2011 Senior Projects

Abstracts

Abstract: Designing robots with basic navigation skills is an obvious stepping stone toward more lofty goals. This project explores using a neural network approach to equipping a mobile robot with vision and decision-making skills. We will investigate a specific type of neural network based on the theory that the human brain does not compute how to do everyday actions, but, through experience, has developed associations (memories) between inputs and outputs, and, using new sensory inputs, selects from which memory to be making predictions to come to an appropriate output. The focus of this project is not necessarily on object-avoidance but on image recognition. Therefore, we will be analyzing the usefulness of this particular type of neural network in recognizing the difference between simple indoor obstacles and unobstructed pathways.

Abstract: My project is an exploration of finding a function from a set of games to a set of numbers, so that we may assign value to a game. During this process, I found that we have to create new numbers to represent the value of some games in order for our function to be consistent. We call our set of game values nimbers because it contains items other than typical numbers. I worked on making this function consistent and exploring various issues that arose during this process.

Abstract: None

Abstract: None

Abstract: Modern security for end-user computing systems is typically handled with passwords, secret phrases that authenticate the potential user as valid. Passwords are problematic in that they must be remembered and can be found by potential assailants rendering the security useless. Passwordless grabs images from any standard webcam and sends it through a series of image processors. These processed images are then sent to facial recognition systems to authenticate the user. The focus of the project is on creating facial recognition systems that utilize techniques from artificial intelligence, particularly self-organizing maps.

Abstract: High-throughput biological technologies rapidly generate massive amounts of gene product expression data, overwhelming the manual analysis approaches traditionally utilized by biologists. Simultaneously, significant work has created publicly available biological pathway models which explain some of the most fundamental biological processes. By incorporating pathway structure into analysis of differentially expressed genes and proteins, Differential Expression Analysis of Pathways (DEAP) improves upon current approaches, notably Gene Set Enrichment Analysis (GSEA), which examine co-expression in the context of gene sets. The utilization of pathway connections and the inhibition or catalysis nature of these connections maximizes inclusion of contextual data for the identification of biologically significant co-expression in pathways.

Abstract: The P vs NP question is the well-known problem in computer science of trying to determine if the complexity classes P and NP are equivalent. In my presentation I will provide descriptions of these two classes and also provide details concerning three barriers to answering this question. These barriers are proof techniques that have been shown to be incapable of solving this problem. These barriers are relativization, algebrization, and natural proofs.

Abstract: Video games are a rapidly expanding medium of entertainment, but have yet to gain widespread acceptance as a legitimate medium for artistic expression. My project is an experiment in game design — an exploration of what a game can do besides be fun to play. Using several different algorithmic approaches in the context of a consistent design, I attempted to inspire a sense of loneliness and isolation in the player.

Abstract: The purpose of this project is to understand the logic behind asset pricing. The value of financial derivatives depends on a number of different variables in addition to the value of the underlying asset. Hence, financial derivatives are complex to value. There are many pricing models in use and the methods used in asset pricing require quantitative tools designed to help manage risk. Some of them are the Ito's Lemma and the Black Scholes models.

Abstract: This expository project explores different aspects of Cryptography; an area in mathematics which comprises the development of methods for encrypting and decrypting messages and signals based on a secret key. The survey goes from the most basic systems based on simple substitution of symbols, to much more sophisticated systems based on complex algorithms involving a wide range of theorems from Number Theory and Algebra. For each system, levels of vulnerability against intruders are analyzed, possible threats are pointed out, and descriptive techniques to crack vulnerable systems are provided. In particular, the efficiency and security of popular cryptosystems such as DES (Data Encryption System), and RSA are closely examined.

Abstract: One of the strategies that underdeveloped nations often apply to improve their economic situations is to invest in education in order to create a workforce that can find solutions to the country's needs. However, when it comes to higher education, the education system in such countries tends to be inadequate. One solution to increase the number of highly educated students is to implement a program of financing the education of selected students in developed countries. The program requires that the students return to the country and apply the learned knowledge to their country's needs. As a student in the Rwandan program, the goal of my project is to create a model that I will use to evaluate the value of the program in terms of metrics of the return-on-investment of the program. I intend to use this model to respond to the question of the success of the program.

Abstract: We begin by proving some basic theorems pertaining to step functions whose discontinuities occur at dyadic points. After laying some theoretical foundations, we prove that such functions are dense in L^p before developing series expansions for a continuous function f in terms of the Haar functions on the unit interval and on an arbitrary interval. After proving L^p convergence for both expansions in the case where f is bounded, we present a simple application: approximating the solution to an integral equation. The computer programs used to produce these approximations, along with those used to interpret the results, are included at the project’s conclusion.

Abstract: For dance instructors and choreographers, it is sometimes difficult to communicate to their dancers any inaccuracies or inconsistencies in their movements. This project utilizes image processing to create comparable representations of dancers. The representations created are used to calculate measurable metrics of difference between two dancers' forms in order to aid in the communication process.