Knot modification of B-spline curves is extensively studied in the past few years. Altering one knot value, curve points move on well-defined paths, the limit of which can be computed if the knot value tends to infinity. Symmetric alteration of two knot values can also be studied in a similar way. The extension of these limit theorems for general synchronized modification of two knots is discus...

In this paper we investigate the computational complexity of knot theoretic problems and show upper and lower bounds for planarity problem of signed and unsigned knot diagrams represented by Gauss words. Due to the fact the number of crossing in knots is unbounded, the Gauss words of knot diagrams are strings over infinite (unbounded) alphabet. For establishing the lower and upper bounds on rec...

This paper describes the "scissor-knot-pusher," an instrument that greatly facilitates the execution of knot tying during laparoscopic operations. The instrument acts in essence as an extension of the surgeon's hand and, given its rigid structure, allows the surgeon full control of the process of knot tying. Additionally, after the knot has been tightened, it is possible to cut the suture witho...

In this paper, we give a precise and workable definition of a quantum knot system, the states of which are called quantum knots. This definition can be viewed as a blueprint for the construction of an actual physical quantum system. Moreover, this definition of a quantum knot system is intended to represent the “quantum embodiment” of a closed knotted physical piece of rope. A quantum knot, as ...

The whitefly Bemisia tabaci is a major pest to agricultural crops. It transmits begomoviruses, such as Tomato yellow leaf curl virus (TYLCV), in a circular, persistent fashion. Transcriptome analyses revealed that B. tabaci knottin genes were responsive to various stresses. Upon ingestion of tomato begomoviruses, two of the four knottin genes were upregulated, knot-1 (with the highest expressio...

K not theory is usually understood to be the study of embeddings of topological spaces in other topological spaces. Classical knot theory, in particular, is concerned with the ways in which a circle or a disjoint union of circles can be embedded in R. Knots are usually described via knot diagrams, projections of the knot onto a plane with breaks at crossing points to indicate which strand passe...

Let K be a rationally null-homologous knot in a three-manifold Y . We construct a version of knot Floer homology in this context, including a description of the Floer homology of a three-manifold obtained as Morse surgery on the knot K. As an application, we express the Heegaard Floer homology of rational surgeries on Y along a null-homologous knot K in terms of the filtered homotopy type of th...

Knot fingerprints provide a fine-grained resolution of the local knotting structure of tight knots. From this fine structure and an analysis of the associated planar graph, one can define a measure of knot complexity using the number of independent unknotting pathways from the global knot type to the short arc unknot. A specialization of the Cheeger constant provides a measure of constraint on ...

We consider the relations ≥ and ≥p on the collection of all knots, where k ≥ k (respectively, k ≥p k) if there exists an epimorphism πk → πk of knot groups (respectively, preserving peripheral systems). When k is a torus knot, the relations coincide and k must also be a torus knot; we determine the knots k that can occur. If k is a 2-bridge knot and k ≥p k, then k is a 2-bridge knot with determ...

This work presents a method for associating a class of constraint satisfaction problems to a three-dimensional knot. Given a knot, one can build a knot quandle, which is a generally an infinite, free algebra. The desired collection of problems is derived from the finite quotients of the knot quandle by applying theory that relates finite algebras to constraint languages. Along the way, notions ...