.
Faculty Nicholas Horton is assistant professor, Department of Mathematics, Smith College
Student Linjuan Qian (Smith College class of 2005) undertook the work during summer 2004 and is currently planning to matriculate into a doctoral program in Statistics at Harvard University.
Fund This work was funded in part by NIH grant MH54693.
 
( 45 )   Recorded at: 9/29/2005      
Title Debugging with Aspects
Journal Journal of the Consortium of Computing Sciences in Colleges, 2005, 20-5, 44-55, John Stamey, Bryan Saunders (Coastal Carolina University).
Description This paper illustrates techniques for tracing the execution of loops, methods and constructors using AOP. The use of aspects to implement debugging can also eliminate the need to install and learn new debugging packages for code tracing.
Faculty John Stamey is a professor of computer science at Coastal Carolina University
Student Bryan Saunders participated in this research during his sophomore year. He is currently still enrolled at Coastal Carolina University as a junior.
 
( 46 )   Recorded at: 9/29/2005      
Title Primitive Ideals of non-Noetherian Down-up Algebras
Journal Communications in Algebra, 2005, 33, 605-622, Iwan Praton, Stephen May (Franklin and Marshall College).
Description We determine generators of all primitive ideals of non-Noetherian down-up algebras. Since primitive ideals of Noetherian down-up algebras have been previously calculated, this work completes the classification of all primitive ideals of down-up algebras-we now have explicit descriptions of all of them.
Faculty Iwan Praton is a faculty member in the mathematics department at Franklin & Marshall College
Student Stephen May participated in this project during the summer after his junior year. He is now in graduate school at North Carolina State University.
Fund The work was supported by Franklin & Marshall's Hackman summer grant.
 
( 47 )   Recorded at: 9/29/2005      
Title Building Infrastructure for an Honors Research Robotics Lab
Journal Proceedings IEEE 6th ACIS International Conference on Software Engineering, Artificial Intelligence, Networking and Parallel/Distributed Computing, Towson, MD, May 23-25, 2005, 352-357, G. Trajkovski, J. Schlosburg, B. Whitman, G. Vincenti (Towson University).
Description This paper overviews the process of adaptation of the Cognitive Agency and Robotics Laboratory (CARoL) at Towson University to host undergraduate research projects, and overviews the ongoing research in the domain of Cognitive and Developmental Robotics. With institution-specific adaptations, based on the student interests and profiles, this lab can be easily replicated on a shoestring.
Faculty Goran Trajkovski is an assistant professor of computer and information Sciences and the director of the Cognitive Agency and Robotics Laboratory at Towson University.
Student Julius Schlosburg, a sophomore, and Brian Whitman, a senior majoring in computer science, have worked in the lab since its inception within a variety of undergraduate research programs at the College of Science and Mathematics and Towson University in general. Giovanni Vincenti is a doctoral student of Trajkovski.
Fund Part of this work was funded by the National Academies of the Sciences.
 
( 48 )   Recorded at: 9/29/2005      
Title The Structure of Optimal Partitions of Orthogonal Polygons into Fat Rectangles
Journal Computational Geometry: Theory and Applications, 28(1) 49-71, 2004, Joseph O'Rourke, Geetika Tewari (Smith College).
Description A VLSI masking problem suggested exploring partitions of a polygon into rectangles that maximize the shortest rectangle side. Thus no rectangle is "thin"; all rectangles are "fat." The shortest side corresponds to the width of the etching electron beam. The research resulted in a polynomial-time algorithm to find this optimal partition.
Faculty Joseph O'Rourke is professor and chair of computer science at Smith College.
Student The work grew out of Geetika Tewari's senior honors thesis of 2002. She is currently a graduate student in computer science at Harvard University.
Fund The research was supported through an NSF-DTS award.
 
( 49 )   Recorded at: 9/29/2005      
Title Ternary Codes Through Ternary Designs
Journal Australasian Journal of Combinatorics, 2004, 30, 21–29, Alexander L. Strehl (College of Charleston).
Description It is known that under certain conditions the incidence matrix of a balanced incomplete block design (BIBD) with parameters (v, b, r, k, ?) can be used to form a binary error-correcting code of size 2(v +1) with wordlength b. In this paper sufficient conditions are given under which the incidence matrix of a balanced ternary design (BTD) can be used to forma ternary error-correcting code, analogous to the binary codes from BIBD’s. Three examples of single-error-correcting ternary codes are constructed illustrating this principle.
Faculty Dinesh G. Sarvate, the faculty mentor for this project, is a professor of mathematics at the College of Charleston.
Student Alexander is currently at Rutgers working towards a PhD in Computer Science. This work was done during 2001 and 2002 during academic year and summer and was part of Alexander's undergraduate Bachelor's Essay.
 
