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We describe how deletion-correcting codes may be enhanced to yield codes with double-strand DNA-sequence codewords. This enhancement involves abstractions of the pertinent aspects of DNA; it nevertheless ensures specificity of binding for all pairs of single strands derived from its codewords—the key desideratum of DNA codes– i.e. with binding feasible only… (More)

Let [t] represent a nite population with t elements. Suppose we have an unknown d-family of k-subsets of [t]. We refer to as the set of positive k-complexes.I nt h egroup testing for complexes problem, must be identied by performing 0, 1 tests on subsets or pools of [t]. A pool is said to be positive if it completely contains a complex; otherwise the pool… (More)

We discuss the concept of t-gap block isomorphic subsequences and use it to describe new abstract string metrics that are similar to the Levenshtein insertion-deletion metric. Some of the metrics that we define can be used to model a thermodynamic distance function on single-stranded DNA sequences. Our model captures a key aspect of the nearest neighbor… (More)

DNA nanotechnology often requires collections of oligonucleotides called "DNA free energy gap codes" that do not produce erroneous crosshybridizations in a competitive muliplexing environment. This paper addresses the question of how to design these codes to accomplish a desired amount of work within an acceptable error rate. Using a statistical… (More)

We present a group testing approach to identify the first d vertices with the highest betweenness centrality. Betweenness centrality (BC) of a vertex is the ratio of shortest paths that pass through it and is an important metric in complex networks. The Brandes algorithm computes the BC cumulatively over all vertices. Approximate BC of a single vertex can… (More)

- Arkadii D’yachkov, Vyacheslav Rykov, David Torney, Sergey Yekhanin
- 2004

— We introduce the distance concept between two q-ary n-sequences, 2 ≤ q < n, called partition distance. This distance is a metric in the space of partitions of a finite n-set, where each partition contains ≤ q disjoint subsets of the n-set. For the metric, we study codes called q-partition codes which can be applied to statistical analysis of psychological… (More)

We will discuss superimposed codes and non-adaptive group testing designs arising from the potentialities of compressed genotyping models in molecular biology. The given paper was motivated by the 30th anniversary of D'yachkov-Rykov recurrent upper bound on the rate of superimposed codes published in 1982. We were also inspired by recent results obtained… (More)