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- Kenneth C Millett, Philip J Davis, Ruben Hersh, Elena Anne
- 1998

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)

- Joanna I Sułkowska, Eric J Rawdon, Kenneth C Millett, Jose N Onuchic, Andrzej Stasiak
- Proceedings of the National Academy of Sciences…
- 2012

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)

- Eric J Rawdon, John C Kern, Michael Piatek, Patrick Plunkett, Andrzej Stasiak, Kenneth C Millett
- 2008

Momentary configurations of long polymers at thermal equilibrium usually deviate from spherical symmetry and can be better described, on average, by a prolate ellipsoid. The asphericity and nature of asphericity (or prolateness) that describe these momentary ellipsoidal shapes of a polymer are determined by specific expressions involving the three principal… (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)

- Kenneth C Millett, Benjamin 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)

- 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)

For a polygonal knot K, it is shown that a tube of radius R(K), the polygonal thickness radius, is an embedded torus. Given a thick configuration K, perturbations of size r < R(K) define satellite structures, or local knotting. We explore knotting within these tubes both theoretically and numerically. We provide bounds on perturbation radii for which we can… (More)

- Eric J Rawdon, Kenneth C Millett, Joanna I Sułkowska, Andrzej Stasiak
- Biochemical Society transactions
- 2013

The backbones of proteins form linear chains. In the case of some proteins, these chains can be characterized as forming linear open knots. The knot type of the full chain reveals only limited information about the entanglement of the chain since, for example, subchains of an unknotted protein can form knots and subchains of a knotted protein can form… (More)

- Michal Jamroz, Wanda Niemyska, Eric J. Rawdon, Andrzej Stasiak, Kenneth C. Millett, Piotr Sułkowski +1 other
- Nucleic Acids Research
- 2015

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)

There is a striking qualitative similarity among the graphs of the relative probabilities of corresponding knot types across a wide range of random polygon models. In many cases one has theoretical results describing the asymptotic decay of these knot probabilities but, in the finite range, there is little theoretical knowledge and a variety of functional… (More)