Mathematics Symposium: "Mathematics Awareness Month at UNO"
Jeremy Trageser, UNO - Department of Mathematics
Developing Statistical Tests to Analyzing the Metaphorical
Use of Secondary Students when Reasoning with Signed Numbers
There have been several studies discussing uses of different
metaphors associated with signed numbers, some of which argue
which metaphor is best. We will be discussing a method for testing
a hypothesis by Dr. Matthews that states successful problem solvers
may shift metaphors to motion and object/canceling metaphors
depending on the type of problem involved such as continuous or
discrete. Identifying which metaphors in mathematics are theory
constitutive metaphors is vital to understanding how to teach
mathematics effectively, and the methods of hypothesis testing
we will be reviewing will give us an effective way of testing for them.
Kodjo Togbey, UNO - Department of Mathematics
Fractal dimension and the 4/5 allometric scaling law for the human brain
One of the most ubiquitous laws in biology is allometric scaling,
whereby a biological variable Y is related to the mass of the
organism by a power law Y = (Y0)(M^b), where b is the so called allometric
exponent. Empirical observations and recent researches showed
that the basal metabolic rate of all organisms is allometrically
scaled by 2/3 (Rubner Law), or 3/4 (Kleiber law). A fractal
analysis of these exponents leads to a 4/5 law that empowers
the human brain with a 5th dimension. We will explain these
dimensions in terms of fractal geometry.
Bryan Kowal, UNO - Department of Mathematics
A Comparison of Mathematical-Programming and
Constraint-Programming Approaches to Tournament
Appraiser Assignment
Every year, dozens of teams enter and compete in
different Destination Imagination competitions and,
in order to enter, each team must supply an appraiser.
These appraisers are eventually assigned to and responsible
for judging a particular panel. The process of assigning
the appraisers to the panels is very time-consuming and
error-prone because there are several factors that must
be taken into account. So, the goal is to create an
Operations Research algorithm in the language OPL to
hopefully streamline the process. Last year, an
Integer-Programming approach was used; this year,
a Constraint-Programming approach will be used so
that it will also be possible to compare both
Integer-Programming and Constraint-Programming.
Wei Chen, UNO - Department of Mathematics
A minimal adaptive sampling plan for finite lot inspection
Quality control is an important part of any manufacturing process.
Ideally, to guarantee outgoing quality meets a certain standard,
every item should be inspected. However, in many instances this is
either not practical or not possible. Thus, sampling must be used.
If the population size is large, statistical theory provides convenient
methods for estimating quality. However, for small population size these methods are not valid.
We have introduced an adaptive sampling plan based on exact confident intervals
for the Hypergeometric Distribution. A key property of our sampling
plan is that the sample size is always the smallest size required to
show that the outgoing quality meets a specified target with a given confidence.
Janyl Jumadinova, UNO - Department of Mathematics
The Pseudo Gradient Search and a Penalty Technique
Used in Classifications
The goal of classification is to build a model of the classifying
attributes based on the predictive attributes. Then this model can
be applied when determinining what class a new observation belongs to.
One way of solving classification problem is to use pseudo gradient search.
In most classifiers, the goal is to reduce the misclassified rate that
is discrete. However, since pseudo gradient
search is a local search, to apply it for classification problem,
objective function has to be real valued. A penalty technique is
used for this purpose.
Kerrigan Award for Excellence in the Teaching of Mathematics, UNO - Department of Mathematics
The award is offered every year to one member of the Mathematics Department
at UNO to recognize their contribution to the teaching of mathematics at
the University of Nebraska at Omaha. The benefactor is Mr. Patrick Kerrigan.
Past winners are listed on the
award site.
Future Leader in Mathematics: Elementary/Middle School Level
It is awarded to those who have demonstrated superior understanding of
mathematics taught at the Elementary and Middle School levels
through their mathematics coursework at UNO.
The 2007 awardees are:
Seeman, Jamie C.;
Tapp, Michael J.;
Stilmock, Kimberly M.;
Wellman, Joseph S.;
Daemon, Holly J.;
Hartmann, Kimberly M.;
Kieselhorst, Courtney;
Suarez-Delgado,Jackel;
Timmerman, Deanna E.;
Winstryg, Glenn L.;
Emily Geopforth;
Holly Strumme.
Dan Harnett, UNO - Department of Mathematics
Error-Correcting Codes for a Steganography Application
Steganography is the process of inserting hidden
messages in an unrelated transmission. An algorithm for
steganography that uses an error-correcting code to
embed messages in a carrier sequence is studied.
A distortion limit theorem from information-theoretic
analysis is given, and optimal code parameters are discussed.
Adam Wermes, UNO - Department of Mathematics
Development of an Interactive Software System for Solving the Transportation Problem
The transportation problem is a specialized problem in Operations Research.
