Quantifying long-range correlations in complex networks beyond nearest neighbors

We propose a fluctuation analysis to quantify spatial correlations in complex networks. The approach considers the sequences of degrees along shortest paths in the networks and quantifies the fluctuations in analogy to time series. In this work, the Barabasi-Albert (BA) model, the Cayley tree at the percolation transition, a fractal network model, and examples of real-world networks are studied. While the fluctuation functions for the BA model show exponential decay, in the case of the Cayley tree and the fractal network model the fluctuation functions display a power-law behavior. The fractal network model comprises long-range anti-correlations. The results suggest that the fluctuation exponent provides complementary information to the fractal dimension

Damage functions for climate-related hazards: Unification and uncertainty analysis

Most climate change impacts manifest in the form of natural hazards. Damage assessment typically relies on damage functions that translate the magnitude of extreme events to a quantifiable damage. In practice, the availability of damage functions is limited due to a lack of data sources and a lack of understanding of damage processes. The study of the characteristics of damage functions for different hazards could strengthen the theoretical foundation of damage functions and support their development and validation. Accordingly, we investigate analogies of damage functions for coastal flooding and for wind storms and identify a unified approach. This approach has general applicability for granular portfolios and may also be applied, for example, to heat-related mortality. Moreover, the unification enables the transfer of methodology between hazards and a consistent treatment of uncertainty. This is demonstrated by a sensitivity analysis on the basis of two simple case studies (for coastal flood and storm damage). The analysis reveals the relevance of the various uncertainty sources at varying hazard magnitude and on both the microscale and the macroscale level. Main findings are the dominance of uncertainty from the hazard magnitude and the persistent behaviour of intrinsic uncertainties on both scale levels. Our results shed light on the general role of uncertainties and provide useful insight for the application of the unified approach

Damage and protection cost curves for coastal floods within the 600 largest European cities

The economic assessment of the impacts of storm surges and sea-level rise in coastal cities requires high-level information on the damage and protection costs associated with varying flood heights. We provide a systematically and consistently calculated dataset of macroscale damage and protection cost curves for the 600 largest European coastal cities opening the perspective for a wide range of applications. Offering the first comprehensive dataset to include the costs of dike protection, we provide the underpinning information to run comparative assessments of costs and benefits of coastal adaptation. Aggregate cost curves for coastal flooding at the city-level are commonly regarded as by-products of impact assessments and are generally not published as a standalone dataset. Hence, our work also aims at initiating a more critical discussion on the availability and derivation of cost curves

How people interact in evolving online affiliation networks

The study of human interactions is of central importance for understanding the behavior of individuals, groups, and societies. Here, we observe the formation and evolution of networks by monitoring the addition of all new links, and we analyze quantitatively the tendencies used to create ties in these evolving online affiliation networks. We show that an accurate estimation of these probabilistic tendencies can be achieved only by following the time evolution of the network. Inferences about the reason for the existence of links using statistical analysis of network snapshots must therefore be made with great caution. Here, we start by characterizing every single link when the tie was established in the network. This information allows us to describe the probabilistic tendencies of tie formation and extract meaningful sociological conclusions. We also find significant differences in behavioral traits in the social tendencies among individuals according to their degree of activity, gender, age, popularity, and other attributes. For instance, in the particular data sets analyzed here, we find that women reciprocate connections 3 times as much as men and that this difference increases with age. Men tend to connect with the most popular people more often than women do, across all ages. On the other hand, triangular tie tendencies are similar, independent of gender, and show an increase with age. These results require further validation in other social settings. Our findings can be useful to build models of realistic social network structures and to discover the underlying laws that govern establishment of ties in evolving social networks

Scaling laws of human interaction activity

Even though people in our contemporary, technological society are depending on communication, our understanding of the underlying laws of human communicational behavior continues to be poorly understood. Here we investigate the communication patterns in two social Internet communities in search of statistical laws in human interaction activity. This research reveals that human communication networks dynamically follow scaling laws that may also explain the observed trends in economic growth. Specifically, we identify a generalized version of Gibrat's law of social activity expressed as a scaling law between the fluctuations in the number of messages sent by members and their level of activity. Gibrat's law has been essential in understanding economic growth patterns, yet without an underlying general principle for its origin. We attribute this scaling law to long-term correlation patterns in human activity, which surprisingly span from days to the entire period of the available data of more than one year. Further, we provide a mathematical framework that relates the generalized version of Gibrat's law to the long-term correlated dynamics, which suggests that the same underlying mechanism could be the source of Gibrat's law in economics, ranging from large firms, research and development expenditures, gross domestic product of countries, to city population growth. These findings are also of importance for designing communication networks and for the understanding of the dynamics of social systems in which communication plays a role, such as economic markets and political systems.Comment: 20+7 pages, 4+2 figure

About the influence of elevation model quality and small-scale damage functions on flood damage estimation

The assessment of coastal flood risks in a particular region requires the estimation of typical damages caused by storm surges of certain characteristics and annualities. Although the damage depends on a multitude of factors, including flow velocity, duration of flood, precaution, etc., the relationship between flood events and the corresponding average damages is usually described by a stage-damage function, which considers the maximum water level as the only damage influencing factor. Starting with different (microscale) building damage functions we elaborate a macroscopic damage function for the entire case study area Kalundborg (Denmark) on the basis of multiple coarse-graining methods and assumptions of the hydrological connectivity. We find that for small events, the macroscopic damage function mostly depends on the properties of the elevation model, while for large events it strongly depends on the assumed building damage function. In general, the damage in the case study increases exponentially up to a certain level and then less steep

The Area and Population of Cities: New Insights from a Different Perspective on Cities

The distribution of the population of cities has attracted a great deal of attention, in part because it sharply constrains models of local growth. However, to this day, there is no consensus on the distribution below the very upper tail, because available data need to rely on the “legal” rather than “economic” definition of cities for medium and small cities. To remedy this difficulty, in this work we construct cities “from the bottom up” by clustering populated areas obtained from high-resolution data. This method allows us to investigate the population and area of cities for urban agglomerations of all sizes. We find that Zipf’s law (a power law with exponent close to 1) for population holds for cities as small as 12,000 inhabitants in the USA and 5,000 inhabitants in Great Britain. In addition the distribution of city areas is also close to a Zipf’s law. We provide a parsimonious model with endogenous city area that is consistent with those findings.