Closed curves and geodesics with two self-intersections on the Punctured torus

We classify the free homotopy classes of closed curves with minimal self intersection number two on a once punctured torus, T , up to homeomorphism. Of these, there are six primitive classes and two imprimitive. The classification leads to the topological result that, up to homeomorphism, there is a unique curve in each class realizing the minimum self intersection number. The classification yields a complete classification of geodesics on hyperbolic T which have self intersection number two. We also derive new results on the Markoff spectrum of diophantine approximation; in particular, exactly three of the imprimitive classes correspond to families of Markoff values below Hall's ray.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41628/1/605_2005_Article_BF01317313.pd

Visualizing Implicit Queries For Information Management and Retrieval

In this paper, we describe the use of similarity metrics in a novel visual environment for storing and retrieving favorite web pages. The similarity metrics, called Implicit Queries, are used to automatically highlight stored web pages that are related to the currently selected web page. Two experiments explored how users manage their personal web information space with and without the Implicit Query highlighting and later retrieve their stored web pages. When storing and organizing web pages, users with Implicit Query highlighting generated slightly more categories. Implicit Queries also led to faster web page retrieval time, although the results were not statistically significant