Student Talks Handout:
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Last updated:
03/23/11, 9:51 p.m.

Friday 3:10 p.m., G219, Crapo Hall



Amber Brown, Greenville College



Title:

Wavelet Analysis and a Computational, TimeDependent Problems



Abstract:

Wavelets are a basis set of functions that can be used to effectively represent images or
other functions. Though most commonly associated with image processing such as FBI fingerprint
storage and jpeg files, wavelets have become popular in the physics and chemistry communities
for solving partial differential equations (PDE's). The most notable features of wavelets are
their multiresolution capabilities and good localization, which together allow for efficient
representations of solutions to PDE's. The performance of two types of wavelets, symmlets and
coiflets, were compared based on their efficiency and error accumulation when used to solve the
quantum displaced harmonic oscillator. After a brief introduction to wavelets and their properties,
specific attention will be given to how wavelets were applied to the aforementioned problem.

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Friday 3:10 p.m., G221, Crapo Hall



Sarah Jabon, RoseHulman Institute of Technology



Title:

Algorithmic Threshold Selection for the PeakOverThreshold Method



Abstract:

In extreme value theory, the peakoverthreshold method is one way to model the tails of
heavy tailed distributions. In this method, a generalized Pareto distribution (GPD) is fit to
the data points that exceed a high threshold. Choosing an appropriate threshold is crucial, as
bias and variance affect the fit of GPD when then threshold is too low or too high respectively.
Currently, graphical techniques are typically employed to identify a suitable threshold given a
data set, as there is no accepted standard for determining a threshold algorithmically. We
compare three original algorithmic techniques that use commonly used plots, the Hill plot and
the exponential quantile plot, as well as one previously proposed method from Zhou et al.
in "A New Method to Choose the Threshold in the POT Model." In order to compare performance,
we apply each method to simulated data from the Pareto, f, Frechet, and Student's t distributions
with multiple data set sizes. One method based on the Hill plot performs particularly well with
regard to identifying a threshold that produces a GPD with a shape parameter close to the true value.
Finally, we apply these techniques to the wellstudied Danish fire data set. These algorithmic
methods can aid in identifying suitable thresholds for the peakoverthreshold approach in extreme
value theory.

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Friday 3:10 p.m., G222, Crapo Hall



Lane Bloome, Millikin University



Title:

Compressed ZeroDivisor Graphs of Finite Commutative Rings



Abstract:

The zerodivisor graph of a commutative ring R , denoted ΓR, is a graph whose
vertices are the nonzero zerodivisors of a ring, and two vertices are connected if and only
if their product is zero. These graphs have been studied for a number of years in the hope
that the graphtheoretic properties of ΓR can help us understand more about the
ringtheoretic properties of R. We slightly alter the definition of the zerodivisor graph
to obtain the compressed zerodivisor graph. In this talk,
we will explore recent developments regarding these structures, including an algorithm for
constructing these graphs.

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Friday 3:40, G219, Crapo Hall



Kyla Lutz, RoseHulman Institute of Technology



Title:

Yeast and Mathematics



Abstract:

Mathematics underlies many biological problems, including the metabolism of Saccharomyces
cerevisiae, or baker's yeast. The metabolic network of this organism is modeled using flux
balance analysis (FBA), which incorporates linear algebra, computer science, and the chemical
reactions within a cell to determine what a single cell is doing while it is in steadystate.
More basic mathematics is also used for this metabolic model. Specifically, Boolean algebra is
used to represent the reactions so that the experimental data can be used accurately in the model.
The metabolites given to the cell initially are collectively called the environment, or medium,
which can be controlled by the user in the model to mimic experimental conditions so that accurate
predictions can be made. Using this tool, some questions that can be asked are "What are the
minimum number of metabolites that the cell needs and what are they?" and "What are the
compositions of all of the possible 'minimal media' in which the cell can survive?" These
questions were addressed in Dr. Jason Papin's Biomedical Engineering laboratory over the
course of an REU at the University of Virginia. Another problem that was addressed is the
connectedness among all of the reactions in a cell and each metabolite with which the cell
interacts. These connections can be found using a modification of the FloydWarshall algorithm
from computer science. Mathematics played a major part in this research project and others very
similar to it.

