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A set of subsets is said to have the Helly property if the condition that each pair of subsets has a non-empty intersection implies that the intersection of all subsets has a non-empty intersection. In 1966, Gallai noticed that the set of all longest paths of a connected graph is pairwise intersecting and asked if the set had the Helly property. While it is not true in general, a number of classes of graphs have been shown to have the property. In this dissertation, we show that K4-minor-free graphs, interval graphs, circular arc graphs, and the intersection graphs of spider graphs are classes that have this property. The accuracy of facial recognition algorithms on images taken in controlled conditions has improved significantly over the last two decades. As the focus is turning to more unconstrained or relaxed conditions and toward videos, there is a need to better understand what factors influence performance. If these factors were better understood, it would be easier to predict how well an algorithm will perform when new conditions are introduced. Previous studies have studied the effect of various factors on the verification rate (VR), but less attention has been paid to the false accept rate (FAR). In this dissertation, we study the effect various factors have on the FAR as well as the correlation between marginal FAR and VR. Using these relationships, we propose two models to predict marginal VR and demonstrate that the models predict better than using the previous global VR.

Transfer models provide a viable means of determining which skills a student needs in order to solve a given problem. However, constructing a good fitting transfer model requires a lot of trial and error. The main goal of this thesis was to develop a procedure for developing better fit transfer models for intelligent tutoring systems. The procedure implements a search method using association rules as a means of guiding the search. The association rules are mined from the instances in the dataset that the transfer model predicts incorrectly. The association rules found in the mining process determines what operation to perform on the current transfer model. Our search algorithm using association rules was compared to a blind search method that finds all possible transfer models for a given set of factors. Our search process was able to find statistically similar models to the ones the blind search method finds in a considerably shorter amount of time. The difference in times between our search process and the blind search method is days to minutes. Being able to find good transfer models quicker will help intelligent tutor system builders as well as cognitive science researchers better assess what makes certain problems hard and other problems easy for students.

In this thesis, I sought to determine whether frequency bands in the human electroencephalogram could be used to predict baseball batting performance. Past electroencephalographic (EEG) studies have found that alpha power in the human electroencephalogram predicts subsequent performance. Specifically, Mathewson and colleagues (2012) found that background brain activity, in particular, frontal alpha, had a direct correlation with one’s ability to learn a video game. Here, we decided to see if a similar result would hold true for baseball batting performance. We used a portable electroencephalographic (EEG) data collection system to record EEG data prior to batting practice. Participants sat quietly in a room with the portable EEG unit affixed to their head. Participants then stared in silence at a fixation cross in the center of a computer screen for 30 seconds and then counted backwards from 1000 by 7’s for 30 seconds as a masking task while background EEG was recorded. Player’s were then immediately given live batting practice and with performance judged by three different coaches on four different criteria. The four criteria were: batting mechanics, power, contact, and the batter’s ability to recognize good and bad pitches. Post-hoc, a frequency decomposition was performed on each participant’s EEG data to obtain power in all frequency bands. A correlation analysis of EEG power and batting performance showed that beta power and not alpha power predicted the subsequent performance of the batter. Importantly, a high correlation and significance show that predicting a batter’s performance with a portable EEG system, specifically the MUSE Headband, is highly plausible. / Graduate / 2018-08-09

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