Complexity of Interlocking Polyominoes

Polyominoes are a subset of polygons which can be constructed from integer-length squares fused at their edges. A system of polygons P is interlocked if no subset of the polygons in P can be removed arbitrarily far away from the rest. It is already known that polyominoes with four or fewer squares cannot interlock. It is also known that determining the interlockedness of polyominoes with an arbitrary number of squares is PSPACE hard. Here, we prove that a system of polyominoes with five or fewer squares cannot interlock, and that determining interlockedness of a system of polyominoes including hexominoes (polyominoes with six squares) or larger polyominoes is PSPACE hard.Comment: 18 pages, 15 figure

Perceiving Personality through Sentiment Analysis

The goal of this project is to find new ways to understand the human personality through the analysis of writing style over long periods of time. Techniques from Natural Language Processing and Sentiment Analysis are used to perform the analysis. The data used for analysis consists of large sets of personal letters written by John Adams, Thomas Jefferson, and George Washington - these three figures were chosen because they all have large, publicly available collections of letters from the Massachusetts Historical Society and the University of Virginia Press, and they were all forced to deal with a similar set of events in their lives. We attempt to analyze the overall writing styles of the presidents and how they change over time. In addition, we try to identify the major events of their life and analyze the ways that these presidents write about them. This analysis allows us to pinpoint differences in the ways that significant life events are perceived, what emotions they trigger, and how each person responds to them; thus, we find new ways to understand the human thought process and how it differs from individual to individual