Tenability of Polya
Urns and Applications
Omri Bar-Mashiah and Kyle
Whittaker
Our research focused on finding a general solution for which a
two-dimensional Polya Urn would be tenable. We were able to solve
three special cases for the nonlinear partial differential equation not
previously solved in the literature. In addition, we were able to find
moment generating functions for several of the linearized partial
differential equations using the method of characteristics.
This research was
conducted at George Washington University, under the supervision
of Dr. Katharine Gurski.
|
MCell And DReAMM
Simulations Of Catecholamine Release Detection Using a Patch Clamp
Technique
Akrita Bhatnagar
Catecholamine ions are released through the channels in the vesicle
membrane. We used the technique of cell-attached patch amperometry. To
represent the models and for mesh generation a blender is used, which
is exported as a Model Description Language (MDL) and run in a MCell3
program to create simulation objects. The meshes are visualized,
imported and edited in DReaMM.
This research was
conducted at the University of Pittsburgh's Pittsburgh
Supercomputing Center..
|
Equilateral Stick Knots
Lauren Blount
We use MatLab to construct equilateral stick knots from given stick
knots. Our algorithms failed for knots whose equilateral stick numbers
are conjectured to be greater than their stick numbers, adding some
computational evidence to support the conjectures.
This research was
conducted at St. Mary's College of Maryland, under the
supervision of Dr. Sandy Ganzell.
|
Cardinal Invariants for
${\mathfrak C}[0,1]$
Jorge Bruno
Relationships between cardinal invariants are well understood for the
continuum, but extensions of this theory to other spaces are partial,
and general claims have not been elaborated. We consider invariants for
the space of continuous function on $[0,1]$, especially those related
to a generalized Lebesgue measure.
This research was
conducted at James Madison University, under the supervision of
Dr. E. Brown.
|
Deterministic
Collections of Minors for Square-Matrices
Stephanie Bush
Our first objective was to find all deterministic collections of minors
in the 3x3 case, and then second to generalize principles to larger
matrices. We have focused our attention on collections of entry
minors with the 4 Sylvestor Minors given. Validation of the
proposed Conjecture is still pending.
This research was
conducted at the College of William and Mary, under the
supervision of Dr. Charles Johnson.
|
How many hours does it
take to model the local atomic structure of a sample?
Two... Four... Six... Six!
Julianne Coxe
NPDF at LANL uses neutrons from a proton beam to determine the local
atomic structure of samples. The experiment currently has neither
a generic time frame in which to measure, nor a set of requirements
after which to stop. This project focused on finding a solution
to this problem.(LA-UR # 07 5447)
This research was
conducted at Los Alamos National Lab, under the supervision of
Dr. Dr. Thomas Proffen.
|
Teacher Adoption of an Interactive Math
Curriculum
Alli Crandell
SimCalc MathWorlds is a dynamic technology-enhanced curriculum that can
deepen mathematical understanding of the mathematics of change and
variation. Its advantages have been documented in small studies;
do these results hold at scale? Sixty-eight teacher interviews in
the context of a randomized, controlled study reveal issues in
technology implementation and mathematical concepts covered.
This research
was
conducted at Virginia Tech, under the supervision of Dr. Deborah
Tatar.
|
HPV Vaccination Modeling
Michael Frempong and Charell
Wingfield
Discrete Models on HPV Vaccinations using two gender populations.
This research
was
conducted at James Madison University, under the supervision of
Dr. Anthony Tongen.
|
Evaluation of Computational Methods in the
Prediction of Protein-Protein Interactions in Arabidopsis thaliana
Lisa Gabor
A study previously conducted by this research group concluded that
supervised machine learning could be used to make predictions regarding
protein interactions based on direct and indirect biological datasets
for yeast cells. We sought to repeat these results for
Arabidopsis thaliana, a model organism for flowering plants, and
defined "protein interactions'' as a physical interaction.
This research was
conducted at Bioengineering and Bioinformatics Summer Institute
(BBSI), a joined program between the University of Pittsburgh, Carnegie
Mellon, and Duquesne University, under the supervision of. Dr. Judith
Klein-Seetharaman, PhD, and Yanjun Qi, PhD candidate.
|
Weighting for Coverage
Bias in Internet Surveys
Donovan Gromet
This research describes several weighting adjustment schemes aimed at
reducing coverage bias in internet surveys. Several schemes are
evaluated by considering the reduction in bias for variables of
interest and the variability of estimates from the schemes. It is
found that several of the proposed schemes are successful in improving
accuracy.
