Related papers: Universality and Shannon entropy of codon usage
Shannon entropies of one- and two-electron atomic structure factors in the position and momentum representations are used to examine the behavior of the off-diagonal elements of density matrices with respect to the uncertainty principle and…
We use the formalism of 'Maximum Principle of Shannon's Entropy' to derive the general power law distribution function, using what seems to be a reasonable physical assumption, namely, the demand of a constant mean "internal order"…
Upper and lower bounds are obtained for the joint entropy of a collection of random variables in terms of an arbitrary collection of subset joint entropies. These inequalities generalize Shannon's chain rule for entropy as well as…
Essential genes constitute the core of genes which cannot be mutated too much nor lost along the evolutionary history of a species. Natural selection is expected to be stricter on essential genes and on conserved (highly shared) genes, than…
The tendencies described in this work were revealed in the course of examination of adenine and uracil distribution in the mRNA encoding sequence. The study also discusses the usage of codons occupied by the amino acid arginine in the table…
Across all kingdoms of biological life, protein-coding genes exhibit unequal usage of synonmous codons. Although alternative theories abound, translational selection has been accepted as an important mechanism that shapes the patterns of…
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…
We consider the Shannon mutual information of subsystems of critical quantum chains in their ground states. Our results indicate a universal leading behavior for large subsystem sizes. Moreover, as happens with the entanglement entropy, its…
We deploy Shannon's information entropy to the distribution of branching fractions in a particle decay. This serves to quantify how important a given new reported decay channel is, from the point of view of the information that it adds to…
We present a framework based on conditional entropy and the Dirichlet distribution for classifying chromosomes based on the degree to which they use synonymous codons uniformly or preferentially, that is, whether or not codons that code for…
Shannon's entropy is one of the building blocks of information theory and an essential aspect of Machine Learning methods (e.g., Random Forests). Yet, it is only finitely defined for distributions with fast decaying tails on a countable…
This paper derives bounds for two omnipresent information theoretic measures, the Shannon entropy and its complementary dual, the extropy. Based on a large size data set from a logconcave model, the said bounds are obtained for the entropy…
An existing conjecture states that the Shannon mutual information contained in the ground state wavefunction of conformally invariant quantum chains, on periodic lattices, has a leading finite-size scaling behavior that, similarly as the…
We study the correlation between the codon usage bias of genetic sequences and the network features of protein-protein interaction (PPI) in bacterial species. We use PCA techniques in the space of codon bias indices to show that genes with…
We analyse forty seven chloroplastid genes of the large subunit of RuBisCO, from the Algal order Ectocarpales, sourced from GenBank. Codon-usage weighted by the nucleotide base bias defines our score called the Codon-Impact-Parameter. This…
We present a statistical model of bacterial evolution based on the coupling between codon usage and tRNA abundance. Such a model interprets this aspect of the evolutionary process as a balance between the codon homogenization effect due to…
We show how universal codes can be used for solving some of the most important statistical problems for time series. By definition, a universal code (or a universal lossless data compressor) can compress any sequence generated by a…
Sufficient conditions are developed, under which the compound Poisson distribution has maximal entropy within a natural class of probability measures on the nonnegative integers. Recently, one of the authors [O. Johnson, {\em Stoch. Proc.…
Since its origin in the thermodynamics of the 19th century, the concept of entropy has also permeated other fields of physics and mathematics, such as Classical and Quantum Statistical Mechanics, Information Theory, Probability Theory,…
1) Harmonic oscillations (HO) in numerous electroencephalograms (EEG) from different humans are introduced. 2) The probability density functions (PDF, p(X)) of the EEG voltages (X) are normal (Gauss) for OO whereas, the plots for the…