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Abstract

In this study, we show how concepts of recurrence microstates (RM) can contribute to and optimize recurrence analysis. In particular, we show two topics of theoretical development in the study of recurrences: a statistical approach for the computation of recurrence quantifiers that brings a substantial reduction in computational time, keeping it precision and increasing the capacity to perform recurrence analyses of long time series; in a second topic, we show how an analysis of the structures and symmetries of RMs allows results based on RMs of different sizes to be studied together. The former analysis allows exact results about the distribution of smaller RMs, based on larger RMs, as well as providing the possibility of approximating results based on larger RMs when only the distribution of small RMs is available. As a last topic we perform an application of the symmetries of the RMs to distinguish random and deterministic signals. Along these lines, new symmetries appear when larger RMs are used, allowing, in principle, very subtle distinctions between systems to be analyzed or quantified. This property presents a strong perspective for applications in non-stationary signals and stochastic signals with temporal correlation.