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Complex systems are everywhere. Ecosystems, financial markets, traffic, the economy, the internet and social media are complex systems. This textbook summarizes our understanding of complex systems and the methodological progress made over the past 20 years in a clear, structured, and comprehensive way

Democratic societies are built around the principle of free and fair elections, and that each citizen's vote should count equally. National elections can be regarded as large-scale social experiments, where people are grouped into usually large numbers of electoral districts and vote according to their references. The large number of samples implies statistical consequences for the polling results, which can be used to identify election irregularities. Using a suitable data representation, we find that vote distributions of elections with alleged fraud show a kurtosis substantially exceeding the kurtosis of normal elections, depending on the level of data aggregation. As an example, we show that reported irregularities in recent Russian elections are, indeed, well-explained by systematic ballot stuffing. We develop a parametric model quantifying the extent to which fraudulent mechanisms are present. We formulate a parametric test detecting these statistical properties in election results. Remarkably, this technique produces robust outcomes with respect to the resolution of the data and therefore, allows for cross-country comparisons.

Democratic societies are built around the principle of free and fair elections, and that each citizen's vote should count equally. National elections can be regarded as large-scale social experiments, where people are grouped into usually large numbers of electoral districts and vote according to their references. The large number of samples implies statistical consequences for the polling results, which can be used to identify election irregularities. Using a suitable data representation, we find that vote distributions of elections with alleged fraud show a kurtosis substantially exceeding the kurtosis of normal elections, depending on the level of data aggregation. As an example, we show that reported irregularities in recent Russian elections are, indeed, well-explained by systematic ballot stuffing. We develop a parametric model quantifying the extent to which fraudulent mechanisms are present. We formulate a parametric test detecting these statistical properties in election results. Remarkably, this technique produces robust outcomes with respect to the resolution of the data and therefore, allows for cross-country comparisons.

The populations of American (Anguilla rostrata) and European eels (Anguilla anguilla) have been declining rapidly in the last decades. Organic contaminants are suspected to be one of the possible causes for the decline; however, so far there have been few investigations of the uptake of specific compounds by different life cycle stages (e.g. freshwater or marine stage) and how the contamination patterns develop throughout the eel's life cycle. In the present study we measured concentrations of polybrominated diphenylethers (PBDEs), alternate brominated flame retardants (alternate BFRs) and Dechloranes (Decs) in different life stages of European and American eels to compare the contamination patterns and their development throughout the eel's life cycle. In general, concentrations of flame retardants (FRs) were similar to or higher in American than in European eels, and a greater number of FRs were detected. PBDE congeners that are characteristic of the Penta-PBDE formulation were the most abundant FRs in all adult eels as well as American glass eels. In European glass eels the alternate BFR 2,3-dibromopropyl-2,4,6-tribromophenylether (DPTE) and Dechlorane Plus were the dominating FRs, with average concentrations of 1.1 ± 0.31 ng g−1 ww and up to 0.32 ng g−1 ww respectively. Of the PBDEs BDE-183 was the most abundant congener in European glass eels. Low concentrations (less than 10% of the total contamination) of Tetra and Penta-PBDEs in juvenile European eels indicated that bans of technical Penta-PBDE in the European Union are effective. Enrichment of PBDEs was observed over the life stages of both European and American eels. However, a greater relative contribution of PBDEs to the sum FR contamination in American eels indicated an on-going exposure to these substances. High contributions of alternate BFRs in juvenile eels indicated an increased use of these substances in recent years. Concentrations seemed to be driven primarily by location, rather than life stage or age.