Related papers: Statistical distributions and entropy consideratio…
The distribution of bases spacing in human genome was investigated. An analysis of the frequency of occurrence in the human genome of different sequence lengths flanked by one type of nucleotide was carried out showing that the distribution…
Although information theoretic characterizations of human communication have become increasingly popular in linguistics, to date they have largely involved grafting probabilistic constructs onto older ideas about grammar. Similarities…
Nature is full of random networks of complex topology describing such apparently disparate systems as biological, economical or informatical ones. Their most characteristic feature is the apparent scale-free character of interconnections…
Genetic sequences are known to possess non-trivial composition together with symmetries in the frequencies of their components. Recently, it has been shown that symmetry and structure are hierarchically intertwined in DNA, suggesting a…
Epidemic disease spreading is conventionally often modelled and analyzed by means of rate and diffusion equations, following the paradigms of well-controlled chemical reactions and diffusive dynamics in a test tube. Yet, serious worries…
Much information is stored in amino acid composition of protein and base composition of DNA. We simulated the evolution of amino acid frequencies and genomic GC content by a linguistic model. It is showed that the evolution of genetic code…
Eukaryote genomes contain excessively introns, inter-genic and other non-genic sequences that appear to have no vital functional role or phenotype manifestation. Their existence, a long-standing puzzle, is viewed from the principle of…
We show how generalized Gibbs-Shannon entropies can provide new insights on the statistical properties of texts. The universal distribution of word frequencies (Zipf's law) implies that the generalized entropies, computed at the word level,…
The statistical methods derived and described in this thesis provide new ways to elucidate the structural properties of text and other symbolic sequences. Generically, these methods allow detection of a difference in the frequency of a…
Biological sequences do not come at random. Instead, they appear with particular frequencies that reflect properties of the associated system or phenomenon. Knowing how biological sequences are distributed in sequence space is thus a…
The number of extant individuals within a lineage, as exemplified by counts of species numbers across genera in a higher taxonomic category, is known to be a highly skewed distribution. Because the sublineages (such as genera in a clade)…
The crossword-like patterns of tiles in Scrabble form connected graphs of occupied sites on a square lattice. We find the most structureless description that reproduces means and covariances observed in real Scrabble games by adapting a…
Correlation of gene histories in the human genome determines the patterns of genetic variation (haplotype structure) and is crucial to understanding genetic factors in common diseases. We derive closed analytical expressions for the…
Evaluating whether large language models (LLMs) capture the structure of natural language beyond local fluency remains an open challenge. Existing evaluation methods, largely based on task performance or short-context behavior, provide…
Superstatistics describes statistical systems that behave like superpositions of different inverse temperatures $\beta$, so that the probability distribution is $p(\epsilon_i) \propto \int_{0}^{\infty} f(\beta) e^{-\beta \epsilon_i}d\beta$,…
Topological features of gene regulatory networks can be successfully reproduced by a model population evolving under selection for short dynamical attractors. The evolved population of networks exhibit motif statistics, summarized by…
Shannon information (SI) and its special case, divergence, are defined for a DNA sequence in terms of probabilities of chemical words in the sequence and are computed for a set of complete genomes highly diverse in length and composition.…
We investigate symbolic sequences and in particular information carriers as e.g. books and DNA--strings. First the higher order Shannon entropies are calculated, a characteristic root law is detected. Then the algorithmic entropy is…
In this paper, we apply persistent entropy, a novel topological statistic, for characterization of images of epithelial tissues. We have found out that persistent entropy is able to summarize topological and geometric information encoded by…
A new approach to estimate the Shannon entropy of a long-range correlated sequence is proposed. The entropy is written as the sum of two terms corresponding respectively to power-law (\emph{ordered}) and exponentially (\emph{disordered})…