Parameter
Influences on Instability of the Keller-Segel Aggregation Model
Ronald C. Anderson, Thiel
College
The Keller-Segel Model suggests amoebae aggregation into fruiting
bodies results from an instability. This talk will introduce an
instability condition for the PDE model proposed by Keller and Segel. A
mathematical and biological analysis of several parameters contributing
to system instability will then be presented.
This research was
conducted at Texas Tech University, under the supervision of Dr. Akif
Ibraguimov.
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Estimating the Eigenvalues of a Covariance
Matrix
Robert Carrico,
University of Mary Washington
The purpose of this research was to produce confidence estimates of the
eigenvalues of a covariance matrix. The confidence intervals were
derived from two different confidence bands for the characteristic
polynomial . Simulations were conducted for a variety of different
pairs for the eigenvalues to see how well the estimators perform.
This research was conducted
at the University of Mary Washington, under the supervision of
Dr. Debra Hydorn . |
A Ribbon Graph Structure on Plane Curves
Michael Chmutov, The Ohio State University
The talk concerns the study of immersions of a circle into the plane
with only transverse double point singularities. In particular, we show
how to capture the information about such a plane curve using a
combinatorial structure of a ribbon graph.
This research was conducted
at Oregon State University, under the supervision of Dr. Juha
Pohjanpelto.
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PascGalois: Pictures and Patterns
Julianne Coxe, JMU
Using PascGaloisJE to implement Pascal's triangle update rule to
graphically represent finite space-time diagrams, I observed patterns
displayed when the modular number and seed were varied. Certain
combinations of powers of 2 and prime numbers resulted in common
patterns in the graphics that may be specific to those number classes.
This research was conducted
at New College of Florida, under the supervision of Dr. Eirini
Poimenidou.
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The Aeroacoustics Of Turbulent Coanda Jet
Flows
Jason Fox, James
Madison University
This paper extends the theory of mathematically predicting the
Turbulent Mixing Noise Emitted by a plane 2D wall jet to the case of a
3D Coanda jet. The effect of key flow characteristics are discussed,
extensions to the model are suggested, and comparison with experimental
results are presented.
This research was
conducted
at James Madison University, under the supervision of Dr.
Caroline Lubert. |
The Distribution of the Number of Shared
Items Between Three Randomly Ordered Lists of N Numbers
Erin Keegan,
University of Mary Washington
Suppose there are three lists of randomly ordered N numbers, and that
we compare the top n numbers in each of these three lists. The
goal was to find the probability distribution for the number of shared
items in each of these three sub-lists, including the mean and variance.
This research was conducted
at University of Mary Washington, under the supervision of Dr.
Debra Hydorn.
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Real Polynomials, Imaginary Roots, and
Enchanting Ellipses
Liza
Lawson, Randolph-Macon College
Investigation of a certain class of polynomials reveals that, as a real
root varies, the nonreal roots of the derivatives of these polynomials
lie on fixed ellipses in the complex plane. Further work shows
that this same configuration can be maintained for a broader class of
polynomials.
This research was conducted
at Randolph-Macon College, under the supervision of Dr. Bruce
Torrence.
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Population Dynamics
of Two Competing Species
Benjamin Leard, James Madison University
Using difference equations and nullclines, we model the population
dynamics of two generic species competing over the same resources in a
closed environment.
This research was conducted
at James Madison University, under the supervision of Dr. Anthony
Tongen and Dr. Brian Walton .
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The Determination of Relative
Concentrations of Hydrogen Isotopes
Laurence A.
Lewis, James Madison University
JMU produces high purity hydrogen deuteride gas for nuclear
experiments. To determine the relative purity of the gas,
chromatography is used, producing overlapping asymmetric gaussian
peaks. Numerical algorithms using functions modeled on these peaks
produce chi-squared fits which allow for extraction of the
concentrations. The method and results of such fits will be discussed.
This research was conducted
at James Madison University, under the supervision of Dr. C. S.
Whisnant.
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Non-Destructive Recovery of Voids within a
Three Dimensional Domain using Thermal Imaging
Victor Oyeyemi,
Goshen College
We develop an algorithm which recovers spherical voids in a three
dimensional object. The algorithm produces the radii and
locations of each void. Our method involves the application of known
heat flux to the object's boundary. The steady temperature of the
boundary is then used to image the voids.
This research was conducted
at the Rose-Hulman Institute of Technology, under the supervision
of Dr. Kurt Bryan.
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Length Sets of Numerical Monoids
Joao
Paixao, Virginia Tech
We
study non-unique factorization of numerical monoids. First, we
determine exact solutions for length sets and then we enumerate V-sets.
Then we look at the problem if equality of the V-sets implies
isomorphism between the monoids. Finally, we investigate if equality of
lengths sets also implies isomorphism.
This research was conducted
at the Trinity Research Experience for Undergraduates, under the
supervision of Dr.Scott Chapman.
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A game of Biblical Proportions
Joan
Pharr, Wake Forest University
The game involves two players: a devil and an angel, hence the name of
the game. The players take turns moving two tokens on a line with
n vertices. The talk will include the details of the game,
proposed strategies and results of our research and a sketch of a proof.
This research was conducted
at Carnegie Mellon University, under the supervision of Dr.
Andrew
Beveridge and Dr. Thomas Bohman.
