Mathematics and Computer Science

# 2012 Senior Theses

# 2012 Senior Projects

Spring 2012 | ||

Monday, April 2, MCRey 315 | ||

3:10 | Jack Sudyka, Test Case Generation From A Model Checked Finite-State Machine | |

3:40 | Hannah Flatau, When False is True: Multi-Valued Logics as a Possible Response to Intuitive Difficulties in Logical Implication | |

4:10 | Alex Koeppel, A System for the Identification of Speed Limit Signs | |

4:40 | Casey Wynn, Hypercyclic Operators in Hilbert Spaces | |

Tuesday, April 3, MCRey 315 | ||

2:40 | Becca Emrick, Categorizing Websites with Machine Learning | |

3:10 | Ross Crocker, The Dependence of Friction Upon Velocity | |

3:40 | Riley Capshaw, Effects of Inference Technique and Similarity Measure on Latent Dirichlet Allocation-Based Feature Location | |

4:10 | Luke Kressin, The Properties of Border Strips on Ferrers Diagrams | |

4:40 | John Nelson Huffman, A Novel Application of Swarm Intelligence |

## Abstracts

**Abstract:** One method of finding features in Java source code is to use Latent Dirichlet Allocation (LDA), which builds a statistical model of the text based on the words used in each method. However, LDA must be approximated, and the performance of such approximations, or inference techniques, when used on source code is not well documented. Also, such models must be queried using some similarity measure to locate the most relevant methods. I compare how well two inference techniques and three similarity measures perform in this domain.

Presenter: | Ross Crocker |

Title: | The Dependence of Friction Upon Velocity |

Presentation: | Tue 3 Apr, 3:10pm, MCRey 315 |

Advisor: | Dr. Duff Campbell |

**Abstract:** It has been suggested that in some physical systems, friction may be related to velocity in variable and nonlinear ways. I investigate different systems and attempt to observe these relationships. I find that in some systems under certain conditions, unexpected and unconventional relationships between friction and velocity do in fact exist.

Presenter: | Becca Emrick |

Title: | Categorizing Websites with Machine Learning |

Presentation: | Tue 3 Apr, 2:40pm, MCRey 315 |

Advisor: | Dr. Gabe Ferrer |

**Abstract:** Categorizing websites is a useful way to increase the performance of search engines as well as discover the underlying structure of the data. Our approach is to categorize websites within specific subjects using machine learning. By using machine learning we are able to find common words among the categories with minimal human involvement.

**Abstract:** This paper surveys several systems of multi-valued logic: Lukasiewics’ and Post’s three valued systems, Bochvar logic, Kleene logic, Probabilistic logic and Modal logic. I evaluate these various logical systems in light of the intuitive difficulties we have identified in the implication connective. Most three valued logics were developed as a response to Aristotle’s problem of future contingents and so do not significantly alter the definition of the implication connective. Modal logic, however, does attempt to reconcile some of the intuitive expectations of reasoning. No logic, though, can fully grasp and formalize the intricacy or flexibility of human reasoning.

Presenter: | John Nelson Huffman |

Title: | A Novel Application of Swarm Intelligence: |

Presentation: | Tue 3 Apr, 4:40pm, MCRey 315 |

Advisor: | Dr. Carl Burch |

**Abstract:** 'Swarm intelligence' is exhibited in natural or artificial systems where collective behaviors emerge through the local interactions of individuals with each other or their environment, such as in ant colony foraging. In my talk, I present the adaptation and use of an ant colony algorithm, originally developed for pathfinding in graphs, to detect anomalous disease patterns in a population."

Presenter: | Alex Koeppel |

Title: | A System for the Identification of Speed Limit Signs |

Presentation: | Mon 2 Apr, 4:10pm, MCRey 315 |

Advisor: | Dr. Dwayne Collins |

**Abstract:** As a stepping stone on the path towards the development of a system which is capable of identifying and interpreting all possible road features, our research focused on identifying a single road feature. Specifically we developed a system to identify U.S. speed limit signs present in a given image or video taken from a moving car. To achieve this goal our system analyzes the edges present in a binarization of the input image, or of the frames of the input video. However, preserving these edges through the binarization process is a non-trivial task. Provided that the edges which correspond to speed limit signs in the input image were preserved through binarization, our system performed well.

Presenter: | Luke Kressin |

Title: | The Properties of Border Strips on Ferrers Diagrams |

Presentation: | Tue 3 Apr, 4:10pm, MCRey 315 |

Advisor: | Dr. David Sutherland |

**Abstract:** This presentation examines the relationship between visual representations of partitions, called Ferrers diagrams, and shapes called border strips. First, the properties of border strips contained within Ferrers diagrams are examined. After this, we will move on to the more interesting properties of border strips which can be appended to Ferrers diagrams. The talk will end with an examination of the properties of border strips independent of any Ferrers diagram.

Presenter: | Jack Sudyka |

Title: | Test Case Generation From A Model Checked Finite-State Machine |

Presentation: | Mon 2 Apr, 3:10pm, MCRey 315 |

Advisor: | Dr. Gabe Ferrer |

**Abstract:** With the continued advances in computer technology the economic risk associated with software bugs has grown significantly. In order to effectively identify these bugs, tests must reliably identify unintended behaviors and must, themselves, be bug free. The project explores a method of limiting the introduction of bugged property tests while ensuring these tests do not conflict with each other and designate specific behavior for every distinct state the program may enter. The system utilizes a finite-state machine to check properties against one another, then builds and runs the property tests through an existing solution.

Presenter: | Casey Wynn |

Title: | Hypercyclic Operators in Hilbert Spaces |

Presentation: | Mon 2 Apr, 4:40pm, MCRey 315 |

Advisor: | Dr. Chris Camfield |

**Abstract:** This talk considers the relationship between hypercyclic operators and the unsolved invariant subspace problem. I begin by finding dense countable subsets of the real plane and R^3. After introducing a space of infinite dimension, little-ell-2, I show that it is a Hilbert space. Finally, I use recent theorems involving hypercyclicity to show the existence of a hypercyclic operator on the ell-p spaces.