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Self-Organized Criticality
01 Jan 1998-
About: The article was published on 1998-01-01 and is currently open access. It has received 610 citations till now.
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TL;DR: The major concepts and results recently achieved in the study of the structure and dynamics of complex networks are reviewed, and the relevant applications of these ideas in many different disciplines are summarized, ranging from nonlinear science to biology, from statistical mechanics to medicine and engineering.
9,441 citations
TL;DR: Viewing the brain in terms of collective dynamics is one approach now yielding some insight.
Abstract: Is the brain on the edge of criticality? Understanding the inner workings of the brain is a task made difficult by the number of elements involved: a hundred billion neurons and a hundred trillion synapses. Viewing the brain in terms of collective dynamics is one approach now yielding some insight.
1,011 citations
TL;DR: An overview of a complex systems approach to large blackouts of electric power transmission systems caused by cascading failure is given and it is suggested that power system operating margins evolve slowly to near a critical point and confirmed using a power system model.
Abstract: We give an overview of a complex systems approach to large blackouts of electric power transmission systems caused by cascading failure. Instead of looking at the details of particular blackouts, we study the statistics and dynamics of series of blackouts with approximate global models. Blackout data from several countries suggest that the frequency of large blackouts is governed by a power law. The power law makes the risk of large blackouts consequential and is consistent with the power system being a complex system designed and operated near a critical point. Power system overall loading or stress relative to operating limits is a key factor affecting the risk of cascading failure. Power system blackout models and abstract models of cascading failure show critical points with power law behavior as load is increased. To explain why the power system is operated near these critical points and inspired by concepts from self-organized criticality, we suggest that power system operating margins evolve slowly to near a critical point and confirm this idea using a power system model. The slow evolution of the power system is driven by a steady increase in electric loading, economic pressures to maximize the use of the grid, and the engineering responses to blackouts that upgrade the system. Mitigation of blackout risk should account for dynamical effects in complex self-organized critical systems. For example, some methods of suppressing small blackouts could ultimately increase the risk of large blackouts.
877 citations
TL;DR: The method allows, for the first time, to define a theoretical framework in terms of an order and control parameter derived from fMRI data, where the dynamical regime can be interpreted as one corresponding to a system close to the critical point of a second order phase transition.
Abstract: Functional magnetic resonance imaging (fMRI) techniques have contributed significantly to our understanding of brain function. Current methods are based on the analysis of gradual and continuous changes in the brain blood oxygenated level dependent (BOLD) signal. Departing from that approach, recent work has shown that equivalent results can be obtained by inspecting only the relatively large amplitude BOLD signal peaks, suggesting that relevant information can be condensed in discrete events. This idea is further explored here to demonstrate how brain dynamics at resting state can be captured just by the timing and location of such events, i.e., in terms of a spatiotemporal point process. The method allows, for the first time, to define a theoretical framework in terms of an order and control parameter derived from fMRI data, where the dynamical regime can be interpreted as one corresponding to a system close to the critical point of a second order phase transition. The analysis demonstrates that the resting brain spends most of the time near the critical point of such transition and exhibits avalanches of activity ruled by the same dynamical and statistical properties described previously for neuronal events at smaller scales. Given the demonstrated functional relevance of the resting state brain dynamics, its representation as a discrete process might facilitate large-scale analysis of brain function both in health and disease.
671 citations
TL;DR: Two experiments demonstrate 1/f scaling (pink noise) in simple reaction times and speeded word naming times, which round out a catalog of laboratory task demonstrations that background noise is pink noise.
Abstract: Background noise is the irregular variation across repeated measurements of human performance. Background noise remains after task and treatment effects are minimized. Background noise refers to intrinsic sources of variability, the intrinsic dynamics of mind and body, and the internal workings of a living being. Two experiments demonstrate 1/f scaling (pink noise) in simple reaction times and speeded word naming times, which round out a catalog of laboratory task demonstrations that background noise is pink noise. Ubiquitous pink noise suggests processes of mind and body that change each other's dynamics. Such interaction-dominant dynamics are found in systems that self-organize their behavior. Self-organization provides an unconventional perspective on cognition, but this perspective closely parallels a contemporary interdisciplinary view of living systems.
659 citations