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In the fifteen years since the first edition of The Mathematical Experience there have been many important efforts to enlarge the public understanding of and support for contemporary mathematics. Despite these efforts little if any progress is apparent. Why? First, the effectiveness of many mathematics teachers, including college and university… (More)

The protein topology database KnotProt, http://knotprot.cent.uw.edu.pl/, collects information about protein structures with open polypeptide chains forming knots or slipknots. The knotting complexity of the cataloged proteins is presented in the form of a matrix diagram that shows users the knot type of the entire polypeptide chain and of each of its… (More)

- Patrick Plunkett, Michael Piatek, Akos Dobay, John C. Kern, Kenneth C. Millett, Andrzej Stasiak +1 other
- 2006

Previous work on radius of gyration and average crossing number has demonstrated that polymers with fixed topology show a different scaling behavior with respect to these characteristics than polymers with unrestricted topology. Using numerical simulations, we show here that the difference in the scaling behavior between polymers with restricted and… (More)

We present here a nonbiased probabilistic method that allows us to consistently analyze knottedness of linear random walks with up to several hundred noncorrelated steps. The method consists of analyzing the spectrum of knots formed by multiple closures of the same open walk through random points on a sphere enclosing the walk. Knottedness of individual "… (More)

While analyzing all available protein structures for the presence of knots and slipknots, we detected a strict conservation of complex knotting patterns within and between several protein families despite their large sequence divergence. Because protein folding pathways leading to knotted native protein structures are slower and less efficient than those… (More)

Polypeptide chains form open knots in many proteins. How these knotted proteins fold and finding the evolutionary advantage provided by these knots are among some of the key questions currently being studied in the protein folding field. The detection and identification of protein knots are substantial challenges. Different methods and many variations of… (More)

Closed macromolecular chains may form physically knotted conformations whose relative occurrence and spatial measurements provide insight into their properties and the mechanisms acting upon them. Under the assumption of a degree of structural homogeneity, equilateral spatial polygons are a productive context within which to create mathematical models of… (More)

Using numerical simulations we investigate how overall dimensions of random knots scale with their length. We demonstrate that when closed non-self-avoiding random trajectories are divided into groups consisting of individual knot types, then each such group shows the scaling exponent of approximately 0.588 that is typical for self-avoiding walks. However,… (More)

- Kenneth C. Millett, Benjamin M. Sheldon, K. C. Millett, B. M. Sheldon
- 2005

A mathematical knot is simply a closed curve in three-space. 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… (More)

- W. B. R. LlCKORISH, K. C. MlLLETT, K. C. MILLETT
- 2004

A short proof is given, using linear skein theory, of the theorem of V.F.R. Jones that the one variable "Jones" polynomial associated to an oriented link is independent of the choice of strand orientations, up to a multiple of the variable. The Jones polynomial of an oriented link K is the element V(K) of Z[t ±ι/2) defined by tV(K +)-Γ ι V(K_) + (t 1 ' 2-r… (More)