Related papers: The naturally designed spherical symmetry in the g…
Using Barnes-Wall lattices and 1-cocycles on finite groups of monomial matrices, we give a procedure to construct tricosine spherical codes. This was inspired by a 14-dimensional code which Ballinger, Cohn, Giansiracusa and Morris…
A self-organizing approach is proposed for gene finding based on the model of codon usage for coding regions and positional preference for noncoding regions. The symmetry between the direct and reverse coding regions is adopted for reducing…
In this paper, we have examined the problem of embedding a cycle of n vertices onto a given set of n points inside a simple polygon. The goal of the problem is that the cycle must be embedded without bends and does not intersect itself and…
In this paper, we propose a sufficient condition for a family of 2-generator self-orthogonal quasi-cyclic codes with respect to Hermitian inner product. Supported in the Hermitian construction, we show algebraic constructions of good…
In the ball-stick model, interatomic cohesions are considered "sticks". But enormous details and features of the "sticks" are usually oversimplified as indexed quantities or equivocated as geometry characteristics. These indexed quantities…
We give sufficient conditions for self-orthogonality with respect to symplectic, Euclidean and Hermitian inner products of a wide family of quasi-cyclic codes of index two. We provide lower bounds for the symplectic weight and the minimum…
The coding space of protein sequences is shaped by evolutionary constraints set by requirements of function and stability. We show that the coding space of a given protein family--the total number of sequences in that family--can be…
A new approach to solve quasicrystalline atomic structures in 3-dimensional (3D) real space is presented: The atomic pair distribution function (PDF) of face centred icosahedral Ho9Mg26Zn65 [a(6D) = 2x5.18(3)A was obtained from in-house…
We present a new complementary strategy to quasicrystalline structure determination: The local atomic structure of simple icosahedral (si) Ho11Mg15Zn74 [a(6D)=5.144(3)A] in a sphere of up to r=17A was refined using the atomic pair…
Quasiperiodic patterns described by polyhedral "atomic surfaces" and admitting matching rules are considered. It is shown that the cohomology ring of the continuous hull of such patterns is isomorphic to that of the complement of a torus…
The standard genetic code multiplet structure as well as the correct degeneracies, class by class, are all extracted from the (unique) number 23, the order of the permutation group of 23 objects.
We present the results of atomistic and ab initio simulation of several different tilt grain boundaries (GB) in silicon. The boundary structures obtained with genetic algorithm turned out to have no coordination defects, i.e. all silicon…
The assembly and maturation of viruses with icosahedral capsids must be coordinated with icosahedral symmetry. The icosahedral symmetry imposes also the restrictions on the cooperative specific interactions between genomic RNA/DNA and coat…
The genetic code is considered to be universal. In order to test if some statistical properties of the coding bacterial genome were due to inherent properties of the genetic code, we compared the autocorrelation function, the scaling…
In this paper, necessary and sufficient conditions for the self-orthogonality of t-generator quasi-cyclic (QC) codes are presented under the Euclidean, Hermitian, and symplectic inner products, respectively. Particularly, by studying the…
The values of molecular polarizabilities and softnesses of the twenty amino acids were computed ab initio (MP2). By using the iterative Hirshfeld scheme to partition the molecular electronic properties, we demonstrate that the values of the…
Quasi-twisted codes are used here as the classical ingredients in the so-called Construction X for quantum error-control codes. The construction utilizes nearly self-orthogonal codes to design quantum stabilizer codes. We expand the choices…
How to represent the genetic code? Despite the fact that it is extensively known, the DNA mapping into proteins remains as one of the relevant discoveries of genetics. However, modern genomic signal processing usually requires converting…
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…
Background The theoretical requirements for a genetic code were well defined and modeled by George Gamow and Francis Crick in the 50-es. Their models failed. However the valid Genetic Code, provided by Nirenberg and Matthaei in 1961,…