Stochastic and Self-Organisation Patterns in a 17-Year PM10 Time Series in Athens, Greece

Abstract

This paper utilises statistical and entropy methods for the investigation of a 17-year PM10 time series recorded from five stations in Athens, Greece, in order to delineate existing stochastic and self-organisation trends. Stochastic patterns are analysed via lumping and sliding, in windows of various lengths. Decreasing trends are found between Windows 1 and 3500–4000, for all stations. Self-organisation is studied through Boltzmann and Tsallis entropy via sliding and symbolic dynamics in selected parts. Several values are below −2 (Boltzmann entropy) and 1.18 (Tsallis entropy) over the Boltzmann constant. A published method is utilised to locate areas for which the PM10 system is out of stochastic behaviour and, simultaneously, exhibits critical self-organised tendencies. Sixty-six two-month windows are found for various dates. From these, nine are common to at least three different stations. Combining previous publications, two areas are non-stochastic and exhibit, simultaneously, fractal, long-memory and self-organisation patterns through a combination of 15 different fractal and SOC analysis techniques. In these areas, block-entropy (range 0.650–2.924) is significantly lower compared to the remaining areas of non-stochastic but self-organisation trends. It is the first time to utilise entropy analysis for PM10 series and, importantly, in combination with results from previously published fractal methods.

Fractal and Complex Patterns Existing in Music: Application to the Composition Diaphonies of Michael Paouris

“…It also accepts as indicators of criticality the areas with antipersistency-persistency interchanges (1.7 < b < 2.3). Both aspects have also been supported by other investigators [34,35,[43][44][45][46]. For these reasons both strong persistent areas with 2.3 <= b <= 3 and in areas of antipersistency-persistency interchanges with 1.7 < b < 2.3 are deemed of extreme importance for the criticality of the analysed music and under this view all results are discussed already and hereafter.…”

“…The reader should emphasise on this categorisation because it is based on arguments expressed in several papers [5,12,[21][22][23][28][29][30][31][32][33][34][35][36][37][38][39][40][41][43][44][45][46]55]. As aforementioned, the Class I category is deemed of prognostic value whereas the Class II ones are non-fractal.…”

“…The reader should consider in relation, that time t corresponds to a whole window. As in other publications, t is taken as the time moment of the first sample of each window under investigation (see e.g., [46] and references therein). In case of sliding window technique, finally all times but the actual t = 0s are considered.…”

Regional Multifractal Variability of the Overall Seismic Activity in Pakistan from 1820 to 2020 via the Application of MDFA on Earthquake Catalogs

“…As with the Fq(s) versus s curves of Figure 4, Flores-Márquez et al [34] report increasing tendencies of Fq(s) versus s both for the Guerrero earthquake magnitudes time series, as well as in each one of the five seismic zones. Comparable increasing trends of Fq(s) versus s are also reported by Telesca et al [48,49], Telesca and Lapenna [91], in other papers for seismic data [12,92,93] and in urban pollution MFDFA data series [94]. In similar plots of h(q) versus q as those of Figure 6, Flores-Márquez et al [34] reports comparable h(q) versus q with overlap.…”

“…This in turn suggests that the pure statistical analysis of seismic sequence data, as the one presented in Figures 3 and 5, and Table 1, is of limited character and can not outline all trends in similar datasets. Fluctuation functions Fq(s) as a function of the scale s for earthquake data are reported by Flores-Márquez et al [34] for seismic five zones in Mexico, by Chamoli and Yadav [72] for seismic series in NW Himalaya, by Telesca et al [48] for seismic series in Italy, by Telesca et al [49] for seismic interspike series in Italy, for other earthquake related series [12,[89][90][91][92][93] and for other types of series [50,94]. As with the Fq(s) versus s curves of Figure 4, Flores-Márquez et al [34] report increasing tendencies of Fq(s) versus s both for the Guerrero earthquake magnitudes time series, as well as in each one of the five seismic zones.…”