Secreted proteins coded by parasitism genes expressed in esophageal gland cells mediate infection and parasitism of plants by root-knot nematodes. An essential parasitism gene, designated as 16D10, encodes a conserved root-knot nematode secretory peptide that stimulates root growth and functions as a ligand for a plant transcription factor. Plants were engineered to silence this parasitism gene...

Tying secure knots is essential in arthroscopic surgery. A new slip knot for arthroscopic shoulder surgery is described. Locking of the knot is accomplished by pulling the post strand. Knot tying is simple and a low-profile, secure knot is produced.

This paper is a self-contained introduction to the Jones polynomial that assumes no background in knot theory. We define the Jones polynomial, prove its invariance, and use it to tackle two problems in knot theory: detecting amphichirality and finding bounds on the crossing numbers. 1. Preliminaries 1.1. Definitions. For the most part, it is enough to think of a knot as something made physicall...

Knot insertion is the operation of obtaining a new representation of a B-spline curve by introducing additional knot values to the defining knot vector. The new curve has control points consisting of the original control points and additional new control points corresponding to the number of new knot values. So knot insertions give additional control points which provide extra shape control wit...

A p–colouring of a knot K is a surjective homomorphism ρ from its knot group G := π1(S − K) to D2p := {t, s|t2 = sp = 1, tst = sp−1} the dihedral group of order 2p, when p is any odd integer. The pair (K, ρ) is called a p–coloured knot. It is a well-known fact that we can encode ρ as a colouring of arcs of a knot diagram by elements of Zp (the cyclic group of order p), subject to the ‘colouring...

The Ramsey number is known for only a few specific knots and links, namely the Hopf link and the trefoil knot (although not published in periodicals). We establish the lower bound of all Ramsey numbers of any knot to be one greater than its stick number. 1 Background and Definitions The study of Ramsey numbers of knots can be found at the intersection of knot theory and graph theory. 1.1 Knot T...

Numerical simulations indicate that there exist conformations of the unknot, tied on a finite piece of rope, entangled in such a manner, that they cannot be disentangled to the torus conformation without cutting the rope. The simplest example of such a gordian unknot is presented. Knots are closed, self-avoiding curves in the 3-dimensional space. The shape and size of a knot, i.e. its conformat...

In [23] we introduced a knot invariant for a null-homologous knot K in an oriented three-manifold Y , which is closely related to the Heegaard Floer homology of Y (c.f. [21]). In this paper we investigate some properties of these knot homology groups for knots in the three-sphere. We give a combinatorial description for the generators of the chain complex and their gradings. With the help of th...

The group of any nontrivial torus knot, hyperbolic 2-bridge knot, or hyperbolic knot with unknotting number one contains infinitely many elements, none the automorphic image of another, such that each normally generates the group.

The knot vectors of a B-spline surface determine the basis functions hereby, together with the control points, the shape of the surface. Knot manipulations and their influence on the shape of curves have been investigated in several papers (see e.g. [4] and [5]). The computations can be made very efficiently, if the basis functions and the vector function of the B-spline surface are represented...