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An observational test of the critical earthquake concept
We test the concept that seismicity prior to a large earthquake can be understood in terms of the statistical physics of a critical phase transition. In this model, the cumulative seismic strainExpand
Robust dynamic classes revealed by measuring the response function of a social system
  • R. Crane, D. Sornette
  • Physics, Medicine
  • Proceedings of the National Academy of Sciences
  • 14 March 2008
TLDR
The relaxation response of a social system after endogenous and exogenous bursts of activity is studied using the time series of daily views for nearly 5 million videos on YouTube to provide a unique framework for the investigation of timing in complex systems. Expand
Critical Phenomena in Natural Sciences: Chaos, Fractals, Selforganization and Disorder: Concepts and Tools
Useful Notions of Probability Theory.- Sums of Random Variables, Random Walks and the Central Limit Theorem.- Large Deviations.- Power Law Distributions.- Fractals and Multifractals.- Rank-OrderingExpand
Stretched exponential distributions in nature and economy: “fat tails” with characteristic scales
Abstract:To account quantitatively for many reported “natural” fat tail distributions in Nature and Economy, we propose the stretched exponential family as a complement to the often used power lawExpand
Discrete scale invariance and complex dimensions
Abstract We discuss the concept of discrete-scale invariance and how it leads to complex critical exponents (or dimensions), i.e. to the log-periodic corrections to scaling. After their initialExpand
Discrete hierarchical organization of social group sizes
TLDR
This study combines data on human grouping patterns in a comprehensive and systematic study and identifies a discrete hierarchy of group sizes with a preferred scaling ratio close to three, which could reflect a hierarchical processing of social nearness by human brains. Expand
Testing the Pareto against the lognormal distributions with the uniformly most powerful unbiased test applied to the distribution of cities.
TLDR
The UMPU test is advocated as a systematic tool to address similar controversies in the literature of many disciplines involving power laws, scaling, "fat" or "heavy" tails, and in order to demonstrate that the procedure works for data sets other than the US city size distribution. Expand
Complex Critical Exponents from Renormalization Group Theory of Earthquakes: Implications for Earthquake Predictions
Several authors have proposed discrete renormalization group models of earthquakes, viewing them as a kind of dynamical critical phenomena. Here, we propose that the assumed discrete scale invarianceExpand
Economic Networks: The New Challenges
TLDR
An approach that stresses the systemic complexity of economic networks and that can be used to revise and extend established paradigms in economic theory will facilitate the design of policies that reduce conflicts between individual interests and global efficiency, as well as reduce the risk of global failure by making economic networks more robust. Expand
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