This work focuses on the complexity of computing exact loop bounds in Multilevel Tiling. Conventional tiling techniques implement tiling using first strip-mining and afterwards loop interchange. Multilevel tiling has typically been implemented applying tiling level by level. We present a new way to implement Multilevel Tiling that deals with all levels simultaneously, performing a loop intercha...

Anderson and Putnam showed that the cohomology of a substitution tiling space may be computed by collaring tiles to obtain a substitution which “forces its border.” One can then represent the tiling space as an inverse limit of an inflation and substitution map on a cellular complex formed from the collared tiles; the cohomology of the tiling space is computed as the direct limit of the homomor...

To cover the receptive field completely and non-redundantly, neurons of certain functional groups arrange tiling of their dendrites. In Drosophila class IV dendrite arborization (da) neurons, the NDR family kinase Tricornered (Trc) is required for homotypic repulsion of dendrites that facilitates dendritic tiling. We here report that Sin1, Rictor, and target of rapamycin (TOR), components of th...

We present a tiling interpretation for kth order linear recurrences, which yields new combinatorial proofs for recurrence identities. Moreover, viewing the tiling process as a Markov chain also yields closed form Binet-like expressions for these recurrences.

In this paper we prove that if two self-similar tiling systems, with respective stretching factors λ1 and λ2, have a common factor which is a non periodic tiling system, then λ1 and λ2 are multiplicatively dependent.

2D oxide quasicrystals (OQCs) are unique structures arising from atoms positioned at the vertices of a dodecagonal triangle–square–rhombus tiling. The prototypical example for OQCs is derived BaTiO3 on Pt(111). Herein, scanning tunneling microscopy (STM) and low-energy electron diffraction (LEED) investigations layers Pd(111) reported. Upon ultrahigh vacuum (UHV) annealing, different long-range...

It takes more than a good algorithm to achieve high performance: inner-loop performance and data locality are also important. Tiling is a well-known method for parallelization and for improving data locality. However, tiling has the potential of being even more beneecial. At the nest granularity, it can be used to guide register allocation and instruction scheduling; at the coarsest level, it c...

Traditional compiler optimization theory distinguishes three separate classes of cache miss – Cold, Conflict and Capacity. Tiling for cache is typically guided by capacity miss counts. Models of cache function have not been effectively used to guide cache tiling optimizations due to model error and expense. Instead, heuristic or empirical approaches are used to select tilings. We argue that con...

In this paper, we examine rigid tilings of the four quadrants in a Cartesian coordinate system by tiling sets consisting of L-shaped polyominoes and notched rectangles. The first tiling sets we consider consist of an L-shaped polyomino and a notched rectangle, appearing from the dissection of an n×n square, and of their symmetries about the first diagonal. In this case, a tiling of a quadrant i...

Annotation of the rice (Oryza sativa) genome has evolved significantly since release of its draft sequence, but it is far from complete. Several published transcript assembly programmes were tested on RNA-sequencing (RNA-seq) data to determine their effectiveness in identifying novel genes to improve the rice genome annotation. Cufflinks, a popular assembly software, did not identify all transc...