Correlações de longo alcance em tamanhos de frases

Abstract

Correlations between mathematical entities have been studied for very long in the complex systems area. The study object of this analysis, assumed to display some degree of self-correlation, is composed of a database concerning sentences lengths in texts, quantified in terms of the number of words within them. These texts are extracted from the second testament of the bible, in Portuguese and other nineteen languages. Correlations are investigated not solely directly from sentences lengths, but also from two additional time series, extracted from the original one. In this study, one verifies that the Hurst exponent points to persistence for length time series in all considered languages, and for those built on the absolute values of sentence lengths differences as well, possibly pointing towards a long-range correlation presence. For time series built on the signs of these same differences, the found exponents indicate anti-persistence or, perhaps, absence of correlations. Quantitatively, the Hurst exponents of length series are generally close to each other, indicating that they are approximately independent on the language in consideration. The same quantitative conclusions were observed for the modules and signs series. The technique that is utilized here for the extraction of such an exponent is the DFA - detrended fluctuation analysis.