Complexity and Random Overlaps

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To investigate the dynamics of social networks and the formation and evolution of online communities in response to extreme events, we collected three datasets from Twitter shortly before and after the 2011 earthquake and tsunami in Japan. We find that while almost all users increased their online activity after the earthquake, Japanese speakers, who are assumed to be more directly affected by the event, expanded the network of people they interact with to a much higher degree than English speakers or the global average. By investigating the evolution of communities, we find that the behavior of joining or quitting a community is far from random: users tend to stay in their current status and are less likely to join new communities from solitary or shift to other communities from their current community. While non-Japanese speakers did not change their conversation topics significantly after the earthquake, nearly all Japanese users changed their conversations to earthquake-related content. This study builds a systematic framework for investigating human behaviors under extreme events with online social network data and our findings on the dynamics of networks and communities may provide useful insight for understanding how patterns of social interaction are influenced by extreme events.

Network Structure and Community Evolution on Twitter: Human Behavior Change in Response to the 2011 Japanese Earthquake and Tsunami
• Xin Lu & Christa Brelsford

Scientific Reports 4, Article number: 6773 http://dx.doi.org/10.1038/srep06773

What allows a creative enterprise—a film studio, a design firm, a start-up—to flourish? It's an old question, but one that has become increasingly relevant in the transition to an information economy. In the new book Collective…

We have known for at least 100 years that a brain is organized as a network of connections between nerve cells. But in the last 10 years there has been a rapid growth in our capacity to quantify the complex topological pattern of brain connectivity, using mathematical tools drawn from graph theory.
Here we bring together articles and reviews from some of the world’s leading experts in contemporary brain network analysis by graph theory. The contributions are focused on three big questions that seem important at this stage in the scientific evolution of the field: How does the topology of a brain network relate to its physical embedding in anatomical space and its biological costs? How does brain network topology constrain brain dynamics and function? And what seem likely to be important future methodological developments in the application of graph theory to analysis of brain networks?
Clearer understanding of the principles of brain network organization is fundamental to understanding many aspects of cognitive function, brain development and clinical brain disorders. We hope this issue provides a forward-looking window on this fast moving field and captures some of the excitement of recent progress in applying the concepts of graph theory to measuring and modeling the complexity of brain networks.

Complex network theory and the brain
Issue compiled and edited by David Papo, Javier M. Buldú, Stefano Boccaletti and Edward T. Bullmore

http://rstb.royalsocietypublishing.org/site/2014/network.xhtml

The importance of complexity is well-captured by Hawking's comment: "Complexity is the science of the 21st century". From the movement of flocks of birds to the Internet, environmental sustainability, and market regulation, the study and understanding of complex non-linear systems has become highly influential over the last 30 years.

In this Very Short Introduction, one of the leading figures in the field, John Holland, introduces the key elements and conceptual framework of complexity. From complex physical systems such as fluid flow and the difficulties of predicting weather, to complex adaptive systems such as the highly diverse and interdependent ecosystems of rainforests, he combines simple, well-known examples -- Adam Smith's pin factory, Darwin's comet orchid, and Simon's 'watchmaker' -- with an account of
the approaches, involving agents and urn models, taken by complexity theory.

Over the past thirty years, a new systemic conception of life has emerged at the forefront of science. New emphasis has been given to complexity, networks, and patterns of organisation leading to a novel kind of 'systemic' thinking. This volume integrates the ideas, models, and theories underlying the systems view of life into a single coherent framework. Taking a broad sweep through history and across scientific disciplines, the authors examine the appearance of key concepts such as autopoiesis, dissipative structures, social networks, and a systemic understanding of evolution. The implications of the systems view of life for health care, management, and our global ecological and economic crises are also discussed. Written primarily for undergraduates, it is also essential reading for graduate students and researchers interested in understanding the new systemic conception of life and its implications for a broad range of professions - from economics and politics to medicine, psychology and law.

A number of social-ecological systems exhibit complex behavior associated with nonlinearities, bifurcations, and interaction with stochastic drivers. These systems are often prone to abrupt and unexpected instabilities and state shifts that emerge as a discontinuous response to gradual changes in environmental drivers. Predicting such behaviors is crucial to the prevention of or preparation for unwanted regime shifts. Recent research in ecology has investigated early warning signs that anticipate the divergence of univariate ecosystem dynamics from a stable attractor. To date, leading indicators of instability in systems with multiple interacting components have remained poorly investigated. This is a major limitation in the understanding of the dynamics of complex social-ecological networks. Here, we develop a theoretical framework to demonstrate that rising variance—measured, for example, by the maximum element of the covariance matrix of the network—is an effective leading indicator of network instability. We show that its reliability and robustness depend more on the sign of the interactions within the network than the network structure or noise intensity. Mutualistic, scale free and small world networks are less stable than their antagonistic or random counterparts but their instability is more reliably predicted by this leading indicator. These results provide new advances in multidimensional early warning analysis and offer a framework to evaluate the resilience of social-ecological networks.

Early Warning Signs in Social-Ecological Networks.

PLoS ONE 9(7): e101851. doi:10.1371/journal.pone.0101851 (2014)

Suweis Samir, D'Odorico Paolo

Code of the analysis available at https://github.com/suweis

http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0101851