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Full-Text Articles in Mathematics
Tropical Algebra, Graph Theory, & Foreign Exchange Arbitrage, Bradley A. Mason
Tropical Algebra, Graph Theory, & Foreign Exchange Arbitrage, Bradley A. Mason
Senior Honors Projects, 2010-2019
We answer the question, given n currencies and k trades, how can a maximal arbitrage opportunity be found and what is its value? To answer this question, we use techniques from graph theory and employ a max-plus algebra (commonly known as tropical algebra). Further, we show how the tropical eigenvalue of a foreign exchange rate matrix relates to arbitrage among the currencies and can be found algorithmically. We finish by employing time series techniques to study the stability of maximal, high-currency arbitrage opportunities.
A Computational Investigation Of Large Gaps In Contingency Tables, Noah J. Watson
A Computational Investigation Of Large Gaps In Contingency Tables, Noah J. Watson
Senior Honors Projects, 2010-2019
Integer programming can be used to find upper and lower bounds on the cells of a multi-dimensional contingency table using the information from the released margins. The linear relaxation of these programs also provides bounds and the discrepancy between these bounds, the integer programming gap, can be large. While the more notable examples of large gaps have been shown to be rare, here we provide some results on the rarity of large gaps on small tables.
Population Projection And Habitat Preference Modeling Of The Endangered James Spinymussel (Pleurobema Collina), Marisa Draper
Population Projection And Habitat Preference Modeling Of The Endangered James Spinymussel (Pleurobema Collina), Marisa Draper
Senior Honors Projects, 2010-2019
The James Spinymussel (Pleurobema collina) is an endangered mussel species at the top of Virginia’s conservation list. The James Spinymussel plays a critical role in the environment by filtering and cleaning stream water while providing shelter and food for macroinvertebrates; however, conservation efforts are complicated by the mussels’ burrowing behavior, camouflage, and complex life cycle. The goals of the research conducted were to estimate detection probabilities that could be used to predict species presence and facilitate field work, and to track individually marked mussels to test for habitat preferences. Using existing literature and mark-recapture field data, these goals were accomplished …