We investigate the instabilities of a flat elastic ribbon subject to twist under tension and develop an integrated phase diagram of the observed shapes and transitions. We find that the primary buckling mode switches from being localized longitudinally along the length of the ribbon to transverse above a triple point characterized by a crossover tension that scales with ribbon elasticity and as...

At the presynaptic active zone, Ca²+ influx triggers fusion of synaptic vesicles. It is not well understood how Ca²+ channel clustering and synaptic vesicle docking are organized. Here, we studied structure and function of hair cell ribbon synapses following genetic disruption of the presynaptic scaffold protein Bassoon. Mutant synapses--mostly lacking the ribbon--showed a reduction in membrane...

Kinesin motors are presumed to transport various membrane compartments within neurons, but their specific in vivo functions, cargoes, and expression patterns in the brain are unclear. We have investigated the distribution of KIF3A, a member of the heteromeric family of kinesins, in the vertebrate retina. We find KIF3A at two distinct sites within photoreceptors: at the basal body of the connect...

Fast neurotransmitter release from ribbon synapses via Ca2+-triggered exocytosis requires tight coupling of L-type Ca2+ channels to release-ready synaptic vesicles at the presynaptic active zone, which is localized at the base of the ribbon. Here, we used genetic, electrophysiological, and ultrastructural analyses to probe the architecture of ribbon synapses by perturbing the function of RIM-bi...

The Interstellar Boundary Explorer (IBEX) observes a remarkable feature, the IBEX ribbon, which has energetic neutral atom (ENA) flux over a narrow region ∼20◦ wide, a factor of 2–3 higher than the more globally distributed ENA flux. Here, we separate ENA emissions in the ribbon from the distributed flux by applying a transparency mask over the ribbon and regions of high emissions, and then sol...

The transformation behavior of an embedded shape memory alloy (SMA) ribbon was investigated experimentally and numerically. Single SMA ribbons (55% Ni, 45% Ti) were pre-strained to 1% and then embedded in a room-temperature-cured epoxy resin. The embedded ribbons were heated resistively to a temperature above the austenite start temperature to induce transformation. The development of displacem...

We investigate the rich morphologies of an electrically charged flexible ribbon, which is a prototype for many beltlike structures in biology and nanomaterials. Long-range electrostatic repulsion is found to govern the hierarchical buckling of the ribbon from its initially flat shape to its undulated and out-of-plane twisted conformations. In this process, the screening length is the key contro...

The Reshetikhin-Turaev invariant, Turaev's TQFT, and many related constructions rely on the encoding of certain ribbon tangles (n-string links, or n-ribbon handles) as n-forms on the coend of a ribbon category. We introduce the monoidal category of Hopf diagrams, and describe a universal encoding of ribbon string links as Hopf diagrams. This universal encoding is an injective monoidal functor a...

This thesis begins with the study of a class of symmetric functions {x} which are generating functions for ribbon tableaux (hereon called ribbon functions), first defined by Lascoux, Leclerc and Thibon. Following work of Fomin and Greene, I introduce a set of operators called ribbon Schur operators on the space of partitions. I develop the theory of ribbon functions using these operators in an ...

In this note, I discuss a dual version of the ribbon graph decomposition of the moduli spaces of Riemann surfaces with boundary and marked points, which I introduced in the unpublished preprint [1], and used in [2] to construct open-closed topological conformal field theories. This dual version of the ribbon graph decomposition is a compact orbi-cell complex with a natural weak homotopy equival...