Mathematics Symposium: "Mathematics Awareness Month at UNO"
Louis Scott Bock, UNO - Mathematics, KRMP
Using 2-Additive Measures in Nonlinear Multiregressions
When a nonlinear integral with respect to a signed fuzzy measure is used in multiregression,
people face a serious problem that, comparing to the number of variables (attributes),
there are exponentially many unknown parameters in the model. However, in many real-world
problems, the higher-order interactions among the variables can be omitted, and then only
consider the second-order one with an acceptable small error in the result. Thus, a
2-additive measure based on the Mobius transformation and its inverse can be used to
replace the signed fuzzy measure. In such a way, the complexity of the computation will
be significantly reduced.
Ray Goodman, UNO - Mathematics, KRMP
Random Boolean networks with number of parents generated by certain probability distributions
Random Boolean networks occur in nature, describing systems such as the neural network of the
human brain, the World Wide Web, and social networks. Studies have shown how these complex
scale free networks are connected following a Power Law distribution. Others have examined
how highly connected networks use a Popularity Model for establishing parent connections.
This study combines the two theories, examining a complex network where the number of parents
are obtained using a Power Law distribution and are connected based on a Popularity Model.
This study found that scale free Boolean networks that have a gamma value less than 1.6,
exhibit chaotic behavior.
Jay Pedersen, UNO - Mathematics, KRMP
Design and Implementation of a Tournament Assignment Algorithm
Destination Imagination (DI) is international creativity and
problem-solving organization for youth. Regional DI tournaments
are held each spring at five sites in Nebraska, with the top finishers
from each region advancing to the state tournament. Other states
hold similar competitions. The winners in each state advance to
the global tournament. Teams compete in one of five central challenges
in one of three levels as well as an instant challenge. As a condition
of entry in a tournament, a team must supply an appraiser (judge) to
work at the tournament. Typically these appraisers are parents or
teachers of the competitors. Assignments of appraisers to the various
challenges and levels is complicated by many factors, not the least of
which is the desire to eliminate any conflicts of interest. Currently
in Nebraska the scheduling is done largely by hand, which is less than
desirable given the number of teams participating (e.g., over 100 teams
in the Omaha-area region). Using data from last year's state tournament,
we tested several optimization approaches and will report on these results
and compare them to those produced by the existing manual approach.
Vladimir Ufimtsev, UNO - Mathematics, KRMP
Group Testing and its Application to Multiple Access Information Transmission Models
A multiple access channel is a medium that allows multiple terminal stations to
communicate with a central station. We will consider a system containing a large
amount of terminal stations and a multiple access OR channel connecting the
terminal stations to the central station. We implement the symmetric model of
group testing and superimposed code constructions to the discussed multiple
access information transmission model, for the calculation of bounds on the
multiple access channel capacity. Recent results in Superimposed Coding Theory
have given us the possibility of improving the known bounds on the multiple
access OR channel capacity.
We present a method based on Choquet integral projections for nonlinear multiregression involving
unknown periodic variation. A signed fuzzy measure is used to represent the contribution rate
of each combination of the predictive attributes towards the objective attribute. Hence,
the interactions among the predictive attributes are reflected. Experimental results
performed on sample datasets are presented in the paper to show its effectiveness.
Chris Goodrich, UNO - Mathematics, KRMP
Robustness Analysis of certain Random Boolean networks
In this talk, we seek to explore both numerically and analytically
the robustness of the well known Rule 126 of cellular automata.
In particular, we explore whether or not the introduction of noise
into the system has any discernable effect on the evolution of the
system. This noise is introduced by changing both one and more
than one node, and new models have been developed for this
purpose. We use MATLAB to run the numerical simulations as well
as to evaluate Lyapunov exponents and to form bifurcation diagrams.
We show that it is possible either to attenuate or to suppress entirely
chaos through the introduction of noise and that the perturbed system
may exhibit very different long-term behavior than that of the unperturbed system.
Finally, some directions for future work are considered.
Nian Yan, UNO - Mathematics, KRMP
Solving nonlinear classifications based on the Choquet integral by LP
Linear programming (LP) based models provide good solutions to classification
problem especially when the data is linearly separable. The assumption of
LP classification models is: the contributions from all attributes towards
the classification model are the sum of contributions of each attribute.
This assumption leads to a weakness of LP classification models when data
is linearly inseparable. The concept of signed fuzzy measure is introduced
and utilized in LP approach in order to enhance the classification power
through capturing all possible interactions among any two or more attributes.
The use of the Choquet integral with respect to a signed fuzzy measure on LP
model is able to separate the data that is linearly inseparable.
Zaher Kmail and Jay Hutfles, UNO - Mathematics
Algorithms for High School Timetabling
Every year, high school administrators face the difficult task of
creating schedules for the following academic year. While the process of
creating either student schedules or teaching assignments individually has
been well researched, little has been written on algorithms which address
both student course requests and faculty teaching preferences at the same time.
Various approaches to the high school timetabling problem will be discussed,
along with details of their implementations and the practicality of using each
in a large high school environment.