On Critical Relative Distance of DNA Codes for Additive Stem Similarity

We consider DNA codes based on the nearest-neighbor (stem) similarity model which adequately reflects the "hybridization potential" of two DNA sequences. Our aim is to present a survey of bounds on the rate of DNA codes with respect to a thermodynamically motivated similarity measure called an additive stem similarity. These results yield a method to analyze and compare known samples of the nearest neighbor "thermodynamic weights" associated to stacked pairs that occurred in DNA secondary structures.Comment: 5 or 6 pages (compiler-dependable), 0 figures, submitted to 2010 IEEE International Symposium on Information Theory (ISIT 2010), uses IEEEtran.cl

On Multistage Learning a Hidden Hypergraph

Learning a hidden hypergraph is a natural generalization of the classical group testing problem that consists in detecting unknown hypergraph $H_{un}=H(V,E)$ by carrying out edge-detecting tests. In the given paper we focus our attention only on a specific family $F(t,s,\ell)$ of localized hypergraphs for which the total number of vertices $|V| = t$, the number of edges $|E|\le s$, $s\ll t$, and the cardinality of any edge $|e|\le\ell$, $\ell\ll t$. Our goal is to identify all edges of $H_{un}\in F(t,s,\ell)$ by using the minimal number of tests. We develop an adaptive algorithm that matches the information theory bound, i.e., the total number of tests of the algorithm in the worst case is at most $s\ell\log_2 t(1+o(1))$. We also discuss a probabilistic generalization of the problem.Comment: 5 pages, IEEE conferenc