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2013 Senior Projects

Abstracts

Abstract: We begin by exploring differences between common voting methods that use ranking ballots. To determine which is more fair, we examine a fairness criterion, the Condorcet criterion. If a Condorcet candidate appears frequently in an election, we can deem it as an appropriate standard for comparing voting methods. We then test the likeliness of having a Condorcet candidate in an election, and find that because it is so common, we can use it to compare the different voting methods.

Abstract: A person can find where they are in an unknown location by using a GPS receiver. However, problems arise when the area that one is in is very dense or requires fine altitude distinction for navigation. I use wireless routers to attempt to locate Android devices on the third floor of MCReynolds.

Abstract: We consider a population distribution where the dependent variable is a function of several independent variables. Then by random sampling the population, the Sample Regression Function (SRF) slope coefficient estimators are obtained by the method of Ordinary Least Squares (OLS). Then, we prove independently the Gauss-Markov Theorem which states that the SRF estimators, under certain assumptions, are the best linear unbiased estimators of the population slope coefficient estimates.

Abstract: With the advent of tablet and touch screen computing, the number of applications that utilize text recognition technologies is rapidly increasing. These applications rely on accurate identification of text characters, which may or may not be oriented uniformly. This project explores methods to identify characters that may have been altered with translation, rotation, or skew. Our approach uses transformation matrices to correct character orientation by manipulating the set of pixels representing the characters. Machine learning was used to identify the properly oriented characters.

Abstract: Shuffle posets are poset variations which contain listings composed of all, some, or none of the elements of ordered alphabets A and B such that the listings preserve the order of the alphabets within their structures. We impose a partial order and display the shuffle posets as lattices, opening the door for the inspection of group-like structures. The subject of this project is the investigation of shuffle poset properties and the nature of their Hasse diagrams. In particular, combinatorics and abstract algebra are used to prove theorems regarding the partial order on shuffle posets and to inspect the graph automorphisms of these Hasse diagrams for isomorphisms to well-known algebraic groups.

Abstract: The current housing process at ºÚÁϲ»´òìÈ is meticulous and requires large amounts of human resources to accomplish repetitive tasks. In my project I explore the creation of a user interface in the context of attempting to update the current housing system.

Abstract: The Internet Protocol, IP, is a system of digital message formats and rules for exchanging message between devices connected to a network. IP supports unique addressing for all the devices on the network for an exchange of information to be established. There are two main Internet Protocol versions; Internet Protocol Version 4, IPv4, and Internet Protocol version 6, IPv6. IPv6 was made available for deployment since 1999 and was designed to respond to the exhaustion of IPv4 available addresses available to allocate. As of now, even though IPv4 available addresses are almost exhausted, IPv6 network traffic remains very small compared to IPv4 network traffic. This project studies past and current statistics of IPv6 deployment to determine why IPv6 has not been fully deployed 14 years after it was made available and when there are no more IPv4 addresses to allocate. The project analyses the main factors that impact IPv6 deployment and makes predictions for the future IPv6 deployment.

Abstract: In a rectangular point lattice of dimensions N vertices down and M vertices across, it is possible to define a path through the vertices from the left-hand side to the right-hand side of the lattice. This project explored the properties of these paths, including the number of total paths on a given lattice, the number of paths associated with each node, and the probabilities of these paths.

Abstract: This project models the set-up of the outpatient clinic and efficiency is the key target, it is measured by the time patients spend waiting for the service and how clinic resources are being used. I allowed the adjustments on initial clinic appointment and nurses, that was done by constructing different scenarios and used queuing theory to examine the possible improvement in efficiency basing on scenarios results.

Abstract: The project focuses on two goals. The first is to recreate the N-Queens problem, that is, to determine the maximum number of queens that can be placed on an NxN chessboard, where N represents the number of squares on the side of the board, such that no two queens are attacking each other. The second goal is to determine the least number of queens that can be placed on a board such that every square on the board is attacked. The project will be completed using a mix of empirically determined data that enumerates piece placement and the patterns that emerge from their placement.

Abstract: I modeled an educational practice called project-based-learning as I discovered how to utilize Markov Chains and elements from linear algebra to analyze different board games. Finding information about the game length of Chutes and Ladders and about which Monopoly properties are most advantageous to invest in, I learned mathematics the way it should be learned: in the context of something you are truly curious about and enjoy.

Abstract: The SLAM problem is known as the Simultaneous Localization and Mapping problem. It is a technique used by robots in order to create maps of an unknown environment while simultaneously localizing itself within the created map. The research does not create a full solution for the SLAM problem but rather attempts to create a solution to a subproblem: robot localization. More specifically, an approximate localization value was calculated by implementing a particle filter. Although this research is a subproblem of a much more complex issue, it is definitely a stepping stone to potentially achieve a full solution for the SLAM problem at an undergraduate level.

Abstract: Real-time object recognition systems are usually expected to analyze and interpret images captured from a substantially non-homogeneous environment. This imposes various additional computational complexities for resolving noise, which is likely not incurred when dealing with images taken from a fairly homogeneous environment. In this project, we attempt to identify speed limit numbers represented in binary images that presumably are captured using a camera mounted on a moving vehicle. By analyzing a shape of a contour representing a digit in the image, we collect features that enable us to accurately characterize the corresponding number.