Black tunnels and hammocks

Extending hammocks for parallelism detection∗

Introduction and basic definitions Finding the independent parts of a Control Flow Graph (CFG) is important for exposing program parallelism. Two types of instruction dependences constrain the order of execution, dataand control-dependences (CD). Abstracting from data-dependences, it is useful to study the idealized parallelism allowed by program control structure. CD’s are assumed as the depen...

Hammocks and the Algorithm of Nazarova-roiter

Unknotting Tunnels and Seifert Surfaces

Let K be a knot with an unknotting tunnel γ and suppose that K is not a 2-bridge knot. There is an invariant ρ = p/q ∈ Q/2Z, p odd, defined for the pair (K, γ). The invariant ρ has interesting geometric properties: It is often straightforward to calculate; e. g. for K a torus knot and γ an annulus-spanning arc, ρ(K, γ) = 1. Although ρ is defined abstractly, it is naturally revealed when K ∪ γ i...

Tunnels in digital objects

An important concept in digital geometry for computer imagery is that of tunnel. In this paper we obtain a formula for the number of tunnels as a function of the number of the object vertices, pixels, holes, connected components, and 2 × 2 grid squares. It can be used to test for tunnel-freedom a digital object, in particular a digital curve.

Enzymes with molecular tunnels.

As a result of recent advances in molecular cloning, protein expression, and X-ray crystallography, it has now become feasible to examine complicated protein structures at high resolution. For those enzymes with multiple catalytic sites, a common theme is beginning to emerge; the existence of molecular tunnels that connect one active site with another. The apparent mechanistic advantages render...