We consider two operations on an edge of an embedded graph (or equivalently a ribbon graph): giving a half-twist to the edge, and taking the partial dual with respect to the edge. These two operations give rise to an action of S3 |E(G)|, the ribbon group, on G. The action of the ribbon group on embedded graphs extends the concepts of duality, partial duality, and Petrie duality. We show that th...

Synaptic ribbons are presynaptic protein structures found at many synapses that convey graded, "analog" sensory signals in the visual, auditory, and vestibular pathways. Ribbons, typically anchored to the presynaptic membrane and surrounded by tethered synaptic vesicles, are thought to regulate or facilitate vesicle delivery to the presynaptic membrane. No direct evidence exists, however, to in...

The goal of this study was to evaluate the mechanisms underlying Vernier acuity, over a range of spatial scales using narrow-band Vernier stimuli and oblique masking. Specifically, the test stimuli consisted of a pair of vertical ribbons of horizontal cosine grating with a vertical Vernier offset between the ribbons. These stimuli have two important advantages for studying Vernier acuity: (1) t...

Why are these synapses special? Because the electrical signals they transmit are not the same as those in other parts of the brain. Conventional synapses convey information arriving as a ‘pulse code’; action potentials lasting a few milliseconds trigger a transient burst of vesicle fusion and the amplitude of the action potential is fixed. But ribbon synapses transmit ‘analogue signals’, such a...

We present ‘Ribbon Proofs’, a graphical proof system for the Logic of Bunched Implications (BI). We give the informal, graphical, notation, we formalise the system algebraically and sketch the proof of its soundness and completeness. We discuss the spatial and geometrical nature of the proof system and its relation to BI’s spatial model theory.