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The fluctuation scaling law has universally been observed in a wide variety of phenomena. For counting processes describing the number of events occurred during time intervals, it is expressed as a power function relationship between the variance and the mean of the event count per unit time, the characteristic exponent of which is obtained theoretically in the limit of long duration of counting windows. Here I show that the scaling law effectively appears even in a short timescale in which only a few events occur. Consequently, the counting statistics of nonstationary event sequences are shown to exhibit the scaling law as well as the dynamics at temporal resolution of this timescale. I also propose a method to extract in a systematic manner the characteristic scaling exponent from nonstationary data.
We develop a method for the multifractal characterization of nonstationary time series, which is based on a generalization of the detrended fluctuation analysis (DFA). We relate our multifractal DFA method to the standard partition function-based mul
Fluctuation scaling has been observed universally in a wide variety of phenomena. In time series that describe sequences of events, fluctuation scaling is expressed as power function relationships between the mean and variance of either inter-event i
For any branching process, we demonstrate that the typical total number $r_{rm mp}( u tau)$ of events triggered over all generations within any sufficiently large time window $tau$ exhibits, at criticality, a super-linear dependence $r_{rm mp}( u tau
Detrended fluctuation analysis (DFA) is a scaling analysis method used to quantify long-range power-law correlations in signals. Many physical and biological signals are ``noisy, heterogeneous and exhibit different types of nonstationarities, which c
In counting experiments, one can set an upper limit on the rate of a Poisson process based on a count of the number of events observed due to the process. In some experiments, one makes several counts of the number of events, using different instrume