Generalized Hurst exponent and multifractal function of original and translated texts mapped into frequency and length time series

Abstract

A nonlinear dynamics approach can be used in order to quantify complexity in written texts. As a first step, a one-dimensional system is examined : two written texts by one author (Lewis Carroll) are considered, together with one translation, into an artificial language, i.e. Esperanto are mapped into time series. Their corresponding shuffled versions are used for obtaining a "base line". Two different one-dimensional time series are used here: (i) one based on word lengths (LTS), (ii) the other on word frequencies (FTS). It is shown that the generalized Hurst exponent $h(q)$ and the derived $f(\alpha )$ curves of the original and translated texts show marked differences. The original "texts" are far from giving a parabolic $f(\alpha )$ function, - in contrast to the shuffled texts. Moreover, the Esperanto text has more extreme values. This suggests cascade model-like, with multiscale time asymmetric features as finally written texts. A discussion of the difference and complementarity of mapping into a LTS or FTS is presented. The FTS $f(\alpha )$ curves are more opened than the LTS ones

preprint for PRE; 2 columns; 10 pages; 6 (multifigures); 3 Tables; 70 references

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