Self-assembly, the process by which objects autonomously come together to form complex structures, is omnipresent in the physical world. A systematic study of self-assembly as a mathematical process has been initiated. The individual components are modelled as square tiles on the infinite two-dimensional plane. Each side of a tile is covered by a specific “glue”, and two adjacent tiles will sti...

(1) BACKGROUND: Many disorders and diseases of agricultural produce change the physical features of surfaces of plant organs; in terms of russet, e.g., of apple or pear, affected fruit peel becomes rough and brown in color, which is associated with changes in light reflection; (2) OBJECTIVE AND METHODS: The objective of the present project was an interdisciplinary approach between horticultural...

Riparian buffers are a proven practice for removing NO from overland flow and shallow groundwater. However, in landscapes with artificial subsurface (tile) drainage, most of the subsurface flow leaving fields is passed through the buffers in drainage pipes, leaving little opportunity for NO removal. We investigated the feasibility of re-routing a fraction of field tile drainage as subsurface fl...

It is shown that an equilateral convex pentagon tiles the plane if and only if it has two angles adding to 180 o or it is the unique equilateral convex pentagon with Although the area of mathematical tilings has been of interest for a long time there is still much to be discovered. We do not even know which convex polygons tile the plane. Furthermore, for those polygons which do tile, new tilin...

Endovascular therapy of arterial occlusive disease has made impressive progress since the first balloon angioplasty conceived by Dr Charles T. Dotter in 1964, followed by the first peripheral balloon angioplasty by Dr Andreas Gruntzig in 1974. Each advancement has frequently faced skepticism after the initial clinical experience. Thankfully, skepticism was met in kind with research seeking faci...

Tile logic extends rewriting logic, taking into account rewriting with side-eeects and rewriting synchronization. Since rewriting logic is the semantic basis of several language implementation eeorts, it is interesting to map tile logic back into rewriting logic in a conservative way, to obtain executable speciications of tile systems. The resulting implementation requires a meta-layer to contr...

Majumder, Reif and Sahu have presented a stochastic model of reversible, error-permitting, two-dimensional tile self-assembly, and showed that restricted classes of tile assembly systems achieved equilibrium in (expected) polynomial time. One open question they asked was how much computational power would be added if the model permitted multiple nucleation, i.e., independent groups of tiles gro...

In this paper we show that passive self-assembly in the context of the tile self-assembly model is capable of performing fuel efficient, universal computation. The tile self-assembly model is a premiere model of self-assembly in which particles are modeled by four-sided squares with glue types assigned to each tile edge. The assembly process is driven by positive and negative force interactions...

By PAUL HELLER, JOHN VAN STONE, DAVID APPLE AND RICHARD D. COLEMAN A RARE FORM of hereditary anemia characterized by hypochromia of the erythrocytes in tile presence of increased iron stores has been designated by Heilmeyer1’2 as “hereditary hypochromic sideroachrestic anemia.” Garby and his co-workers3 and Hei1meyer1’ ’ have suggested that in this disorder heme synthesis is disturbed possibly ...

We study the minimal complexity of tilings of a plane with a given tile set. We note that any tile set admits either no tiling or some tiling with O(n) Kolmogorov complexity of its (n× n)squares. We construct tile sets for which this bound is tight: all (n × n)-squares in all tilings have complexity Ω(n). This adds a quantitative angle to classical results on non-recursivity of tilings – that w...