( 50 )   Recorded at: 9/29/2005      
Title Microsoft .NET and Security Provided by High-Level Internet Protocols
Journal The 2005 International Conference on Parallel and Distributed Processing Techniques and Applications (PDPTA'05), 2005, Tatiana Melnik, Zornitza Prodanoff (University of North Florida).
Description This paper describes a class of insecure .NET client applications, which avoid higher layer protocol protection through using a raw sockets API. By compiling and executing client applications using the "raw" sockets interface, we demonstrate a serious security risk - insecure clients can be written with minimal programming effort (lines of code).
Faculty Zornitza Prodanoff is an assistant professor of computer science and information systems at the Department of Computer and Information Sciences of the University of North Florida.
Student Tatiana Melnik participated in this research during the summer of 2004 as a directed independent study student after her junior year. She then completed her honors thesis in the Fall of 2004.
Fund The research was supported through a UNF Undergraduate Research grant.
 
( 51 )   Recorded at: 9/29/2005      
Title Monitor Color and Repetition as Factors in Human-Computer Interaction
Journal Proceedings of the 43rd ACM Southeast Conference, March 18-20, 2005, 2, 118-119, Katja A. Rodgers (University of West Florida).
Description Recall of new information is the basis for reading comprehension and is a fundamental skill that affects virtually every area of human activity in which information is displayed. Because the computer has become the primary means by which information is disseminated, Human-Computer Interaction (HCI) factors play an important role in the effectiveness of the process. The effect of repetition and color on the recall of new information was tested by briefly presenting colored text to participants and measuring how accurately they recall the text. A unique aspect of this study is that a computer monitor, rather than the normally used print media, was used for the experiment. Differences were found both in repetition and color selection. This result points out the need for a return to a more structured approach to the learning process and the need for additional study to help determine a more effective means by which information is displayed by way of computer monitors.
Faculty
Student
 
( 52 )   Recorded at: 9/29/2005      
Title Classification of Signature Curves Using Latent Semantic Analysis
Journal LNCS, 2005, 3519, 152-162, Cheri Shakiban and Ryan Lloyd (University of St. Thomas).
Description We described the Euclidean signature curves for two dimensional closed curves in the plane and gave a discrete numerical method for finding such invariant curves. Further we described an analog of Latent Semantic Analysis (LSA) and presented data and noise reduction techniques as well as an optimal combination of normalizing transformations to categorize signature curves. We then gave an example for sorting out leaves of two types of trees regardless of their orientation using their signature curves
Faculty Cheri Shakiban is a professor of mathematics at University of St. Thomas.
Student Ryan Lloyd, a math major, participated in this research the summer after his junior year and continued during his senior year. He is currently employed in industry.
Fund The research was supported partly through a NSF grant and partly through an internal grant.
 
( 53 )   Recorded at: 9/12/2005      
Title Performance Evaluation of an Internet Friendly Transport Protocol over Networks with Lossy Links
Journal Applied Telecommunication Symposium; Spring Simulation Multiconference, San Diego, California, April 2-8 2005, , H. ElAarag, A. Moedinger (Stetson University).
Description The growing need for Internet friendly streaming protocols prompted us to develop IFTP (Internet Friendly Transport Protocol). To improve the performance of IFTP on lossy links, we developed a variant, IFTP-W, which specifies an error-sensitive section. In this paper we present the performance of IFTP-W with varying error-sensitive section lengths on networks with varying link qualities. The results indicate the increase of IFTP-W=92s performance as the error-sensitive section length is decreased. This paper also describes the object oriented discrete event networking simulator we wrote in C# to evaluate the performance of our design.
Faculty H.ElAarag is an assistant professor of computer science at Stetson University.
Student A. Moedinger participated in this research in Fall 2004 of his junior year through an independent study and is still enrolled at Stetson University.
 
