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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

Nowadays, a large number of countries combine formal democratic institutions with authoritarian practices. Although in these countries the ruling elites may receive considerable voter support, they often use several manipulation tools to control election outcomes. A common practice of these regimes is the coercion and mobilization of large numbers of voters. This electoral irregularity is known as voter rigging, distinguishing it from vote rigging, which involves ballot stuffing or stealing. We develop a statistical test to quantify the extent to which the results of a particular election display traces of voter rigging. Our key hypothesis is that small polling stations are more susceptible to voter rigging because it is easier to identify opposing individuals, there are fewer eyewitnesses, and interested parties might reasonably expect fewer visits from election observers. We devise a general statistical method for testing whether voting behavior in small polling stations is significantly different from the behavior in their neighbor stations in a way that is consistent with the widespread occurrence of voter rigging. On the basis of a comparative analysis, the method enables third parties to conclude that an explanation other than simple variability is needed to explain geographic heterogeneities in vote preferences. We analyze 21 elections in 10 countries and find significant statistical anomalies compatible with voter rigging in Russia from 2007 to 2011, in Venezuela from 2006 to 2013, and in Uganda in 2011. Particularly disturbing is the case of Venezuela, where the smallest polling stations were decisive to the outcome of the 2013 presidential elections.

In the wake of the 2008 financial crisis, the role of strongly interconnected markets in causing systemic instability has been increasingly acknowledged. Trade networks of commodities are susceptible to cascades of supply shocks that increase systemic trade risks and pose a threat to geopolitical stability. We show that supply risk, scarcity, and price volatility of nonfuel mineral resources are intricately connected with the structure of the worldwide trade networks spanned by these resources. At the global level, we demonstrate that the scarcity of a resource is closely related to the susceptibility of the trade network with respect to cascading shocks. At the regional level, we find that, to some extent,region-specific price volatility and supply risk can be understood by centrality measures that capture systemic trade risk. The resources associated with the highest systemic trade risk indicators are often those that are produced as by products of major metals. We identify significant strategic shortcomings in the management of systemic trade risk, in particular in the European Union.

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 preferences. 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.

With a majority of 'Yes' votes in the Constitutional Referendum of 2017, Turkey continued its drift towards an autocracy. By the will of the Turkish people, this referendum transferred practically all executive power to president Erdoğan. However, the referendum was confronted with a substantial number of allegations of electoral misconducts and irregularities, ranging from state coercion of 'No' supporters to the controversial validity of unstamped ballots. Here we report the results of an election forensic analysis of recent Turkish elections to clarify to what extent it is plausible that these voting irregularities were present and able to influence the outcome of the referendum. We apply statistical forensics tests to identify the specific nature of the alleged electoral malpractices. In particular, we test whether the data contains fingerprints for ballot stuffing (submission of multiple ballots per person during the vote) and voter rigging (coercion and intimidation of voters). Additionally, we perform tests to identify numerical anomalies in the election results. For the 2017 Constitutional Referendum we find systematic and highly significant statistical support for the presence of both ballot stuffing and voter rigging. In 11% of stations we find signs for ballot stuffing with a standard deviation (uncertainty of ballot stuffing probability) of 2.7% (4 sigma event). Removing such ballot-stuffing-characteristic anomalies from the data would tip the overall balance from 'No' to a majority of 'Yes' votes. The 2017 election was followed by early elections in 2018 to directly vote for a new president who would now be head of state and government. We find statistical irregularities in the 2018 presidential and parliamentary elections similar in size and direction to those in 2017. These findings validate that our results unveil systematic and potentially even fraudulent biases that require further attention in order to combat electoral malpractices.

Reliable estimates of indirect economic losses arising from natural disasters are currently out of scientific reach. To address this problem, we propose a novel approach that combines a probabilistic physical damage catastrophe model with a new generation of macroeconomic agent-based models (ABMs). The ABM moves beyond the state of the art by exploiting large data sets from detailed national accounts, census data, and business information, etc., to simulate interactions of millions of agents representing \backslashemph{each} natural person or legal entity in a national economy. The catastrophe model introduces a copula approach to assess flood losses, considering spatial dependencies of the flood hazard. These loss estimates are used in a damage scenario generator that provides input for the ABM, which then estimates indirect economic losses due to the event. For the first time, we are able to link environmental and economic processes in a computer simulation at this level of detail. We show that moderate disasters induce comparably small but positive short- to medium-term, and negative long-term economic impacts. Large-scale events, however, trigger a pronounced negative economic response immediately after the event and in the long term, while exhibiting a temporary short- to medium-term economic boost. We identify winners and losers in different economic sectors, including the fiscal consequences for the government. We quantify the critical disaster size beyond which the resilience of an economy to rebuild reaches its limits. Our results might be relevant for the management of the consequences of systemic events due to climate change and other disasters.