We present ribbon proofs, a diagrammatic proof system for separation logic. Inspired by an eponymous system due to Bean, ribbon proofs emphasise the structure of a proof, so are intelligible and hence useful pedagogically. Because they contain less redundancy than proof outlines, and allow each proof step to be checked locally, they are highly scalable (and we illustrate this with a ribbon proo...

Synaptic ribbons are proteinaceous specialized electron-dense presynaptic structures found in nonspiking sensory cells of the vertebrate nervous system. Understanding the function of these structures is an active area of research (reviewed in Matthews G, Fuchs P. Nat Rev Neurosci 11: 812-822, 2010). Previous work had shown that ribbons could be effectively labeled and visualized using peptides ...

Mutations in the gene encoding Cav 1.4, CACNA1F, are associated with visual disorders including X-linked incomplete congenital stationary night blindness type 2 (CSNB2). In mice lacking Cav 1.4 channels, there are defects in the development of "ribbon" synapses formed between photoreceptors (PRs) and second-order neurons. However, many CSNB2 mutations disrupt the function rather than expression...

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...