Critical Phenomena in Natural Sciences: Chaos, Fractals, Selforganization and Disorder: Concepts and Tools

By S. Franz. 2004

643 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/ef509c9d5744f3d30041d788f17a24f850d6f0aa

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In Economics and Econometrics

Citations in the corpus

Power-law distributions in binned empirical data (2012, background): “…properties, which sometimes lead to surprising consequences, and for their appearance in a wide range of natural and man-made phenomena, spanning physics, chemistry, biology, computer science, economics and the social sciences [Mitzen-macher (2004), Newman (2005), Sornette (2006), Gabaix (2009)].”
Early warning signals also precede non-catastrophic transitions (2013, background): “In the case of ecosystems, but also more generally of complex systems (Sornette 2002, 2003, Peters and Pielke linear autoregressive model of first order (AR(1), xt 1 2 m 5 a1(xt 2 m) e, where a1 is the autoregressive coefficient of order 1, m the mean of the timeseries and e an error i.i.d term)…”
Seismic precursory patterns before a cliff collapse and critical point phenomena (2005, background): “Many observables of the system dynamics are supposed to diverge (as measured by power law behavior) when the system moves toward the critical point [Sornette, 2000].”
Heavy-Tailed Universality Predicts Trends in Test Accuracies for Very Large Pre-Trained Deep Neural Networks (2019, background): “In Statistical Physics, Universality of PL exponents is very non-trivial, and it suggests the presence of a deeper, underlying, Universal mechanism driving the system dynamics [21, 22].”
Predictability of catastrophic events: Material rupture, earthquakes, turbulence, financial crashes, and human birth (2001, background): “Predictability of catastrophic events: Material rupture, earthquakes, turbulence, financial crashes, and human birth”
Implicit Self-Regularization in Deep Neural Networks: Evidence from Random Matrix Theory and Implications for Learning (2018, methodology): “A different mechanism for this has been described by Sornette, who suggests it can arise more generally in natural Self-Organizing systems, without needing to tune specific exogenous control parameters [134].”
Systemic Risks in Society and Economics (2010, neutral): “[1] D. Sornette (2006) Critical Phenomena in Natural Sciences: Chaos, Fractals, Selforganization and Disorder.”
Power law distributions in entrepreneurship: : Implications for theory and research (2015, background): “A PL distribution has unstable means, near-infinite variance, and a greater proportion of extreme events (Sornette, 2006).”
25 Years of Self-Organized Criticality: Solar and Astrophysics (2014, neutral): “3.11 in Sornette 2004).”
Mainshocks are aftershocks of conditional foreshocks: How do foreshock statistical properties emerge from aftershock laws (2002, methodology): “…variables with distribution p(x) ∼ 1/x1+m with m < 2, we can use the generalized central limit theorem to obtain that PN(X) converges for large N to a stable Lévy law Lm with index equal to the exponent m and scale factor ∑N j=1 Kmj [Gnedenko and Kolmogorov, 1954; Sornette, 2000]: PN (SN) →N→∞ Lm”
Power laws and Self-Organized Criticality in Theory and Nature (2013, background): “For additional information with respect to several alternative mechanisms, not mentioned here, we refer the reader to several sources [115, 121, 151, 145].”
Dragon-kings: Mechanisms, statistical methods and empirical evidence (2012, positive): “Many phenomena in the physical, natural, economic and social sciences can be characterized by power-law statistics, for which there are many different mechanisms (Mitzenmacher, 2003; Newman, 2005; Sornette, 2006).”
Recent advances in percolation theory and its applications (2015, background): “This however neither means that the connectivity transition at pc is characterized by a usual power-law divergence of the order parameter [184, 185, 186] nor that it cannot be followed by multiple discontinuous transitions.”