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We consider the effects of long-range temporal correlations in many-particle systems, focusing particularly on fluctuations about the typical behaviour. For a specific class of memory dependence we discuss the modification of the large…
In condensed matter physics, simplified descriptions are obtained by coarse-graining the features of a system at a certain characteristic length, defined as the typical length beyond which some properties are no longer correlated. From a…
The evolution in coding DNA sequences brings new flexibility and freedom to the codon words, even as the underlying nucleotides get significantly ordered. These curious contra-rules of gene organisation are observed from the distribution of…
This is a review of a set of recent papers with some new data added. After a brief biological introduction a visualization scheme of the string composition of long DNA sequences, in particular, of bacterial complete genomes, will be…
The review summarizes the main methodological concepts used in studying natural language from the perspective of complexity science and documents their applicability in identifying both universal and system-specific features of language in…
Counts of galaxies as a function of apparent magnitude are among the most time-honored observations in cosmology. In this Letter, we focus on some statistical properties of these counts which are fundamental in order to characterize the…
We analyze subsamples of Abell and ACO cluster catalogs, in order to study the spatial properties of the large scale matter distribution. The subsamples analyzed are estimated to be nearly complete and are the standard ones used in the…
Chargaff once said that "I saw before me in dark contours the beginning of a grammar of Biology". In linguistics, "grammar" is the set of natural language rules, but we do not know for sure what Chargaff meant by "grammar" of Biology.…
Infectious diseases and computer malwares spread among humans and computers through the network of contacts among them. These networks are characterized by wide connectivity fluctuations, connectivity correlations and the small-world…
Recognition of pathogens relies on families of proteins showing great diversity. Here we construct maximum entropy models of the sequence repertoire, building on recent experiments that provide a nearly exhaustive sampling of the IgM…
Present human languages display slightly asymmetric log-normal (Gauss) distribution for size [1-3], whereas present cities follow power law (Pareto-Zipf law)[4]. Our model considers the competition between languages and that between cities…
Some authors have recently argued that a finite-size scaling law for the text-length dependence of word-frequency distributions cannot be conceptually valid. Here we give solid quantitative evidence for the validity of such scaling law,…
Zipf's law is found when the vocabulary of long written texts is ranked according to the frequency of word occurrences, establishing a power-law decay for the frequency vs rank relation. This law is a robust statistical property observed…
We present results from our quantitative study of statistical and network properties of literary and scientific texts written in two languages: English and Polish. We show that Polish texts are described by the Zipf law with the scaling…
Herein it is shown that in order to study the statistical properties of DNA sequences in bacterial chromosomes it suffices to consider only one half of the chromosome because they are similar to its corresponding complementary sequence in…
Quantitative linguistics has provided us with a number of empirical laws that characterise the evolution of languages and competition amongst them. In terms of language usage, one of the most influential results is Zipf's law of word…
According to Zipf's meaning-frequency law, words that are more frequent tend to have more meanings. Here it is shown that a linear dependency between the frequency of a form and its number of meanings is found in a family of models of…
Despite being a paradigm of quantitative linguistics, Zipf's law for words suffers from three main problems: its formulation is ambiguous, its validity has not been tested rigorously from a statistical point of view, and it has not been…
We show, that the specific distribution of gene's length, which is observed in natural genomes, might be a result of a growth process, in which a single length scale $L(t)$ develops that grows with time as $t^{1/3}$. This length scale could…
Coherently moving flocks of birds, beasts or bacteria are examples of living matter with spontaneous orientational order. How do these systems differ from thermal equilibrium systems with such liquid-crystalline order? Working with a…