Compositional Structure of the Genome: A Review.

As the genome carries the historical information of a species' biotic and environmental interactions, analyzing changes in genome structure over time by using powerful statistical physics methods (such as entropic segmentation algorithms, fluctuation analysis in DNA walks, or measures of compositional complexity) provides valuable insights into genome evolution. Nucleotide frequencies tend to vary along the DNA chain, resulting in a hierarchically patchy chromosome structure with heterogeneities at different length scales that range from a few nucleotides to tens of millions of them. Fluctuation analysis reveals that these compositional structures can be classified into three main categories: (1) short-range heterogeneities (below a few kilobase pairs (Kbp)) primarily attributed to the alternation of coding and noncoding regions, interspersed or tandem repeats densities, etc.

On the Validity of Detrended Fluctuation Analysis at Short Scales.

Detrended Fluctuation Analysis (DFA) has become a standard method to quantify the correlations and scaling properties of real-world complex time series. For a given scale of observation, DFA provides the function F(ℓ), which quantifies the fluctuations of the time series around the local trend, which is substracted (detrended). If the time series exhibits scaling properties, then F(ℓ)∼ℓα asymptotically, and the scaling exponent α is typically estimated as the slope of a linear fitting in the logF(ℓ) vs.

Driven progressive evolution of genome sequence complexity in Cyanobacteria.

Progressive evolution, or the tendency towards increasing complexity, is a controversial issue in biology, which resolution entails a proper measurement of complexity. Genomes are the best entities to address this challenge, as they encode the historical information of a species' biotic and environmental interactions. As a case study, we have measured genome sequence complexity in the ancient phylum Cyanobacteria.

Transforming Gaussian correlations. Applications to generating long-range power-law correlated time series with arbitrary distribution.

The observable outputs of many complex dynamical systems consist of time series exhibiting autocorrelation functions of great diversity of behaviors, including long-range power-law autocorrelation functions, as a signature of interactions operating at many temporal or spatial scales. Often, numerical algorithms able to generate correlated noises reproducing the properties of real time series are used to study and characterize such systems. Typically, many of those algorithms produce a Gaussian time series.

Comparison of methods for the assessment of nonlinearity in short-term heart rate variability under different physiopathological states.

Despite the widespread diffusion of nonlinear methods for heart rate variability (HRV) analysis, the presence and the extent to which nonlinear dynamics contribute to short-term HRV are still controversial. This work aims at testing the hypothesis that different types of nonlinearity can be observed in HRV depending on the method adopted and on the physiopathological state. Two entropy-based measures of time series complexity (normalized complexity index, NCI) and regularity (information storage, IS), and a measure quantifying deviations from linear correlations in a time series (Gaussian linear contrast, GLC), are applied to short HRV recordings obtained in young (Y) and old (O) healthy subjects and in myocardial infarction (MI) patients monitored in the resting supine position and in the upright position reached through head-up tilt.