We analyze the stability of naturally curved, inextensible elastic ribbons. In experiments, we first show that a loop formed using a metallic strip can become unstable if its radius is smaller than its natural radius of curvature (undercurved case): the loop then folds onto itself into a smaller, multiply-covered loop. Conversely, a multi-covered, overcurved metallic strip can unfold dynamicall...

The ribbon synapse can release a stream of transmitter quanta at very high rates. Although the ribbon tethers numerous vesicles near the presynaptic membrane, most of the tethered vesicles are held at a considerable distance from the plasma membrane. Therefore, it remains unclear how their contents are released. We evoked prolonged bouts of exocytosis from a retinal bipolar cell, fixed within s...

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...