We discuss a new general phenomenon pertaining to tiling models of quasicrystal growth. It is known that with Penrose tiles no (de-terministic) local matching rules exist which guarantee defect-free tiling for regions of arbitrary large size. We prove that this property holds quite generally: namely, that the emergence of defects in quasicrystal growth is unavoidable for all aperiodic tiling mo...

Statistical analysis on tiling array data is extremely challenging due to the astronomically large number of sequence probes, high noise levels of individual probes and limited number of replicates in these data. To overcome these difficulties, we first developed statistical error estimation and weighted ANOVA modeling approaches to high-density tiling array data, especially the former based on...

A regular n-sided polygon can be split into n n-part spidrons. Alternate forms of linked triangular structures such as ladders and creepers can also be used to subdivide regular polygons. In the present paper new symmetric designs with inscribed regular polygons are constructed using n 6-part ladders. Also several new tiling patterns are created using these designs General Terms Tiling, Algorit...

MOTIVATION Chromatin immunoprecipitation followed by hybridization to a genomic tiling microarray (ChIP-chip) is a routinely used protocol for localizing the genomic targets of DNA-binding proteins. The resolution to which binding sites in this assay can be identified is commonly considered to be limited by two factors: (1) the resolution at which the genomic targets are tiled in the microarray...

Statistical analysis on tiling array data is extremely challenging due to the astronomically large number of sequence probes, high noise levels of individual probes and limited number of replicates in these data. To overcome these difficulties, we first developed statistical error estimation and weighted ANOVA modeling approaches to high-density tiling array data, especially the former based on...

A musical rhythm pattern is a sequence of note onsets. We consider repeating rhythm patterns, called rhythm cycles. Many typical rhythm cycles from Africa are asymmetric, meaning that they cannot be broken into two parts of equal duration. More precisely: if a rhythm cycle has a period of 2n beats, it is asymmetric if positions x and x + n do not both contain a note onset. We ask the questions ...

We investigate the dynamics of tiling dynamical systems and their deformations. If two tiling systems have identical combinatorics, then the tiling spaces are homeomorphic, but their dynamical properties may differ. There is a natural map I from the parameter space of possible shapes of tiles to H of a model tiling space, with values in R. Two tiling spaces that have the same image under I are ...