( 54 )   Recorded at: 6/3/2005      
Title Data Exploration Tools for the Gene Ontology Database
Journal Bioinformatics, 2004 20:3442-3454, Elizabeth Shoop, Paulo Casaes, Getiria Onsongo, Lisa Lesnett, Erla Osk Petursdottir, Edward Kofi Yeboah Donkor, Dennis Tkach, Michael Cosimini (Macalester College)
Description Our goal for this project was to improve the ability of biologists (both researchers and students) to ask biologically interesting questions of the Gene Ontology (GO) database and to interactively explore the ontologies. To meet this goal, we built two novel tools, called goGet and goView. GoGet has a user interface that enables users to ask biologically interesting questions, such as: 'What are the DNA binding proteins involved in DNA repair, but not in DNA replication?'. The results of such queries can be viewed in a collapsed tabular format that eases the burden of getting through large tables of data. GoView enables users to explore the large directed acyclic graph structure of the ontologies in the GO database.
Faculty Elizabeth Shoop is an assistant professor of computer science.
Student Lisa Lesnett, Erla Osk Petursdottir, Edward Donkor, and Dennis Tkach worked on this project during the summer of 2002. Dennis Tkach is now in graduate school at the University of Chicago. Lisa, Erla, and Edward are employed in industry. Paulo Casaes and Getiria Onsongo worked during the 2002 summer, the 2003 summer, and during their senior year, 2003-2004. Getiria Onsongo is now in graduate school at the University of Minnesota, planning to study bioinformatics. Paulo Casaes has returned to his home country of Brazil and is working in the software industry there. Michael Cosimini worked during the summers of 2003 and 2004, and is currently enrolled at Macalester College.
Fund The work was funded by grants from the Howard Hughes Medical Institute and the Keck Foundation.
 
( 55 )   Recorded at: 6/3/2005      
Title PDA-Based Boolean Function Simplification: A Useful Educational Tool
Journal Informatics, 2004, 15, 323-326, Ledion Bitincka, George A. Antoniou (Montclair State University)
Description In this paper a useful educational tool is presented for minimizing low order Boolean expressions. The algorithm follows the Karnaugh map looping approach and provides optimal results. For the implementation, C++ was used on the CodeWarrior for Palm Operating System environment. In order to make the overall implementation efficient, the object oriented approach was used. Two step-by-step examples are presented to illustrate the efficiency of the proposed algorithm. The proposed application can be used by students and professors in the fields of electrical and computer engineering and computer science.
Faculty George Antoniou is a professor of computer science.
Student Ledion Bitincka participated in this research (independent study) during his senior year. Mr. Bitincka is a graduate student in the Department of Biochemistry and Biophysics of the University of California San Francisco.
Fund The research was supported by a MSU Faculty-Student award.
 
( 56 )   Recorded at: 8/18/2004      
Title Exponential Modeling, Washout Curve Reconstruction, and Estimation of Half-Life of Toluene and its Metabolites
Journal Journal of Toxicology and Environmental Health, 2004, 67, 1131-58, Crispin H. Pierce, Yili Chen, William Hurtle, Michael S. Morgan (University of Wisconsin-Eau Claire)
Description Elimination rates of exhaled 2H8-toluene and urinary metabolites were analyzed from 33 exposures of males to 50 ppm 2H8-toluene for 2 hours at rest. It was hypothesized that the shapes from our decay curves would be applicable to any occupational or environmental toluene exposure. Our approach was able to reconstruct data from studies where exposure duration ranged from 10 min-7 hours, and where activity level ranged from rest-150W (strenuous exercise).
Faculty Crispin Pierce is a professor of environmental and public health at UW-Eau Claire. William Hurtle is a chronopharmacokinetics specialist with the US Air Force. Michael Morgan is a professor of environmental and occupational health at the University of Washington.
Student Yili Chen participated in this research during his junior year, and is currently in law school.
Fund This work was supported by the Superfund Basic Research program, NIEHS, NIOSH SERCA, and NIH.
 
( 57 )   Recorded at: 8/18/2004      
Title From Simple Rules to Cycling in Community Assembly
Journal Oikos, 2004, 105, 349-358, Sebastian J. Schreiber, S. Rittenhouse (College of William and Mary)
Description A system consisting of two predators and two prey competing for a shared resource was analyzed. Simple dominance rules (i.e. R¤ and P¤ rules) were shown to lead to cycling between subcommunities consisting of predator-prey pairs; predator and prey invasions alternatively lead to prey displacement via apparent competition and predator displacement via exploitative competition. These cycles are often dynamically unstable in the population phase space. More specifically, while for too slow invasion rates the system cycles indefinitely, faster invasion rates lead to coexistence of all species. In the later case, the assembly dynamics exhibit transient cycling between predator-prey subcommunities and the length of these transients decreases with the invasion rate and increases with habitat productivity.
Faculty Sebastian Schreiber is an associate professor of mathematics.
Student Seth was an undergraduate at Western Washington University, participated in this research throughout his senior year, and is currently a physics Ph.D. student at the University of Colorado, Boulder.
Fund The research was funded through a NSF-RUI grant.
 
