Recently S. Chmutov introduced a generalization of the dual of a ribbon graph (or equivalently an embedded graph) and proved a relation between Bollobás and Riordan’s ribbon graph polynomial of a ribbon graph and of its generalized duals. Here I show that the duality relation satisfied by the ribbon graph polynomial can be understood in terms of knot theory and I give a simple proof of the rela...

We consider codimension-2 ribbon knottings of circles and 2-spheres. We find that if a given ribbon knot has two ribbon disks, those disks are related by ambient isotopy together with a finite number of local modifications to be described. This allows a complete set of moves to be developed for the representation of ribbon 2-knots by abstract or planar graphs. Similar results hold for classical...

An open ribbon is a square with one side called the seam. A closed ribbon is a cylinder with one boundary component called the seam. We sew an open (resp. closed) ribbon onto a graph by identifying the seam with an open (resp. closed) walk in the graph. A ribbon complex is a graph with a nite number of ribbons sewn on. We investigate when a ribbon complex embeds in 3-dimensional Euclidean space...

Fluorescence in situ hybridization (FISH) has opened new perspectives for the identification and classification of radiation induced chromosome aberrations. Selective staining of individual human chromosomes by chromosome painting allows a rapid microscopic observation of dicentric and translocation chromosomes. Methods of automated digital image analysis accelerate the evaluation of FISH label...

Andruskiewitsch and Schneider classify a large class of pointed Hopf algebras with abelian coradical. The quantum double of each such Hopf algebra is investigated. The quantum doubles of a family of Hopf algebras from the above classification are ribbon Hopf algebras. Introduction Quasitriangular Hopf algebras have an universal R-matrix which is a solution of the Yang-Baxter equation and their ...

BACKGROUND AND PURPOSE Large admission DWI infarct volume (>70 mL) is an established marker for poor clinical outcome in acute stroke. Outcome is more variable in patients with small infarcts (<70 mL). Percentage insula ribbon infarct correlates with infarct growth. We hypothesized that percentage insula ribbon infarct can help identify patients with stroke likely to have poor clinical outcome,...