 
Summary: June 15, 2005 18:7 WSPC/Trim Size: 9in x 6in for Review Volume chapter11
CHAPTER 11
TYING DOWN OPEN KNOTS: A STATISTICAL METHOD
FOR IDENTIFYING OPEN KNOTS WITH APPLICATIONS
TO PROTEINS
Kenneth C. Millett
Department of Mathematics, University of California, Santa Barbara
Santa Barbara, CA 93016, USA
Email: millett@math.ucsb.edu
Homepage: http://www.math.ucsb.edu/~millett/KM.html
Benjamin M. Sheldon
Department of Mathematics, University of California, Santa Barbara
Santa Barbara, CA 93016, USA
Email: bensheldon@umail.ucsb.edu
A mathematical knot is simply a closed curve in threespace. Classifying
open knots, or knots that have not been closed, is a relatively unexplored
area of knot theory. In this note, we report on our study of open random
walks of varying length, creating a collection of open knots. Following
the strategy of Millett, Dobay and Stasiak, an open knot is closed by
connecting its two open endpoints to a third point, lying on a large
