Related papers: The multiplet structure of the genetic code, in on…
Decoding sequences that stem from multiple transmissions of a codeword over an insertion, deletion, and substitution channel is a critical component of efficient deoxyribonucleic acid (DNA) data storage systems. In this paper, we consider a…
We introduce an algorithm that conjectures the structure of a permutation class in the form of a disjoint cover of "rules"; similar to generalized grid classes. The cover is usually easily verified by a human and translated into an…
Nowadays there are several classes of constrained codes intended for different applications. The following two large classes can be distinguished. The first class contains codes with local constraints; for example, the source data must be…
In this study we determine the structure of reversible DNA codes obtained from skew cyclic codes. We show that the generators of such DNA codes enjoy some special properties. We study the structural properties of such family of codes and we…
All known terrestrial proteins are coded as continuous strings of ~20 amino acids. The patterns formed by the repetitions of elements in groups of finite sequences describes the natural architectures of protein families. We present a method…
We supply basic tools for the study of the topological order of a multiplet which is an eigenspace of a finite-dimensional normal operator with continuous parameters. We allow intrinsic degeneracies within the multiplet where a well-known…
Present day data allow significant reconsideration of ideas on mechanisms underlying the degeneracy in the genetic code. Here a hypothesis is presented which links the degeneracy to possible conformational alterations in the codon-anticodon…
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,…
We give algorithms to compute decompositions of a given polynomial, or more generally mixed tensor, as sum of rank one tensors, and to establish whether such a decomposition is unique. In particular, we present methods to compute the…
With the number of sequenced genomes now over one hundred, and the availability of rough functional annotations for a substantial proportion of their genes, it has become possible to study the statistics of gene content across genomes. Here…
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,…
A primitive $k$-batch code encodes a string $x$ of length $n$ into string $y$ of length $N$, such that each multiset of $k$ symbols from $x$ has $k$ mutually disjoint recovering sets from $y$. We develop new explicit and random coding…
A permutation-invariant quantum code on $N$ qudits is any subspace stabilized by the matrix representation of the symmetric group $S_N$ as permutation matrices that permute the underlying $N$ subsystems. When each subsystem is a complex…
It is a well-known fact that genetic sequences may contain sections with repeated units, called repeats, that differ in length over a population, with a length distribution of geometric type. A simple class of recombination models with…
We introduce a geometric invariant of knots in the three-sphere, called the first-order genus, that is derived from certain 2-complexes called gropes, and we show it is computable for many examples. While computing this invariant, we draw…
Motivated by the sequence reconstruction problem from traces in DNA-based storage, we consider the problem of designing codes for the deletion channel when multiple observations (or traces) are available to the decoder. We propose simple…
Imposing a minimum principle in the framework of the so called crystal basis model of the genetic code, we determine the structure of the minimum set of 22 anticodons which allows the translational-transcription for animal mitochondrial…
To synthesize peptides alongside the RNAs making the so-called RNA world, some genetic coding involving RNA had to develop. Herein, it is proposed that the first real-coding setup was a direct one, made up of continuous poly-tRNA-like…
A system-level genetic code is a hypothetical genetic code that exclusively or preferentially codes systems of interacting coadapted parts. System-level genetic codes differ from part-level genetic codes in which each discrete part is coded…
This note presents a descending method that allows us to classify quotients of Reed-Muller codes of lenghth 128 under the action of the affine general linear group.