Probability Distributions in Complex Systems

Sornette, Didier

doi:10.1007/978-1-4614-1800-9_142

Cited by 11 publications

(11 citation statements)

References 79 publications

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“…The study of the statistics and dynamics of series of events with approximate global models has been one of the most popular topics in the last twenty years, specially within the interdisciplinary study of complex systems. Probability distribution functions with a heavy tailed dependence in terms of event or object sizes seem to be ubiquitous statistical features of self-organized natural and social complex systems [7]. The appearance of algebraic distributions, specially power laws, is often thought to be the signature of hierarchy, robustness, criticality and universal subjacent mechanisms [8].…”

Section: Probability Distribution Analysismentioning

confidence: 99%

Analysis of major failures in Europe’s power grid

Rosas-Casals

Solé

2011

International Journal of Electrical Power & Energy Systems

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Power grids are prone to failure. Time series of reliability measures such as total power loss or energy not supplied can give significant account of the underlying dynamical behavior of these systems, specially when the resulting probability distributions present remarkable features such as an algebraic tail, usually considered the footprint of self-organization and the existence of critical points. In this paper, 7 years (from 2002 to 2008) of Europe’s transport of electricity network failure events have been analyzed and the best fit for this empirical data probability distribution is presented. With the actual span of available data and although there exists a moderate support for the power-law model, the relatively small amount of events contained in the function’s tail suggests that causal factors other than self-organization or a critical state might be significantly ruling these systems’ dynamics.Peer ReviewedPostprint (author’s final draft

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Section: Probability Distribution Analysismentioning

confidence: 99%

Analysis of major failures in Europe’s power grid

Rosas-Casals

Solé

2011

International Journal of Electrical Power & Energy Systems

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“…Davy et al, 1990;Sornette et al, 1993;Cowie et al, 1995). Although power-law distributions have been used to describe scaling laws of faults and other structures in Earth Science, the validity of a power law fit to a dataset should be tested (Sornette, 2009). The detection of power laws is complicated by the large fluctuations that occur in the tail of the distribution.…”

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confidence: 99%

Scaling of fault attributes: A review

Torabi

Berg

2011

Marine and Petroleum Geology

309

191

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“…The scale-free property of the highly-skewed distributions has been a source of fascination for many physicists that sought deep analogies with other scale-free phenomena such as fractals, phase transitions and critical phenomena. [2,[8][9][10][11][12] Complex networks provide an abundant source of highly-skewed distributions. [13] The first object identified as a complex network was citations to scientific papers.…”

Section: Introductionmentioning

confidence: 99%

Power-Law Citation Distributions are Not Scale-Free

Golosovsky¹

2019

SpringerBriefs in Complexity

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We analyze time evolution of statistical distributions of citations to scientific papers published in one year. While these distributions can be fitted by a power-law dependence we find that they are nonstationary and the exponent of the power law fit decreases with time and does not come to saturation. We attribute the nonstationarity of citation distributions to different longevity of the low-cited and highly-cited papers. By measuring citation trajectories of papers we found that citation careers of the low-cited papers come to saturation after 10-15 years while those of the highly-cited papers continue to increase indefinitely: the papers that exceed some citation threshold become runaways. Thus, we show that although citation distribution can look as a power-law, it is not scale-free and there is a hidden dynamic scale associated with the onset of runaways. We compare our measurements to our recently developed model of citation dynamics based on copying/redirection/triadic closure and find explanations to our empirical observations.

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Probability Distributions in Complex Systems

Cited by 11 publications

References 79 publications

Analysis of major failures in Europe’s power grid

Analysis of major failures in Europe’s power grid

Scaling of fault attributes: A review

Power-Law Citation Distributions are Not Scale-Free

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