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Friday 3:40 p.m., G221, Crapo Hall



Alicia DeHart, Northern Michigan University



Title:

Modified Fibonacci Sequence



Abstract:

The Fibonacci sequence is often described with a population model, where the population
exists under the most ideal conditions. If a change is made in the conditions, how
does the sequence change? Is there a formula we may use to generate this new sequence?
These questions, and more, will be answered in this presentation.

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Friday 3:40 p.m., G222, Crapo Hall



Darrin Weber, Millikin University



Title:

A Preliminary Look at Compressed ZeroDivisor Graphs and ZeroDivisor Lattices



Abstract:

The zerodivisor graph of a commutative ring R is a graph whose vertices are the nonzero
zerodivisors of a ring, and two vertices are connected if their product is zero. These
graphs have been studied for a number of years in the hope that the graphtheoretic properties
can help us understand more about the ringtheoretic properties of R. We slightly alter the
definition of the zerodivisor graph to obtain the compressed zerodivisor graph. Also, we
look to expand on the idea of zerodivisor graphs of rings into lattices on those rings. We
take the zerodivisors of a ring, examine their annihilator sets, assign an order to them, and
then place these annihilators into a lattice structure. We take a preliminary look at the
relationships between the zerodivisor graph, compressed zerodivisor graph, and the zerodivisor
lattice.

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Friday 4:20 p.m., G219, Crapo Hall



Joseph Gasper, Kent State University



Title:

If Knot Theory and Knot Invariants, Then What?



Abstract:

We will give a brief introduction to Knot Theory with consideration of Knot Invariants and examples.

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Friday 4:20 p.m., G221, Crapo Hall



Tim Ekl, RoseHulman Institute of Technology



Title:

Local Warming



Abstract:

Much attention has been given recently to the validity of global warming claims. We
present a modelbased look at local weather data in an attempt to identify whether global
warming exists on a much smaller, local scale. We use a linear model and statistical analysis
to find the amount of "local warming," if any, that exists in and around Terre Haute, IN.

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Friday 4:20 p.m., G222, Crapo Hall



Taole Zhu, Illinois Wesleyan University



Title:

Bcoloring in regular graphs



Abstract:

A bcoloring is a vertex coloring in which every color class contains a vertex that has a
neighbor in all other color classes. The bchromatic number b(G) of a graph G is the largest
integer k such that G has a bcoloring with k colors. We discuss various approaches to a
conjecture on bcoloring in regular graphs and prove that for any dregular graph with
girth = 5, the bchromatic number is at least floor((d + 1)/2).

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Friday 4:20 p.m., G317, Crapo Hall



David Irwin, Miami University Middletown



Title:

Nice Numbers



Abstract:

Find the number of Representations of Nice numbers as sum of consecutive integers.

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Friday, 4:50 p.m., G219, Crapo Hall



Nathan Poirier, Aquinas College



Title:

Alhazen's Billiard Problem in Hyperbolic Geometry



Abstract:

Alhazen's billiard problem gives points A and B inside a circle and seeks an inscribed isosceles
triangle with a given point on each leg. In our summer research, we found a bijection between
Euclidean solutions and hyperbolic solutions. The constructible Euclidean cases pair up with the
constructible hyperbolic cases. We will prove the bijection and give some examples.

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Friday 4:50 p.m., G221, Crapo Hall



Jonathon Strauser, RoseHulman Institute of Technology



Title:

Protein structure alignment and classification using dynamic programming



Abstract:

Biological molecules called proteins are compared on the basis of the threedimensional
folds that define their shape and function. A mathematical description of a protein's fold
is created so that proteins can be aligned. A dynamic programming algorithm is used to compare
proteins in a data set consisting of 300 proteins of known family classification. The algorithm
has been optimized for both speed and accuracy.

