Probability distribution of intersymbol distances in random symbolic sequences: Applications to improving detection of keywords in texts and of amino acid clustering in proteins

Disordered beta thinned ensemble with applications

It recently has been found that methods of the statistical theories of spectra can be a useful tool in the analysis of spectra far from levels of Hamiltonian systems. The purpose of the present study is to deepen this kind of approach by performing a more comprehensive spectral analysis that measures both the local- and long-range statistics. We have found that, as a common feature, spectra of this kind can exhibit a situation in which local statistics are relatively quenched while the long-range ones show large fluctuations. By combining three extensions of the standard random matrix theory (RMT) and considering long spectra, we demonstrate that this phenomenon occurs when disorder and level incompleteness are introduced in an RMT spectrum. Consequently, the long-range statistics follow Taylor's law, suggesting the presence of a fluctuation scaling (FS) mechanism in this kind of spectra. Applications of the combined ensemble are then presented for spectra originate from several very diverse areas, including complex networks, COVID-19 time series, and quantitative linguistics, which demonstrate that short- and long-range statistics reflect the rigid and elastic characteristics of a given spectrum, respectively. These observations may shed some light on spectral data classification.

Analyzing similarities in genome sequences

This article investigates aspects of similarity between complete sequences of mitochondrial DNA by determining the distribution of the relative frequencies of words with different lengths and the characteristics of their relevance throughout the sequences. The degree of similarity is obtained by comparing the distances between words contained within these sequences. Our results indicate that the best groupings among different species depend on the lengths of words and their respective relative frequencies. We also observed that the longer the word the more consistent the grouping between the sequences becomes. The application of our results, together with the perspective of analyzing DNA sequences belonging to a single biological species, may be important for the construction of phylogenetic trees, which are appropriate structures for understanding the evolutionary history of the species.