Related papers: On the optimality of the standard genetic code: th…
We present a unifying approach to quantum error correcting code design that encompasses additive (stabilizer) codes, as well as all known examples of nonadditive codes with good parameters. We use this framework to generate new codes with…
We calculate the optimality of a doublet precursor to the canonical genetic code with respect to mitigating the effects of point mutations and compare our results to corresponding ones for the canonical genetic code. We find that the…
Although several synonymous codons can encode the same aminoacid, this symmetry is generally broken in natural genetic systems. In this article, we show that the symmetry breaking can result from selective pressures due to the violation of…
We demonstrate how a genetic algorithm solves the problem of minimizing the resources used for network coding, subject to a throughput constraint, in a multicast scenario. A genetic algorithm avoids the computational complexity that makes…
The codons, sixtyfour in number, are distributed over the coding parts of DNA sequences. The distribution function is the plot of frequency-versus-rank of the codons. These distributions are characterised by parameters that are almost…
Gene expression levels carry information about signals that have functional significance for the organism. Using the gap gene network in the fruit fly embryo as an example, we show how this information can be decoded, building a dictionary…
Stopping sets play a crucial role in failure events of iterative decoders over a binary erasure channel (BEC). The $\ell$-th stopping redundancy is the minimum number of rows in the parity-check matrix of a code, which contains no stopping…
Graph codes play an important role in photonic quantum technologies as they provide significant protection against qubit loss, a dominant noise mechanism. Here, we develop methods to analyse and optimise measurement-based tolerance to qubit…
In this work, we investigate a challenging problem, which has been considered to be an important criterion in designing codewords for DNA computing purposes, namely secondary structure avoidance in single-stranded DNA molecules. In short,…
This paper studies two problems that are motivated by the novel recent approach of composite DNA that takes advantage of the DNA synthesis property which generates a huge number of copies for every synthesized strand. Under this paradigm,…
The genesis of the stand genetic code is considered as a result of a fusion of two AU- and GC-codes distributed in two dominant and two recessive domains. The fusion of these codes is described with simple empirical rules. This formal…
A (tandem) duplication of length $ k $ is an insertion of an exact copy of a substring of length $ k $ next to its original position. This and related types of impairments are of relevance in modeling communication in the presence of…
Evolutionary theorizing resembles building an aircraft while also piloting it; new results change the scaffold for older ideas, requiring revised strategy to remain airborne. A calculated kinetic pathway exists that, under explicit…
Encoding data as a set of unordered strings is receiving great attention as it captures one of the basic features of DNA storage systems. However, the challenge of constructing optimal redundancy codes for this channel remained elusive. In…
When polygenic traits are under stabilizing selection, many different combinations of alleles allow close adaptation to the optimum. If alleles have equal effects, all combinations that result in the same deviation from the optimum are…
The rank-modulation scheme has been recently proposed for efficiently storing data in nonvolatile memories. Error-correcting codes are essential for rank modulation, however, existing results have been limited. In this work we explore a new…
We consider the problem of slotted asynchronous coded communication, where in each time frame (slot), the transmitter is either silent or transmits a codeword from a given (randomly selected) codebook. The task of the decoder is to decide…
This note represents the further progress in understanding the determination of the genetic code by Golden mean (Rakocevic, 1998). Three classes of amino acids that follow from this determination (the 7 "golden" amino acids, 7 of their…
We generalize the notion of the stopping redundancy in order to study the smallest size of a trapping set in Tanner graphs of linear block codes. In this context, we introduce the notion of the trapping redundancy of a code, which…
Due to its high data density and longevity, DNA is considered a promising medium for satisfying ever-increasing data storage needs. However, the diversity of errors that occur in DNA sequences makes efficient error-correction a challenging…