Suppose that K ⊆ G is a graph embedded in some surface and F is a face of K with singular branches e and f such that F ∪ ∂F is homeomorphic to the torus minus an open disk. An embedding extension of K to G is a simple embedding if each K-bridge embedded in F is attached to at most one appearance of e and at most one appearance of f on ∂F . Combinatorial structure of minimal obstructions for exi...

Forces in the spindle that align and segregate chromosomes produce a steady poleward flux of kinetochore microtubules (MTs [kMTs]) in higher eukaryotes. In several nonmammalian systems, flux is driven by the tetrameric kinesin Eg5 (kinesin 5), which slides antiparallel MTs toward their minus ends. However, we find that the inhibition of kinesin 5 in mammalian cultured cells (PtK1) results in on...

In Graph Minors III, Robertson and Seymour conjecture that the tree-width of a graph and that of its dual differ by at most one. In this paper, we prove that given a hypergraph H on a surface of Euler genus k, the tree-width of H∗ is at most the maximum of tw(H) + 1 + k and the maximum size of a hyperedge of H∗ minus one.

If G = (V, E, σ) is a finite signed graph, a function f : V → {−1, 0, 1} is a minusdominating function (MDF) of G if f(u) +summation over all vertices v∈N(u) of σ(uv)f(v) ≥ 1 for all u ∈ V . In this paper we characterize signed paths and cycles admitting an MDF.

The properties of the small fraction of tetrodotoxin (TTX)-sensitive Na channels that remain open in the steady state were studied in internally dialyzed voltage clamped squid giant axons. The observed Ussing flux ratio exponent (n') of 0.97 plus minus 0.03 (calculated from simultaneous measurements of TTX-sensitive current and (22)Na efflux) and nonindependent behavior of Na current at high in...