In this work, by considering superstatistics we investigate the short-range correlations (SRCs) and the fluctuations in the distribution of lengths of strings of nucleotides. To this end, a stochastic model provides the distributions of the size of the exons based on the $q$-Gamma and inverse $q$-Gamma distributions. Specifically, we define a time series for exon sizes to investigate the SRC and the fluctuations through the superstatistics distributions. To test the model's viability, we use the Project Ensembl database of genes to extract the time evolution of exon sizes, calculated in terms of the number of base pairs (bp) in these biological databases. Our findings show that, depending on the chromosome, both distributions are suitable for describing the length distribution of human DNA for lengths greater than 10 bp. In addition, we used Bayesian statistics to perform a selection model approach, which revealed weak evidence for the inverse q-Gamma distribution for a considerable number of chromosomes.

The nongravitational interaction between the dark components of the Universe could lead to the variation of dark matter energy density standard evolution law. When we assume this scenario, the dark matter energy density follows ${\rho }_{dm}\sim (1+z{)}^{3+\epsilon (z)}$ [where $\epsilon (z)=0$ corresponds to the standard dark matter density evolution]. In this paper, we perform a Bayesian analysis to test three parametrizations for $\epsilon (z)$, namely, $\epsilon (z)={\epsilon }_0$, $\epsilon (z)={\epsilon }_0+{\epsilon }_1\frac{z}{1+z}$, and $\epsilon (z)={\epsilon }_0+{\epsilon }_1\frac{z(1+z)}{1+z^2}$, where the first one is motivated through fundamental grounds and the others are on phenomenological grounds. Through the Gaussian process regression, our method uses galaxy cluster gas mass fraction measurements, Type Ia supernovae observations, cosmic chronometers, and Baryon Acoustic Oscillations data. No specific cosmological model is considered. In all possibilities analyzed, the standard evolution law ($\epsilon (z)=0$) is within $2\sigma \mathrm{C}.\mathrm{L}.$ The investigated cases generally indicated scenarios of inconclusive or weak evidence toward the simplest model from the Bayesian standpoint.

The short and long statistical correlations are essential in the genomic sequence. Such correlations are long-range for introns, whereas, for exons, these are short. In this study, we employed superstatistics to investigate correlations and fluctuations in the distribution of nucleotide sequence lengths of the Cucurbitaceae family. We established a time series for exon sizes to probe these correlations and fluctuations. We used data from the National Center for Biotechnology Information (NCBI) gene database to extract the temporal evolution of exon sizes, measured in terms of the number of base pairs (bp). To assess the model’s viability, we utilized a timescale extraction method to determine the statistical properties of our time series, including the local distribution and fluctuations, which provide the exon size distributions based on the q-Gamma and inverse q-Gamma distributions. From the Bayesian statistics standpoint, both distributions are excellent for capturing the correlations and fluctuations from the data.

Earthquake frequency–magnitude distributions in subduction zones provide fundamental constraints on the physical processes governing rupture nucleation and propagation. Although the classical Gutenberg–Richter law offers an approximate description of these data, systematic deviations have motivated the use of generalized statistical models grounded in non-extensive statistical mechanics and fragmentation frameworks. Here, we perform a Bayesian comparative analysis of four models applied to twelve subduction zones along the circum-Pacific belt, using National Earthquake Information Center catalogs with and without correction for magnitude of completeness. We show that catalog incompleteness exerts a first-order control on both model ranking and inferred parameters. After completeness correction, fragmentation-based models exhibit superior stability in describing moderate-to-large magnitude seismicity, highlighting the importance of accounting for detection biases in comparative statistical seismology.