( 58 )   Recorded at: 8/16/2004      
Title Classifying Polygonal Chains of Six Segments
Journal Journal of Knot Theory and its Ramifications, 2004, 13, 479-514, Thomas Clark, Gerard Venema (Calvin College)
Description A polygonal chain is the union of a finite number of straight line segments in 3-space that are connected end-to-end. Two chains are considered to be equivalent if there is a motion of space that moves one chain to the other while keeping the segments rigid. Chains may be knotted and stuck in this category even though all chains are topologically trivial. Polygonal chains with five or fewer segments had previously been classified. In this paper, polygonal chains of six segments are classified.
Faculty Gerard Venema is a professor of mathematics.
Student Thomas Clark began work on this research in the summer following his sophomore year as an REU student. Tom continued the work during the following two years and did an honors project and senior thesis in mathematics education that was based on this work. He has accepted a teaching position in California.
Fund The project was funded by an NSF-REU supplement to an NSF-RUI grant.
 
( 59 )   Recorded at: 8/16/2004      
Title Electronic Color Charts for Dielectric Films on Silicon
Journal Optics Express, 2004, 12 1464-1470, Justin Henrie, Spencer Kellis, Stephen M. Schultz, Aaron Hawkins (Brigham Young University)
Description The calculation of the perceived color of dielectric films on silicon is presented. A procedure is shown for computing the perceived color for an arbitrary light source, light incident angle, and film thickness.
Faculty Aaron Hawkins and Stephen Schultz are associate professors in the electrical and computer engineering department.
Student Justin Henrie and Spencer Kellis participated in this research during their junior year under the University's Office of Research and Creative Activities funding program. Spencer is completing an internship with Intel Corporation and Justin is continuing research at BYU over the summer. Both will be seniors this year.
Fund The research was supported through university-sponsored grants.
 
( 60 )   Recorded at: 5/5/2004      
Title Central Groupoids, Central Digraphs, and Zero-One Matrices A Satisfying A^2 =J
Journal Journal of Combinatorial Theory, Series A, 2004, 105, 35-50, Frank Curtis, John Drew, Chi-Kwong Li, Daniel Pragel (College of William and Mary)
Description A study was conducted of central groupoids, central digraphs, and zero-one matrices A satisfying A^2 = J. A survey of known results was generated, including short proofs for some of them; new results and techniques were developed, and conjectures were settled. Open questions and new conjectures were provided.
Faculty John Drew and Chi-Kwong Li are professors of mathematics.
Student Frank Curtis and Daniel Pragel conducted their research in the summer during an NSF supported REU program at the College of William and Mary. Frank Curtis is now a graduate student in applied science at Northwestern University, while Daniel Pragel is a graduate student in mathematics at California Institute of Technology.
 
( 61 )   Recorded at: 5/5/2004      
Title Linear Maps Leaving Invariant Subsets of Nonnegative Symmetric Matrices
Journal Bulletin of Australian Mathematics Society, 2003, 68, 221-231, Hanley Chiang, Chi-Kwong Li (College of William and Mary)
Description A study was conducted of certain sets of nonnegative symmetric matrices, such as the set of symmetric doubly stochastic matrices or the set of symmetric permutation matrices. It was proven that a linear transformation mapping such a set S onto S must be of the form T(X) = (P^t)XP for some permutation matrix P, except for several low dimensional cases.
Faculty Chi-Kwong Li is a professor of mathematics.
Student Hanley Chiang participated in this research as part of his honors thesis work during his senior year. He is now a graduate student in economics at Harvard University.
 
