The Festival of Science was held on April 24, 2015

Here are the abstracts for the Math, Computer Science, and Statistics students who presented at the Festival. Here are some photos with students and their poster presentations.

Thomas Ball / Advisor:  Choong-Soo Lee
Title: Mobile App Approach to Improve Customer Experience at the Northstar Café
At noon every day, the North Star café becomes swamped with students all trying to get food in the brief time they have between classes. Heavy load on dining services often results in orders that are not fill in time for the next class period, and these late orders are wasted. The understaffed café had to cut services such as allowing orders to be phoned in to avoid wasted food, causing customer dissatisfaction. While both Thelmo and Dining services are trying to find a solution for dealing with the lunch rush in an efficient manner, I would like to propose my own solution. An electronic system of placing and paying for orders allows the dining services to receive orders remotely that are already sorted to the right station without taking an employee away from his/her duty. My SYE focuses on building a consumer side interface, an Android app, with which users can browse the menu and place and pay for orders. The orders are stored in a database and can be accessed by users and café staff.  Surveying a pool of customers and researching the application cycle and required network resources, I developed an Android app that currently supports menu browsing and storing orders in a database as a proof of concept. The system can be expanded to accept payments and allow the café staff to receive and analyze orders to meet the customers’ needs better.

Dave DiStefano / Advisor:  Sam Vandervelde
Title: An Application - Based Understanding of the Catalan Numbers
The Catalan numbers are an important, famous, and recursive sequence of integers that appear in over 600 counting problems. This project begins with a quick but detailed introduction to these numbers along with an example to illustrate the recurrence found within this sequence. Next, research is presented regarding an exploration into "Tri - Catalan" numbers, which are applicable to Catalan number counting problems that occur in three dimensional space. Lastly, further research and observations are presented regarding Dyck Paths, a particularly famous problem involving Catalan numbers.

Danny Driscoll / Advisor:  Michael Schuckers
Title: Clustering of NHL Goalies
Predicting the career path of an NHL goalie has important consequences for an NHL franchise. In this project we use data on NHL goalies since the 2000 season, focusing particularly on goalie age, save percentage, and number of shots faced. Using save percentage and number of shots faced as performance metrics, we attempt to identify different clusters, and determine which cluster each goalie belongs to using not just their performance but their trajectory as they age.  To do this we apply a new approach for the clustering of multivariate longitudinal data developed by Komaraek and Komarkova (2013) to the career trajectories of NHL goalies.  In this talk we focus on identifying different clusters of NHL goalies.

Jacob Hurlbut / Advisor:  Lisa Torrey
Title: Applying Web Development to the Total Hockey Rating
The Total Hockey Rating, developed by Dr. Michael Schuckers and James Curro ’12, is a method of rating forwards and defensemen in the National Hockey League based on the number of goals they help their own team score, and the number of goals they help prevent from being scored against their team. This method provides a total evaluation of a player’s value, hence the Total Hockey Rating name. The solution currently being used by Dr. Schuckers to share the Total Hockey Rating results is a basic Excel spreadsheet that can be downloaded. For my SYE, I developed a website to provide a more sophisticated retrieval system for this data. Using the R Shiny package, I designed an interactive and easy to use website to view the calculation results. This website is underpinned by a PostgreSQL database, making data retrieval speedy, efficient, and scalable in the future. This project will make accessing the Total Hockey rating much easier for the community of hockey fans who value advanced statistics, and will allow Dr. Schuckers to showcase the work he has put into creating the Total Hockey Rating.

Alaina Larkin / Advisor:  Sam Vandervelde
Title: Untangling Knot Theory
Aptly named, knot theory is the study of knots, which are simple closed curves in three-space. One way to tell knots apart is to find a knot invariant, in which a value is assigned to a knot that stays the same regardless of the knot diagram.  We have developed a knot invariant that detects chirality and is relatively simple to compute.  Our method involves the idea of ‘smoothing’ each crossing in a knot diagram to obtain a single loop that covers every arc of the knot diagram, then computing a sum over all such smoothings.  (This approach is based on the Kauffman Polynomial invariant.)  There are other knot invariants that also detect chirality, such as the Jones Polynomial and the Vassiliev Invariant; however, they are computationally intensive.  Our method cuts down on the time spent computing the invariant from exponential time to what we believe to be quadratic time.

Brandon Lustig / Advisor:  Robin Lock
Title: Head-to-Head Comparison Models to Rank PGA Tour Players
The current ranking systems for professional golfers, such as the Official World Golf rankings and the Fed Ex Cup standings, put emphasis on winning tournaments and finishing near the top instead of looking at every round played with equal importance. To provide alternatives that are not so heavily weighted on winning tournaments and give more emphasis on playing consistently well, we use models, such as Bradley-Terry, that rely on head-to-head comparisons for all pairs of players for every tournament round. We discuss the details of finding ratings using these models, estimating the probability of a player beating another in a round, and compare the results using data from the 2013-2014 PGA tour season.

