@article{KralemannPikovskijRosenblum2014,
  author    = {Kralemann, Bjoern and Pikovskij, Arkadij and Rosenblum, Michael},
  title     = {Reconstructing effective phase connectivity of oscillator networks from observations},
  series = {New journal of physics : the open-access journal for physics},
  volume    = {16},
  journal   = {New journal of physics : the open-access journal for physics},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/16/8/085013},
  pages     = {21},
  year      = {2014},
  abstract  = {We present a novel approach for recovery of the directional connectivity of a small oscillator network by means of the phase dynamics reconstruction from multivariate time series data. The main idea is to use a triplet analysis instead of the traditional pairwise one. Our technique reveals an effective phase connectivity which is generally not equivalent to a structural one. We demonstrate that by comparing the coupling functions from all possible triplets of oscillators, we are able to achieve in the reconstruction a good separation between existing and non-existing connections, and thus reliably reproduce the network structure.},
  language  = {en}
}
@article{KralemannPikovskijRosenblum2014,
  author    = {Kralemann, Bjoern and Pikovskij, Arkadij and Rosenblum, Michael},
  title     = {Reconstructing connectivity of oscillator networks from multimodal observations},
  series = {Biomedizinische Technik = Biomedical engineering},
  volume    = {59},
  journal   = {Biomedizinische Technik = Biomedical engineering},
  publisher = {De Gruyter},
  address   = {Berlin},
  issn      = {0013-5585},
  doi       = {10.1515/bmt-2014-4089},
  pages     = {S220 -- S220},
  year      = {2014},
  language  = {en}
}
@article{KralemannFruehwirthPikovskijetal.2013,
  author    = {Kralemann, Bjoern and Fruehwirth, Matthias and Pikovskij, Arkadij and Rosenblum, Michael and Kenner, Thomas and Schaefer, Jochen and Moser, Maximilian},
  title     = {In vivo cardiac phase response curve elucidates human respiratory heart rate variability},
  series = {Nature Communications},
  volume    = {4},
  journal   = {Nature Communications},
  publisher = {Nature Publ. Group},
  address   = {London},
  issn      = {2041-1723},
  doi       = {10.1038/ncomms3418},
  pages     = {9},
  year      = {2013},
  abstract  = {Recovering interaction of endogenous rhythms from observations is challenging, especially if a mathematical model explaining the behaviour of the system is unknown. The decisive information for successful reconstruction of the dynamics is the sensitivity of an oscillator to external influences, which is quantified by its phase response curve. Here we present a technique that allows the extraction of the phase response curve from a non-invasive observation of a system consisting of two interacting oscillators-in this case heartbeat and respiration-in its natural environment and under free-running conditions. We use this method to obtain the phase-coupling functions describing cardiorespiratory interactions and the phase response curve of 17 healthy humans. We show for the first time the phase at which the cardiac beat is susceptible to respiratory drive and extract the respiratory-related component of heart rate variability. This non-invasive method for the determination of phase response curves of coupled oscillators may find application in many scientific disciplines.},
  language  = {en}
}