CIM Seminar with Tommaso Alberti

Abstract:

Observations and measurements of complex systems and their dynamical phenomena are genuinely obtained as time series or spatio-temporal data whose dynamics usually manifests a nonlinear multiscale (in terms of time and space) behavior. Despite the intrinsic morphological and/or physical difference between complex systems, they are all characterized by dynamical patterns and structures, with signatures of chaos at large scales, an apparently random behavior at small scales, and emergent phenomena. This motivates to bring together different disciplines, from dynamical system theory to statistics and decomposition methods to gain novel insights on a great diversity of phenomena like weather and climate dynamics, turbulence in fluids and plasmas, or chaos in dynamical systems and to inform us on its predictability, persistence and synchronization.

In this talk, I will provide an overview on a selection of contemporary topics related with complex systems based approaches and their utilization across different disciplines to explore the active number of degrees of freedom and the predictability horizon of multiscale complex systems. I will briefly discuss a newly introduced framework in comparison with classical approaches, based on generalized fractal dimensions, Lyapunov exponents, and Renyi entropies. Finally, I will demonstrate the suitability of this novel formalism to trace the instantaneous scale-dependent features of complex systems, pointing out how the predictability horizon, the persistence and synchronization of complex systems is a matter of scales.

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