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

ABSTRACTS – Symposia
Ciliates are single celled organisms hosting two types of
nuclei, one an encrypted version of the other. In some species
this encryption is nontrivial. During certain events in the
ciliate life-cycle nuclei are updated through a process that
involves decryption of the encrypted version. Mathematical
models for the decryption process postulate certain specific
molecular computations that achieve this decryption. In this
work we seek to: (1) determine the molecular computational
steps taking place during decryption by examining
intermediate DNA products of the process; (2) determine the
elements of the symmetric group that are invertible by the
ciliate decryption apparatus; (3) determine the computational
complexity of the several steps to be taken in modeling
elements and operations of symmetric groups in the ciliate
computing environment.
All four authors contributed equally under the mentorship of Prof. Marion
Scheepers, Boise State University. We acknowledge NSF grant DMS
1062857 and Boise State University for supporting this work.
35 Exploring Phylogenetic Relationships in Drosophila
with Ciliate Operations, MARION SCHEEPERS 1 , ANNA
NELSON 1 *, and JACOB HERLIN 2 . ( 1 Department of
Mathematics, Boise State University, 1910 University Drive,
Boise, ID 83725; 2 Department of Mathematical Sciences,
University of Northern Colorado, 2901 South 27th Avenue,
Greeley, CO 80631; annanelson1@u.boisestate.edu).
Phylogenetics is the study of evolutionary relationships
among groups of organisms. It is known that the genomes
of some species are related by permutations of gene locations
on chromosomes. The central research question that
arises from this finding is to find mathematical operations
on permutations that most faithfully model the evolutionary
steps by which genome rearrangements arise. Classical work
on the question hypothesize that genome rearrangements
arise through reversals only. Data about the developmental
genome remodeling events in ciliates suggest that there are
additional genome rearrangement operations that could also
be routinely involved in the evolutionary process. Ciliates
are capable of permuting DNA segments using merge, swap,
and reverse operations. We created a deterministic algorithm
that simulates permuting DNA sequences using these three
ciliate operations. It determines in polynomial time evolutionary
distances among scrambled genomes. After implementing
our algorithm in Python we applied it to extensive
data about genome rearrangements in fruit-fly species. We
found a correlation between the published evolutionary distances
of the fly species, found by other means by others, and
the number of ciliate reversal operations used by our algorithm.
For all but one of the eight species we found this correlation
also held for the total number of uses of the reversal
and swap operations used. Our research was supported by
the NSF Mathematics REU site grant DMS 1062857 and by
Boise State University.
36 Geometry, Topology, and Complexity of Virtual Knots,
ASHLEY EARLS 1 *, GABRIEL ISLAMBOULI 2 *, and
RACHAEL KELLER 3 * ( 1 Department of Mathematics, St
Olaf College, 1500 St. Olaf Ave, Northfield, MN 55057,
earls@stolaf.edu; 2 Department of Mathematics, University
of Virginia, Charlottesville, VA 22904, gfi8ps@virginia.edu;
3
Department of Mathematics, Louisiana State University,
Baton Rouge, LA 70803, rkell18@tigers.lsu.edu).
Knots, strings tangled in 3-space, are objects with which
everyone is familiar. The mathematical theory of knots is
highly sophisticated, incorporating many classical areas
including topology, geometry, combinatorics and group theory.
Currently, the study of knots is finding application in
fields as diverse as biology, physics and computing.
A knot, when drawn on a piece of paper, is a planar
4-regular graph. A virtual knot, from a graph theoretic point
of view, is an arbitrary (not necessarily planar) 4-regular
graph. Many questions which have been answered for classical
knots are still unanswered for virtual knots. In our talk
we will introduce virtual knots and explain their relevance to
long standing conjectures, such as Whitehead’s asphericity
conjecture.
All three authors contributed equally under the mentorship of Prof. Jens
Harlander, Boise State University. We acknowledge NSF grant DMS
1062857 and Boise State University for supporting this work.
Responses of Sagebrush-Steppe
Ecosystems to a Changing Climate
Monday, 1:30 p.m. in SALMON RIVER
37 Changes in Soil Aggregate Dynamics and Carbon Storage
Following 18 Years of Experimentally Increased Precipitation
in a Cold Desert Ecosystem, MARIE-ANNE de
GRAAFF 1 *, JESS van der VEEN 2 , MATTHEW GER-
MINO 2 , and JAMIE HICKS 1 ( 1 Department of Biological
Sciences, Boise State University, Boise, ID 38725; 2 USGS
Forest and Rangeland Ecosystem Science Center, Boise, ID
83706; marie-annedegraaff@boisestate.edu).
Climate change is expected to alter the amount and
timing of precipitation in semi-arid ecosystems of the Intermountain
West, and the net effect of these changes on soil
C sequestration is not well understood. Soil C sequestration
is regulated by the incorporation of C into soil aggregates,
where they are physically protected from microbial degradation.
With this study we assessed: (1) how precipitation
shifts affect soil aggregate formation and associated soil
organic carbon (SOC) contents in semi arid ecosystems,
and (2) how plants mediate precipitation impacts on soil
C sequestration. Soil was collected from an ecohydrology
study situated at INL. The experimental field site consists
of subplots planted with either sagebrush (Artemisia tridentata)
or crested wheatgrass (Agropyron cristatum) and
has been exposed to three precipitation treatments: ambient
(i.e.control), winter (200mm) or summer (4x50mm) for 18
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