This research was
conducted at San Diego State University, under the supervision of
Dr. Kristin Duncan.
|
Bayesian Multiple
Comparisons for Treatments with a Control
Dustin Hevener
Comparison of $k$ treatment means with a control mean is considered. In
this setting, the pioneering work by Dunnett is well known. We propose
both two-sided and one-sided multiple-comparison procedures using a
Bayesian hierarchical model. The proposed method flexibly accommodates
heterogeneity of variances and unequal sample sizes, and can be
utilized in many areas where treatments vs. control is of primary
interest.
This research was
conducted at James Madison University, under the supervision of
Dr. Kane Nashimoto.
|
Book Embeddings of
Chessboard Graphs
Casey James
Hufford
A pawn is placed on an $n \times n$ chessboard and a graph is created
based on potential queen movement. A book embedding linearly
orders vertices in the spine and assigns edges to pages with
restrictions. Upper and lower bounds on the book thickness of this
graph are established.
This research
was
conducted at Morehead State University, under the supervision of
Dr. Robin Blankenship.
|
Power to the People:
Solving the Problem of Gerrymandering
Allison
Johnson, Benjamin Leard, and
Megan Mifflin
Gerrymandering, the redrawing of state district lines with the goal of
increasing a political party's chances of winning future elections,
causes an unequal representation of voter preferences. To confront this
issue, we provide an algorithm that draws district lines independent of
political factors, generates simple district shapes, and allots
approximately equal populations to each district.
This
research was
conducted at James Madison University, under the
supervision of Dr. Brian Walton.
|
Modeling Atomic Force
Microscope Deformation of Fibrin Fibers
Callie
Johnson
One use for an Atomic Force Microscope (AFM) is to measure the force
used to deform a cylindrical tube; one example is fibrin fibers.
One-dimensional analysis yields the boundary conditions used for more
complicated models and verifies experimental results of rupture. The
nonlinear three-dimensional study yields valuable information on the
comparative behavior of biological tissue deformation.
This research
was
conducted at James Madioson University, under the supervision of
Dr. Anthony Tongen.
|
The Relationship between Drug Abuse and
HIV/AIDS incidence among different ethnicities
Isaac A.
Kpodonou and Faraz A Shaikh
We investigate the relationship drug abuse and ethnicity among
people 13 years and older in the Washington area. HIV/AIDS incidence
and mortality rate among the African American community are compared to
other races. Data were accessed from the Center for Disease Control and
Prevention. Graphs and numerical results are presented.
This
research was
conducted at the University of the District of Columbia, under the
supervision of Dr. Valbona Bejleri.
|
Post Marketing Drug Surveillance
Chris LaVallee
We will explore Bayesian logistic regression models and methods to deal
with count data and contingency tables. Our ultimate goal is to look
for adverse drug reaction signals in real data from the FDA Adverse
Event Reporting System (AERS).
This research was
conducted at Rutgers University, under the supervision of Dr.
Ivan Zorych.
|
Dynamics of a
Ratio-Dependent Predator-Prey Model with Nonconstant Harvesting Policies
Benjamin
Leard
Predator-Prey models have been used in ecology, biology and economics
to understand and predict the behavior of predator/prey interactions.
We analyze a Ratio-Dependent Predator-Prey model that involves
harvesting on the prey population. Our findings include calculating a
maximum sustainable yield and detecting multiple bifurcations and
connecting orbits.
This
research was
conducted at Missouri State University, under the supervision of
Dr. Jorge Rebaza.
|
Eigenvalue Multiplicity of Hermitian
Matrices whose Graphs are Trees
Paul McMichael and Jonathan
Nuckols
Our research deals with trees (undirected, acyclic, connected graphs)
and what can be inferred about possible eigenvalue multiplicities of
Hermitian matrices from their trees. Specifically, we are concerned
with the minimum number of eigenvalues whose multiplicity is 1 for a
given tree.
This research was
conducted at the College of William and Mary, under the supervision of
Dr. Charles R. Johnson.
|
A Linear Algebraic Interpretation of
Majority Rule Outcomes
Lauren Merrill
We may represent the societal outcome of majority rule as a complete
asymmetric diagraph (CAD). A natural question arises: can an arbitrary
CAD be obtained as the result of majority rule applied to some society?
We present a linear algebraic approach to this question and similar
questions concerning majority rule.
