We study the evolution of a social network with friendly/enmity connections into a balanced state by introducing a dynamical model with an intrinsic randomness, similar to Glauber dynamics in statistical mechanics. We include the possibility of the tension promotion as well as the tension reduction in our model. Such a more realistic situation enables the system to escape from local minima in its energy landscape and thus to exit out of frozen imbalanced states, which are unwanted outcomes observed in previous models. On the other hand, in finite networks the dynamics takes the system into a balanced phase, if the randomness is lower than a critical value. For large networks, we also find a sharp phase transition at the initial positive link density of ρ * 0 = 1/2, where the system transitions from a bipolar state into a paradise. This modifies the gradual phase transition at a nontrivial value of ρ * 0 ≃ 0.65, observed in recent studies.I.

We report on a stochastic analysis of Earth's vertical velocity time series by using methods originally developed for complex hierarchical systems and, in particular, for turbulent flows. Analysis of the fluctuations of the detrended increments of the series reveals a pronounced transition in their probability density function from Gaussian to non-Gaussian. The transition occurs 5-10 hours prior to a moderate or large earthquake, hence representing a new and reliable precursor for detecting such earthquakes.

Emergent extreme events are a key characteristic of complex dynamical systems. The main tool for detailed and deep understanding of their stochastic dynamics is the statistics of time intervals of extreme events. Analyzing extensive experimental data, we demonstrate that for the velocity time series of fully-developed turbulent flows, generated by (i) a regular grid; (ii) a cylinder; (iii) a free jet of helium, and (iv) a free jet of air with the Taylor Reynolds numbers Reλ from 166 to 893, the interoccurrence time distributions P(τ) above a positive threshold Q in the inertial range is described by a universal q- exponential function, P(τ) = β(2 − q)[1 − β(1 − q)τ]1/(1−q), which may be due to the superstatistical nature of the occurrence of extreme events. Our analysis provides a universal description of extreme events in turbulent flows.

An information-theoretic approach for detecting causality and information transfer is used to identify interactions of solar activity and interplanetary medium conditions with the Earth’s magnetosphere–ionosphere systems. A causal information transfer from the solar wind parameters to geomagnetic indices is detected. The vertical component of the interplanetary magnetic field (Bz) influences the auroral electrojet (AE) index with an information transfer delay of 10 min and the geomagnetic disturbances at mid-latitudes measured by the symmetric field in the H component (SYM-H) index with a delay of about 30 min. Using a properly conditioned causality measure, no causal link between AE and SYM-H, or between magnetospheric substorms and magnetic storms can be detected. The observed causal relations can be described as linear time-delayed information transfer.