REU Mini-Symposium ~ August 2, 2012

Clapp Laboratory (Map), Mount Holyoke College



Click here for a PDF of the program.

 

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

Edge-Disjoint Spanning Trees and Inductive Constructions

11:00

Zachariah Button, Mount Holyoke REU

The Effect of Forest Characteristics on Hemlock-Loving 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 Bar-and-Body 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 Body-and-cad 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 K-means 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 non-generic persistence.

 

Zachariah Button, Mount Holyoke REU

The Effect of Forest Characteristics on Hemlock-Loving 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 Rd, and due to Laman, these conditions are also sufficient for planar frameworks.  However, sufficiency doesn't extend into R3, 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 tree-moves:  NNI (nearest neighbor interchange) and TBR (tree bisection and reconnection).

 

James Farre, Mount Holyoke REU

Finding Special Embeddings of Bar-and-Body 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

Edge-Disjoint Spanning Trees and Inductive Constructions

Combinatorial characterizations of rigidity models are often tied to edge-disjoint 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. Mixed-effect models were applied to the data, and then alternative characteristics were used to suggest rationale for the clusters which appear. As a follow-up 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 non-vaccinated 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 Body-and-cad Rigidity

Motivated by computer aided design software, I develop a complete rigidity theory for 2D body-and-cad 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 foreign-born person in the United States. With the goal of analyzing the cost-effectiveness of implementing pre-entry testing and treatment of latent TB infection, we construct an individual-based 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 policy-makers.