No abstract

This book is a comprehensive introduction to quantitative approaches to complex adaptive systems. Practically all areas of life on this planet are constantly confronted with complex systems, be it ecosystems, societies, traffic, financial markets, opinion formation, epidemic spreading, or the internet and social media. Complex systems are systems composed of many elements that interact with each other, which makes them extremely rich dynamical systems showing a huge range of phenomena. Properties of complex systems that are of particular importance are their efficiency, robustness, resilience, and proneness to collapse. The quantitative tools and concepts needed to understand the co-evolutionary nature of networked systems and their properties are challenging. The intention of the book is to give a self-contained introduction to these concepts so that the reader will be equipped with a conceptual and mathematical toolset that allows her to engage in the science of complex systems. Topics covered include random processes of path-dependent processes, co-evolutionary dynamics, the statistics of driven nonequilibrium systems, dynamics of networks, the theory of scaling, and approaches from statistical mechanics and information theory. The book extends well beyond the early classical literature in the field of complex systems and summarizes the methodological progress over the past twenty years in a clear, structured, and comprehensive way. The book is intended for natural scientists and graduate students.

Non-pharmaceutical interventions (NPIs) to mitigate the spread of SARS-CoV-2 were often implemented under considerable uncertainty and a lack of scientific evidence. Assessing the effectiveness of the individual interventions is critical to inform future preparedness response plans. Here we quantify the impact of 4,579 NPIs implemented in 76 territories on the effective reproduction number, Rt, of COVID-19. We use a hierarchically coded data set of NPIs and propose a novel modelling approach that combines four computational techniques, which together allow for a worldwide consensus rank of the NPIs based on their effectiveness in mitigating the spread of COVID-19. We show how the effectiveness of individual NPIs strongly varies across countries and world regions, and in relation to human and economic development as well as different dimensions of governance. We quantify the effectiveness of each NPI with respect to the epidemic age of its adoption, i.e., how early into the epidemics. The emerging picture is one in which no one-fits-all solution exists, and no single NPI alone can decrease Rt below one and that a combination of NPIs is necessary to curb the spread of the virus. We show that there are NPIs considerably less intrusive and costly than lockdowns that are also highly effective, such as certain risk communication strategies and voluntary measures that strengthen the healthcare system. By allowing to simulate ``what-if'' scenarios at the country level, our approach opens the way for planning the most likely effectiveness of future NPIs.

Many countries have passed their first COVID-19 epidemic peak. Traditional epidemiological models describe this as a result of nonpharmaceutical interventions pushing the growth rate below the recovery rate. In this phase of the pandemic many countries showed an almost linear growth of confirmed cases for extended time periods. This new containment regime is hard to explain by traditional models where either infection numbers grow explosively until herd immunity is reached or the epidemic is completely suppressed. Here we offer an explanation of this puzzling observation based on the structure of contact networks. We show that for any given transmission rate there exists a critical number of social contacts, Dc, below which linear growth and low infection prevalence must occur. Above Dc traditional epidemiological dynamics take place, e.g., as in susceptible–infected–recovered (SIR) models. When calibrating our model to empirical estimates of the transmission rate and the number of days being contagious, we find Dc∼7.2. Assuming realistic contact networks with a degree of about 5, and assuming that lockdown measures would reduce that to household size (about 2.5), we reproduce actual infection curves with remarkable precision, without fitting or fine-tuning of parameters. In particular, we compare the United States and Austria, as examples for one country that initially did not impose measures and one that responded with a severe lockdown early on. Our findings question the applicability of standard compartmental models to describe the COVID-19 containment phase. The probability to observe linear growth in these is practically zero.

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.

Social networks exhibit scaling laws for several structural characteristics, such as degree distribution, scaling of the attachment kernel and clustering coefficients as a function of node degree. A detailed understanding if and how these scaling laws are inter-related is missing so far, let alone whether they can be understood through a common, dynamical principle. We propose a simple model for stationary network formation and show that the three mentioned scaling relations follow as natural consequences of triadic closure. The validity of the model is tested on multiplex data from a well-studied massive multiplayer online game. We find that the three scaling exponents observed in the multiplex data for the friendship, communication and trading networks can simultaneously be explained by the model. These results suggest that triadic closure could be identified as one of the fundamental dynamical principles in social multiplex network formation.

Based on a unique dataset comprising all 325,000 Austrian patients that were under pharmaceutical treatment for diabetes during 2006 and 2007, we measured the excess risk of developing diabetes triggered by undernourishment in early life. We studied the percentage of all diabetes patients in the total population specifically for each year of birth, from 1917 to 2007. We found a massive excess risk of diabetes in people born during the times of the three major famines and immediately after, which occurred in Austria in the 20th century : 1918-1919, 1938, and 1946-1947. Depending on the region, there was an up to 40% higher chance of having diabetes when born in 1919-1921, compared with 1918 or 1922, where age-specific typical diabetes ratios are observed. The excess risk for diabetes was practically absent in those provinces of Austria that were less affected by the famines. We show that diabetes rates exhibit nontrivial, age-specific sex differences, and correlate with the economic wealth of the region. Our results might be of relevance for establishing higher awareness in the health system for those born in high-risk years, and underline the importance of ensuring sufficient nutrition in prenatal and early stages of life.epidemic | glucose tolerance | intrauterine programming | massive data analysis | fetal development

SARS-CoV-2=severe acute respiratory syndrome coronavirus 2. Further details are available in the appendix.