Modelling the influence of photospheric turbulence on solar flare statistics

Mendoza, M.; Kaydul, A.; Arcangelis, L. de; Andrade, José S.; Herrmann, Hans J.

doi:10.1038/ncomms6035

Cited by 17 publications

(17 citation statements)

References 38 publications

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“…In Fig. 3 the duration distributions of up and down-states indeed show that down-states can last much longer that up-states, in agreement with experimental data on rat visual cortex [40] and simulations of integrate and fire neuron networks [41].…”

Section: Up-states and Down-statessupporting

confidence: 84%

Avalanche Dynamics and Correlations in Neural Systems

Lombardi

Herrmann²,

Arcangelis

2019

Springer Series on Bio- And Neurosystems

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The existence of power law distributions is only a first requirement in the validation of the critical behavior of a system. Long-range spatio-temporal correlations are fundamental for the spontaneous neuronal activity to be the expression of a system acting close to a critical point. This chapter focuses on temporal correlations and avalanche dynamics in the spontaneous activity of cortex slice cultures and in the resting fMRI BOLD signal. Long-range correlations are investigated by means of the scaling of power spectra and of Detrended Fluctuations Analysis. The existence of 1/ f decay in the power spectrum, as well as of power-law scaling in the root mean square fluctuation function for the appropriate balance of excitation and inhibition suggests that long-range temporal correlations are distinctive of "healthy brains". The corresponding temporal organization of neuronal avalanches can be dissected by analyzing the distribution of inter-event times between successive events. In rat cortex slice cultures this distribution exhibits a non-monotonic behavior, not usually found in other natural processes. Numerical simulations provide evidences that this behavior is a consequence of the alternation between states of high and low activity, leading to a dynamic balance between excitation and inhibition that tunes the system at criticality. In this scenario, inter-times show a peculiar relation with avalanche sizes, resulting in a hierarchical structure of avalanche sequences. Large avalanches correspond to low-frequency oscillations, and trigger cascades of smaller ones that are part of higher frequency rhythms. The selfregulated balance of excitation and inhibition observed in cultures is confirmed at

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Section: Up-states and Down-statessupporting

confidence: 84%

Avalanche Dynamics and Correlations in Neural Systems

Lombardi

Herrmann²,

Arcangelis

2019

Springer Series on Bio- And Neurosystems

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“…SOC systems are characterized by their avalanche dynamics resulting from slow driving of the system. Vortex avalanche dynamics in type II superconductors [6], earthquakes [7], solar flares [8], microfracturing processes [9], fluid flow in porous media [10], phase transition-like behavior of the magnetosphere [11], bursts in filters [12], phase transitions in jammed granular matter [3], and avalanches dynamics in the rat cortex [13] are some natural examples for SOC. This large class of natural systems inspired theoretical models with the aim of capturing the dominant internal dynamics that causes the avalanches.…”

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confidence: 99%

Geometry-induced nonequilibrium phase transition in sandpiles

et al. 2020

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We study the sandpile model on three-dimensional spanning Ising clusters with the temperature T treated as the control parameter. By analyzing the three dimensional avalanches and their twodimensional projections (which show scale-invariant behavior for all temperatures), we uncover two universality classes with different exponents (an ordinary BTW class, and SOCT =∞), along with a tricritical point (at Tc, the critical temperature of the host) between them. The SOCT =∞ universality class is characterized by the exponent of the avalanche size distribution τ T =∞ = 1.27 ± 0.03, consistent with the exponent of the size distribution of the Barkhausen avalanches in amorphous ferromagnets (Phys. Rev. L 84, 4705 (2000)). The tricritical point is characterized by its own critical exponents and also some additional scaling behavior in its vicinity. In addition to the avalanche exponents, some other quantities like the average height, the spanning avalanche probability (SAP) and the average coordination number of the Ising clusters change significantly the behavior at this point, and also exhibit power-law behavior in terms of ≡ T −Tc Tc , defining further critical exponents. Importantly the finite size analysis for the activity (number of topplings) per site shows the scaling behavior with exponents β = 0.19 ± 0.02 and ν = 0.75 ± 0.05. A similar behavior is also seen for the SAP and the average avalanche height. The fractal dimension of the external perimeter of the two-dimensional projections of avalanches is shown to be robust against T with the numerical value D f = 1.25 ± 0.01.In the context of out-of-equilibrium critical phenomena, self-organized critical (SOC) systems have attracted much attention because of their role in a wide range of systems, from finance [1] and biological [2] to granular matter [3], the brain [4] and neural networks in general [5]. SOC systems are characterized by their avalanche dynamics resulting from slow driving of the system. Vortex avalanche dynamics in type II superconductors [6], earthquakes [7], solar flares [8], microfracturing processes [9], fluid flow in porous media [10], phase transition-like behavior of the magnetosphere [11], bursts in filters [12], phase transitions in jammed granular matter [3], and avalanches dynamics in the rat cortex [13] are some natural examples for SOC. This large class of natural systems inspired theoretical models with the aim of capturing the dominant internal dynamics that causes the avalanches.Here we find evidence for a novel non-equilibrium universality class, and propose a new type of outof-equilibrium phase transition between SOC models induced by the geometry of the underlying graph upon which the model is defined. It might be applicable to experiments with spatial flow patterns of transport in heterogeneous porous media [14], which involve the toppling of fluid [15]. Another example is the Barkhausen effect in magnetic systems [16], for which the avalanches have been shown to exhibit scaling behavior with an avalanche size exponent 1.27 ± 0....

