We prove that if a set X ⊆ Z2 weakly self-assembles at temperature 1 in a deterministic (Winfree) tile assembly system satisfying a natural condition known as pumpability, then X is a finite union of semi-doubly periodic sets. This shows that only the most simple of infinite shapes and patterns can be constructed using pumpable temperature 1 tile assembly systems, and gives evidence for the the...

We present an technique for developing a single, aperiodic (or universal) tile that does not overlap. We provide two examples, constructed by converting overlapping regions of Gummelt’s decagon cover to interleaved regions in a porous tile. Each is a bounded, dense, sponge-like set of points in 2 that tiles the plane aperiodically. One tile has measure zero, the other has positive measure every...

Algorithmic self-assembly, a generalization of crystal growth, has been proposed as a mechanism for bottom-up fabrication of complex nanostructures and autonomous DNA computation. In principle, growth can be programmed by designing a set of molecular tiles with binding interactions that enforce assembly rules. In practice, however, errors during assembly cause undesired products, drastically re...

A subset V ⊆ Fn2 is a tile if F n 2 can be covered by disjoint translates of V . In other words, V is a tile if and only if there is a subset A ⊆ Fn2 such that V + A = Fn2 uniquely (i.e., v + a = v ′ + a′ implies that v = v′ and a = a′ where v, v′ ∈ V and a, a′ ∈ A). In some problems in coding theory and hashing we are given a putative tile V , and wish to know whether or not it is a tile. In t...

Self-assembly is a fundamental process by which supramolecular species form spontaneously from their components. This process is ubiquitous throughout the life chemistry and is central to biological information processing. Algorithms for solving many mathematical and computational problems via tile self assembly has been proposed by many researchers in the last decade. In particular tile set fo...

In this paper, we introduce a novel approach to guide tile size selection by employing analytical models to limit empirical search within a subspace of the full search space. Two analytical models are used together: 1) an existing conservative model, based on the data footprint of a tile, which ignores intra-tile cache block replacement, and 2) an aggressive new model that assumes optimal cache...

Tile logic extends rewriting logic by taking into account side-eeects and rewriting synchronization. These aspects are very important when we model process calculi, because they allow us to express the dynamic interaction between processes and \the rest of the world". Since rewriting logic is the semantic basis of several language implementation eeorts, an executable speciication of tile system...

Installing subsurface tile drain systems in poorly drained claypan soils to improve corn ( L.) yields could potentially increase environmental phosphorus (P) loss through the tile drainage system. The objectives of the study were to quantify the average concentration and loss of ortho-P in tile drain water from a claypan soil and to determine whether managed subsurface drainage (MD) could reduc...

An aperiodic tile set was first constructed by R. Berger while proving the undecidability of the domino problem. It turned out that aperiodic tile sets appear in many topics ranging from logic (the Entscheidungsproblem) to physics (quasicrystals). We present a new construction of an aperiodic tile set that is based on Kleene’s fixed-point construction instead of geometric arguments. This constr...

Actinomvcosis is now so widely known as a patilological entity that the presentation of another series of cases should be justified by at least some unusual feature of the syndrome or a contribution to tile treatment of this difficult disease. The fact that over 80 per cent of cases in humans occur in tile gastro-intestinal or respiratory system (Boyd 1943) is strong evidence in favour of infec...