Related papers: Microbial genome as a fluctuating system: Distribu…
We checked that the distribution of words in text should uniform, which gives Heaps' law as natural result, that is, the number of types of words can be expressed as a power law of the number of tokens within text. We developed a…
We study the convergence of certain subseries of the harmonic series corresponding to increasing sequences of integers whose digits in a certain base are not uniformly distributed. We also discuss the case of irregular sequences, where the…
Research done during the previous century established our Standard Cosmological Model. There are many details still to be filled in, but few would seriously doubt the basic premise. Past surveys have revealed that the large-scale…
Complexity metrics and machine learning (ML) models have been utilized to analyze the lengths of segmental genomic entities like: exons, introns, intergenic and repeat/unique DNA sequences, in each of the 22 human chromosomes. The purpose…
The frequency of occurrence of prime numbers at unit number spacing intervals exhibits selfsimilar fractal fluctuations concomitant with inverse power law form for power spectrum generic to dynamical systems in nature such as fluid flows,…
The rank ordered distribution of the codon usage frequencies for 123 bacteriae is best fitted by a three parameters function that is the sum of a constant, an exponential and a linear term in the rank n. The parameters depend (two…
Work fluctuations and work probability distributions are fundamentally different in systems with short- ranged versus long-ranged correlations. Specifically, in systems with long-ranged correlations the work distribution is extraordinarily…
We introduce a method to estimate the complexity function of symbolic dynamical systems from a finite sequence of symbols. We test such complexity estimator on several symbolic dynamical systems whose complexity functions are known exactly.…
In a genetic algorithm, fluctuations of the entropy of a genome over time are interpreted as fluctuations of the information that the genome's organism is storing about its environment, being this reflected in more complex organisms. The…
We study numerically statistical properties and dynamical disease propagation using a percolation model on a one dimensional small world network. The parameters chosen correspond to a realistic network of school age children. We found that…
Signal propagation over long distances is a ubiquitous feature of multicellular communities. In biofilms of the bacterium Bacillus subtilis, we recently discovered that some, but not all, cells participate in the propagation of an…
We study the influence of a dissipation process on diffusion dynamics triggered by fluctuations with long-range correlations. We make the assumption that the perturbation process involved is of the same kind as those recently studied…
A weak correlation between the diffusion-exponent fluctuations and the temperature fluctuations is discussed based on recent experimental observations for protein diffusion inside bacteria. Its existence is shown to be essential for…
Phoneme frequency distributions exhibit robust statistical regularities across languages, including exponential-tailed rank-frequency patterns and a negative relationship between phonemic inventory size and the relative entropy of the…
Heaps' or Herdan's law is a linguistic law describing the relationship between the vocabulary/dictionary size (type) and word counts (token) to be a power-law function. Its existence in genomes with certain definition of DNA words is…
Zipf's law is the main regularity of quantitative linguistics. Despite of many works devoted to foundations of this law, it is still unclear whether it is only a statistical regularity, or it has deeper relations with information-carrying…
The empirical studies of city-size distribution show that Zipf's law and the hierarchical scaling law are linked in many ways. The rank-size scaling and hierarchical scaling seem to be two different sides of the same coin, but their…
Statistical studies of languages have focused on the rank-frequency distribution of words. Instead, we introduce here a measure of how word ranks change in time and call this distribution \emph{rank diversity}. We calculate this diversity…
In the framework of the Gibbs statistical theory, the question of the size of the particles forming the statistical system is investigated. This task is relevant for a wide variety of applications. The distribution for particle sizes and…
We study the primary DNA structure of four of the most completely sequenced human chromosomes (including chromosome 19 which is the most dense in coding), using Non-extensive Statistics. We show that the exponents governing the decay of the…