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“…Bursty dynamics characterizes a wide variety of physical systems. Examples include earthquakes in the earth’s crust 1 , chemical reactions 2 , solar flares 3 4 or Barkhausen noise in ferromagnets 5 , to cite only a few. In neuronal networks, both in vitro and in vivo , bursts arise from the near synchronous firing of many neurons 6 7 8 9 10 11 12 13 14 .…”

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confidence: 99%

“…In order to better understand the relationship between quiescence and activity, here we propose an alternative approach to the study of correlations in spontaneous cortical activity, which has been successfully introduced to address the longstanding problem of magnitude correlations in seismic and solar flare activity 3 4 42 and has recently been applied to the analysis of the fMRI BOLD signal 43 44 . This approach is based on the method of surrogate data 45 and consists in a systematic comparison of conditional probabilities evaluated in the real time series with the ones evaluated in a time series where avalanche sizes are randomly reshuffled.…”

mentioning

confidence: 99%

“…This approach is based on the method of surrogate data 45 and consists in a systematic comparison of conditional probabilities evaluated in the real time series with the ones evaluated in a time series where avalanche sizes are randomly reshuffled. Such a procedure is very efficient in case of large statistical fluctuations in the data 3 4 42 , as for the avalanche time series we analyze. Indeed, in the Supplementary Information (SI) we show that both correlation functions and scatter plots, which are commonly used to investigate the relationship between avalanche sizes and quiet times, are strongly affected by statistical noise, exhibiting fluctuations as large as the ones measured in uncorrelated data sets ( Supplementary Figs S1–S3 ).…”

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confidence: 99%

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Temporal correlations in neuronal avalanche occurrence

Lombardi

Herrmann

Plenz³

et al. 2016

Sci Rep

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Ongoing cortical activity consists of sequences of synchronized bursts, named neuronal avalanches, whose size and duration are power law distributed. These features have been observed in a variety of systems and conditions, at all spatial scales, supporting scale invariance, universality and therefore criticality. However, the mechanisms leading to burst triggering, as well as the relationship between bursts and quiescence, are still unclear. The analysis of temporal correlations constitutes a major step towards a deeper understanding of burst dynamics. Here, we investigate the relation between avalanche sizes and quiet times, as well as between sizes of consecutive avalanches recorded in cortex slice cultures. We show that quiet times depend on the size of preceding avalanches and, at the same time, influence the size of the following one. Moreover we evidence that sizes of consecutive avalanches are correlated. In particular, we show that an avalanche tends to be larger or smaller than the following one for short or long time separation, respectively. Our analysis represents the first attempt to provide a quantitative estimate of correlations between activity and quiescence in the framework of neuronal avalanches and will help to enlighten the mechanisms underlying spontaneous activity.

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Modelling the influence of photospheric turbulence on solar flare statistics

Cited by 17 publications

References 38 publications

Avalanche Dynamics and Correlations in Neural Systems

Avalanche Dynamics and Correlations in Neural Systems

Geometry-induced nonequilibrium phase transition in sandpiles

Temporal correlations in neuronal avalanche occurrence

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