Mathematics and Computer Science

2007 Senior Theses

Spring 2007
Wednesday, April 4, MCRey 317
3:00Jeremy Crosmer, Counting Mazes
3:30Samuel Hwang, Game Theoretic Analysis of the U.S.-North Korea Relations
4:00Jared Keahey, Localization for a Tricycle Gear Robot
4:30Neil Bledsoe, Concurrency Issues, Motor and Servo Control, and Obstacle Avoidance in Robotics
5:00Tony Schraml, Shuffles of Partially Ordered Sets
Thursday, April 5, MCRey 317
3:00Ian Hill, Algorithms for Detecting Humans Using Motion Detection and Template Images
3:30Lee Kaufman, A Map Subsystem for a Messenger Robot
4:00Thomas Przybylinski, Category Theory and Sequential Machines
4:30Russel Reed, Intelligent Manipulation of Video Game Audio


Presenter:Neil Bledsoe
Title:Concurrency Issues, Motor and Servo Control, and Obstacle Avoidance in Robotics
Presentation:Wed 4 Apr, 4:30pm, MCRey 317
Advisor:Dr. Gabriel Ferrer

Abstract: This project explores issues related to communication between separate control modules of the TinkerTrike robot and also explores any concurrency issues involved therein. This project is also a module itself which acts as the brainstem of the robot - in particular, the module associated with this project communicates higher-order functions, such as following paths, to the robot's motors and servos. Finally, this project explores obstacle avoidance with limited-distance range finders.

Presenter:Jeremy Crosmer
Title:Counting Mazes
Presentation:Wed 4 Apr, 3:00pm, MCRey 317
Advisor:Dr. David Sutherland

Abstract: This project consists entirely of the student's constructs which are independent of outside resources. The main goal of the project is to establish a text-book style study of mazes. In this study, the concept of a simple-path maze is stated in precise mathematical terms, and then a number of different ways to count mazes is developed from this defined concept. These counting methods involve both rough estimates for a general square maze and precise answers for more specific cases.

Presenter:Ian Hill
Title:Algorithm for Detecting Humans Using Motion Detection and Template Images
Presentation:Thu 5 Apr, 3:00pm, MCRey 317
Advisor:Dr. Gabriel Ferrer

Abstract: An algorithm for finding humans in a video stream is described. The algorithm first attempts to segment areas of the video that possibly contain humans by using a motion-detecting visual filter. It then tries to match the 'area of interest' found by the filter to generate template images, bitmaps which represent the average intensity and importance of pixels over many pictures of a specific feature (e.g. face templates, body templates). The algorithm then creates a heuristic value for the human content of the segmented area—based on the difference in intensity at every pixel as well as the pixel's corresponding weight—and judges the presence or absence of a human by it. This algorithm is intended to find humans with a robot-mounted camera for the purpose of delivering messages. The robot is employed on a particular floor of a university building consisting primarily of hallways and offices. The algorithm assumes many of the conditions of the specific task and environment: lighting values, faces of residents and the ability to stop for observation. The algorithm is thus primarily engineered for these particular conditions, but with the intent of incrementally evolving it for more general use in other tasks and environments.

Presenter:Samuel Hwang
Title:Game Theoretic Analysis of the U.S.-North Korea Relations
Presentation:Wed 4 Apr, 3:30pm, MCRey 317
Advisor:Dr. Duff Campbell

Abstract: North Korea's repeated provocations have threatened the political stability of Northeast Asia and consequently the normalization of the U.S.-North Korea relations have been delayed. In this presentation North Korea's repeated provocations will be analyzed in the context of a game theoretic model, Asymmetric Deterrence Model (ADM). Also, suggestions for future policies of the U.S. towards North Korea are made using the ADM, including how the U.S. should capitalize the Six Party Talk.

Presenter:Lee Kaufman
Title:A Map Subsystem for a Messenger Robot
Presentation:Thu 5 Apr, 3:30pm, MCRey 317
Advisor:Dr. Carl Burch

Abstract: For my Senior Project I implemented the Map system of the joint Messenger Robot project. The job of the Map system is to find a path between the Robot's current position given by the Localization unit and its destination. Then send an instruction to the Controller Unit that can move the Robot. The map allows the robot to search all of the rooms in the map in an attempt to locate a target human.

Presenter:Jared Keahey
Title:Localization for a Tricycle Gear Robot
Presentation:Wed 4 Apr, 4:00pm, MCRey 317
Advisor:Dr. Carl Burch

Abstract: This project explores the challenges of implementing a Localization module to allow the Hendrix College Computer Science Department's robot to estimate its location as it moves. There are two main components of the module. The first is a system that uses estimation functions, derived from empirical data, that are based on the relationship observed between the commands issued and the resulting heading and distance traveled. The second uses two light sensors that read alternating black and white patterns on the rear wheels to estimate distance traveled and resulting heading. The presentation will examine the synthesis of these two components as well as the robot itself in detail.

Presenter:Thomas Przybylinski
Title:Category Theory and Sequential Machines
Presentation:Thu 5 Apr, 4:00pm, MCRey 317
Advisor:Dr. Ze'ev Barel and W. Dwayne Collins

Abstract: Category Theory is novel approach to mathematics that concentrates on the relationships between mathematical objects. We will use this theory to analyze several properties and components of a simple theoretical computer known as a sequential machine. This will allow us to describe one machine's properties in terms of maps to and from other sequential machines and will give allow us to gain a different insight into these properties.

Presenter:Russel Reed
Title:Intelligent Manipulation of Video Game Audio
Presentation:Thu 5 Apr, 4:30pm, MCRey 317
Advisor:Dr. W. Dwayne Collins

Abstract: Video games and video game music are two inseparable concepts. In the vast majority of cases, the music is an immediate reaction to some change in the state of the game. This project explores the potential for a game in which the soundtrack suggests the actions of the player, instead of the other way around. Through artificial intelligence, a soundtrack can be modified in anticipation of actions based on the player's past actions in a similar situation. The project explores two possible implementations of such an intelligent system.

Presenter:Tony Schraml
Title:Shuffles of Partially Ordered Sets
Presentation:Wed 4 Apr, 5:00pm, MCRey 317
Advisor:Dr. David Sutherland

Abstract: This project strives to identify structural characteristics of the poset of shuffles as described by Richard Stanley and Curtis Greene. The characteristics are then used to help construct an isomorphic relation and several automorphism groups. From this construction, several theorems are proposed generalizing automorphism group construction for posets of shuffles.