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intro

Welcome to the web-page of the IJCNN Tutorial

Self-Organized Criticality: Avalanches in Neural Networks, Active Learning, and Intelligent Control.

Organizers: J. Michael Herrmann, Anna Levina

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Power-law distributions are frequently found in the sciences that study ``complex'' systems. They are observed, for instance, in the population sizes of cities, in the sizes of earthquakes, the frequencies of words in a text, in neurological data, in the severity of violent conflicts, and in the migration of albatrosses. The multitude of examples includes in particular problems such as the function of the brain, ecosystems, and society, which are of vital interest to all of us.

It is natural to think that the prevalence of spatio-temporal power-law statistics is not accidental. On the contrary, it is most likely that there exists an underlying pattern. The pursuit of such a pattern attracted many scientists; as a result, there exist dozens of model algorithms to generate power-law distributions []. However, most algorithms lack a unifying concept, which would not only provide power-law distributions, but also explain their role and highlight the similarity of the systems where they appear. A concept which filled this gap was proposed by Bak, Tang and Wiesenfeld [1] and is called self-organized criticality (SOC). The idea of SOC is indeed very simple: it proposes that the system has a critical state as an attractor. It is well known in statistical physics that near a phase transition observable of the system has a power-law distribution. However, in equilibrium systems, the critical point is reached only by tuning a control parameter precisely, which makes it rather rare to be found stable in freely developing systems. Thus, SOC proposes to have a look at non-equilibrium systems instead.

Starting with the first article in 1987, more than 8000 articles have been published on SOC, and more than 1000 over the last two years (data from Google scholar). Regardless of the number of publications, there are still many questions to be answered; some have not even been asked

Anna Levina and J. Michael Herrmann