Related papers: Universality and Shannon entropy of codon usage
We introduce a simple geometrical construction similar to covariant holographic entanglement entropy but with the addition of a new term proportional to boundary region volume. This new procedure has properties strongly resembling classical…
We study an entropy measure for quantum systems that generalizes the von Neumann entropy as well as its classical counterpart, the Gibbs or Shannon entropy. The entropy measure is based on hypothesis testing and has an elegant formulation…
A method for estimating the Shannon differential entropy of multidimensional random variables using independent samples is described. The method is based on decomposing the distribution into a product of the marginal distributions and the…
A physically unclonable function (PUF) is an electronic circuit that produces an intrinsic identifier in response to a challenge. These identifiers depend on uncontrollable variations of the manufacturing process, which make them hard to…
Shannon entropy is widely used to measure the complexity of DNA sequences but suffers from saturation effects that limit its discriminative power for long uniform segments. We introduce a novel metric, the entropy rank ratio R, which…
For statistical systems that violate one of the four Shannon-Khinchin axioms, entropy takes a more general form than the Boltzmann-Gibbs entropy. The framework of superstatistics allows one to formulate a maximum entropy principle with…
The Shannon entropy, one of the cornerstones of information theory, is widely used in physics, particularly in statistical mechanics. Yet its characterization and connection to physics remain vague, leaving ample room for misconceptions and…
In this paper we will analyze discrete probability distributions in which probabilities of particular outcomes of some experiment (microstates) can be represented by the ratio of natural numbers (in other words, probabilities are…
Probability distributions having power-law tails are observed in a broad range of social, economic, and biological systems. We describe here a potentially useful common framework. We derive distribution functions $\{p_k\}$ for situations in…
We propose a method to derive the stationary size distributions of a system, and the degree distributions of networks, using maximisation of the Gibbs-Shannon entropy. We apply this to a preferential attachment-type algorithm for systems of…
The behavior of the Kozachenko - Leonenko estimates for the (differential) Shannon entropy is studied when the number of i.i.d. vector-valued observations tends to infinity. The asymptotic unbiasedness and L^2-consistency of the estimates…
We study the length distribution of a particular class of DNA sequences known as 5'UTR exons. These exons belong to the messanger RNA of protein coding genes, but they are not coding (they are located upstream of the coding portion of the…
Shannon Entropy is the preeminent tool for measuring the level of uncertainty (and conversely, information content) in a random variable. In the field of communications, entropy can be used to express the information content of given…
We show that the essential properties of entropy (monotonicity, additivity and subadditivity) are consequences of entropy being a monoidal natural transformation from the under category functor $-/\mathsf{LProb}_{\rho}$ (where…
We have presented a new axiomatic derivation of Shannon Entropy for a discrete probability distribution on the basis of the postulates of additivity and concavity of the entropy function.We have then modified shannon entropy to take account…
Understanding the way in which random entities interact is of key interest in numerous scientific fields. This can range from a full characterization of the joint distribution to single scalar summary statistics. In this work we identify a…
Selection pressures on proteins are usually measured by comparing homologous nucleotide sequences (Zuckerkandl and Pauling 1965). Recently we introduced a novel method, termed `volatility', to estimate selection pressures on protein…
In special coordinates (codon position--specific nucleotide frequencies) bacterial genomes form two straight lines in 9-dimensional space: one line for eubacterial genomes, another for archaeal genomes. All the 348 distinct bacterial…
The Shannon entropy in the atomic, molecular and chemical physics context is presented by using as test cases the hydrogenic-like atoms $H_c$, ${He_c}^+$ and ${Li_c}^{2+}$ confined by an impenetrable spherical box. Novel expressions for…
We study the problem of choosing the copula when the marginal distributions of a random vector are not all continuous. Inspired by four motivating examples including simulation from copulas, stress scenarios, co-risk measures, and…