This paper describes Ribbon (Ruby Instructions Becoming Basic Object Notation), a new representation written in a text-based data format using Ruby syntax. The design principle of Ribbon is good readability and simplicity of structured data representation. An important feature of Ribbon is an executable representation. Once Ribbon-related definitions are loaded into a Ruby interpreter, the repr...

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...

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...

The ribbon graph decomposition of moduli space is a non-compact orbi-cell complex homeomorphic to Mg,n×R>0. This was introduced by Harer-Mumford-Thurston [Har86] and Penner [Pen87], and used to great effect by Kontsevich [Kon92, Kon94] in his proof of the Witten conjecture and his construction of classes in moduli spaces associated to A∞ algebras. In this note, I discuss in some detail the dual...

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...

Giant synaptic terminals of goldfish bipolar neurons allow direct studies of presynaptic mechanisms underlying neurotransmitter release and its modulation. Calcium influx via L-type calcium channels of the terminal triggers synaptic vesicle exocytosis, which can be monitored in isolated terminals by means of the associated changes in membrane capacitance. Information about the kinetics and calc...

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...

Adviser: Professor Carina Curto Mathematical modeling has broad applications in neuroscience whether we are modeling the dynamics of a single synapse or the dynamics of an entire network of neurons. In Part I, we model vesicle replenishment and release at the photoreceptor synapse to better understand how visual information is processed. In Part II, we explore a simple model of neural networks ...