Many kinds of complex systems exhibit characteristic patterns of temporal correlations that emerge as the result of functional interactions within a structured network. One such complex system is the brain, composed of numerous neuronal units linked by synaptic connections. The activity of these neuronal units gives rise to dynamic states that are characterized by specific patterns of neuronal activation and co-activation. These patterns, called functional connectivity, are possible neural correlates of perceptual and cognitive processes. Which functional connectivity patterns arise depends (...) on the anatomical structure of the underlying network, which in turn is modified by a broad range of activity-dependent processes. Given this intricate relationship between structure and function, the question of how patterns of anatomical connectivity constrain or determine dynamical patterns is of considerable theoretical importance. The present study develops computational tools to analyze networks in terms of their structure and dynamics. We identify different classes of network, including networks that are characterized by high complexity. These highly complex networks have distinct structural characteristics such as clustered connectivity and short wiring length similar to those of large-scale networks of the cerebral cortex. (shrink)

How can our societies be stabilized in a crisis? Why do we enjoy and understand Shakespeare? Why are fruitflies uniform? How do omnivorous eating habits aid our survival? What makes the Mona Lisa's smile beautiful? How do women keep their social structures intact? -- Could there possibly be a single answer to all these questions? This book shows that the statement 'weak links stabilize complex systems' provides the key to understanding each of these intriguing puzzles, and many others too. The (...) author...uses weak (low affinity, low probability) interactions as a thread to introduce a vast variety of networks from proteins to economics and ecosystems. --From publisher description. (shrink)

Self-organized criticality (SOC) is based upon the idea that complex behavior can develop spontaneously in certain multi-body systems whose dynamics vary abruptly. This book is a clear and concise introduction to the field of self-organized criticality, and contains an overview of the main research results. The author begins with an examination of what is meant by SOC, and the systems in which it can occur. He then presents and analyzes computer models to describe a number of systems, and he explains (...) the different mathematical formalisms developed to understand SOC. The final chapter assesses the impact of this field of study, and highlights some key areas of new research. The author assumes no previous knowledge of the field, and the book contains several exercises. It will be ideal as a textbook for graduate students taking physics, engineering, or mathematical biology courses in nonlinear science or complexity. (shrink)