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**Kerrin Ehrensbeck** - Faculty Sponsor: Ivan Ramler*“Using Bayesian Analysis to Maintain the Management of Plutonium at the Los Alamos National Laboratory”*

The Los Alamos National Laboratory (LANL) was founded in 1943 as part of the Manhattan Project. LANL is infamous for its work with nuclear material. On July 6, 1945 LANL produced the first nuclear bomb Trinity. Trinity was successfully dropped in the Jornada del Muerto desert. To this day LANL regulates and maintains the remaining nuclear material for the National Aeronautics and Space Administration (NASA). One way in which they regulate the nuclear material is by using calorimeters. A calorimeter is a type of measurement system that is used to measure the heat that an item emits. One problem that applications using calorimeters have is a residual heat effect that results in a correlated data set. The focus of this project is to find a method to model this autocorrelation that can easily be applied to all applications that generate correlated data sets. Using Bayesian statistics, a Metropolis-Hastings algorithm, multiplicative errors and non-linear regression, this project suggests one possible method to model the autocorrelation of a data set and implement it into a plutonium management model.

**Ryan Godard** - Faculty Sponsor: Lisa Torrey*“Question Answering on the Web”*

This project explains the technology behind question-answering systems, and details the process behind building one. Unlike a web search with Google, which responds to queries with a list of relevant documents, question-answering (QA) systems try to determine the single most likely answer to a question. I trained a simple QA system on a set of sample questions from the game of Trivial Pursuit. Given a question, my system attempts to classify the entity the question is asking for into one of three types: Person, Location, or Organization. Then it searches the web, scrapes relevant web pages, and compiles potential answers. Finally, it presents the user with what it judges to be the most likely answer.

**Luke Horton**- Faculty Sponsor: Ed Harcourt*“Quanundrum”*

My goal was to achieve a better understanding of the iOS development process, and to publish to the App Store a purchase-worthy mobile game. The iOS platform requires working in Objective-C using the MVC design pattern. I utilized the well-established Cocos2D game engine mixed with elements of Apple's UIKit and other third-party operations including ShareKit. I have a completed game published on the App Store. I have learned that game development has many, many hurdles and is not for the faint of heart. One must discover and learn the tools, workflow processes, and design patterns necessary for effective Ios development.

**Shelley Kandola** - Faculty Sponsor: Lisa Torrey*“An Analysis of RSA Encryption”*

A cryptographic algorithm is used for safely and securely transferring sensitive data. The data is encrypted, sent, and then decrypted in such a way that only the recipient can know the contents of the message. This project explores a specific algorithm used in cryptography known as RSA. Encrypting messages in RSA involves a variety of mathematical operations, such as modular exponentiation, finding multiplicative inverses, and generating very large prime numbers. These operations can be implemented in a variety of ways that can optimize qualities such as speed, security, or accuracy. In this project I explored a variety of implementations and evaluated their effects on the speed of the RSA algorithm.

**Alex Laird** - Faculty Sponsor: Sam Vandervelde*“Burning Bridges: A Graph Theory Game”*

Burning Bridges is a two-player game on a connected graph. The players alternate turns by moving along edges from vertex to vertex. A move must be made to a vertex adjacent to the one previously selected, and each edge can only be used once. The object of the game is to reach a position in which the other player is not able to move, resulting in their loss. For certain graphs, the outcome is clear just by inspection. For example, the first player always wins on a cycle graph with an odd number of edges. There are strategies for other graphs as well, such as complete graphs, which we will discuss so that you are able to defeat your neighbor in Burning Bridges.

**Lucy Mellor** - Faculty Sponsor: Sam Vandervelde*“A Chromatic Duel on Simple Graphs”*

We will provide a brief survey of the historical and mathematical background of graph edge-coloring as well as several known results pertaining to the edge-coloring of simple graphs. We will then introduce the following edge-coloring game. Given a particular simple graph G, two players alternate coloring an edge of G using one of k available colors in such a way that the coloring remains proper; that is to say, no two adjacent edges receive the same color. The game is won by the player who makes the last valid move that maintains the proper edge-coloring of G. We will analyze the winning strategies for several classes of graphs, including both paths and cycles. We will conclude with a discussion of further avenues of exploration regarding the edge-coloring game.

**Zach Nelson** - Faculty Sponsor: Michael Schuckers*“How to Build an Optimal Team Under a Salary Cap: A stochastic optimization methodology for allocation of resources across positions, applicable to the National Hockey League”*

In this project we considered the question of how to build an efficient professional hockey team. To do this we utilized data from the National Hockey League (NHL). Wins created, our measure of player value, is determined by the Total Hockey Rating (THoR) of Schuckers and Curro (2013), based upon data from the 2010-11 and 2011-12 regular seasons and for goalies, using Schuckers’ (2011) Defense Independent Goalie Ratings (DIGR). Salary data were taken to be the indexed average cap hit for these two years, using 2010 as the base year. The relationship between wins created and salary was estimated with nonparametric quantile regression for each type of player. For the NHL, we used three types of players: Forwards, Defensemen and Goalies. We next considered how to distribute funds between positions to optimize the number of wins given a fixed total salary. Constraining our hypothetical team to have 16 forwards (64% of the roster), 7 Defensemen (28%) and 2 goalies (8%) and a total salary under $70,000,000, we found that approximately 85% of a team’s salary should be into forwards, 10% into defensemen and 5% into goalies. In large part the discrepancy between percent of roster by position and salary allocated to a position is due to the large amount of variability in defensemen.

**Luke Reed** - Faculty Sponsor: Daniel M. Look*“Compartmental Models: An Epidemiological Application of Ordinary Differential Equations”*

Ordinary Differential Equations can be used to create epidemiological models to study the spread of infections. The traditional SIR model splits a population into three separate categories: Susceptible, Infected and Removed. This model provides a basic understanding of the progress of an infection, but it overlooks important details. By splitting these categories into smaller subgroups, it becomes possible to understand the various stages of the infection and study it within the contexts of populations with varying interaction and transmission rates. Tracking the populations of these subgroups enables deeper understanding of a given infection, and applications of these models extend beyond the bounds of traditional epidemiology.

**Alex Root** - Faculty Sponsor: Daniel M. Look*“Easy Complex Dynamics”*

Visualizations of the Mandelbrot Set appear in popular culture frequently. Its mysterious fractal form can be recognized by mathematicians and non-mathematicians alike. Although the mathematics required to understand the Mandelbrot Set is complex, it can be created using ideas from high-school mathematics and simple programming. We will discuss what the Mandelbrot Set is, some simple properties that it has, and how it can be generated by a computer program. We will also discuss some variations on the Mandelbrot Set.

**Brian Thomas** - Faculty Sponsors: Ed Harcourt & Catherine Jahncke*“Building a 4-bit Computer”*

As technological advances occur, and the ability to produce progressively smaller electronics grows, the computational power and complexity of computers also increases. Although computers have become an integral part of society, many still do not understand the basics behind how these machines operate. In this experiment, I construct a computer at its basic level. Using the essential building blocks of computers today, transistor-transistor logic (TTL) gates, I implement the core components of modern computers: an arithmetic logic unit (ALU) and registers. Combining these two components with a clock, I am able to implement a fully functioning 4-bit central processing unit (CPU).