A complex process is often a balance between nonscaling and scaling components. We show how the nonextensive Tsallis g-entropy indicator may be interpreted as a measure of the nonscaling condition in time series. This is done by applying the nonextensive entropy formalism to the diffusion entropy analysis (DEA). We apply the analysis to the study of the teen birth phenomenon. We find that the number of unmarried teen births is strongly influenced by social processes that induce an anomalous memory in the data. This memory is related to the strength of the nonscaling component of the signal and is more intense than that in the married teen birth time series. By using a wavelet multiresolution analysis, we attempt to provide a social interpretation of this effect…. One of the most exciting and rapidly developing areas of modern research is the quantitative study of "complexity." Complexity has special interdisciplinary impacts in the fields of physics, mathematics, information science, biology, sociology, and medicine. No definition of a complex system has been universally embraced, so here we adopt the working definition, "an arrangement of parts so intricate as to be hard to understand or deal with." Therefore, the main goal of the science of complexity is to develop mathematical methods in order to discriminate among the fundamental microscopic and macroscopic constituents of a complex system and to describe their interrelations in a concise way. Experiments usually yield results in the form of time series for physical observables. Typically, these time series contain both a slow regular variation, usually called a "signal," and a rapid erratic fluctuation, usually called "noise." Historically, the techniques applied to processing such time series have been based on equilibrium statistical mechanics and, therefore, they are not applicable to phenomena far from equilibrium. Among the fluctuating phenomena, a particularly important place is occupied by those phenomena characterized by some type of self-similar or scaling-fractal structures [4]. In this chapter we show that the nonextensive Tsallis g-entropy indicator may be interpreted as a measure of the strength of the nonscaling component of a time series.
Multifractal diffusion entropy analysis: Optimal bin width of probability histograms
