Extended Alexander groups are used to define an invariant for open virtual strings. Examples of non-commuting open strings and a ribbon-concordance obstruction are given. An example is given of a slice open virtual string that is not ribbon. Definitions are extended to open n-strings.

Connes and Kreimer have discovered the Hopf algebra structure behind the renormalization of Feynman integrals. We generalize the Hopf algebra to the case of ribbon graphs, i.e. to the case of theories with matrix fields. The Hopf algebra is naturally defined in terms of surfaces corresponding to ribbon graphs. As an example, we discuss the renormalization of Φ4 theory and the 1/N expansion.

We describe a general algorithm for generating various families of ribbon tableaux and computing their spin polynomials. This algorithm is derived from a new matricial coding. An advantage of this new notation lies in the fact that it permits one to generate ribbon tableaux with skew shapes.

We determine which among the 3-stranded pretzel knots P (p, q, r) with p, q, r odd are smoothly slice. We show that each of these is in fact ribbon thus proving the slice-ribbon conjecture for this family of knots.

The submillimeter wave or terahertz (THz) band (1 mm-100 microm) is one of the last unexplored frontiers in the electromagnetic spectrum. A major stumbling block hampering instrument deployment in this frequency regime is the lack of a low-loss guiding structure equivalent to the optical fiber that is so prevalent at the visible wavelengths. The presence of strong inherent vibrational absorptio...

The rod photoreceptor's synaptic terminal (or spherule) uses an elaborate synaptic structure to signal absorption of one or more photons to its postsynaptic targets. This structure includes one or two synaptic ribbons inside the terminal and a pouch-like "invagination" outside the terminal, into which enter a widely variable number of incoming fibers and postsynaptic targets-central elements su...

We report an experimental and theoretical study of single mode, guided wave propagation in plastic ribbons. Using cylindrical THz optics, we obtain excellent quasioptic coupling between freely propagating THz waves and a single TM 0 waveguide mode. Dispersive, low-loss propagation is observed within the experimental bandwidth of 0.1–3.5 THz for 2-cm-wide, high-density polyethylene ribbon wavegu...

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...