REU
MiniSymposium ~ August 2, 2012
Clapp
Laboratory (Map), Mount Holyoke College
10:30
– 10:45 
Welcome & Coffee
(Clapp 416) 

10:45
– 11:45 
Session IA (Clapp 401) 
Session IB (Clapp 402) 
10:45 
Christopher
Clement, Mount Holyoke REU Hyperbananas:
A Family of Flexible Frameworks 
Laura
Gioco, Mount Holyoke REU EdgeDisjoint
Spanning Trees and Inductive Constructions 
11:00 
Zachariah
Button, Mount Holyoke REU The
Effect of Forest Characteristics on HemlockLoving Insect Populations 
Xueying
Zhao,
Mount Holyoke Domestic
return on overseas LTBI testing and treatment 
11:15 
James
Farre, Mount Holyoke REU Finding
Special Embeddings of BarandBody Frameworks 
Helen
Jenne & Ceara Somerville, Mount Holyoke REU Estimating
the Prevalence of Tuberculosis Infection 
11:30 
Dominic
Spadacene, Williams REU Spaces
of Trees 

11:45
– 1:00 
Lunch
(Clapp 416) 

1:00
– 2:00 
Keynote (Clapp 402) Satyan
Devadoss, Williams College Robot
Motion Planning What
is the space of all possible ways robots can move in a room? What happens
when we place obstacles in their path? We not only look at the important
subject of robot motions but look at the ideas behind robot collisions.
This leads to worlds of polyhedra, tilings, string theory, and
phylogenetic trees. During this adventure, we visually learn what
multiplication is really about as well as learning to draw in higher
dimensions. This talk is heavily based on pictures and no background is
needed. 

2:00
– 2:15 
Break 

2:15
– 3:15 
Session IIA (Clapp
401) 
Session IIB (Clapp
402) 
2:15 
Craig
Corsi,
Williams REU Spaces
of Oranges 
David
Breese, Mount Holyoke REU Swarms
of robots maintaining formation 
2:30 
Daoji
Huang, Williams REU Quotients
of Tree Spaces 
Jed Chou
and Ben Whitney, UConn REU Frobenius
Splitting of Projective Toric Varieties 
2:45 
Linnea
LaMon, Mount Holyoke REU A Combinatorial Characterization of 2D Bodyandcad Rigidity 

3:00 
Nathan
Blyler, Mount Holyoke REU A
Clustering Approach to Image Compression 
Tara
Hudson, Mount Holyoke REU Carbon
Dioxide Flux due to Soil Respiration 
3:15
– 3:45 
Tea
(Clapp 416) 
Titles
and Abstracts (alphabetically by last name)
Nathan Blyler, Mount Holyoke REU
A Clustering Approach to Image Compression
We use the Kmeans clustering algorithm to downsample images
before JPEG compression. We
compare our methods to JPEG's current downsampling method's problems of color
bleeding, color gradient, and compression ratio.
David Breese, Mount Holyoke REU
Swarms of robots maintaining formation
We develop the notion of persistence of a formation of robots
modeled as bodies in R^n. We then give several results and conjectures about
the characterization of generic and nongeneric persistence.
Zachariah Button, Mount Holyoke REU
The Effect of Forest Characteristics on HemlockLoving Insect
Populations
Two species of insects, the Hemlock Woolly Adelgid and the
Elongate Hemlock Scale, are wreaking havoc upon hemlock populations in the
northeastern United States. In
this talk, I'll discuss which characteristics of the forest may affect the
movement of these populations, from a statistical perspective.
Jed Chou and Ben Whitney, UConn REU
Frobenius Splitting of Projective Toric Varieties
We will explain how to construct a projective toric variety from a
lattice polytope. Then we will describe how we tried to classify the diagonally
Frobenius split projective toric varieties using a polyhedral characterization
of this property due to Sam Payne (2008).
Christopher Clement, Mount Holyoke REU
Hyperbananas: A Family of Flexible Frameworks
Maxwell's counting conditions are necessary for rigidity in R^{d},
and due to Laman, these conditions are also sufficient for planar
frameworks. However, sufficiency
doesn't extend into R^{3}, as the double banana is a classical example of a
flexible framework satisfying these conditions. In this talk, we discuss a family of flexible Maxwell graphs
called hyperbananas, which includes the double banana example.
Craig Corsi, Williams REU
Spaces of Oranges
We construct another tree space, introduced by Kim (2000), which
captures the relation between two treemoves: NNI (nearest neighbor interchange) and TBR (tree bisection
and reconnection).
James Farre, Mount Holyoke REU
Finding Special Embeddings of BarandBody Frameworks
The study of frameworks provides a mathematically rigorous way to
approach problems concerning the rigidity of structures coming from engineering
and the natural sciences. We use the existing infrastructure of a class of
algorithms called pebble games in order to obtain geometric interpretations of
special positions of frameworks.
Laura Gioco, Mount Holyoke REU
EdgeDisjoint Spanning Trees and Inductive Constructions
Combinatorial characterizations of rigidity models are often tied
to edgedisjoint unions of spanning trees. In this talk, we describe an
inductive construction for a specific class of graphs that arise in Computer
Aided Design applications.
Daoji Huang, Williams REU
Quotients of Tree Spaces
A novel set of discrete folding moves are introduced to understand
the relation between tree spaces, based on the combinatorics of isolating sets.
Tara Hudson, Mount Holyoke REU
Carbon Dioxide Flux due to Soil Respiration
A significant amount of carbon dioxide is emitted from the
respiration of microorganisms in the soil, which unfortunately is difficult to
estimate. The goal of this project was to analyze the data gathered by
researchers at Harvard Forest to determine trends in the emission of carbon
dioxide. Mixedeffect models were applied to the data, and then alternative
characteristics were used to suggest rationale for the clusters which appear.
As a followup analysis, a model was selected to predict the carbon dioxide
flux given the site in Harvard Forest.
Helen Jenne and Ceara Somerville, Mount Holyoke REU
Estimating the Prevalence of Tuberculosis Infection
We used mixture modeling to determine the prevalence of
tuberculosis infection based on skin test data from a 1975 South Korean survey that
included both vaccinated and nonvaccinated individuals. Using the EM
algorithm, we found the maximum likelihood estimates for the parameters of
several different mixture models.
Linnea LaMon, Mount Holyoke REU
A Combinatorial Characterization of 2D Bodyandcad Rigidity
Motivated by computer aided design software, I develop a complete
rigidity theory for 2D bodyandcad structures composed a bodies connected with
coincidence, angular, and distance constraints. I focus on two basic
constraints and outline the complete theory.
Dominic Spadacene, Williams REU
Spaces of Trees
A classical problem in computational biology is the construction
of a phylogenetic tree from a sequence alignment of $n$ species. Based on the work by Billera, Holmes,
and Vogtmann (2001), we provide a construction of a space of such metric trees.
Xueying
Zhao, Mount Holyoke
Domestic
return on overseas LTBI testing and treatment
Increased
risk for tuberculosis (TB) disease has been identified among foreignborn
person in the United States. With the goal of analyzing the costeffectiveness
of implementing preentry testing and treatment of latent TB infection, we
construct an individualbased model using Netlogo software to track and record
the future costs and health status of each visa applicant from a certain
country. The results from the
simulation will provide quantitative data to public health policymakers.