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

摘要

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