Apr 13, 2018 | 14:00—15:30
“More is different,” wrote P.W. Anderson  in order to characterize the behaviour of complex systems, consisting of many interacting elements, which cannot be explained by a simple extrapolation of the laws describing the behaviour of a few elements. In order to understand complex dynamics and emergent phenomena we need to understand interactions among system components. Interacting subsystems can mutually exchange information and influence each other; or one system can causally influence another one by a directed information flow. The mathematical formulation of causality in measurable terms of predictability was given by the father of cybernetics N. Wiener  and formulated for time series by C.W.J. Granger . The Granger causality is based on the evaluation of predictability in bivariate autoregressive models. This concept has been generalized for nonlinear systems using methods rooted in information theory [4, 5]. Complexity observed in such systems as the human brain or the Earth climate stems not only from the fact that they consist of many subsystems. Their variability covers large ranges of spatial and temporal scales and the nonlinear character of these systems leads to interactions of dynamics across scales. For instance, dynamical processes on large time scales influence variability on shorter time scales. In order to detect cross-scale causal interactions we have recently introduced a methodology  which starts with a wavelet decomposition of a multi-scale signal into quasi-oscillatory modes of a limited bandwidth, described using their instantaneous phases and amplitudes. Then their statistical associations are tested using the information-theoretic formulation of the Granger causality. The analysis of long-term air temperature records uncovers causal influence and information transfer from large-scale modes of climate variability with characteristic time scales from years to almost a decade to regional temperature variability on short time scales. The phenomenon of cross-scale interactions has non-negligible influence on the air temperature variability in the European mid-latitudes . In the tropical Pacific, the interactions of the annual cycle with slower modes of atmospheric and oceanic variability are of special interest in order to better understand the El Niño Southern Oscillation. The cross-frequency interactions and information transfer can be observed in brain dynamics, where the cross-frequency coupling enriches the cooperative behaviour of neuronal networks and apparently plays an important functional role in neuronal computation, communication, and learning.
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