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- ItemA unified and automated approach to attractor reconstruction(London : IOP, 2021) Kraemer, K. H.; Datseris, G.; Kurths, J.; Kiss, I. Z.; Ocampo-Espindola, J. L.; Marwan, N.We present a fully automated method for the optimal state space reconstruction from univariate and multivariate time series. The proposed methodology generalizes the time delay embedding procedure by unifying two promising ideas in a symbiotic fashion. Using non-uniform delays allows the successful reconstruction of systems inheriting different time scales. In contrast to the established methods, the minimization of an appropriate cost function determines the embedding dimension without using a threshold parameter. Moreover, the method is capable of detecting stochastic time series and, thus, can handle noise contaminated input without adjusting parameters. The superiority of the proposed method is shown on some paradigmatic models and experimental data from chaotic chemical oscillators.
- ItemTowards dynamical network biomarkers in neuromodulation of episodic migraine(Berlin : De Gruyter, 2013) Dahlem, M.A.; Rode, S.; May, A.; Fujiwara, N.; Hirata, Y.; Aihara, K.; Kurths, J.Computational methods have complemented experimental and clinical neurosciences and led to improvements in our understanding of the nervous systems in health and disease. In parallel, neuromodulation in form of electric and magnetic stimulation is gaining increasing acceptance in chronic and intractable diseases. In this paper, we firstly explore the relevant state of the art in fusion of both developments towards translational computational neuroscience. Then, we propose a strategy to employ the new theoretical concept of dynamical network biomarkers (DNB) in episodic manifestations of chronic disorders. In particular, as a first example, we introduce the use of computational models in migraine and illustrate on the basis of this example the potential of DNB as early-warning signals for neuromodulation in episodic migraine.
- ItemSupermodeling by combining imperfect models(Amsterdam : Elsevier B.V., 2011) Selten, F.M.; Duane, G.S.; Wiegerinck, W.; Keenlyside, N.; Kurths, J.; Kocarev, L.SUMO (Supermodeling by combining imperfect models) is a three-year project funded under FET Open program with a starting date October, 1, 2010. We review some basic facts and findings of the SUMO project.