Self-assembly, the process by which objects autonomously come together to form complex structures, is omnipresent in the physical world. Recent experiments in self-assembly demonstrate its potential for the parallel creation of a large number of nanostructures, including possibly computers. A systematic study of self-assembly as a mathematical process has been initiated by L. Adleman and E. Win...

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graph decomposition of the moduli spaces of Riemann surfaces with boundary and marked points, which I introduced in the unpublished preprint [1], and used in [2] to construct open-closed topological conformal field theories.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...

We show that every trivial 3-strand braid diagram contains a disk, defined as a ribbon ending in opposed crossings. Under a convenient algebraic form, the result extends to every Artin–Tits group of dihedral type, but it fails to extend to braids with 4 strands and more. The proof uses a partition of the Cayley graph and a continuity argument.

Synaptic depression at conventional synapses is usually caused by strong or prolonged stimuli, like tetanic bursts of afferent fiber discharge at high frequencies. In this issue of Neuron, Dunn and Rieke report that, in the retina, even the weakest stimuli, single photons, can lead to synaptic depression at ribbon-type synapses and adaptation of neuronal output to ambient light levels.

We show that every trivial 3-strand braid diagram contains a disk, defined as a ribbon ending in opposed crossings. Under a convenient algebraic form, the result extends to every Artin–Tits group of dihedral type, but it fails to extend to braids with 4 strands and more. The proof uses a partition of the Cayley graph and a continuity argument.

We prove that a crossing change along a double point circle on a 2-knot is realized by ribbon-moves for a knotted torus obtained from the 2-knot by attaching a 1-handle. It follows that any 2-knots for which the crossing change is an unknotting operation, such as ribbon 2-knots and twistspun knots, have trivial Khovanov-Jacobsson number. A surface-knot or -link is a closed surface embedded in 4...

Hair cells, like retinal photoreceptors and bipolar cells, encode stimuli with graded changes in membrane potential and transmit that signal through ribbon synapses to drive action potentials in associated afferent neurons (Sterling and Matthews 2005). Thus one would expect transmitter release from ribbons to vary in interesting ways from that evoked by action potentials at conventional chemica...

This paper explores the effect of impeller design on the chaotic mixing in a helical ribbon mixer. Numerical simulations using the Smoothed Particle Hydrodynamics (SPH) method are used to solve for the fluid flow around the moving impellor. The mixing flow is visualised by extracting the hyperbolic Lagrangian Coherent Structures (LCS) of the flow from the Finite-Time Lyapunov Exponent (FTLE) fi...

W. H. Tutte’s 1947 paper on a ring generated by graphs satisfying a contraction-deletion relation is extended to ribbon graphs. This ring of ribbon graphs is a polynomial ring on an infinite set of one-vertex ribbon graphs. Acknowledgements: The LSU Research Experience for Undergraduates Program is supported by a National Science Foundation grant, DMS-0648064. Page 16 RHIT Undergrad. Math. J., ...

A closed duplex DNA molecule relaxed and containing nucleosomes has a different linking number from the same molecule relaxed and without nucleosomes. What does this say about the structure of the nucleosome? A mathematical study of this question is made, representing the DNA molecule by a ribbon. It is shown that the linking number of a closed ribbon can be decomposed into the linking number o...