HRUMC 2014 Titles and Abstracts

Twenty-Six Mathematics, Computer Science and Statistics students and five faculty participated in the the 21st Annual Hudson River Undergraduate Mathematics Conference at Marist College in Poughkeepsie, New York on Saturday April 26.
Eleven students presented their senior research projects. The most of any university participating.

Zachary Felix
Pitch Classification Using Major League Baseball’s Pitchf/x Data
Abstract: Pitchf/x is a baseball tracking system that uses cameras to record measures such as the velocity, movement, and location of every pitch thrown in Major League Baseball games since 2006. We use an R package called pitchRx to access and store data from the online Pitchf/x files. We examine methods, such as k-means clustering and multinomial logistic regression, for classifying the type of pitch (fastball, curveball, etc.) based on Pitchf/x characteristics.

Jack Holby
Geometric Variations on the Euclidean Steiner Tree Problem
Abstract: The Euclidean Steiner Tree Problem (ESTP) attempts to create a minimal spanning network of a set of points by allowing the introduction of new points, called Steiner points. This poster discusses a variation on this classic problem by introducing a single “Steiner line” in addition to the Steiner points, whose weight is not counted in the resulting network. For small sets, we have arrived at a complete geometric solution. We discuss heuristic algorithms for solving this variation on larger sets. We believe that in general, this problem is NP-hard.

Tom Lehmann
Examining Allometric Scaling Laws in Biology and Cross-Sectional Area Preservation in Trees
Abstract: A unique ¾ power relationship between metabolic rate and mass in organisms exists, spanning 21 magnitudes of body size and applicable to "organisms" from trees to cities to living cells. The mathematical foundations of this unique quarter-power relationship have been a topic of debate ever since its first observance in 1932.  In 1997, a team of physicists developed a groundbreaking derivation of the “¾ power law” using the physical limitations of self-similar fractal-like distribution networks that minimize energy dissipation. This derivation spurred heated discussion. Necessary premises to the derivation, such as cross-sectional area-preserving branching, may not hold true in reality and have fueled this discussion. In our study, we review the methods of the 1997 derivation, and examine if trees exhibit area-preserving branching, first proposed by Leonardo Da Vinci, through field measurements of a variety of confer and deciduous trees.

Daniel Look
It Came From......The Fourth Dimension!!
Abstract: Comic books are rarely used as mathematical resources. However, artistically, comic books have an advantage over other visual media in terms of conveying higher dimensional spaces. We will focus on an issue of Steven Bissette and Alan Moore's 1963 Comics featuring an invader from \The Fourth Dimension" to explore how the artistic space created by the panels of a comic book lend themselves to portraying higher dimensions.

Brian Magovney
Bradley Terry Model for Ranking Division III Baseball Teams
Abstract: The ranking athletic teams, particularly college teams, is often debated and discussed, especially when there may be large differences in strengths of schedules between different teams or leagues. Who is the best?  How do you determine what team deserves to be ranked where? We use a Bradley Terry Model to generate a function to determine team rankings based on schedule information and game results scraped from the web using an R package.

Robert Montgomery
Paired Kidney Donation:  Optimal and Equitable Matchings in Bipartite Graphs
Abstract: If a donor is not a good match for a kidney transplant recipient, the donor/recipient pair can be combined with other pairs to find a sequence of pairings that is more effective. The group of donor/recipient pairs, with information on how strong a match each donor is to each recipient, forms a weighted bipartite graph. The Hungarian method allows us to find an optimal matching for such a graph. However, the outcome which is optimal for the group might not be the most equitable for the individual patients involved. We examine several modifications to the Hungarian method which consider a balance between the optimal score for the group and the most uniformly equitable score for the individuals. We examine the strengths and weaknesses of these modifications within the current climate of kidney allocation in the United States. Finally, we expand these findings to other fields where these revised algorithms may also hold particular significance.

Spencer Nelson
Cuves Derived From Circular Motion And Guilloch_E Patterns
Abstract: Imagine you and a friend attend your local carnival which features two ferris wheels that are oriented in the same plane. You proceed to the _rst ferris wheel and attach a bungee cord to your gondola while your friend does the same at the other ferris wheel. If there is a blinking strobe light at the midpoint of the bungee cord, what shape does it trace for onlookers as the ride progresses? We will explore a number of curves created by circular motion and analyze the parameters that determine the curve. Additionally, we will generalize this problem to three circles and examine the curves created by the centroid and other points associated with the triangle de_ned by three points on three circles. We will also consider the relation between these curves and Guilloch_e patterns, which are decorative designs that commonly appear in architecture and _ne metal workings.

Michael Orlando
Mapping the National Survey of Reaction and the Environment Data
Abstract: The NSRE dataset contains information on 162 variables measuring attitudes about the environment and recreation for almost 100,000 respondents. To help analyze and display this data we have developed a set of R functions to generate choropleths, maps that are colored to display quantitative information along a color gradient. We discuss some of the interesting findings the maps reveal about the NSRE data as well as the challenges of automatically producing choropleths.

Tafadzwa Pasipanodya
Automated Multi-Document Summarization
Abstract: We live in a world with a wealth of information. It is essential to be able to deduce concise and comprehensive facts from this wealth of information in order to reduce information overload. For example, being able to write short summaries of longer documents is a useful skill.  In this talk, we will discuss an automated approach to document summarization.  The technique most often used to create summaries is called sentence extraction. This approach builds a summary by selecting sentences from within the original document that best capture its meaning. We implemented two document summarizers; one that simply picks the sentences that are most similar to a query sentence, and one that considers a document as a graph, and judges the importance of sentences based on their relationships within this graph. We found that different approaches worked better for different documents, and that there were noticeable differences in efficiency between these approaches.

Addie Peterson
Statistical Analysis of Survival Models for Biological Data
Abstract: We examine methods for estimating survival curves and comparing life expectancies with applications to biological events. The analysis addresses the idea of determining the proportion of a population that will survive past a particular time. We use Kaplan-Meier curves to estimate survival functions and perform inference on curves using computer simulation methods, such as randomization tests and bootstrapping. We illustrate these methods modeling the lifetimes of C. elegans (worms) used in a study of treatments for brain disease involving free radicals.

Devlin Rutherford
Applications of Fractal Geometry to Volcanology
Abstract: We explore the basic mathematics behind fractal geometry, examining fractal sets such as the Sierpinski Triangle, Koch Snowflake, and the Cantor middle-thirds set. Additionally, we explore a problem involving the measurement of the coastline of Britain. Finally, this problem leads us to one application of fractal geometry in the field of geology, namely, classifying volcanic particles.

Vir Seth
CSA Squash Ratings Using a Bradley-Terry Model
Abstract: We use a Bradley--‐Terry Model to generate rankings of the squash teams in the College Squash Association (CSA). The model takes into account several factors such as the number of matches played, the strength of schedule and the win-loss records. At the end of the regular season, the top 8 teams in the nation are invited to compete for the Potter Cup, a single elimination draw to crown the National Champion.  How do the rankings for the 2014 Potter Cup compare to the rankings obtained by using our Bradley--‐Terry model?