High cognitive abilities, a large flexibility in vocal production, and advanced social interactions together constitute fundamental prerequisites to evolve such abilities.
It is known that many marine mammals, specifically dolphins, simultaneously form a variety of social interactions, have high cognitive abilities and are flexible in sound production.
Matrilineal whales, in particular killer whales (Orcinus Orca) and long-finned pilot whales (Glophicephala Melas), developed an advanced communication system resulting from intra- and inter-group social interactions and environmental factors. Their vocal repertoires consist of a variety of sounds such as pulsed calls, whistles, clicks and buzzes. There is evidence that two or three sounds are sometimes used in systematic combination and that killer whales may communicate by exchanging vocal signals. How vocal signals are combined and how vocal exchange patterns are organized and used, however, is largely unknown.
Systems with a complex time evolution that generate great impact events from time to time are ubi-
quitous. Examples include electrical activity of human brain with rare epileptic seizures, fluctuations
of prizes for financial assets in economy with rare market crashes, changing weather conditions with
rare disastrous storms, landslides, fluid flow with rare intermittent bursts, and also fluctuations of
on-line diagnostics of technical machinery and networks with rare breakdowns or black-outs.
Besides the explorations done for each type of events in specific disciplines, there are also general approaches, which aim in accessing common features of extreme events. Many of these general approaches use concepts and methods of complex systems science, such as cellular automata models, self orga- nized criticality or synchronization. A second type of general approaches is based on the statistical characterization of extreme events, via extreme value theory or the theory of large deviations.
My research follows a different general approach, namely the characterization of extreme events in time series of observations. Special emphasis is given to the identification of precursory structures, which can can serve to predict extreme events. A simple but powerful method to identify precursors is statistical inference. In the past I focussed mainly on the question why larger and thus more extreme events can under certain circumstances be better predicted than average events. A condition which tests for the dependence on the magnitude of the event was studied for predictions of events in various stochastic processes, data of intermittent fluid flow and wind speed recordings. Recent research aims at the development of efficient prediction techniques for practical applications.
It has been demonstrated that the spatiotemporal dynamics of characteristic Lyapunov vectors in spatially extended chaotic systems can be related to properties of scale invariant growing surfaces.
This is based on a Hopf Cole transformation, which reveales that the Lyapunov vectors corresponding to the largest Lyapunov exponents are ``piecewise copies'' of the first Lyapunov vector.
We study now, whether similar scaling properties, can also be observed for bred vectors, which are used in the context of data assimilation for weather forecasting.
We study the generalized extreme value distributions (GEV) of extreme temperature and precipitation events in observations and different regional climate models.
> ζ-functions are an important concept in different fields of theoretical physics, like equilibrium statistical mechanics, nonlinear dynamics, or semiclassical descriptions of chaotic quantum systems. Of particular interest are analytical properties of ζ -functions as they reflect nontrivial features like dynamical instabilities or phase transitions, e.g., ferromagnetic phase transitions in spin systems.