Fault-tolerance is a critical issue for biochemical computation. Recent theoretical work on algorithmic self-assembly has shown that error correcting tile sets are possible, and that they can achieve exponential decrease in error rates with a small increase in the number of tile types and the scale of the construction [24, 4]. Following [17], we consider the issue of applying similar schemes to...

The number of distinguishable inherent structures of a liquid is the key component to understanding the thermodynamics of glass formers. In the case of hard potential systems such as hard discs, spheres and ellipsoids, an inherent structure corresponds to a collectively jammed configuration. This work develops a tiling based approach to counting inherent structures that constructs packings by c...

Introduction: The relationship between elevated level of gas and particulate pollutants with increased mortality resulting from cardiovascular and respiratory diseases has been presented in epidemiological studies. Although the principal mechanisms of diseases are still unknown, inflammatory and homeostatic processes have been known to be related to this issue. Accordingly, this study was condu...

Tiling or supernode transformation has been widely used to improve locality in multi-level memory hierarchies, as well as to efficiently execute loops onto parallel architectures. However, automatic code generation for tiled loops can be a very complex compiler work due to non-rectangular tile shapes and arbitrary iteration space bounds. In this paper, we first survey code generation methods fo...

Agglutinative languages presenl rich morphology and for sonic applications they lleed deep analysis at word level. Tile work here presenled proposes a model for designing a full nlorphological analyzer. The model integrates lhe two-level fornlalisnl alld a ullificalion-I)asod fornialisni. In contrast to other works, we propose to separate the treatment of sequential and non-sequetTtial mou)hola...

Molecular self-assembly, the formation of large structures by small pieces of matter sticking together according to simple local interactions, is a ubiquitous phenomenon. A challenging engineering goal is to design a few molecules so that large numbers of them can self-assemble into desired complicated target objects. Indeed, we would like to understand the ultimate capabilities and limitations...

Self-assembly is fundamental to both biological processes and nanoscience. Key features of self-assembly are its probabilistic nature and local programmability. These features can be leveraged to design better self-assembled systems. The conventional Tile Assembly Model (TAM) developed by Winfree using Wang tiles is a powerful, Turing-universal theoretical framework which models varied self-ass...

The tile packing problem is a challenging combinatorial puzzle based on tiles with colored edges or colored corners. In its different incarnations, the puzzle gives rise to a number of interesting problems. In this paper, we sketch the background of the tile packing problem and present solutions to the puzzle. We hope that this work will stimulate further interest in this puzzle amongst readers...

We study the problem of covering Rd by overlapping translates of a convex polytope, such that almost every point of Rd is covered exactly k times. Such a covering of Euclidean space by a discrete set of translations is called a k-tiling. The investigation of simple tilings by translations (which we call 1-tilings in this context) began with the work of Fedorov [5] and Minkowski [15], and was la...

In this paper we design tile self-assembly systems which assemble arbitrarily close approximations to target squares with arbitrarily high probability. This is in contrast to previous work which has only considered deterministic assemblies of a single shape. Our technique takes advantage of the ability to assign tile concentrations to each tile type of a self-assembly system. Such an assignment...