Emmanuel Ngenoh / Advisor:  Lisa Torrey
Title: Hockey Statistical Analysis Tool
This Computer Science SYE produced a Java application for web data extraction. The application is targeted at webpages that have information on college hockey teams. It extracts statistics about goals recorded during hockey games over the past few years. All the statistics are consolidated and cached to avoid repeated data extraction, which is time consuming. When launched, the application loads the cached information and provides a user interface that displays the data. The user interface has filtering features for viewing interesting subsets of the data. It can also generate a data matrix for statistical analysis.  Coaches could potentially use this application to develop play strategies ahead of an upcoming game.

Abigail Ross / Advisor:  Sam Vandervelde
Title: A Multi-Dimensional Generalization of the Catalan Numbers
The central goal of this research was to take the Catalan numbers, a well-known number series, and understand how they can be defined and computed in multiple dimensions. This project begins with a basic introduction to the Catalan numbers in two dimensions. We then use mathematical intuition and computer code to conjecture a formula for higher dimensions. Finally, we prove our conjecture about multi-dimensional Catalan numbers and discuss extra explorations on the topic of Catalan numbers.

Nathaniel Shenton / Advisor:  Robin Lock
Title: The Double Pendulum: A Case Study of Chaotic Behavior
The double pendulum is a dynamical system in which a second pendulum is connected to the first, allowing the second to swing freely. The motion of the resulting dynamical system will depend upon the motion of the first pendulum.  This system experiences both periodic and chaotic tendencies.  We will use this example to show what it means for a system to be considered chaotic.  To do this we will explore the known visual tools that can help detect chaos, including an actual built pendulum.

Molly Sneden / Advisor:  Jessica Chapman
Title: Exploring Wine Characteristics Through Hierarchical Cluster Analysis
Hierarchical cluster analysis is a method of cluster analysis that builds a hierarchy of groups based on similarities in the data.  I will be using hierarchical clustering to group together different Vinho Verde wines based on their chemical composition, such as acidity, amount of residual sugar, chloride, and sulfur dioxide and alcohol percentage. Using these clusters, I investigate the similarities and differences in wine quality and type. The wine I will be looking at is from the Minho region in the far north of Portugal.  The Vinho Verdes are light, fresh, young wines, meaning they are meant to be drunk within a year of production.

Jennifer Street / Advisor:  Michael Schuckers
Title: Adjusting Grade Point Averages for Course Difficulty
Class rank is a measure of a student's performance compared to the performance of other students in his or her class. The conventional method for determining a student's grade point average involves the earned grades and the number of units or credits that the student receives from each course. However, this process does not include a way to incorporate course difficulty, which can vary due to the nature of the course material or the particular grading standards of a professor, among other defining characteristics. The purpose of this project is to analyze ten years' worth of anonymized grade history for St. Lawrence University and build a model that provides a student's grade point average after adjusting for course difficulty. By doing so, we are able to re-rank students within each class in order to more accurately provide a comparison of classmates. We find that incorporating course difficulty into the ranking process does impact the order of class rankings, though the biggest factor impacting class rankings is the individual student.

Yunsi Yang / Advisor:  Robin Lock
Title: ANOVA and Beyond: When is a difference really a difference?
Analysis of variance (ANOVA) is a common statistical tool to look for differences between groups. The goal is to detect differences that really exist (power), but avoid calling two groups different that are really the same (Type 1 Error). Power and Type 1 Error rate depend on various factors, such as sample sizes, number of groups, variability within groups, and variability between groups. We use simulations to explore some of these relationships and also look at alternatives to the traditional ANOVA test based on randomization procedures.

Yunsi Yang / Advisor:  Duncan Melville
Title: Forecast of Impact of the Decreasing Oil Price on Oil Companies and Major Airlines
U.S. crude oil prices started to decrease dramatically in the fourth quarter of 2014, and did not stabilize until recently. The objective of my project is to analyze how decreasing oil prices influenced domestic oil companies and passenger airlines by observing how these companies’ stock prices changed. I collected historical stock prices for the top 10 U.S. oil and gas companies and 10 major U.S. airlines between March 2014 and February 2015. To have an overview of these two industries, I created two indices, using the weighted mean of daily stock prices of oil companies and airlines separately; the weights are determined by annual revenue. I performed a statistical analysis on these three variables (oil price, the index for oil companies and the index for airlines), including a t-test for significance of correlation and an ARIMA model to forecast the future price. Stock prices in March 2015 are used to test the accuracy of ARIMA model. The pricing of index options is accomplished by the Black-Scholes formula and the GARCH model.