Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scale Invariant Avalanches: A Critical Confusion   The "Self-organized criticality" (SOC), introduced in 1987 by Bak, Tang and
Wiesenfeld, was an attempt to explain the 1/f noise, but it rapidly evolved
towards a more ambitious scope: explaining scale invariant avalanches. In two
decades, phenomena as diverse as earthquakes, granular piles, snow avalanches,
solar flares, superconducting vortices, sub-critical fracture, evolution, and
even stock market crashes have been reported to evolve through scale invariant
avalanches. The theory, based on the key axiom that a critical state is an
attractor of the dynamics, presented an exponent close to -1 (in two
dimensions) for the power-law distribution of avalanche sizes. However, the
majority of real phenomena classified as SOC present smaller exponents, i.e.,
larger absolute values of negative exponents, a situation that has provoked a
lot of confusion in the field of scale invariant avalanches. The main goal of
this chapter is to shed light on this issue. The essential role of the exponent
value of the power-law distribution of avalanche sizes is discussed. The
exponent value controls the ratio of small and large events, the energy balance
--required for stationary systems-- and the critical properties of the
dynamics. A condition of criticality is introduced. As the exponent value
decreases, there is a decrease of the critical properties, and consequently the
system becomes, in principle, predictable. Prediction of scale invariant
avalanches in both experiments and simulations are presented. Other sources of
confusion as the use of logarithmic scales, and the avalanche dynamics in well
established critical systems, are also revised; as well as the influence of
dissipation and disorder in the "self-organization" of scale invariant
dynamics.

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The categories of this paper are: alg-geom
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: math
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The categories of this paper are: supr-con
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: cs