( 62 )   Recorded at: 5/5/2004      
Title A Sensitivity Study of Parallel I/O under PVFS: Lessons Learned Using a Parallel File System on PC Clusters
Journal Parallel I/O for Cluster Computing, C. Cerin, H. Jin, Eds, Stylus Publishing, 2004, 93-105, Jens Mache, Joshua Bower-Cooley, Robert Broadhurst, Jennifer Cranfill, Clark Kirkman IV. (Lewis & Clark College)
Description Using the Parallel Virtual File System (PVFS) and a ray tracing application, the sensitivity of parallel I/O performance, the overlapping of I/O nodes with compute nodes and the exploitation of local data were studied. Parallel I/O throughput not only depended on hardware (disk speed and network bandwidth), but also on configuration and programming choices.
Faculty Jens Mache is an assistant professor of computer science.
Student Joshua Bower-Cooley, Robert Broadhurst, Jennifer Cranfill and Clark Kirkman IV participated in this research the summer after their junior years. Jennifer is currently employed in industry. The other three started graduate school.
Fund The research was supported through the John S. Rogers Science Research Program.
 
( 63 )   Recorded at: 5/5/2004      
Title An Alternate Approach to the Total Probability Formula
Journal International Journal of Mathematical Education in Science and Technology, 2004, 35, 144-148, Dane W. Wu, Laura M. Bangerter (Pacific Lutheran University)
Description A simpler approach than the Total Probability Formula (TPF) was developed for computing probabilities of certain events after sequential random shifts. A recursive formula was derived to solve probability problems that are virtually impossible to solve by the TPF. The results can potentially be applied to estimating the demographic distribution of students after a chain of transfers as well as to studies of biological mutation.
Faculty Dane Wu is an associate professor of mathematics.
Student Laura Bangerter participated in this research as an independent study project in her senior year and is now employed in industry.
 
( 64 )   Recorded at: 12/15/2003      
Title Minimal Enclosings of Triple Systems I: Adding One Point
Journal Ars Combinatoria, 2003, 68, 145-159, Spencer P. Hurd, Patrick Munson, Dinesh G. Sarvate (Citadel/College of Charleston)
Description This paper solves the problem of the existence of a minimal enclosing for a triple system into another. A new necessary condition is derived and some general results are obtained for larger values of the index.
Faculty Spencer Hurd is a professor of mathematics at the Citadel. Dinesh Sarvate is a professor of mathematics at the College of Charleston.
Student Patrick Munson performed his part of the research as an independent study project and then as a non-credit research experience during his senior year. Patrick is currently an officer in the US Air Force.
 
( 65 )   Recorded at: 9/8/2003      
Title Taking the Sting out of Wasp Nests: A Dialogue on Modeling in Mathematical Biology
Journal The College Mathematics Journal, 2003, 34, 207-215, Jennifer C. Klein, Thomas Q. Sibley (College of St. Benedict, Saint John’s University)
Description We developed mathematical formulas to compute the number of walls in actual nests based on the number of cells and exterior cells and to compute the optimal number of walls for a given number of cells. These formulas provide the entomologist a fast, accurate way to compare nests of different species with optimal arrangements and so test various hypotheses about the observed variation.
Faculty Tom Sibley is a professor of mathematics at St. John's University.
Student Jennifer Klein participated in the research for this article in 2001 as a junior chemistry major from the College of St. Benedict in a mathematical biology class taught by Tom Sibley, a professor of mathematics at St. John's University. Jennifer has finished her first year of graduate studies in the Biochemistry, Molecular Biology and Biophysics program at the University of Minnesota.
 
( 66 )   Recorded at: 5/27/2003      
Title Evolutionary Music and the Zipf-Mandelbrot Law: Developing Fitness Functions for Pleasant Music
Journal Springer-Verlag Lecture Notes in Computer Science, (LNCS 2611), 2003, 522-534, Bill Manaris, Dallas Vaughan, Christopher Wagner, Juan Romero, Robert Davis (College of Charleston)
Description A study on a 220-piece corpus (baroque, classical, romantic, 12-tone, jazz, rock, DNA strings, and random music) reveals that aesthetically pleasing music may be describable under the Zipf-Mandelbrot law. Various Zipf-based metrics have been developed and evaluated. Zipf distributions across certain music dimensions appear to be a necessary, but not sufficient condition for pleasant music. Statistical analyses suggest that combinations of Zipf-based metrics can be used to identify genre and/or composer. An evolutionary music framework is presented, which utilizes Zipf-based metrics as fitness functions.
Faculty Bill Manaris is in the Department of Computer Science at College of Charleston. Juan Romero is in the Creative Computer Group - RNASA Lab - Faculty of Computer Science, University of A Coruña, Spain. Robert Davis is in the Department of Mathematics and Statistics, Miami University.
Student Dallas and Christopher participated in this research as part of a yearlong bachelors essay research project in their senior year.
Fund The work was supported by a grant from the College of Charleston.
 
