Related papers: Statistical distributions and entropy consideratio…
The paper makes the observation that all orders of information entropy are equal in signals composed of repeating units of distinct symbols where the units can be classified as a member of a symmetry group. This leads to an improved metric…
Boolean network models of strongly connected modules are capable of capturing the high regulatory complexity of many biological gene regulatory circuits. We study numerically the previously introduced basin entropy, a parameter for the…
There are different ways of measuring diversity in complex systems. In particular, in language, lexical diversity is characterized in terms of the type-token ratio and the word entropy. We here investigate both diversity metrics in six…
We propose a new thermodynamic, relativistic relationship between information and entropy, which is closely analogous to the classic Maxwell electro-magnetic equations. Determination of whether information resides in points of…
We use large language models (LLMs) to uncover long-ranged structure in English texts from a variety of sources. The conditional entropy or code length in many cases continues to decrease with context length at least to $N\sim 10^4$…
In the human genomes, recombination frequency between homologous chromosomes during meiosis is highly correlated with their physical length while it differs significantly when their coding density is considered. Furthermore, it has been…
Rooted trees with probabilities are used to analyze properties of a variable length code. A bound is derived on the difference between the entropy rates of the code and a memoryless source. The bound is in terms of normalized informational…
In this work we seek clusters of genomic words in human DNA by studying their inter-word lag distributions. Due to the particularly spiked nature of these histograms, a clustering procedure is proposed that first decomposes each…
We begin with the extraordinary observation that the length distribution of 80 million proteins in UniProt, the Universal Protein Resource, measured in amino acids, is qualitatively identical to the length distribution of large collections…
In this work we present a systematic mathematical approximation scheme that exposes the way that information, about the evolutionary forces of selection and random genetic drift, is encoded in gene-frequency trajectories. We determine…
In the near future, all the human genes will be identified. But understanding the functions coded in the genes is a much harder problem. For example, by using block entropy, one has that the DNA code is closer to a random code then written…
Given a random text over a finite alphabet, we study the frequencies at which fixed-length words occur as subsequences. As the data size grows, the joint distribution of word counts exhibits a rich asymptotic structure. We investigate all…
Many computational linguistic methods have been proposed to study the information content of languages. We consider two interesting research questions: 1) how is information distributed over long documents, and 2) how does content…
Important aspects of the process of information storage and retrieval in DNA and RNA, and its evolution, are the role of the anticodons and associated $t$RNA's, and correlations between anticodons and amino acids; the degeneracy of the…
Unraveling the evolutionary forces shaping bacterial diversity can today be tackled using a growing amount of genomic data. While the genome of eukaryotes is highly stable, bacterial genomes from cells of the same species highly vary in…
The information entropies in coordinate and momentum spaces and their sum ($S_r$, $S_k$, $S$) are evaluated for many nuclei using "experimental" densities or/and momentum distributions. The results are compared with the harmonic oscillator…
A rigorous methodology is proposed to study cell division data consisting in several observed genealogical trees of possibly different shapes. The procedure takes into account missing observations, data from different trees, as well as the…
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…
Networks of genetic expression can be modelled by hypergraphs with the additional structure that real coefficients are given to each vertex-edge incidence. The spectra, i.e. the multiset of the eigenvalues, of such hypergraphs, are known to…
The concept of entropy in statistical physics is related to the existence of irreversible macroscopic processes. In this work, we explore a recently introduced entropy formula for a class of stochastic processes with more than one absorbing…