Related papers: The multiplet structure of the genetic code, in on…
To increase the information capacity of DNA storage, composite DNA letters were introduced. We propose a novel channel model for composite DNA in which composite sequences are decomposed into ordered standard non-composite sequences. The…
Biologists have long sought a way to explain how statistical properties of genetic sequences emerged and are maintained through evolution. On the one hand, non-random structures at different scales indicate a complex genome organisation. On…
A Z2-triple cyclic code of block length (r,s,t) is a binary code of length r+s+t such that the code is partitioned into three parts of lengthsr,s andt such that each of the three parts is invariant under the cyclic shifts of the…
The classical family of Reed-Solomon codes consist of evaluations of polynomials over the finite field $\mathbb{F}_q$ of degree less than $k$, at $n$ distinct field elements. These are arguably the most widely used and studied codes, as…
Based on the generic construction of linear codes, we construct linear codes over the ring $\Bbb Z_4$ via posets of the disjoint union of two chains. We determine the Lee weight distributions of the quaternary codes. Moreover, we obtain…
In this paper, we consider the degenerate multi-poly-Bernoulli numbers and polynomials which are defined by means of the multiple polylogarithms and degenerate versions of the multi-poly-Bernoulli numbers and polynomials. We investigate…
A quadratic line complex is a three-parameter family of lines in projective space P^3 specified by a single quadratic relation in the Plucker coordinates. Fixing a point p in P^3 and taking all lines of the complex passing through p we…
In answer to a question of Eggleton, we prove that the complete multigraph on 5 vertices with edge multiplicity 6, namely $K_{5}^{(6)}$, has a decomposition into 5 copies of the family of trees of order 5 and that $K_{7}^{(22)}$ has a…
Several genetic programming systems are created, each solving a different problem. In these systems, the median number of generations G needed to evolve a working program is measured. The behavior of G is observed as the difficulty of the…
Living organisms produce metabolites of many types via their metabolisms. Especially, flavonoids, a kind of secondary metabolites, of plant species are interesting examples. Since plant species are believed to have specific flavonoids with…
This work deals with the presence of defect structures in generalized sine-Gordon models. The models are described by periodic potentials, with substructure having one, two, three or more distinct topological sectors, with multiplicity one,…
We prove that the clique number of the Paley graph is at most $\sqrt{p/2} + 1$, and that any supposed additive decompositions of the set of quadratic residues can only come from co-Sidon sets.
Gene assembly in ciliates is one of the most involved DNA processings going on in any organism. This process transforms one nucleus (the micronucleus) into another functionally different nucleus (the macronucleus). We continue the…
A typical protein structure is a compact packing of connected alpha-helices and/or beta-strands. We have developed a method for generating the ensemble of compact structures a given set of helices and strands can form. The method is tested…
We study a minimal model for genome evolution whose elementary processes are single site mutation, duplication and deletion of sequence regions and insertion of random segments. These processes are found to generate long-range correlations…
A heuristic diagram of the evolution of the standard genetic code is presented. It incorporates, in a way that resembles the energy levels of an atom, the physical notion of broken symmetry and it is consistent with original ideas by Crick…
The genetic code has a high level of error robustness. Using values of hydrophobicity scales as a proxy for amino acid character, and the Mean Square measure as a function quantifying error robustness, a value can be obtained for a genetic…
In the near future, all the human genes will be identified. But understanding the functions coded in the genes is a much harder problem. For example, by using block entropy, one has that the DNA code is closer to a random code then written…
Due to their sequential nature, traditional DNA synthesis methods are expensive in terms of time and resources. They also fabricate multiple copies of the same strand, introducing redundancy. This redundancy can be leveraged to enhance the…
This paper shows that an arbitrary generic submanifold in a complex manifold can be deformed into a 1-parameter family of generic submanifolds satisfying strong nondegeneracy conditions. The proofs use a careful analysis of the jet spaces…