Related papers: Representations of Genetic Tables, Bimagic Squares…
The conception of multi-alphabetical genetics is represented. Matrix forms of the representation of the multi-level system of molecular-genetic alphabets have revealed algebraic properties of this system. These properties are connected with…
A \emph{magic square} is an $n \times n$ array of distinct positive integers whose sum along any row, column, or main diagonal is the same number. We compute the number of such squares for $n=4$, as a function of either the magic sum or an…
The usage frequencies for codons belonging to quartets are analized, over the whole exonic region, for 92 biological species. Correlation is put into evidence, between the usage frequencies of synonymous codons with third nucleotide A and C…
Statements of Shannon's Noiseless Coding Theorem by various authors, including the original, are reviewed and clarified. Traditional statements of the theorem are often unclear as to when it applies. A new notation is introduced and the…
We use the results of AG/0406290 to discuss the counting formulas of network flow polytopes and magic squares, i.e. the formula for the corresponding Ehrhart polynomial in terms of residues. We also discuss a description of the big cells…
The article continues an analysis of the genetic 8-dimensional Yin-Yang-algebra. This algebra was revealed in a course of matrix researches of structures of the genetic code and it was described in the author's articles arXiv:0803.3330 and…
The systematics of indices of physico-chemical properties of codons and amino acids across the genetic code are examined. Using a simple numerical labelling scheme for nucleic acid bases, data can be fitted as low-order polynomials of the 6…
Whereas Shannon entropy is related to the growth rate of multinomial coefficients, we show that the quadratic entropy (Tsallis 2-entropy) is connected to their $q$-deformation; when $q$ is a prime power, these $q$-multinomial coefficients…
In this paper, some general properties of Shannon information measures are investigated over sets of probability distributions with restricted marginals. Certain optimization problems associated with these functionals are shown to be…
The metaphor of a potential epigenetic differentiation landscape broadly suggests that during differentiation a stem cell follows the steepest descending gradient toward a stable equilibrium state which represents the final cell type. It…
Matrix forms of the representation of the multi-level system of molecular-genetic alphabets have revealed algebraic properties of this system. Families of genetic (4*4)- and (8*8)-matrices show unexpected connections of the genetic system…
We discuss algorithms for estimating the Shannon entropy h of finite symbol sequences with long range correlations. In particular, we consider algorithms which estimate h from the code lengths produced by some compression algorithm. Our…
The distribution functions of the codon usage probabilities, computed over all the available GenBank data, for 40 eukaryotic biological species and 5 chloroplasts, do not follow a Zipf law, but are best fitted by the sum of a constant, an…
Permutation matrices play an important role in understand the structure of magic squares. In this work, we use a class of symmetric permutation matrices than can be used to categorize magic squares. Many magic squares with a high degree of…
This article introduces the physics of information in the context of molecular biology and genomics. Entropy and information, the two central concepts of Shannon's theory of information and communication, are often confused with each other…
This work considers new entropy-based proofs of some known, or otherwise refined, combinatorial bounds for bipartite graphs. These include upper bounds on the number of the independent sets, lower bounds on the minimal number of colors in…
In this paper it is shown that within a Combined Genetic Code Table, realized through a combination of Watson-Crick Table and Codon Path Cube it exists, without an exception, a strict distinction between two classes of enzymes…
Observed neutrino mixing can be described by a tribimaximal MNS matrix. The resulting neutrino mass matrix in the basis of a diagonal charged lepton mass matrix is both 2-3 symmetric and magic. By a magic matrix, I mean one whose row sums…
We propose a new interpretation of measures of information and disorder by connecting these concepts to group theory in a new way. Entropy and group theory are connected here by their common relation to sets of permutations. A combinatorial…
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…