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...

During the realist revival in the early years of this century, philosophers of various persuasions were concerned to investigate the ontology of truth. That is, whether or not they viewed truth as a correspondence, they were interested in the extent to which one needed to assume the existence of entities serving some role in accounting for the truth of sentences. Certain of these entities, such...

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...

In this paper, we study a class of polycubes that tile the space by translation in a non lattice periodic way. More precisely, we construct a family of tiles indexed by integers with the property that Tk is a tile having k ≥ 2 has anisohedral number. That is k copies of Tk are assembled by translation in order to form a metatile. We prove that this metatile is lattice periodic while Tk is not a...

ABSfRACf The Pitman closeness criterion is an intrinsic measure of the comparative behavior of two estimators. based solely on their joint distribution. It generally entails less stringent regulari ty condi tions than in other measures. But. there are some undesirable features of this measure. The past few years have witnessed some developments on Pitman-closeness in its tributaries. and a crit...

We prove that for every nite tile set, isometric copies of which can tile euclidean n-space, there is a tiling with the local iso-morphism property.

We settle a number of questions in variants of Winfree’s abstract Tile Assembly Model (aTAM), a model of molecular algorithmic self-assembly. In the “hierarchical” aTAM, two assemblies, both consisting of multiple tiles, are allowed to aggregate together, whereas in the “seeded” aTAM, tiles attach one at a time to a growing assembly. Adleman, Cheng, Goel, and Huang (Running Time and Program Siz...