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Modeling the Oscillations of Acoustically
Coupled Bubbles
Joseph
Roberts, Pennsylvania State University
The Rayleigh-Plesset equation is a well known ordinary differential
equation that describes the acoustic oscillations of a single spherical
bubble. We have derived a model for a two bubble system using a
similar approach. Our numerical simulations have indicated
complex dynamics. Poincare plots are analyzed and Lyapunov
exponents are calculated.
This research was conducted
at the W.G. Pritchard Labs, Pennsylvania State University, under the
supervision of Professor Andrew Belmonte.
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An Algorithm for Producing Arrow Diagram
Formulas for the Coefficients of the Conway Polynomial
Alfred
Rossi, Ohio State University
The coefficients of the Conway Polynomial are Vassiliev invariants of
links. We give an algorithm for producing the arrow diagram formula for
the n-th coefficient from the corresponding formula of the n-1
coefficient.
This research was conducted
at Ohio State University, under the supervision of Dr. Sergei Chmutov. |
Computations of Quantum Entanglement
Robert Schaeffer, Lebanon Valley College
The purpose of this research was to understand the mathematical notion
of quantum bits (qubits) and their entanglement types. Hence I
developed several code segments to test qubits for entanglement
properties. These tests yielded counterexamples and helped in various
proofs. This research aided in the exploration of 'Irreducible Quantum
Entanglement'.
This research was conducted
at Lebanon Valley College, under the supervision of Dr. David Lyons.
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Tweakable Block Ciphers under Exponential
Attacks
Hakan
Seyalioglu, The College of William and Mary
A tweakable block cipher is a block cipher in which an additional
input, the tweak, is used to construct an essentially different
instance of the block cipher. Motivated by Patarinâ's recent
results on exponential security, we explore the notion of exponential
security for tweakable blockciphers.
This research was conducted
at The College of William and Mary, under the supervision of
Professor Moses Liskov.
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Hamiltonicity of <2,4,t> Cayley
Graphs
James
Sharpnack, The Ohio State University
Which Cayley graphs have Hamilton cycles remains unsolved. By
considering certain types of Euler paths in a reduced ribbon graph of
the original graph, we know that Cayley graphs with <2,4,t>
presentations have Hamilton cycles.
This research was conducted
at The Ohio State University, under the supervision of Dr. Sergei
Chmutov.
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Classifying Hand-written Digits With
Persistent Barcodes
Mandy Smith,
Centre College
We discuss a new approach to shape recognition using persistent
homology, which incorporates both topological and geometric features of
objects into "shape descriptors" that enable a computer to match new
objects with others of similar shape. We focus on classifying
scanned-in numbers from the MNIST database of hand-written digits.
This research was conducted
at Centre College, under the supervision of Dr. Anne Collins.
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Interpolation of linear subspaces by
P-matrices
Christian
Sykes, University of North Carolina, Greensboro
A $P$-matrix is a matrix whose principal minors are positive. Let $X$,
$Y$ be $n \times k$ real matrices of rank $k$. We consider the problem
of what conditions are necessary and sufficient for the existence
of a $P$-matrix $A$ such that $AX = Y$.
This research was conducted
at the 2006 REU in Matrix Analysis at The College of William &
Mary, under the supervision of Dr. Charles R. Johnson.
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Tuning in: a variation of radio labeling
Desmond Torkornoo, University of Richmond
An L(3,2,1)-labeling of graph G is f:V(G)~W>N such that for x,y in
V(G): d(x,y)=1 implies |f(x)-f(y)|>=3; d(x,y)=2 implies
|f(x)-f(y)|>=2; and d(x,y)=3 implies |f(x)-f(y)|>=1. The
L(3,2,1)-number of G is the smallest k such that G has
L(3,2,1)-labeling f with k=max{f(V(G))}. We have determined the
L(3,2,1)-number for simple graphs.
This research was conducted
at the Valparaiso University Summer REU 2006, under the supervision
of Dr. Zsuzsanna Szaniszlo.
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Classification of Ice Crystals through
Fractal Analysis
Heather Umberger, Shenandoah University
Using methods of fractal analysis, a new classification system for ice
crystals can be established. The current analysis involves the
use of two-dimensional, digital images and the use of FracTop
software. Consideration to practical use of the classification
system will be given.
This research was conducted
at Shenandoah University, under the supervision of Dr. Elaine
Magee.
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Thistlethwaite's Theorem for Virtual Links
Jeremy Voltz, Ohio State University
Thistlethwaite's theorem relates the Jones polynomial of a link
to the Tutte polynomial of a corresponding planar graph. We give
a generalization of this theorem to virtual links by way of ribbon
graphs and the Bollobás-Riordan polynomial.
This research was conducted
at The Ohio State University, under the supervision of Dr. Sergei
Chmutov. |
Minimizing Ropelength of Composite Knots
and Links
Rachel Whitaker, University of Georgia
Through developing computer programs and exploiting link symmetry, we
created a library of composite links by connected summing the
well-understood prime links. By tightening links to their minimum
ropelength configuration we hope to demonstrate the correlation of
ropelength to the behavior of a subatomic particle, the glueball.
This research was conducted
at University of Georgia, under the supervision of Dr. Jason Cantarella
.
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The Hamiltonicity of Cayley Graphs
Justin Wiser, Ohio State University
This talk will examine the famous conjecture that all Cayley graphs are
Hamiltonian from an algebraic perspective. We will use basic
representation theory to present a new geometric method that might be
used to eventually prove the conjecture.
This research was conducted
at Ohio State University, under the supervision of Dr. Sergei Chmutov .
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