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Friday 4:50 p.m., G222, Crapo Hall



Mark Bissler, Kent State University



Title:

Group Theory Applications to Rubik's Cubes



Abstract:

We will speak on elementary group theoretics applied to the coolest toy known to man.

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Friday 4:50 p.m., G317, Crapo Hall



Gina Luciano, Millikin University



Title:

Using Data Mining to Determine Academic Success in College



Abstract:

Data mining is the process of finding useful patterns in data. A data mining program called
Rattle was used to analyze admission data for Millikin University. The purpose of analyzing
this set of data was to find patterns that could determine the success of students who were
academically at risk at the time of their application. An original data set of variables was
processed and analyzed to find characteristics of students who thrive academically at Millikin
although they were "at risk" when they applied. The results could also determine if an
academically at risk student would remain at risk and potentially transfer throughout their
college career. The findings were relayed to the Office of Admission to help them more
effectively reach out to students to at risk students.

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Saturday 10:10 a.m., G219, Crapo Hall



Brian McDonald, Carmel High School



Title:

A formula for the integral of an inverse function in terms of the integral of the function.



Abstract:

Most calculus texts give a formula for the derivative of an inverse function in terms of the
derivative of the function. They do not give a corresponding result for the integration of
inverse functions. We derive the integral formula by looking at the graph of the function.
Our derivation does not depend on integration by parts.

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Saturday 10:10 a.m., G221, Crapo Hall



Michael PridalLoPiccolo, RoseHulman Institute of Technology



Title:

Analysis of Keccak, a SHA3 Finalist



Abstract:

Hash functions are cryptographic primitives used in a variety of important applications.
Recent attacks against the industry standard functions have motivated the search for new,
more secure functions. This presentation focuses on the security of one candidate algorithm,
Keccak.

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Saturday 10:10 a.m., G222, Crapo Hall



Matthew Grimm, Kent State University



Title:

Minkowski Length of 3D Polytopes



Abstract:

The Minkowski sum of two polytopes is the set pairwise sums of their points. We will look at the
Minkowski length L(P) of a lattice polytope P. We will explain an algorithm for computing L(P) and
look at indecomposable polytopes. Our result extends a previously known result with polygons. Our
methods are substantially different from those used in the twodimensional case.

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Saturday 10:40 a.m., G219, Crapo Hall



Xin Ma, Trinity University



Title:

Estimating bacterial lag phase: a branching process approach.



Abstract:

Before a population of bacteria (or other cells) starts growing exponentially, there may also
be an initial phase, the lag phase, when the bacterium adjusts to a new environment. Accurate
estimation of the lag phase is important in the field of predictive food microbiology.

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Saturday 10:40 a.m., G221, Crapo Hall



Jack Pringle, RoseHulman Institute of Technology



Title:

Secret Sharing Schemes: An Application of Projective Geometry



Abstract:

We will introduce secret sharing schemes. Then we will discuss finite projective geometries and
other useful properties associated with them. Then we will show how to use finite projective
geometry to construct a secret sharing scheme. Finally, we show why this construction is superior
to other secret sharing schemes.

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Saturday 10:40 a.m., G222, Crapo Hall



Scott Rexford, Northern Illinois



Title:

An overlooked reference from the last book of Euclid's Elements.



Abstract:

Did Euclid suggest an alternate construction for the pentagon in the 13th book of elements?
It would seem so. In this talk the construction will be presented, and its correctness will be proven.
We will also give a brief definition of the affine geometric transformation known as circle
inversion. This will lead up to a posed problem involving an infinite summation of circles packed
within an arbelos.

