First located at the Laboratory of Condensed Matter Physics (University of Nice, France), then at the Earth and Space Department (UCLA, USA), the group is now at ETH-Zurich (Switzerland) since March 2006.

[2] This in turn leads to a power-law acceleration of moment and strain release, up to the macroscopic failure time of the sample (i.e. a large earthquake in nature).

The existence of such oscillations stems from interactions between seismogenic structures (see below for the case of faults and fractures), but also offers a better constraint to identify areas within which a large event may occur.

Sornette's group has contributed significantly to the theoretical development and study of the properties of the now standard Epidemic Type Aftershock Sequence (ETAS) model.

The main reason is that this model predicts future seismicity rates quite accurately, but fails to put constraints on the magnitudes (which are assumed to be distributed according to the Gutenberg-Richter law, and to be independent of each other).

Another unambiguous interesting result of this work is that the Earth crust in Southern California has quite a short memory of past stress fluctuations lasting only about 3 to 4 months.

Solving it analytically allowed them to predict that each event triggers some aftershocks with a rate decaying in time according to the Omori law, i.e. as 1/tp, but with a special twist that had not been recognized heretofore.

[12][13] This result thus shows that small events may trigger a smaller number of aftershocks than large ones, but that their cumulative effect may be more long-lasting in the Earth crust.

A new technique has also recently introduced, called the barycentric fixed mass method, to improve considerably the estimation of multifractal structures of spatio-temporal seismicity expected from the MSA model.

[14] A significant part of the activity of Sornette's group has also been devoted to the statistical physics modelling as well as properties of fractures and faults at different scales.

The geometrical and dynamical complexity of faults and earthquakes is shown to result from the interplay between spatio-temporal chaos and an initial featureless quenched heterogeneity.

Lee et al. (1999) [27] demonstrated the intrinsic intermittent nature of seismic activity on faults, which results from their competition to accommodate the tectonic deformation.

[29][30][31] These transition scales (which quantify the horizontal distribution of brittle structures) can be nicely correlated with the vertical mechanical layering of the host medium (the Earth crust).

By mapping some joints within the crystalline basement in the same area, it was found that their spatial organization (spacing distribution) displayed discrete scale invariance over more than four decades.

[32] Using some other dataset and a theoretical model, Huang et al. also showed that, due to interactions between parallel structures, the length distribution of joints displays discrete scale invariance.

Those reconstructed 3D fault networks offer a good correlation with focal mechanisms, but also provide a significant gain when using them as the proxy of earthquakes locations in forecasting experiments.

This project is originally rooted in the rigorous theoretical and experimental solid-state physics of Prof. Friedemann Freund,[38][39] whose theory is able to explain the whole spectrum of electromagnetic type phenomena that have been reported before large earthquakes for decades, if not centuries: when submitting rocks to significant stresses, electrons and positive holes are activated; the latter flow to less stressed domains of the material thus generating large-scale electric currents.

Those in turn induce local geoelectric and geomagnetic anomalies, stimulated infrared emission, air ionization, increase levels of ozone and carbon monoxide.

Applications include tests of chaos of the discrete logistic map,[45][46] an endo-exo approach to the classification of diseases,[47][48] the introduction of delayed feedback of population on the carrying capacity to capture punctuated evolution,[49][50] symbiosis,[51][52][53] deterministic dynamical models of regime switching between conventions and business cycles in economic systems,[54][55] the modelling of periodically collapsing bubbles,[56] interactions between several species via the mutual dependences on their carrying capacities.

With their PhD student, they have applied this methodology to the valuation of Zynga before its IPO and have shown its value by presenting ex-ante forecasts leading to a successful trading strategy.

The LPPLS model considers the faster-than-exponential (power law with finite-time singularity) increase in asset prices decorated by accelerating oscillations as the main diagnostic of bubbles.

[69] The formal analogy between mechanical ruptures, earthquakes and financial crashes was further refined within the rational expectation bubble framework of Blanchard and Watson[70] by Johansen, Ledoit and Sornette.

Inspired by the research of Ernst Fehr and his collaborators, Darcet and Sornette proposed that the paradox of human cooperation and altruism (without kinship, direct or indirect reciprocity) emerges naturally by an evolutionary feedback selection mechanism.

[82] The corresponding generalised cost-benefit accounting equation has been tested and supported by simulations of an agent-based model mimicking the evolution selection pressure of our ancestors:[83][84] starting with a population of agents with no propensity for cooperation and altruistic punishment, simple rules of selection by survival in interacting groups lead to the emergence of a level of cooperation and altruistic punishment in agreement with experimental findings.

To describe the inherent sociability of Homo Sapiens, the UCLA professor of anthropology, Alan Fiske, has theorised that all human interactions can be decomposed into just four "relational models", or elementary forms of human relations: communal sharing, authority ranking, equity matching and market pricing (to these are added the limiting cases of asocial and null interactions, whereby people do not coordinate with reference to any shared principle).

The relationships generated by this representation aggregate into six exhaustive and disjoint categories that match the four relational models, while the remaining two correspond to the asocial and null interactions defined in RMT.

[89][90] The term "dragon-kings" (DK) embodies a double metaphor implying that an event is both extremely large (a "king" [91]), and born of unique origins ("dragon") relative to its peers.

Based on the mathematics of Hilbert spaces, it embraces uncertainty and enjoys non-additive probability for the resolution of complex choice situations with interference effects.

The method consists of constructing a distance matrix based on the matching of all sample data pairs between the two time series, as in recurrence plots.

Then, the lag–lead structure is searched for as the optimal path in the distance matrix landscape that minimizes the total mismatch between the two time series, and that obeys a one-to-one causal matching condition.