Encoding Color Sequences in Active Tile Self-Assembly

Constructing patterns is a well-studied problem in both theoretical and experimental self-assembly with much of the work focused on multi-staged assembly. In this paper, we study building 1D patterns in a model of active self assembly: Tile Automata. This is a generalization of the 2-handed assembly model that borrows the concept of state changes from Cellular Automata. In this work we further develop the model by partitioning states as colors and show lower and upper bounds for building patterned assemblies based on an input pattern. Our first two sections utilize recent results to build binary strings along with Turing machine constructions to get Kolmogorov optimal state complexity for building patterns in Tile Automata, and show nearly optimal bounds for one case. For affinity strengthening Tile Automata, where transitions can only increase affinity so there is no detachment, we focus on scaled patterns based on Space Bounded Kolmogorov Complexity. Finally, we examine the affinity strengthening freezing case providing an upper bound based on the minimum context-free grammar. This system utilizes only one dimensional assemblies and has tiles that do not change color

Haplotype Assembly: An Information Theoretic View

This paper studies the haplotype assembly problem from an information theoretic perspective. A haplotype is a sequence of nucleotide bases on a chromosome, often conveniently represented by a binary string, that differ from the bases in the corresponding positions on the other chromosome in a homologous pair. Information about the order of bases in a genome is readily inferred using short reads provided by high-throughput DNA sequencing technologies. In this paper, the recovery of the target pair of haplotype sequences using short reads is rephrased as a joint source-channel coding problem. Two messages, representing haplotypes and chromosome memberships of reads, are encoded and transmitted over a channel with erasures and errors, where the channel model reflects salient features of high-throughput sequencing. The focus of this paper is on the required number of reads for reliable haplotype reconstruction, and both the necessary and sufficient conditions are presented with order-wise optimal bounds.Comment: 30 pages, 5 figures, 1 tabel, journa