We study the structures of a ribbon or ladder polymer immersed in poor solvents. The anisotropic bending rigidity coupled with the surface tension leads ribbon polymers to spontaneous formation of highly anisotropic condensates in poor solvents. Unlike ordinary flexible polymers these condensates undergo a number of distinct layering transitions as a function of chain length or solvent quality,...

Synaptic ribbons are presynaptic structures formed by the self-association of RIBEYE-the main structural component of ribbon synapses. RIBEYE consists of two domains: a unique N-terminal A-domain and a C-terminal B-domain that is identical to the transcription co-repressor C-terminal binding protein 2 (CtBP2). Previous studies in cell lines have shown that RIBEYE A-domain alone is sufficient to...

A ribbon is a first-order thickening of a non-singular curve. We show that a compactification of the moduli space of generalized line bundles on a ribbon is given by the Simpson moduli space of semi-stable sheaves. We then describe the geometry of this space, determining the irreducible components, connectedness, and the smooth locus.

This paper gives mathematical models for flat knotted ribbons, and makes specific conjectures for the least length of ribbon (for a given width)) needed to tie the trefoil knot and the figure eight knot. The first conjecture states that (for width one) the least length of ribbon needed to tie an open-ended trefoil knot is

We determine the (smooth) concordance order of the 3-stranded pretzel knots P (p, q, r) with p, q, r odd. We show that each one of finite order is, in fact, ribbon, thereby proving the slice-ribbon conjecture for this family of knots. As corollaries we give new proofs of results first obtained by Fintushel-Stern and Casson-Gordon.

By studying “points of the underlying quantum groups”of coquasitriangular Hopf (face) algebras, we construct ribbon categories for each lattice models without spectral parameter of both vertex and face type. Also, we give a classification of the braiding and the ribbon structure on quantized classical groups and modular tensor categories closely related to quantum SU(N)Linvariants of 3-manifolds.

We give necessary conditions of a surface-knot to be ribbon concordant to another, by introducing a new variant of the cocycle invariant of surface-knots in addition to using the invariant already known. We demonstrate that twist-spins of some torus knots are not ribbon concordant to their orientation reversed images.

We show that the fundamental group of a ribbon disc complement in the four ball associated with certain prime dense and alternating surface arc projections are CAT(0) and δ-hyperbolic. Using this we produce an infinite class of free-by-cyclic CAT(0), δ-hyperbolic multi ribbon disc groups. AMS Subject classification: 57M05, 57M50, 20F65, 20F67.

Nanohelices of cadmium sulfide (CdS) have been made by the mineralization of supramolecular organic ribbons. A schematic representation of how coiled CdS helices (yellow) can be templated from a twisted ribbon (blue) by growth along one face of the ribbon is shown top right.