In December 2011 Computer Science and Math students held Capstone Presentations. Below are a sampling of the students’ Capstones with abstracts of their research:
“The set chromatic number of a graph”
Angela Adams, Ashley Knappenberger, Meagan Leas and Alyssa
The abstract: The paper “The Set Chromatic Number of a Graph” by Chartrand, Okamoto, Zhang, and Rasmussen defines the set chromatic number of a graph as well as defines propositions that relate to finding the set chromatic number. The set chromatic number of G, χs(G) is a generalization of χ(G). It uses neighborhood color sets in order to color every adjacent vertex in a graph G. The minimum number of neighbor-distinguishing colors required is called the set chromatic number χs(G).
“Investing stock market volatility in bull and bear markets”
Xiana Clark and Yanra Pichardo
The abstract: To observe how bullish and bearish economic periods affect stock market volatility. Using these observations to create a linear regresin model which can predict how correlated volatility is with average daily returns, average rate of trading volume, exchange rate, unemployment, inflation, presidential approval, oil and gold.
“Geodesic Graphs with an Exploration of Their Cartesian Products”
Yunus Akkaya, Heather Urban, Marlana Young and Rommy Marquez
The abstract: To introduce a concept, geodesic graphs, from a vertex in a connected graph. We researched some properties of geodesic graphs. We showed that a geodesic graph from a vertex x forms a bipartite graph. We also investigate the double geodesics of a graph, Cartesian product graphs, and the Cartesian product of geodesic graphs.
“A time series approach to analyzing stock market volatility and returns”
Talal Butt and Arteid Memaj
The abstract: Our project tests whether the returns and volatility from 1970-2010 of the Dow Jones Industrial Average and S&P 500 could be modeled applying well-known time-series models including the Autoregressive AR (p) model, Moving Average MA (q) model and a combination of the two known as ARMA(p,q). The results suggest that the return series are too random to model effectively. The volatility series, however, fits an ARMA (p,q). After using the autocorrelation and partial autocorrelation of previous lags to determine the order of the model, we were able to forecast volatility of both portfolios for 2011. Comparisons of the forecasted data to the actual data confirm the accuracy of the prediction. The second hypothesis tested by our project is whether the series before 1970 and after 1970 fit different models. However, we found that despite the increase in the volume of stocks traded after 1970, the best-fit model was the same for both time periods.
Other Capstones included: “Grinvin: a graph conjecturing engine” by Daniel Cohen; “Re-sampling and exact statistical methodologies” by Nicole Coolbaugh, Anthony Hennigan, and Megan Gillespie; “Using independent tests to analyze dependent data: what does wrong” by Samantha Brown; and “A new version of the Busy Beaver problem” by David Abdul-Malak and Megan Gillespie.