Threaded Rings that Swim in Excitable Media.

Cardiac tissue and the Belousov-Zhabotinsky reaction provide two notable examples of excitable media that support scroll waves, in which a filament core is the source of spiral waves of excitation. Here we consider a novel topological configuration in which a closed filament loop, known as a scroll ring, is threaded by a pair of counterrotating filaments that are perpendicular to the plane of the ring and end on the boundary of a thin medium. We simulate the dynamics of this threaded ring (thring) in the photosensitive Belousov-Zhabotinsky excitable medium, using the modified Oregonator reaction-diffusion equations. These computations reveal that the threading topology induces an exotic motion in which the thring swims in the plane of the ring. We propose a light templating protocol to create a thring in the photosensitive Belousov-Zhabotinsky medium and provide experimental confirmation that this protocol indeed yields a thring.

Almost positive links are strongly quasipositive.

We prove that any link admitting a diagram with a single negative crossing is strongly quasipositive. This answers a question of Stoimenow's in the (strong) positive. As a second main result, we give a simple and complete characterization of link diagrams with quasipositive canonical surface (the surface produced by Seifert's algorithm). As applications, we determine which prime knots up to 13 crossings are strongly quasipositive, and we confirm the following conjecture for knots that have a canonical surface realizing their genus: a knot is strongly quasipositive if and only if the Bennequin inequality is an equality.

Unknotting the interactive effects of learning processes on cultural evolutionary dynamics.

Forms of non-random copying error provide sources of inherited variation yet their effects on cultural evolutionary dynamics are poorly understood. Focusing on variation in granny and reef knot forms, we present a mathematical model that specifies how these variant frequencies are affected by non-linear interactions between copying fidelity, mirroring, handedness and repetition biases. Experiments on adult humans allowed these effects to be estimated using approximate Bayesian computation and the model is iterated to explain the prevalence of granny over reef knots in the wild. Our study system also serves to show conditions under which copying fidelity drives heterogeneity in cultural variants at equilibrium, and that interaction between unbiased forms of copying error can skew cultural variation.

Normal and premature rupture of fetal membranes at term delivery differ in regional chemotactic activity and related chemokine/cytokine production.

A gradient of immunological mediators exists in the fetal membranes from the periplacental zone (PZ) to the rupture zone (RZ) at term delivery (rupture of fetal membranes [ROM]). However, it is unknown if this gradient is different in premature rupture of these tissues (premature rupture of fetal membranes [PROM]). We therefore analyzed leukocyte chemotactic activity and chemokine/cytokine production in fetal membrane zones in ROM and PROM. In ROM, leukocyte chemotactic activity increased from the PZ to the RZ; however, this did not occur in PROM. This was due to consistently elevated leukocyte chemotactic activity in PROM compared to ROM tissues. In the RZ, ROM was characterized by increased T-cell attraction and high levels of chemokine (C-X-C motif) ligand 8 (CXCL-8)/interleukin 8, and PROM by increased granulocyte attraction and high levels of granulocyte-macrophage colony-stimulating factor and CXCL-10/interferon gamma-induced protein 10. We conclude that normal and premature rupture of fetal membranes differ in regional chemotactic activity and related chemokine/cytokine production, which may represent evidence for differential mechanisms of rupture at term delivery.