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Saturday 11:20 a.m., G219, Crapo Hall



Andy Milluzzi, RoseHulman Institute of Technology



Title:

Lego: The Intersection of Art and Engineering



Abstract:

Everyone has played with LEGO Bricks, but what happens when you take it to the next level?
There is a thriving community of adult fans that use those plastic bricks as much more than
a toy. From models of the White House to robotic arms, LEGO mixes art and engineering in a
way that captures the inner child in everyone.

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Saturday 11:20 a.m., G221, Crapo Hall



Steven Hayman, Illinois Wesleyan



Title:

Tabulating Irreducible Polynomials over GF(2)



Abstract:

This focus of this presentation is the tabulation of irreducible polynomials
over GF(2). The last tabulation was up to degree 5,000. The goal for my
research project was to tabulate up to degree 100,000.

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Saturday 11:20 a.m., G222, Crapo Hall



William Karr, IUPUI



Title:

Level density and levelspacing distributions of random, selfadjoint, nonHermitian matrices



Abstract:

We investigate the leveldensity σ(x) and levelspacing distribution p(s)
of random matrices M = AF ≠ M^{†} where F is a (diagonal) innerproduct and A
is a random, real symmetric or complex Hermitian matrix with independent entries drawn from a
probability distribution q(x) with zero mean and finite higher moments. Although not Hermitian,
the matrix M is selfadjoint with respect to F and thus has purely real eigenvalues.
We find that the level density σ_{F(x)} is independent of the underlying
distribution q(x), is solely characterized by F, and therefore generalizes Wigner's
semicircle distribution σ_{W(x)}. We find that the levelspacing distributions
p(s) are independent of q(x), are dependent upon the innerproduct F and whether
A is real or complex, and therefore generalize the Wigner's surmise for level spacing. Our
results suggest Fdependent generalizations of the wellknown Gaussian Orthogonal Ensemble
(GOE) and Gaussian Unitary Ensemble (GUE) classes.

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Saturday 11:50 a.m., G219, Crapo Hall



Kelly Ruder, Siena Heights University



Title:

Mathematics Vocabulary and Comprehension



Abstract:

Some say mathematics has a language all its own, while others say that math is the universal
language. If, indeed, "Mathematics has a language all of its own" and "Mathematics is
the universal language", then students should be able to comprehend and apply the vocabulary
of the discipline. Mathematics vocabulary however, can present a major challenge to many learners,
and even though vocabulary is stressed in the elementary grades, this practice is not typically
continued in the secondary grades. The issue of vocabulary can also lead to an increase in
mathematics anxiety, which discourages many students to continue taking math courses. Thus,
this research questions stems from these ideas: Does developing a working vocabulary in statistic
students increase comprehension and decrease math anxiety? This presentation will detail the
approach that will be taken.

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Saturday, 11:50 a.m., G221, Crapo Hall



Eric Crockett, RoseHulman Institute of Technology



Title:

Algebraic Solutions to NonLinear Systems



Abstract:

Many cryptographic algorithms such as AES rely on the difficulty of solving
nonlinear systems of equations over a finite field, which is NPhard in the general case.
When the system is overdetermined, it is sometimes possible to find a solution in polynomial
time. We examine two algorithms for solving nonlinear systems which work by finding new
linearly independent equations and using them to solve the system. We will also discuss the
implications of these algorithms on modern cryptography.

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Saturday 11:50 a.m., G222, Crapo Hall



Tyler Foxworthy, IUPUI



Title:

Explicit representations of characteristic polynomial
coefficients associated with an nbyn symmetric matrix



Abstract:

We obtained explicit representations of the zeroth and the first order coefficient of the
characteristic polynomial associated with an nbyn symmetric matrix, E^{∞}. It is the
asymptotic limit of a matrix associated with fitting data at regular intervals to a sum of
exponentials. Through functional iteration with these coefficients, one can find estimates for
the largest and smallest eigenvalues of the symmetric matrix. In this presentation computational
results and motivational examples will be given to highlight the significance of such problems.

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