Related papers: Statistical distributions and entropy consideratio…
Genomic evolution can be viewed as string-editing processes driven by mutations. An understanding of the statistical properties resulting from these mutation processes is of value in a variety of tasks related to biological sequence data,…
Aging is a universal consequence of life, yet researchers have identified no universal theme. This manuscript considers aging from the perspective of entropy, wherein things fall apart. We first examine biological information change as a…
The frequency distributions of DNA k-mers are shaped by fundamental biological processes and offer a window into genome structure and evolution. Inspired by analogies to natural language, prior studies have attempted to model genomic k-mer…
Beyond the local constraints imposed by grammar, words concatenated in long sequences carrying a complex message show statistical regularities that may reflect their linguistic role in the message. In this paper, we perform a systematic…
This work explores entropy analysis as a tool for probing information distribution within Transformer-based architectures. By quantifying token-level uncertainty and examining entropy patterns across different stages of processing, we aim…
Large scale databases are available that contain homologous gene families constructed from hundreds of complete genome sequences from across the three domains of Life. Here we discuss approches of increasing complexity aimed at extracting…
We present a framework based on conditional entropy and the Dirichlet distribution for classifying chromosomes based on the degree to which they use synonymous codons uniformly or preferentially, that is, whether or not codons that code for…
We analyse the statistical properties of genealogical trees in a neutral model of a closed population with sexual reproduction and non-overlapping generations. By reconstructing the genealogy of an individual from the population evolution,…
When the same set of genes appear in two top ranking gene lists in two different studies, it is often of interest to estimate the probability for this being a chance event. This overlapping probability is well known to follow the…
We propose that the distribution of DNA words in genomic sequences can be primarily characterized by a double Pareto-lognormal distribution, which explains lognormal and power-law features found across all known genomes. Such a distribution…
Much of the on-going statistical analysis of DNA sequences is focused on the estimation of characteristics of coding and non-coding regions that would possibly allow discrimination of these regions. In the current approach, we concentrate…
This article presents the calculation of the entropy of a system with Zipfian distribution and shows that a communication system tends to present an exponent value close to one, but still greater than one, so that it might maximize entropy…
Shannon entropy is often a quantity of interest to linguists studying the communicative capacity of human language. However, entropy must typically be estimated from observed data because researchers do not have access to the underlying…
Recent attacks of various viruses with having deep and extensive impact at a global scale has warranted that microbiome be studied extensively and in a robust analytic framework. Microbiome typically refers to the collective genomes of such…
A pattern of a sequence is a sequence of integer indices with each index describing the order of first occurrence of the respective symbol in the original sequence. In a recent paper, tight general bounds on the block entropy of patterns of…
Properties of networks are often characterized in terms of features such as node degree distributions, average path lengths, diameters, or clustering coefficients. Here, we study shortest path length distributions. On the one hand, average…
Assuming the validity of random matrices for describing the statistics of a closed chaotic quantum system, we study analytically some statistical properties of the S-matrix characterizing scattering in its open counterpart. In the first…
The entropy of network ensembles characterizes the amount of information encoded in the network structure, and can be used to quantify network complexity, and the relevance of given structural properties observed in real network datasets…
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…
There is given a characterization of hyperbolic secant distribution by the independence of linear forms with random coefficients. We provide a characterization by the identic distribution property. Keywords: hyperbolic secant distribution;…