A Wang tile [12] is a unit square with each edge colored from a finite set of colors Σ. A set S of Wang tiles is said to tile a planar grid Z if copies of tiles from S can be placed, one at each grid position, such that abutting edges of adjacent tiles have the same color. Multiple copies of any tile may be used, with no restriction on the number. If we allow the tiles to be rotated or reflecte...

The CERES-Maize model was developed to investigate how variations in environmental conditions, management decisions, and genetics interact to a€ect crop development and growth. A tile drainage subroutine was incorporated into CERES-Maize to improve soil-water and nitrogen leaching under subsurface tile drainage conditions. The purpose of this work was to evaluate the soil-water, soil-nitrogen, ...

Sommerville [10] and Davies [2] classified the spherical triangles that can tile the sphere in an edge-to-edge fashion. Relaxing this condition yields other triangles, which tile the sphere but have some tiles intersecting in partial edges. This paper determines which right spherical triangles within certain families can tile the sphere.

While the complexity of concept satisfiability in both ALCO, the basic description logic ALC enriched with nominals, and ALC(D), the extension of ALC with concrete domains, is known to be PSpace-complete, in this article we show that the combination ALCO(D) of these two logics can have a NExpTime-hard concept satisfiability problem (depending on the concrete domain D used). The proof is by a re...

Chinese medicine needs a new pan for a roast that has grown since ancient times in size and shape, a metaphorical roast that we call the industrial and information revolution. Man has not changed, but the forces that impinge on him have enormously, and the signs which had particular meanings at one time in history are no longer the same. The Tight pulse is no longer a sign of internal cold, in ...

We discuss branch points of a ne coverings and their e ects on Veech groups. In particular, this allows us to show that even if one polygon tiles another, the respective Veech groups are not necessarily commensurable. We also show that there is no universal bound on the number of Teichm uller disks passing through the same point of Teichm uller space and having incommensurable lattice Veech g...

We consider the problem of finding, for a given 2D pattern of coloured tiles, a minimal set of tile types self-assembling to this pattern in the abstract Tile Assembly Model of Winfree (1998). This Patterned self-Assembly Tile set Synthesis (PATS) problem was first introduced by Ma and Lombardi (2008), and subsequently studied by Göös and Orponen (2011), who presented an exhaustive partition-se...

Sommerville [8] and Davies [2] classified the spherical triangles that can tile the sphere in an edge-to-edge fashion. Relaxing this condition yields other triangles, which tile the sphere but have some tiles intersecting in partial edges. This paper shows that no right triangles in a certain subfamily can tile the sphere, although multilayered tilings are possible.

It is shown that the (infinite) tiling problem byWang tiles is undecidable even if the given tile set is deterministic by all four corners, i.e. a tile is uniquely determined by the colors of any two adjacent edges. The reduction is done from the Turing machine halting problem and uses the aperiodic tile set of Kari and Papasoglu. © 2008 Elsevier B.V. All rights reserved.

Herein we demonstrate that flexible DNA architectures with larger cavities can be efficiently constructed by first assembling a relatively more rigid DNA tile architecture and subsequently subtracting a center tile through fuel strand displacement; such structures are otherwise difficult to obtain if the center tile is missing in the beginning, proving a new strategy for DNA self-assembly.