Self-assembly is a process found everywhere in the Nature. In particular, it is known that DNA self-assembly is Turing universal. Thus one can do arbitrary computations or build nano-structures using DNA self-assembly. In order to understand the DNA self-assembly process, many mathematical models have been proposed in the literature. In particular, abstract Tile Assembly Model (aTAM) received m...

We propose an iterative approach to constructing regular shapes by self-assembly. Unlike previous approaches, which construct a shape in one go, our approach constructs a final shape by alternating the steps of assembling and disassembling, increasing the size of the shape iteratively. This approach is embedded into an extended hexagonal tile assembly system, with dynamic strength transformatio...

We present a tile system for assembling a counter of width K and height N = 2 on top of a seed-row in optimum time Θ(N). Our counter works at temperature 2. Earlier known constructions either took sub-optimal time or required temperature 3. Using existing techniques, our system for assembling a counter from a seed row can be extended into a system for assembling an N × N square in optimum time ...

The purpose of this paper is to study optimality of circular neighborbalanced block designs when neighbor effects are present in the model. In the literature many optimality results are established for direct effects and neighbor effects separately, but few for total effects, that is, the sum of direct effect of treatment and relevant neighbor effects. We show that circular neighbor-balanced de...