Vol 31, Part I - forums.sou.edu • Index page - Southern Oregon ...

ABSTRACTS – Contributed Oral Papers
temperatures were summarized to identify the first and last
days of a 1500 growing-degree-day growing season. Precipitation
was accumulated from the end of the growing season
the previous year through 31 December, 1 January through
the beginning of the current year growing season, and during
the current growing season. These weather records were then
subjected to principal components analysis. The eight years
characterizing extremes in each of the five principal components
were identified. Extreme year effects on calf growth
were contrasted for each principal component. Irrespective
of the pattern of precipitation before the growing season and
with near or above average precipitation during the growing
season, calves reared in years characterized by longer,
cooler growing seasons gained more weight from birth to
weaning than those reared in opposing years. This retrospective
analysis indicates a general increase in temperature in
the Northern Great Plains is expected to reduce the growth
of calves from birth to weaning.
MATHEMATICS
Monday, starting at 10:30 a.m. in PONDEROSA PINES 1 & 2
123 Perfect Stripes from a General Turing Model in Different
Geometries, JEAN SCHNEIDER (Department of
Mathematics, Boise State University, 1910 University Drive,
Boise, ID 83725; jeanschneider@u.boisestate.edu).
We explore a striped pattern generated by a general
Turing model in three different geometries. We look at the
square, disk, and hemisphere and make connections between
the stripes in each spatial direction. In particular, we gain a
greater understanding of when perfect stripes can be generated
and what causes defects in their patterns. In this investigation
we look at the difference between the solutions due
to the different domain shapes. In the end we lay out a reason
why stripes from a reaction-diffusion system can be perfect
on a square or hemisphere, but can never be perfect on a disk.
124 Markov Chains on the Symmetric Groups Converging to
Non-uniform Measures, YUNJIANG JIANG (Department
of Mathematics, Stanford University, building 380, Stanford,
California 94305; yunjiangster@gmail.com).
The study of random walks on finite groups, and in
particular symmetric groups, viewed as card-shuffling models,
has seen tremendous activities in recent decades. An
extremely challenging set of problems concerns the mixing
time in total variation as well as other distances on the space
of probability measures. These problems have many practical
consequences ranging from the effectiveness of Monte-
Carlo simulation to number of times one needs to shuffle a
deck of cards to mix it properly. Here we introduce several
other important measures on the symmetric groups other
than the uniform, construct natural Markov chains converging
to them, and analyze their mixing times in sharp form
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via results from symmetric function theory. We also introduce
more general families of measures given by class functions,
and analyze the associated Metropolis chains using
the so-called path method. In particular we give a small
degree polynomial bound for the uniform sampling chain on
derangements, based on the random transposition walk. We
will also mention a few open problems towards the end.
125 Nondefective Secant Varieties of Split Varieties, DOUG-
LAS A TORRANCE (Department of Mathematics, University
of Idaho, 300 Brink Hall, Moscow, ID 83844; torrance@
vandals.uidaho.edu).
Suppose R is the polynomial ring in n+1 variables with
coefficients in an algebraically closed field of characteristic
zero k. The set of all homogeneous polynomials in R of
degree d can be considered as a vector space over k. By considering
two nonzero polynomials to be equivalent if they
are scalar multiples of each other, we can define a projective
space. The split variety, or variety of completely decomposable
forms, consists of all points in this projective space
which correspond to polynomials that are the product of d
linear factors.
For every s distinct points lying on this variety, there
is an (s-1)-plane containing them. We define the closure of
the union of all these (s-1)-planes as the secant variety. We
expect that the secant variety of a split variety will either fill
up the projective space or have dimension s(dn+1). In this
case, the secant variety is said to be nondefective. Otherwise,
it is said to be defective.
It is conjectured that the secant variety to a split variety
will be defective if and only if d = 2 and 2 ≤ s ≤ n/2. It
remains to show that the remaining cases are nondefective.
In this talk, we discuss new results in this area.
Mathematics oral presentations continue on Tuesday.
Please refer to page 90 in these Proceedings.
CELL and MOLECULAR BIOLOGY
Tuesday, starting at 8:40 a.m. in WILLOWS 2
126 A Role for Inflammatory Cytokines in Breast Cancer
Cell EMT, HUNTER COVERT*, NICOLE ANKEN-
BRANDT, RANDY RYAN, and CHERYL JORCYK
(Department of Biological Sciences, Boise State University,
1910 University Drive, Boise, ID 83725; Huntercovert@u.
boisestate.edu).
Inflammatory cytokines are expressed in high levels during
breast tumor development. Tumor cells, as well as monocytes,
macrophages, and neutrophils, secrete these cytokines.
Our preliminary results have shown certain inflammatory
cytokines cause an increase in cell detachment as well
as a change in morphology. The change in cell morphology
can be studied by looking at cellular markers which are
expressed when a cell displays an epithelial or mesenchymal