Student Talks Handout:
Downloadable PDF File
Changes to the schedule and the talks may occur. Please check back for the most recent update as needed.
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, Time-Dependent 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.
|
»
BACK TO TOP
|
Friday 3:10 p.m., G221, Crapo Hall
|
|
|
Sarah Jabon, Rose-Hulman Institute of Technology
|
|
|
Title:
|
Algorithmic Threshold Selection for the Peak-Over-Threshold Method
|
|
|
Abstract:
|
In extreme value theory, the peak-over-threshold 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 well-studied Danish fire data set. These algorithmic
methods can aid in identifying suitable thresholds for the peak-over-threshold approach in extreme
value theory.
|
»
BACK TO TOP
|
Friday 3:10 p.m., G222, Crapo Hall
|
|
|
Lane Bloome, Millikin University
|
|
|
Title:
|
Compressed Zero-Divisor Graphs of Finite Commutative Rings
|
|
|
Abstract:
|
The zero-divisor graph of a commutative ring R , denoted ΓR, is a graph whose
vertices are the nonzero zero-divisors 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 graph-theoretic properties of ΓR can help us understand more about the
ring-theoretic properties of R. We slightly alter the definition of the zero-divisor graph
to obtain the compressed zero-divisor graph. In this talk,
we will explore recent developments regarding these structures, including an algorithm for
constructing these graphs.
|
»
BACK TO TOP
|
Friday 3:40, G219, Crapo Hall
|
|
|
Kyla Lutz, Rose-Hulman 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 steady-state.
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 Floyd-Warshall algorithm
from computer science. Mathematics played a major part in this research project and others very
similar to it.
|
»
BACK TO TOP
|
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.
|
»
BACK TO TOP
|
Friday 3:40 p.m., G222, Crapo Hall
|
|
|
Darrin Weber, Millikin University
|
|
|
Title:
|
A Preliminary Look at Compressed Zero-Divisor Graphs and Zero-Divisor Lattices
|
|
|
Abstract:
|
The zero-divisor graph of a commutative ring R is a graph whose vertices are the nonzero
zero-divisors 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 graph-theoretic properties
can help us understand more about the ring-theoretic properties of R. We slightly alter the
definition of the zero-divisor graph to obtain the compressed zero-divisor graph. Also, we
look to expand on the idea of zero-divisor graphs of rings into lattices on those rings. We
take the zero-divisors 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 zero-divisor graph, compressed zero-divisor graph, and the zero-divisor
lattice.
|
»
BACK TO TOP
|
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.
|
»
BACK TO TOP
|
Friday 4:20 p.m., G221, Crapo Hall
|
|
|
Tim Ekl, Rose-Hulman Institute of Technology
|
|
|
Title:
|
Local Warming
|
|
|
Abstract:
|
Much attention has been given recently to the validity of global warming claims. We
present a model-based 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.
|
»
BACK TO TOP
|
Friday 4:20 p.m., G222, Crapo Hall
|
|
|
Taole Zhu, Illinois Wesleyan University
|
|
|
Title:
|
B-coloring in regular graphs
|
|
|
Abstract:
|
A b-coloring is a vertex coloring in which every color class contains a vertex that has a
neighbor in all other color classes. The b-chromatic number b(G) of a graph G is the largest
integer k such that G has a b-coloring with k colors. We discuss various approaches to a
conjecture on b-coloring in regular graphs and prove that for any d-regular graph with
girth = 5, the b-chromatic number is at least floor((d + 1)/2).
|
»
BACK TO TOP
|
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.
|
»
BACK TO TOP
|
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.
|
»
BACK TO TOP
|
Friday 4:50 p.m., G221, Crapo Hall
|
|
|
Jonathon Strauser, Rose-Hulman Institute of Technology
|
|
|
Title:
|
Protein structure alignment and classification using dynamic programming
|
|
|
Abstract:
|
Biological molecules called proteins are compared on the basis of the three-dimensional
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.
|
»
BACK TO TOP
|
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.
|
»
BACK TO TOP
|
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.
|
»
BACK TO TOP
|
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.
|
»
BACK TO TOP
|
Saturday 10:10 a.m., G221, Crapo Hall
|
|
|
Michael Pridal-LoPiccolo, Rose-Hulman Institute of Technology
|
|
|
Title:
|
Analysis of Keccak, a SHA-3 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.
|
»
BACK TO TOP
|
Saturday 10:10 a.m., G222, Crapo Hall
|
|
|
Matthew Grimm, Kent State University
|
|
|
Title:
|
Minkowski Length of 3-D 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 two-dimensional case.
|
»
BACK TO TOP
|
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.
|
»
BACK TO TOP
|
Saturday 10:40 a.m., G221, Crapo Hall
|
|
|
Jack Pringle, Rose-Hulman 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.
|
»
BACK TO TOP
|
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.
|
»
BACK TO TOP
|
Saturday 11:20 a.m., G219, Crapo Hall
|
|
|
Andy Milluzzi, Rose-Hulman 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.
|
»
BACK TO TOP
|
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.
|
»
BACK TO TOP
|
Saturday 11:20 a.m., G222, Crapo Hall
|
|
|
William Karr, IUPUI
|
|
|
Title:
|
Level density and level-spacing distributions of random, self-adjoint, non-Hermitian matrices
|
|
|
Abstract:
|
We investigate the level-density σ(x) and level-spacing distribution p(s)
of random matrices M = AF ≠ M† where F is a (diagonal) inner-product 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 self-adjoint with respect to F and thus has purely real eigenvalues.
We find that the level density σF(x) is independent of the underlying
distribution q(x), is solely characterized by F, and therefore generalizes Wigner's
semicircle distribution σW(x). We find that the level-spacing distributions
p(s) are independent of q(x), are dependent upon the inner-product F and whether
A is real or complex, and therefore generalize the Wigner's surmise for level spacing. Our
results suggest F-dependent generalizations of the well-known Gaussian Orthogonal Ensemble
(GOE) and Gaussian Unitary Ensemble (GUE) classes.
|
»
BACK TO TOP
|
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.
|
»
BACK TO TOP
|
Saturday, 11:50 a.m., G221, Crapo Hall
|
|
|
Eric Crockett, Rose-Hulman Institute of Technology
|
|
|
Title:
|
Algebraic Solutions to Non-Linear Systems
|
|
|
Abstract:
|
Many cryptographic algorithms such as AES rely on the difficulty of solving
non-linear systems of equations over a finite field, which is NP-hard 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 non-linear 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.
|
»
BACK TO TOP
|
Saturday 11:50 a.m., G222, Crapo Hall
|
|
|
Tyler Foxworthy, IUPUI
|
|
|
Title:
|
Explicit representations of characteristic polynomial
coefficients associated with an n-by-n symmetric matrix
|
|
|
Abstract:
|
We obtained explicit representations of the zeroth and the first order coefficient of the
characteristic polynomial associated with an n-by-n 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.
|
»
BACK TO TOP
|