Abstract: A CWATset is a subset
of n copies of Z_{2}
that is closed with a twist under componentwise addition.
We will define a gc-set, which generalizes the cwatset
structure, and determine some of its basic properties. Some of
the group theoretic properties gc-sets will then be explored.

Abstract: Direct contact
communicable diseases continue to exist. The threat of bio-terrorism
could create additional problems with the introduction of smallpox
or microbial pathogens. We simulate the spread of direct
contact viruses in two-dimensional space, having initially considered
the case where all people are in fixed locations and, more recently,
removing the restriction of fixed positions, allowing people to
interact. We will examine the results and look for patterns
explaining how diseases spread so that protocols of effective
quarantine and cure can be developed.

A
Cost-Benefit Analysis of International Cigarette Smuggling
Using Computationally-Intensive Mathematical Models David Maduram, University of Illinois at Chicago

Abstract: This study uses a stochastic
Markov model to investigate the economics of tobacco smuggling.
By using Norton's model of international smuggling risks
as well as Chaloupka's cigarette demand equations, this study
attempts to assess the profit gained by smuggling tobacco products
between countries and the effects of localized tax reforms on
the smuggling economy.

Analysis
of Disease Mutations By Evolutionary Comparison and Codon
Position Jacob Reidhead, Arizona State University

Abstract: Recent accumulation
of genome sequence data of humans and other species has opened
the door for interesting interspecies comparisons and phylogenetic
analysis. The availability of data about mutations that
cause disease in humans allows us to characterize genetic disease
in humans with respect to evolutionary history. Previous
work has compared the severity, location, and type frequency of
disease mutations and interspecies changes, and has pointed out
distinct differences between the two. Disease causing mutations
were of greater severity (in terms of the biochemical differences)
than those observed in the long-term evolutionary history, occurred
with higher frequency at evolutionarily conserved sites, and comprised
a unique type frequency signature. We have conducted similar
comparisons within putative protein domains. We find that
similar types of domains exhibit similar ranges of tolerated mutation
severity, propensity for mutations at corresponding key sites,
and similar types of frequency signatures. These computational
analyses help in uncovering the nature of disease causing mutations
and provide insights into the contrast between the genome diversity
between species and that in disease mutations. Information
of this kind may ultimately be useful in the future to better
understand the function of different domains of a gene and be
useful in the genetic disease diagnosis.

Three-Minute
Dating and Other Social Mixers Tyrel Fisher, Valparaiso University

Abstract: Suppose you have
k people sitting at each of n tables. They
are allowed to get up and rearrange themselves under the following
conditions: 1) no person may sit at the same table more than once,
and 2) no two people may sit together more than once. How
many times x can a new seating be generated? Using
properties of families of orthogonal Latin Squares, we obtain
solutions to this problem when k = 1, k = 2, k
≥ n, and n = p^{t},
where p is some prime number.

Abstract: We will offer
basic definitions concerning binary quadratic forms and discuss
properties of an equivalence relation on binary quadratic forms.
Examples of equivalence classes of definite quadratic forms
will be considered, and a program in Maple that determines the
class number of definite quadratic forms will be demonstrated.

Abstract: Given k circles
in the Euclidean plane, and a set S of n arcs of
these circles, define the circular arc graph G(S)
as a graph on n vertices such that each vertex represents
an arc in S, and two vertices are adjacent precisely when
the corresponding arcs have a nonempty intersection. Which
graphs can arise in this way? The question for k
= 1 has been well studied. In 2001, Ross M. McConnell published
a linear-time algorithm for recognizing simple circular arc graphs.
Some aspects of simple circular arc graphs (k = 1) will
be summarized, after which some original results on double circular
arc graphs (k = 2) will be presented, including a number
of examples of nonrepresentable graphs.

Abstract:
The distribution of a sum of independent Bernoulli random variables is, in general, complex. We can
approximate this distribution with that of a sum of two independent
almost-binomial variables whose parameters are chosen so that
the first four moments of the approximating distribution agree
with the first four moments of the sum of Bernoulli random variables.
In this talk, we model the errors we get using this approximation
method. They are shown to be typically quite small, and
our model of the errors is shown to be very accurate.

Abstract: Let the vertices of
a graph G be ordered along a line L. A book
embedding of G is an assignment of each edge of G
to exactly one half-plane, called a page, with L
as its boundary, such that the edges on any page do not intersect.
Define the bookthickness of G to be the least number
of pages into which G has a proper book embedding, taken
over all vertex orderings. In this talk, I will discuss
results on the bookthickness of special classes of graphs.

Abstract: A quasi p-group
is any finite group generated by all of its Sylow p-subgroups.
At last year's conference, I presented a classification of the
quasi p-groups of order less than 24. During that
presentation, a member of the audience asked the question, "Can
a group be a quasi p-group for more than one prime p?"
My answer at the time was somewhat limited. In this talk
we will discuss the properties of a quasi [p,q]-group.

Abstract: This study is
a continuation of work done last year investigating a family of
graphs created from essentially equivalent lattice paths.
To obtain these graphs, each path in an m × n lattice
corresponds to a vertex in the graph; two paths are considered
equivalent if they share more than k edges and therefore
their corresponding vertices in the graph are connected.
We denote such a graph by G(m, n, k).
This year we identified some interesting complete sub-graphs and
determined the number of edges in G(m, 2, 0), G(m,
2, 1), and G(m, 2, m - 1). We also
generated data sets giving the number of edges to use in further
investigations of this type.

Abstract: This talk is a follow-up to
an article written by Dr. Gary J. Sherman on the card-game war.
The motivating question is whether or not it is necessary for
a game of war to end. In order to obtain a more manageable
problem, the game was abstracted by removing suits and considering
a deck with fewer cards. Non-terminating, or cyclic, games
were found in this abstracted version of war, and the purpose
of this talk is to characterize these games. Terminating
games will be discussed briefly along with possibilities for further
study.