An axis-aligned string is a simple polygonal path, where each line segment is parallel to an axis in R. Given a graph G, a string contact representation Ψ of G maps the vertices of G to interior disjoint axis-aligned strings, where no three strings meet at a point, and two strings share a common point if and only if their corresponding vertices are adjacent in G. The complexity of Ψ is the mini...

We define and study the Magnus representation for homology cylinders generalizing the work of Kirk, Livingston and Wang [KLW] which treats the case of string links. Using this, we give a factorization formula of Alexander polynomials for three dimensional manifolds obtained by closing homology cylinders. We also show a relationship between the Gassner representation for string links and the Mag...

The 2D string approaches provide a natural way of constructing iconic indexing for images. The 2D C-string representation with an efficient cutting mechanism is more characteristic of spatial knowledge and efficient in the representation of iconic images. However, the computation of object ranks in a 2D C-string might make the inference of spatial reasoning somewhat complicated. This shortcomin...

In its recogniser form, Earley’s algorithm for testing whether a string can be derived from a grammar is worst case cubic on general context free grammars (CFG). Earley gave an outline of a method for turning his recognisers into parsers, but it turns out that this method is incorrect. Tomita’s GLR parser returns a shared packed parse forest (SPPF) representation of all derivations of a given s...

The AdS/CFT correspondence establishes a string representation for Wilson loops in N = 4 SYM theory at large N and large ’t Hooft coupling. One of the clearest manifestations of the stringy behaviour in Wilson loop correlators is the string breaking phase transition. It is shown that resummation of planar diagrams without internal vertices predicts the strong-coupling phase transtion in exactly...