Research Experience for Undergraduates
I am an active participant in Westfield State University’s Research Experience for Undergraduates (2015). This is a program created by the WSU Mathematics Department to give students the opportunity to do mathematical research at the undergraduate level. Below is my original abstract.
I began working on this project with my faculty advisor, Dr. Julian F. Fleron, during the Spring semester of 2014 and worked on it during my free time. As our research progressed, we quickly realized that this was a much more involved problem. In the Fall semester 2015, our project proposal was approved to be my REU project as well as the topic for my Senior Honors Thesis.
Our final intention in regards to this project is to incorporate our findings into GIS (beta-versions of code and sample exercises can be found on the ICAI page) and our results in terms of optimization to be published in a mathematical journal.
Intercardinal Adjacencies: A New Landscape Metric
Geographic Information Systems (GIS) have become crucial to daily life.
They are particularly useful in scientific areas, including landscape ecology
where they can measure the density of land relative to water using landscape
indices. Current landscape indices like FRAGSTATS’ aggregation index only
measure cardinal adjacencies – edge to edge adjacencies in the N/S/E/W direc-
tions. Essential to this method is knowledge of the optimal congurations, a
result established by Haray and Harboth in “Extremal Animals” (1976).
GIS experts have asked us to help them develop a method of measuring
adjacencies which include diagonal, or corner to corner, adjacencies as well. We
call these intercardinal adjacencies. Essential is the determination of optimal
configurations – which polyominoes of each size have the greatest number of
intercardinal adjacencies. We have discovered a family of archetypes for the
optimal configurations and have found a closed-term expression for the number
of intercardinal adjacencies. We are working to prove that these families are
indeed optimal. Once completed we will work with GIS experts on integrating
this new method, called the intercardinal metric, into GIS systems.
The Intercardinal Aggregation Index
More detailed information about this work can be located directly on the Intercardinal Aggregation Index page, located under the Research tab.
Currently, this webpage is under construction and a password restriction has been implemented. If you are interested in viewing its preliminary contents, please contact me.