This research was
conducted at College of William & Mary, under the supervision
of Dr. Charles R. Johnson.
|
Thin Film Evolution
Kumnit Nong
Braun and Fitt came up with the thin film equation, which include the
impact of fluid dynamic, pressure, gravity and more. Rather than
looking at the original equation, instead we will study two
modification equations to explain the characteristic behavior of the
fluid velocity and viscosity on the shear stress on the surface of an
eye.
This research was
conducted at George Mason University's Undergraduate
Research Computational Mathematics, under the supervision of Dr. Daniel
M. Anderson.
|
Barrel Vibrations Of
Medium Caliber Rapid- Firing Guns
Catherine Schwartz
Gun barrel vibrations arise from the natural droop of the barrel due to
gravity and frictional forces associated with the projectile traveling
thru the barrel. With rapid firing guns, the free vibrations may
not die out in between rounds. The model developed studied the
effects of these parameters and relates barrel dynamics to dispersion.
This research was
conducted under the supervision of Drs. Luke A. Martin of NAVSEA,
and Tom Dawson of USNA
|
Protein Stability of a
21 Residue Alanine Based Peptide
Rusty A. Stough
A short polyalanine 21 residue peptide, immersed in different
environments, has been studied, through molecular dynamics, to
understand the role ions play in peptide stability. This
knowledge will be useful in understanding the folding problem for much
larger proteins.
This research was
conducted at Duquesne University, under the supervision of Dr.
Dr. Jeffry Madura.
|
How far from being prime are you?
(Additively Speaking)
Desmond
Torkornoo
Let $M$ be a commutative, cancellative, atomic, $BFM$ and $x$ a nonunit
in $M$. We define an $\omega$-measure that determines how far from
being prime $x$ is in $M$. We give an algorithm for computing
$\omega(x)$ in any numerical monoid. Also we give simple formulas for
special cases and a simpler algorithm for two generator monoids. With
these tools we study some interesting properties of $\omega$-Measure.
This
research was
conducted at the University of Richmond.
|
Collatz Tree: Inductive
and Deductive approaches to the Collatz conjecture
Jeff Troy
An exploration of the Collatz conjecture (a recursive algorithm in
which to obtain the successive entry, you must divide by two if the
previous entry is even, or multiply by three and add one if the
previous entry is odd) using three approaches. First, a direct
computational approach. Second, a deductive back-to-front approach,
Finally, an inductive computational approach.
This research was
conducted at Lynchburg College, under the supervision of Dr.
Danny Cline.
|
Development of a
Graphical and Analytical Ternary Analysis for Mixed Hydrocarbon Flame
Strength Studies
Sarah Vaden
Hydrocarbon fuels have potential benefits for scramjets. Extinction
limits were collected of various binary and ternary hydrocarbon
mixtures. Standard two-dimensional plotting was inadequate for
accommodating the total mixing effect on flame strength. Thus, a
ternary graphing and analytical manipulation was developed to
accommodate the data and define a surrogate mixture.
This research was
conducted at NASA Langley Research Center, under the supervision
of Dr. Gerald Pellett and Mrs. Linda Hanks.
|
The Equivalence Number
and Transit Graphs for Chessboard Graphs
B. Nicholas Wahle
For large enough N-by-N chessboards, N+K nonattacking queens can be
placed given K pawns blocking their attack. These pawns remove
many edges of the N-by-N queens graph. Considering the
equivalence number and transit graphs provides a new perspective to the
N+K queens problem and allows consideration of other chess pieces.
This research was
conducted at Morehead State University, under the supervision of
Drs Doug Chatham and Duane Skaggs.
|
Scaling of
nearest-neighbor trees for a Poisson point field in R^n
Ellen Webb
We study scaling properties of the nearest-neighbor spanning tree for
a Poisson point field. The focus is on Horton-Strahler and
Tokunaga rankings that characterize the tree's branching structure. We
overview the existing results and report new findings for homogeneous
Poisson point fields in a bounded region of n-dimensional Euclidean
space.
This research
was
conducted at University of Nevada, Reno, under the supervision of
Dr.Ilya Zaliapin.
|
Cardinal Invariants
Beyond the Continuum
Charell Wingfield
We discuss generalizations of cardinal invariants associated with the
continuum, to the space of continuous functions on $[0,1]$. To
reasonably generalize invariants associated with Lebesgue measure on
$\mathbb R$, we introduce a natural measure on this space.
This
research was
conducted at James Madison University, under the supervision of
Dr. E. Brown.
|
