Global warming, extreme climate events, earthquakes and their accompanying
socioeconomic disasters pose significant risks to humanity. Yet due to the nonlinear …

Transformers-based models, such as BERT, have been one of the most successful deep
learning models for NLP. Unfortunately, one of their core limitations is the quadratic …

The study of correlation structure in the primary sequences of DNA is reviewed. The issues
reviewed include: symmetries among 16 base-base correlation functions; accurate …

We develop a method for the multifractal characterization of nonstationary time series, which
is based on a generalization of the detrended fluctuation analysis (DFA). We relate our …

Traditional approaches to measuring the complexity of biological signals fail to account for
the multiple time scales inherent in such time series. These algorithms have yielded …

LéVY flights are a special class of random walks whose step lengths are not constant but
rather are chosen from a probability distribution with a power-law tail. Realizations of Lévy …

Here we propose a new method, detrended cross-correlation analysis, which is a
generalization of detrended fluctuation analysis and is based on detrended covariance. This …

We examine the detrended fluctuation analysis (DFA), which is a well-established method
for the detection of long-range correlations in time series. We show that deviations from …

For stationary time series, the cross-covariance and the cross-correlation as functions of time
lag n serve to quantify the similarity of two time series. The latter measure is also used to …

We study the temporal correlations in the atmospheric variability by 14 meteorological
stations around the globe, the variations of the daily maximum temperatures from their …