Constrained randomization of time series data

A new method is introduced to create artificial time sequences that fulfil given constraints but are random otherwise. Constraints are usually derived from a measured signal for which surrogate data are to be generated. They are fulfilled by minimizing a suitable cost function using simulated annealing. A wide variety of structures can be imposed on the surrogate series, including multivariate, nonlinear, and nonstationary properties. When the linear correlation structure is to be preserved, the new approach avoids certain artifacts generated by Fourier-based randomization schemes.Comment: 4 pages, 2 figure

The human ECG - nonlinear deterministic versus stochastic aspects

We discuss aspects of randomness and of determinism in electrocardiographic signals. In particular, we take a critical look at attempts to apply methods of nonlinear time series analysis derived from the theory of deterministic dynamical systems. We will argue that deterministic chaos is not a likely explanation for the short time variablity of the inter-beat interval times, except for certain pathologies. Conversely, densely sampled full ECG recordings possess properties typical of deterministic signals. In the latter case, methods of deterministic nonlinear time series analysis can yield new insights.Comment: 6 pages, 9 PS figure

Localization and conductance in the quantum Coulomb glass

We consider the combined influence of disorder, electron-electron interactions and quantum hopping on the properties of electronic systems in a localized phase, approaching an insulator-metal transition. The generic models in this regime are the quantum Coulomb glass and its generalization to electrons with spin. After introducing these models we explain our computational method, the Hartree-Fock based diagonalization. We then discuss the conductance and compare spinless fermions and electrons. It turns out that spin degrees of freedom do not play an essential role in the systems considered. Finally, we analyze localization and decay of single-particle excitations. We find that interactions generically tend to localize these excitations which is a result of the Coulomb gap in the single-particle density of states.Comment: Contribution to the Festschrift dedicated to Prof. Michael Pollak on the occasion of his 75th birthda