A heavenly example of scale-free networks and self-organized criticality

Paczuski, Maya; Hughes, David

doi:10.1016/j.physa.2004.04.073

Cited by 22 publications

(19 citation statements)

References 12 publications

(9 reference statements)

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“…These bursts can reach sufficiently high energies to pose a risk to astronauts, spacecraft, or airplanes following polar routes. In addition they exhibit a number of empirical features associated with SOC [9,15,16,17,18,19]. For instance, the distribution of event durations and quiet times is a power-law for both solar flux and the BTW sandpile [9], once physically relevant detection thresholds are taken into account to compare these time series on an equal basis.…”

Section: Solar X-ray Fluxmentioning

confidence: 99%

Activity-dependent branching ratios in stocks, solar x-ray flux, and the Bak-Tang-Wiesenfeld sandpile model

2010

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We define an activity dependent branching ratio that allows comparison of different time series Xt. The branching ratio bx is defined as bx = E[ξx/x]. The random variable ξx is the value of the next signal given that the previous one is equal to x, so ξx = {Xt+1|Xt = x}. If bx > 1, the process is on average supercritical when the signal is equal to x, while if bx < 1, it is subcritical. For stock prices we find bx = 1 within statistical uncertainty, for all x, consistent with an "efficient market hypothesis". For stock volumes, solar X-ray flux intensities, and the Bak-Tang-Wiesenfeld (BTW) sandpile model, bx is supercritical for small values of activity and subcritical for the largest ones, indicating a tendency to return to a typical value. For stock volumes this tendency has an approximate power law behavior. For solar X-ray flux and the BTW model, there is a broad regime of activity where bx ≃ 1, which we interpret as an indicator of critical behavior. This is true despite different underlying probability distributions for Xt, and for ξx. For the BTW model the distribution of ξx is Gaussian, for x sufficiently larger than one, and its variance grows linearly with x. Hence, the activity in the BTW model obeys a central limit theorem when sampling over past histories. The broad region of activity where bx is close to one disappears once bulk dissipation is introduced in the BTW model -supporting our hypothesis that it is an indicator of criticality.

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Section: Solar X-ray Fluxmentioning

confidence: 99%

Activity-dependent branching ratios in stocks, solar x-ray flux, and the Bak-Tang-Wiesenfeld sandpile model

2010

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“…It is convenient to quote the seminal work by Voss and Clarke [5]. These authors have found in fact that music composition yields a 1/f noise spectrum, which is generally regarded as a complexity manifestation [6,7,8,9].…”

Section: Introductionmentioning

confidence: 99%

Brain, music, and non-Poisson renewal processes

et al. 2007

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In this paper we show that both music composition and brain function, as revealed by the electroencephalogram ͑EEG͒ analysis, are renewal non-Poisson processes living in the nonergodic dominion. To reach this important conclusion we process the data with the minimum spanning tree method, so as to detect significant events, thereby building a sequence of times, which is the time series to analyze. Then we show that in both cases, EEG and music composition, these significant events are the signature of a non-Poisson renewal process. This conclusion is reached using a technique of statistical analysis recently developed by our group, the aging experiment ͑AE͒. First, we find that in both cases the distances between two consecutive events are described by nonexponential histograms, thereby proving the non-Poisson nature of these processes. The corresponding survival probabilities ⌿͑t͒ are well fitted by stretched exponentials ͓⌿͑t͒ ϰ exp (−͑␥t͒ ␣ ), with 0.5Ͻ ␣ Ͻ 1.͔ The second step rests on the adoption of AE, which shows that these are renewal processes. We show that the stretched exponential, due to its renewal character, is the emerging tip of an iceberg, whose underwater part has slow tails with an inverse power law structure with power index =1+␣. Adopting the AE procedure we find that both EEG and music composition yield Ͻ 2. On the basis of the recently discovered complexity matching effect, according to which a complex system S with S Ͻ 2 responds only to a complex driving signal P with P ഛ S , we conclude that the results of our analysis may explain the influence of music on the human brain.

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“…The distribution of magnetic concentration sizes on the photosphere is also scale invariant, and the coronal magnetic network embodies a scale-free network [4,5]. In fact, a model of self-organized criticality (SOC) with avalanches of reconnecting flux tubes reproduces the observed scale-free network structure [4,6].As part of the debate on the characterization of magnetohydrodynamic turbulence in this regime [1,4,5,6,7,8,9], interest has focused on comparing interoccurrence times between flares with those in models of SOC. Analyses of flare catalogs have indicated scale invariance of the waiting times, but the behavior was found to vary with the phase of the solar cycle [10] and with the methods used to analyze the catalogs.…”

mentioning

confidence: 99%

Intensity Thresholds and the Statistics of the Temporal Occurrence of Solar Flares

2006

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Introducing thresholds to analyze time series of emission from the Sun enables a new and simple definition of solar flare events, and their interoccurrence times. Rescaling time by the rate of events, the waiting and quiet time distributions both conform to scaling functions that are independent of the intensity threshold over a wide range. The scaling functions are well described by a two parameter function, with parameters that depend on the phase of the solar cycle. For flares identified according to the current, standard definition, similar behavior is found.PACS numbers: 96.60. Rd, 05.45.Tp, 05.65.+b The solar corona is a very high Reynolds number turbulent plasma producing intermittent bursts of radiation. Plasma forces twist the coronal magnetic fields until stresses are suddenly released, an avalanching process governed by magnetic reconnection [1]. The released magnetic energy induces radiative emission that can be detected as a flare. Flares exhibit scale invariant statistics. For instance, the probability distribution of flare energies is a power law spanning more than eight orders of magnitude [2,3], similar to the Gutenberg-Richter law for earthquakes. The distribution of magnetic concentration sizes on the photosphere is also scale invariant, and the coronal magnetic network embodies a scale-free network [4,5]. In fact, a model of self-organized criticality (SOC) with avalanches of reconnecting flux tubes reproduces the observed scale-free network structure [4,6].As part of the debate on the characterization of magnetohydrodynamic turbulence in this regime [1,4,5,6,7,8,9], interest has focused on comparing interoccurrence times between flares with those in models of SOC. Analyses of flare catalogs have indicated scale invariance of the waiting times, but the behavior was found to vary with the phase of the solar cycle [10] and with the methods used to analyze the catalogs. (See e.g. Ref. [10,11].) The prior belief that avalanches occur with Poissonian waiting times in the well-known BTW sandpile model [12] (giving an exponential distribution of waiting times) argued against the SOC hypothesis [8]. However, including a finite detection threshold leads to a power law distribution of quiet times even for the BTW model [13], when durations and quiet times are measured with the same clock. Since the turnover time scale for flux to be regenerated in the corona is of the order of ten hours [14], while the correlated waiting time intervals between flares can extend up to years, the physical mechanism(s) responsible for these correlations resides in the turbulent convective region beneath the photosphere that generates magnetic flux and drives it into the corona. Systematic studies of the temporal pattern of flares can give insight into the dynamics of magnetic flux in the convective region, or the solar dynamo, which is difficult to observe directly.Here we show that the interoccurrence times between flares has a hierarchical scaling structure when flares are defined as intervals during which the emissi...

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A heavenly example of scale-free networks and self-organized criticality

Cited by 22 publications

References 12 publications

Activity-dependent branching ratios in stocks, solar x-ray flux, and the Bak-Tang-Wiesenfeld sandpile model

Activity-dependent branching ratios in stocks, solar x-ray flux, and the Bak-Tang-Wiesenfeld sandpile model

Brain, music, and non-Poisson renewal processes

Intensity Thresholds and the Statistics of the Temporal Occurrence of Solar Flares

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