It has been shown [6] that, within the McAlister inverse monoid [9], whose elements can be seen as overlapping one-dimensional tiles, the class of languages recognizable by finite monoids collapses compared with the class of languages definable in Monadic Second Order Logic (MSO). This paper aims at capturing the expressive power of the MSO definability of languages of tiles by means of a weake...

We present a theoretical model for self-assembling tiles with flexible branches motivated by DNA branched junction molecules. We encode an instance of a “problem” as a pot of such tiles, and a “solution” as an assembled complete complex without any free sticky ends (called ports), whose number of tiles is within predefined bounds. We develop an algebraic representation of this self-assembly pro...

We study self-affine tiles which tile the n-dimensional real vector space with respect to a crystallographic group. First we define classes of graphs that allow to determine the neighbors of a given tile algorithmically. In the case of plane tiles these graphs are used to derive a criterion for such tiles to be homeomorphic to a disk. As particular application, we will solve a problem of Gelbri...

Equal bit rate is assigned to all tiles of an image when compressed with JPEG2000 standard. This bit rate is selected without taking information contents of the tiles into account. This results into poor performance of JPEG2000 standard for the tiles that have higher complexity. We can improve performance of JPEG2000 by assigning higher bit rates to complex tiles. An entropy based weighted bit ...

A web geographical information system is a typical service-intensive application. Tile prefetching and cache replacement can improve cache hit ratios by proactively fetching tiles from storage and replacing the appropriate tiles from the high-speed cache buffer without waiting for a client's requests, which reduces disk latency and improves system access performance. Most popular prefetching st...

In this paper we introduce a simple probabilistic model, hierarchical tiles, for 0–1 data. A basic tile (X, Y, p) specifies a subset X of the rows and a subset Y of the columns of the data, i.e., a rectangle, and gives a probability p for the occurrence of 1s in the cells of X × Y . A hierarchical tile has additionally a set of exception tiles that specify the probabilities for subrectangles of...

A new approach to automatic generation of tile mosaic images containing square tiles suitable for the information hiding purpose is proposed. The generated tile mosaic image contains no overlapping tiles, and the orientations of the tiles are deterministic. The properties of the generated image allow simple tile feature detection, and result in efficient data embedding and extraction. The orien...

The Wang Tiles method is a successful and effective technique for the representation of 2D-texture or 3D-geometry. In this paper we present a new method to fill Wang tiles with a 2D-FON distribution or a 3D-geometry in order to achieve a more efficient runtime. We extend the Wang Tiles method to include information about their position. We further demonstrate how the individual tiles are filled...

Deciding if a given set of Wang tiles admits a tiling of the plane is decidable if the number of Wang tiles (or the number of colors) is bounded, for a trivial reason, as there are only finitely many such tilesets. We prove however that the tiling problem remains undecidable if the difference between the number of tiles and the number of colors is bounded by 43. One of the main new tool is the ...

1 Methods Estimated bound on effective error rates: Given an assembly of tiles on a scaffold of N repeat units in which each tile has a mismatch with its lower or right neighbor with independent probability = 1−p, we would like to bound the probability that the assembly contains a particular pattern of M tiles that has been observed. In particular, we are interested in the probability of seeing...