Iteration space tiling is a well-explored programming and compiler technique to enhance program locality. Its performance benefit appears obvious, as the ratio of processor versus memory speed increases continuously. In an effort to include a tiling pass into an advanced parallelizing compiler, we have found that the interaction of tiling and parallelization raises unexplored issues. Applying e...

Tiling is a key transformation used for coarsening the granularity of parallelism and improving locality. It is known that current stateof-the-art compiler approaches for tiling affine loop nests make use of sufficient, i.e., conservative conditions for the validity of tiling. These conservative conditions, which are used for static scheduling, miss tiling schemes for which the tile schedule is...

The gap-labelling group, which provides the set of possible values of the integrated density of states on gaps in the spectrum of a Hamiltonian describing particles in a tiling, is frequently related to the cohomology of the tiling. We present explicit results for the cohomology of many well-known tilings obtained from the cut and projection method with codimension 2, including the (generalized...

We describe a neural network model in which the tiling of the input array is learned by performing a joint localization and classification task. After training, the optimal tiling that emerges resembles the eccentricity dependent tiling of the human retina.

A monotypic simple tiling by a 14-face polyhedron that does not admit an isohedral tiling is described. The tiling is triclinic and contains four distinct, but combinatorially equivalent, kinds of tile.