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 scaling that appear at small time scales become stronger in higher orders of DFA, and suggest a modified DFA method to remove them. The improvement is necessary especially for short records that are affected by non-stationarities. Furthermore, we describe how crossovers in the correlation behavior can be detected reliably and determined quantitatively and show how several types of trends in the data affect the different orders of DFA.

The paddlefish perceives its world through an array of electroreceptor organs spread over its rostrum. Using Detrended-Fluctuation Analysis (DFA) we find long-range anticorrelations in sequences of time intervals between neural action potentials recorded from spontaneously firing electroreceptor afferents. In contrast, spontaneous discharges from mechanoreceptor afferents in the crayfish tailfan lack long-range correlations altogether. We interpret this finding as a consequence of the self-sustained oscillatory nature of the electroreceptor organ compared with the threshold-type dynamics of the mechanoreceptor.Short-time anti-correlations have been known in sensory biology for many years. An early report on electroreceptors similar to those studied here [1] showed that short time intervals tend to be followed by long time intervals and vice versa. This phenomenon has been attributed to the action of a noise-mediated, subthreshold oscillator [2]. A noise excursion may cause a premature threshold crossing (generating a spike) prior to the maximum in one cycle leading to a short time interval. The next spike will occur near the maximum of the subsequent cycle, lengthening the following time interval. Such anti-correlations must therefore decay with time constants comparable to the period of the slow oscillator (typically 20-300 milliseconds), and indeed such anti-correlations with characteristic timescales up to a few hundred milliseconds were recently reported for electroreceptor organs of the catfish [2] and the knifefish [3], using standard Markovian analysis.In contrast, we report here observations of long-range (time) anti-correlations (LRACs) (in the range 10-200 seconds) in fluctuations of the time intervals generated by the spontaneous firing of unstimulated ampullary electroreceptors (ER) [4] of the paddlefish, Polyodon spathula.

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