The Reshetikhin-Turaev invariant, Turaev’s TQFT, and many related constructions rely on the encoding of certain tangles (n-string links, or ribbon n-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 and admi...

Recently, Dasbach, Futer, Kalfagianni, Lin, and Stoltzfus extended the notion of a Tait graph by associating a set of ribbon graphs (or equivalently, embedded graphs) to a link diagram. Here we focus on Seifert graphs, which are the ribbon graphs of a knot or link diagram that arise from Seifert states. We provide a characterization of Seifert graphs in terms of Eulerian subgraphs. This charact...

Piccolo is the largest known cytomatrix protein at active zones of chemical synapses. A growing number of studies on conventional chemical synapses assign Piccolo a role in the recruitment and integration of molecules relevant for both endo- and exocytosis of synaptic vesicles, the dynamic assembly of presynaptic F-actin, as well as the proteostasis of presynaptic proteins, yet a direct functio...

The activity of individual afferent neurones in the mammalian cochlea can be driven by neurotransmitter released from a single synaptic ribbon in a single inner hair cell. Thus, a ribbon synapse must be able to transmit all the information on sound frequency, intensity and timing carried centrally. This task is made still more demanding by the process of binaural sound localization that utilize...

In vivo cellulose ribbon assembly by the Gram-negative bacterium Acetobacter xylinum can be altered by incubation in carboxymethylcellulose (CMC), a negatively charged water-soluble cellulose derivative, and also by incubation in a variety of neutral, water-soluble cellulose derivatives. In the presence of all of these substituted celluloses, normal fasciation of microfibril bundles to form the...

The Golgi apparatus is composed of stacks of cisternae laterally connected by tubules to form a ribbon-like structure. At the onset of mitosis, the Golgi ribbon is broken down into discrete stacks, which then undergo further fragmentation. This ribbon cleavage is required for G2/M transition, which thus indicates that a 'Golgi mitotic checkpoint' couples Golgi inheritance with cell cycle transi...

A promising energy source for many current and future applications is a ribbon-like device that could simultaneously harvest and store energy. Due to the high flexibility and weavable property, a fabric/matrix made using these ribbons could be highly beneficial for powering wearable electronics. Unlike the approach of using two separate devices, here we report a ribbon that integrates a solar c...

In [LLT] Lascoux, Leclerc and Thibon introduced symmetric functions Gλ which are spin and weight generating functions for ribbon tableaux. This article is aimed at studying these functions in analogy with Schur functions. In particular we will describe: • a Pieri and dual-Pieri formula for ribbon functions, • a ribbon Murnaghan-Nakayama formula, • ribbon Cauchy and dual Cauchy identities, • and...

A closer look at an example introduced by Livingston & Melvin and later studied by Miyazaki shows that a plumbing of two fibered ribbon knots (along their fiber surfaces) may be algebraically slice yet not ribbon. Trivially, the connected sum (i.e., 2-gonal Murasugi sum) of ribbon knots is ribbon. Non-trivially [6, 1], any Murasugi sum of fibered knots (along their fiber surfaces) is fibered. I...

Excitatory and inhibitory neurons in the CNS are distinguished by several features, including morphology, transmitter content, and synapse architecture [1]. Such distinctions are exemplified in the vertebrate retina. Retinal bipolar cells are polarized glutamatergic neurons receiving direct photoreceptor input, whereas amacrine cells are usually monopolar inhibitory interneurons with synapses a...