@misc{TopcuFruehwirthMoseretal.2018,
  author    = {Top{\c{c}}u, {\c{C}}ağda{\c{s}} and Fr{\"u}hwirth, Matthias and Moser, Maximilian and Rosenblum, Michael and Pikovskij, Arkadij},
  title     = {Disentangling respiratory sinus arrhythmia in heart rate variability records},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  number    = {913},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-43631},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-436315},
  pages     = {15},
  year      = {2018},
  abstract  = {Objective: Several different measures of heart rate variability, and particularly of respiratory sinus arrhythmia, are widely used in research and clinical applications. For many purposes it is important to know which features of heart rate variability are directly related to respiration and which are caused by other aspects of cardiac dynamics. Approach: Inspired by ideas from the theory of coupled oscillators, we use simultaneous measurements of respiratory and cardiac activity to perform a nonlinear disentanglement of the heart rate variability into the respiratory-related component and the rest. Main results: The theoretical consideration is illustrated by the analysis of 25 data sets from healthy subjects. In all cases we show how the disentanglement is manifested in the different measures of heart rate variability. Significance: The suggested technique can be exploited as a universal preprocessing tool, both for the analysis of respiratory influence on the heart rate and in cases when effects of other factors on the heart rate variability are in focus.},
  language  = {en}
}
@article{TopcuFruehwirthMoseretal.2018,
  author    = {Top{\c{c}}u, {\c{C}}ağda{\c{s}} and Fr{\"u}hwirth, Matthias and Moser, Maximilian and Rosenblum, Michael and Pikovskij, Arkadij},
  title     = {Disentangling respiratory sinus arrhythmia in heart rate variability records},
  series = {Physiological Measurement},
  volume    = {39},
  journal   = {Physiological Measurement},
  number    = {5},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {0967-3334},
  doi       = {10.1088/1361-6579/aabea4},
  pages     = {12},
  year      = {2018},
  abstract  = {Objective: Several different measures of heart rate variability, and particularly of respiratory sinus arrhythmia, are widely used in research and clinical applications. For many purposes it is important to know which features of heart rate variability are directly related to respiration and which are caused by other aspects of cardiac dynamics. Approach: Inspired by ideas from the theory of coupled oscillators, we use simultaneous measurements of respiratory and cardiac activity to perform a nonlinear disentanglement of the heart rate variability into the respiratory-related component and the rest. Main results: The theoretical consideration is illustrated by the analysis of 25 data sets from healthy subjects. In all cases we show how the disentanglement is manifested in the different measures of heart rate variability. Significance: The suggested technique can be exploited as a universal preprocessing tool, both for the analysis of respiratory influence on the heart rate and in cases when effects of other factors on the heart rate variability are in focus.},
  language  = {en}
}
@misc{StraubePikovskij2011,
  author    = {Straube, Arthur V. and Pikovskij, Arkadij},
  title     = {Pattern formation induced by time-dependent advection},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch Naturwissenschaftliche Reihe},
  number    = {575},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-41314},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-413140},
  pages     = {138-147},
  year      = {2011},
  abstract  = {We study pattern-forming instabilities in reaction-advection-diffusion systems. We develop an approach based on Lyapunov-Bloch exponents to figure out the impact of a spatially periodic mixing flow on the stability of a spatially homogeneous state. We deal with the flows periodic in space that may have arbitrary time dependence. We propose a discrete in time model, where reaction, advection, and diffusion act as successive operators, and show that a mixing advection can lead to a pattern-forming instability in a two-component system where only one of the species is advected. Physically, this can be explained as crossing a threshold of Turing instability due to effective increase of one of the diffusion constants.},
  language  = {en}
}
@misc{PolitiPikovskijUllner2017,
  author    = {Politi, Antonio and Pikovskij, Arkadij and Ullner, Ekkehard},
  title     = {Chaotic macroscopic phases in one-dimensional oscillators},
  series = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe},
  number    = {721},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-42979},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-429790},
  pages     = {20},
  year      = {2017},
  abstract  = {The connection between the macroscopic description of collective chaos and the underlying microscopic dynamics is thoroughly analysed in mean-field models of one-dimensional oscillators. We investigate to what extent infinitesimal perturbations of the microscopic configurations can provide information also on the stability of the corresponding macroscopic phase. In ensembles of identical one-dimensional dynamical units, it is possible to represent the microscopic configurations so as to make transparent their connection with the macroscopic world. As a result, we find evidence of an intermediate, mesoscopic, range of distances, over which the instability is neither controlled by the microscopic equations nor by the macroscopic ones. We examine a whole series of indicators, ranging from the usual microscopic Lyapunov exponents, to the collective ones, including finite-amplitude exponents. A system of pulse-coupled oscillators is also briefly reviewed as an example of non-identical phase oscillators where collective chaos spontaneously emerges.},
  language  = {en}
}