The purpose of this paper is to discuss the development of a program designed
to solve the transportation problem. The program is used as an educational
tool to learn how to solve the transportation problem and can be used as a
tool to solve the problem without the educational parts. The logical
development of the program includes a discussion of the steps to solve
the transportation problem. The first step in the process is the
collection of the information about the transportation problem. After
collecting the data check to see if the problem is balanced, look for
a basic feasible solution, then check to see if it is optimal.
A detailed discussion of each step is included, but the focus is
on the development of the program. The code and program flow is
the central theme of this paper. Screen shots from the program are
included as well as code and flow to understand the processes of
the program and how it relates to the solution of the transportation problem.
Honggang Wang, UNO - Department of Mathematics
Nonlinear Classification by Genetic Algorithm with Signed Fuzzy Measure
In this paper, we propose a new nonlinear classier based on a generalized
Choquet integral with signed fuzzy measures to enhance the classification power
by capturing all possible interactions among two or more attributes. A special
genetic algorithm is designed to implement this classification optimization
with fast convergence. Instead of using a discrete misclassification rate, the
objective function to be optimized in this research is a continuous Choquet
distance with a penalty coefficient for misclassified points. The numerical
experiment shows that the special genetic algorithm effectively solves the
nonlinear classification problem and this nonlinear classifier accurately
identifies classes.
Yan Wu, UNO - Department of Mathematics
Using 2-interactive Measures in Nonlinear Classifications
Within the classification algorithms based on signed
fuzzy measures, an obvious limitation is the complexity
of the algorithms due to the large number of interactions
among attributes. For a data set with n attributes, the
complexity of classification algorithm would be O(2n).
But in the practical problems, the higher-order interactions
among attributes are often not significant enough to the
classification, so sometimes omitting them just sacrifices
the accuracy a little but will save a lot of time and energy.
Hence, a 2-interactive measure may be used to reduce the
calculation complexity into O(n^2). In this study, the Mobius
Transformation and its reverse --- Zeta Transformation are
used to calculate the 2-interactions among attributes for
the records. A comprehensive discussion on the semantic and
geometric meanings of the parameters is given. The weighted
Choquet integral with respect to the signed fuzzy measure
serves as an aggregation tool to project the feature space
onto a real axis to make the classification simple. To implement
the classification, we need to determine the values of the
signed fuzzy measure and the other parameters. This can be
done by running an adaptive genetic algorithm based on the
given training data. The new classifier is tested by recovering
the preset parameters from a set of artificial training data
generated from these parameters.
Poster Session Titles and Abstracts
Jessica Ali
The Golden Mean in Mathematics and Life
This report will discuss the many appearances of the Golden Ratio
(also represented as Phi) in nature and in the arts and its association with beauty.
The Golden Ratio is not just a number because of its amazing characteristics
and its amazing ability to fascinate humankind throughout the centuries because
of its ubiquity. It is an entire subject in itself because it is so complex
and yet it is so beautifully simple. The Fibonacci Number Sequence often
occurs in nature and that fact that this series converges to the Golden
Ratio is nothing but incredible. The Golden Ratio is often associated
with beauty but it has been argued that the connection between the Golden Ratio
and beauty is vague. An attempt will be made to connect the mathematical
information and the intuitive nature of Phi.
Oliver Bonham-Carter
A Study of Genetic Entropy
We investigate differences across DNA subsequences using entropy
with associated ideas and concepts from Information Theory. We
form conclusions which help distinguish one kind of sequence
from another thanks to differing levels of disorder in single,
double and triple subsequence sets or word frequencies. The
data is drawn from nine typical DNA sequences which code for
common wild-type cellular receptor sites. The sequences were
randomly selected from the on-line genetics database at The
National Center for Biotechnology Information,
(http://www.ncbi.nlm.nih.gov/). The kinds of selected DNA fit
into three main categories: bacterial (e. coli), virus
(from the common cold), and human (liver). Each genetic
sequence was analyzed by a computer program which was written
in the programming language of Maple version 10 (Maplesoft)
to calculate the entropy levels and to collect the related
information which we present. The values of entropy from the
subsequences are used as a measurement to detect the differences
and similarities between one whole sequence and the next. The
study draws general conclusions concerning each kind of sequence
in relation to the others as well as explanations for the kinds
of entropy values which were detected. Markov Models drawn from
the sequences are also investigated.
Wei Chen
An algorithm for identification of belief measures
The connection of belief measures and basic probability assignments is
recalled in the report. Then the identification of belief measure
is discussed. An algorithm is developed to search for the best
fitting basic probability assignment based on a given "blank" of
belief measure. Through the algorithm, an exact identification
can be obtained if it exists. When the exact identification fails,
a genetic algorithm is activated to search for a global optimal
solution and obtain an approximate identification.