( 67 )   Recorded at: 5/27/2003      
Title Persistence of Thin Ice Regions in Europa’s Ice Crust
Journal Geophysical Research Letters, 2002, 29, 12-1, L. Buck, C.F. Chyba, M. Goulet, A. Smith, P.J. Thomas (University of Wisconsin-Eau Claire)
Description An application of a two-dimensional thermal model to the analysis of the refreezing of a hole in the icy crust of Europa following a breach event. The model incorporates heat produced by tidal heating of Europa by basal heating from the core, and by flexing of the ice sheet. We find that catastrophic breaches in Europa's ice crust may produce regions of relatively thin ice persisting up to one million years.
Faculty Chris Chyba is the Carl Sagan Chair for the Study of Life at the SETI Institute. Marc Goulet is an associate professor of mathematics, Alex Smith a professor of mathematics, and Paul Thomas a professor of physics and astronomy at UW-Eau Claire.
Student Leon Buck worked on this project during his sophomore year and is still enrolled in UW-Eau Claire.
Fund Funding was provided by UWEC.
 
( 68 )   Recorded at: 5/16/2003      
Title Linear Codes Through Latin Squares Modulo n
Journal Bulletin of the Institute of Combinatorics and Applications, 2003, 37, 73-81, Dinesh G. Sarvate, Alexander L. Strehl (College of Charleston)
Description A method of construction of codes from Latin squares over Zn that satisfies the linear property was obtained. Necessary and sufficient conditions on the family of Latin squares were described and a method for constructing a maximal family of mutually orthogonal Latin squares that form linear codes was developed. On the other extreme it was shown that no pair of mutually orthogonal Latin codes of even order generate a linear code.
Faculty Dinesh G. Sarvate is a professor of mathematics at the College of Charleston.
Student Alex's research was initiated in the summer and then continued into the academic year as a yearlong senior bachelors essay project. Alex is currently a Ph.D. student in Computer Science at Rutgers.
Fund The Departments of Mathematics and Computer Science supported the research in the summer.
 
( 69 )   Recorded at: 10/1/2002      
Title A Stirling EnCOUNTer with Harmonic Numbers
Journal Mathematics Magazine, 2002, 75, 95-103, Arthur T. Benjamin, Gregory O. Preston, Jennifer J. Quinn (Harvey Mudd College)
Description A combinatorial definition of the Harmonic Number H_n = 1 + 1/2 + 1/3 + … + 1/n is given, leading to interesting combinatorial proof of many indentities.
Faculty Arthur Benjamin is professor of mathematics. Jennifer Quinn is associate professor of mathematics.
Student Greg Preston conducted the work as a senior thesis and is employed as a consultant.
 
( 70 )   Recorded at: 6/26/2002      
Title Polygonal Chains Cannot Lock in 4D
Journal Computational Geometry: Theory and Applications, 2001, 20, 105-129, Roxana Cocan, Joseph O'Rourke. (Smith College)
Description It was proven that polygonal chains (chains of rigid bars connected by universal joints) cannot lock (i.e., be "stuck") in four and all higher dimensions. Reconfigurations of the chain do not permit bars to cross through one another. It was known that chains can lock in 3D, but it was an unsolved problem to determine if they could in 2D, or in 4D and higher. The latter question was settled.
Faculty Joseph O'Rourke is a professor of Computer Science.
Student Roxana Cocan carried out the work as part of her senior honors thesis project. Roxana is now employed as a software architect.
Fund The work was supported by the NSF.
 
( 71 )   Recorded at: 3/11/2002      
Title The Gaussian Zoo
Journal Experimental Mathematics, 2001, 10, 161-173, John Renze, Stan Wagon, Brian Wick
Description The patterns of prime numbers in the Gaussian integers were examined. Several errors in the literature were corrected, a famous theorem of Mertens to the Gaussian integers was extended, and the generation of Hardy-Littlewood formulas for prime patterns was automated.
Faculty Stan Wagon is in the Department of Mathematics and Computer Science at Macalester College.
Student John Renze did the work during the academic year and is currently in the Ph. D. program at Northwestern University.
 

 

  
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