Related papers: Sum rules of codon usage probabilities
We consider the probability of knotting in equilateral random polygons in Euclidean 3-dimensional space, which model, for instance, random polymers. Results from an extensive Monte Carlo dataset of random polygons indicate a universal…
Convergent evolution provides powerful evidence for natural selection, yet its molecular basis is typically sought in protein-coding amino acid substitutions. Whether adaptive pressures can drive the convergent evolution of synonymous codon…
The chord length probability density of the regular octahedron is explicitly evaluated throughout its full range of distances by separating it into three contributions respectively due to the pairs of facets opposite to each other or…
The algebraic structures of the genetic code are most important to obtain additional information about the semantic code and its applications. In this paper we define two dual Boolean codon lattices of the genetic code using hydrogen bond…
The density matrix positivity is a natural counterpart of unitarity. The resulting constraints for various parton distribution and correlations are considered. Their compatibility with leading order QCD evolution is guaranteed by the…
Using basic properties of p-adic numbers, we consider a simple new approach to describe main aspects of DNA sequence and genetic code. Central role in our investigation plays an ultrametric p-adic information space which basic elements are…
Codifference is a commonly used measure of dependence for stable vectors and processes for which covariance is infinite. However, we argue that it can also be used for other heavy-tail distributions and it provides useful information for…
The shape-dependent universality of the excess percolation cluster number and cross-configuration probability on a torus is discussed. Besides the aspect ratio of the torus, the universality class depends upon the twist in the periodic…
The paper represents three supplements to the source paper, q-bio/0610044 [q-bio.OT], with three new series of harmonic structures of the genetic code, determined by Gauss arithmetical algorithm; by Table of Minimal Adding, as in…
We investigated the error-minimization properties of putative primordial codes that consisted of 16 supercodons, with the third base being completely redundant, using a previously derived cost function and the error minimization percentage…
The statistical model of the hadron as a quarkonium system suggests the dimensional dependence of some of the properties of the hadron like the scaling in its probability density with the anomalous dimension as the exponent,the…
It is shown that there is a sense in splitting Genetic Code Table (GCT) into three parts using the harmonic mean, calculated by the formula H (a, b) = 2ab / (a + b), where a = 63 and b = 31.5. Within these three parts, the amino acids (AAs)…
Some properties of diagonal binomial coefficients were studied in respect to frequency of their units digits. An approach was formulated that led to use of difference tables to predict if certain units digits can appear in the values of…
We investigate the theoretical stability of the predictions of tri-bimaximal neutrino mixing with respect to third family wave-function corrections. Such third family wave-function corrections can arise from either the canonical…
Given independent normally distributed points A,B,C,D in Euclidean 3-space, let Q denote the plane determined by A,B,C and D^ denote the orthogonal projection of D onto Q. The probability that the tetrahedron ABCD is acute remains…
We discuss the statistical properties of parton distributions within the framework of the NNPDF methodology. We present various tests of statistical consistency, in particular that the distribution of results does not depend on the…
Complex systems with tightly coadapted parts frequently appear in living systems and are difficult to account for through Darwinian evolution, that is random variation and natural selection, if the constituent parts are independently coded…
We determine the cobordism distance between all positive 3-braid links and connected sums of trefoil knots, up to a constant error. This may be seen as a reinterpretation of Coxeter's finiteness result on the braid group on three strands…
We study the structure of local baryon fields using the method of QCD sum rule. We only consider the single baryon fields and calculate their operator product expansions. We find that the octet baryon fields belonging to the chiral…
We introduce a family of copulas which are locally piecewise uniform in the interior of the unit cube of any given dimension. Within that family, the simultaneous control of tail dependencies of all projections to faces of the cube is…