A knot is an embedding of a circle S in a 3-manifold M , usually taken to be R or S. In the 1920’s Alexander and Briggs [2, §4] and Reidemeister [23] observed that questions about ambient isotopy of polygonal knots in R can be reduced to combinatorial questions about knot diagrams. These are labeled planar graphs with overcrossings and undercrossings marked, representing a projection of the kno...

Knots can occur in biopolymers such as DNA and peptides. In our previous study, we systematically investigated the effects of intra-chain interactions on knots and found that long-range repulsions can surprisingly tighten knots. Here, we use this knowledge to trap a knot into tight conformations in Langevin dynamics simulations. By trapping, we mean that the free energy landscape with respect t...

BACKGROUND Suturing and knot tying are basic skills for surgeons. Performing these tasks laparoscopically can be a tedious, time-consuming endeavor associated with much frustration. We evaluated a mechanically assisted suture and pretied knot device (Quik-Stitch) for performing the basic tasks of suturing and knot tying. METHODS We performed a time study using 1) intracorporeal suturing and k...

We introduce disk matrices which encode the knotting of all subchains in circular knot configurations. The disk matrices allow us to dissect circular knots into their subknots, i.e. knot types formed by subchains of the global knot. The identification of subknots is based on the study of linear chains in which a knot type is associated to the chain by means of a spatially robust closure protoco...

Bjorklund, L. & Moberg, L. 1999. Modelling the inter-tree variation of knot properties for Pinus syluestris in Sweden. Studia Forestalia Suecica 207. 23 pp. ISSN 0039-3150. With the help of the Swedish Scots Pine Stem Bank, the variation of internal knot properties was studied between stems and stands in sections in which the vertical variation was small. By means of explanatory site, stand and...

Knot polynomials have been used to detect and classify knots in biomolecules. Computation of knot polynomials in DNA and protein molecules have revealed the existence of knotted structures, and provided important insight into their topological structures. However, conventional knot polynomials are not well suited to study RNA molecules, as RNA structures are determined by stem regions which are...

This is an expository paper discussing some parallels between the Khovanov and knot Floer homologies. We describe the formal similarities between the theories, and give some examples which illustrate a somewhat mysterious correspondence between them.

To record what has happened, ancient people tie knots. | I ching, the Chinese classic of 1027{771 B.C. Knots are fascinating objects. When fastening a rope, the distinction between a knot and a \slip-knot" (one that can be undone by pulling) must have been recognized very early in human history. We even developed a subconscious about knots: When we are puzzled or troubled, we have a feeling of ...

We say that a given knot J ⊂ S is detected by its knot Floer homology and A-polynomial if whenever a knot K ⊂ S has the same knot Floer homology and the same A-polynomial as J , then K = J . In this paper we show that every torus knot T (p, q) is detected by its knot Floer homology and A-polynomial. We also give a one-parameter family of infinitely many hyperbolic knots in S each of which is de...

It was predicted recently that sufficiently complex knots on a linear wormlike chain can have a metastable size, preventing their spontaneous expansion. We tested this prediction via computer simulations for 7(1) and 10(151) knots. We calculated the equilibrium distributions of knot size S for both knots. By using the umbrella sampling, we were able to obtain the distributions over a wide range...