@incollection{OsterhageBialonskiStanieketal.2008,
  author    = {Osterhage, Hannes and Bialonski, Stephan and Staniek, Matth{\"a}us and Schindler, Kaspar and Wagner, Tobias and Elger, Christian E. and Lehnertz, Klaus},
  title     = {Bivariate and multivariate time series analysis techniques and their potential impact for seizure prediction},
  series = {Seizure Prediction in Epilepsy: From Basic Mechanisms to Clinical Applications},
  booktitle = {Seizure Prediction in Epilepsy: From Basic Mechanisms to Clinical Applications},
  publisher = {Wiley-VCH},
  address   = {Weinheim},
  isbn      = {978-3-527-62519-2},
  doi       = {10.1002/9783527625192.ch15},
  pages     = {189 -- 208},
  year      = {2008},
  language  = {en}
}
@article{LehnertzBialonskiHorstmannetal.2009,
  author    = {Lehnertz, Klaus and Bialonski, Stephan and Horstmann, Marie-Therese and Krug, Dieter and Rothkegel, Alexander and Staniek, Matth{\"a}us and Wagner, Tobias},
  title     = {Synchronization phenomena in human epileptic brain networks},
  series = {Journal of neuroscience methods},
  volume    = {183},
  journal   = {Journal of neuroscience methods},
  number    = {1},
  issn      = {0165-0270},
  doi       = {10.1016/j.jneumeth.2009.05.015},
  pages     = {42 -- 48},
  year      = {2009},
  language  = {en}
}
@incollection{LehnertzBialonskiHorstmannetal.2010,
  author    = {Lehnertz, Klaus and Bialonski, Stephan and Horstmann, Marie-Therese and Krug, Dieter and Rothkegel, Alexander and Staniek, Matth{\"a}us and Wagner, Tobias},
  title     = {Epilepsy},
  series = {Reviews of Nonlinear Dynamics and Complexity, Volume 2},
  booktitle = {Reviews of Nonlinear Dynamics and Complexity, Volume 2},
  publisher = {Wiley-VCH},
  isbn      = {9783527628001},
  doi       = {10.1002/9783527628001.ch5},
  pages     = {159 -- 200},
  year      = {2010},
  language  = {en}
}
@article{HorstmannBialonskiNoenningetal.2010,
  author    = {Horstmann, Marie-Therese and Bialonski, Stephan and Noenning, Nina and Mai, Heinke and Prusseit, Jens and Wellmer, J{\"o}rg and Hinrichs, Hermann and Lehnertz, Klaus},
  title     = {State dependent properties of epileptic brain networks: Comparative graph-theoretical analyses of simultaneously recorded EEG and MEG},
  series = {Clinical Neurophysiology},
  volume    = {121},
  journal   = {Clinical Neurophysiology},
  number    = {2},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {1388-2457},
  doi       = {10.1016/j.clinph.2009.10.013},
  pages     = {172 -- 185},
  year      = {2010},
  abstract  = {Objective To investigate whether functional brain networks of epilepsy patients treated with antiepileptic medication differ from networks of healthy controls even during the seizure-free interval. Methods We applied different rules to construct binary and weighted networks from EEG and MEG data recorded under a resting-state eyes-open and eyes-closed condition from 21 epilepsy patients and 23 healthy controls. The average shortest path length and the clustering coefficient served as global statistical network characteristics. Results Independent on the behavioral condition, epileptic brains exhibited a more regular functional network structure. Similarly, the eyes-closed condition was characterized by a more regular functional network structure in both groups. The amount of network reorganization due to behavioral state changes was similar in both groups. Consistent findings could be achieved for networks derived from EEG but hardly from MEG recordings, and network construction rules had a rather strong impact on our findings. Conclusions Despite the locality of the investigated processes epileptic brain networks differ in their global characteristics from non-epileptic brain networks. Further methodological developments are necessary to improve the characterization of disturbed and normal functional networks. Significance An increased regularity and a diminished modulation capability appear characteristic of epileptic brain networks.},
  language  = {en}
}
@article{BialonskiHorstmannLehnertz2010,
  author    = {Bialonski, Stephan and Horstmann, Marie-Therese and Lehnertz, Klaus},
  title     = {From brain to earth and climate systems: Small-world interaction networks or not?},
  series = {Chaos: An Interdisciplinary Journal of Nonlinear Science},
  volume    = {20},
  journal   = {Chaos: An Interdisciplinary Journal of Nonlinear Science},
  number    = {1},
  publisher = {AIP Publishing},
  address   = {Melville, NY},
  issn      = {1089-7682},
  doi       = {10.1063/1.3360561},
  pages     = {013134},
  year      = {2010},
  abstract  = {We consider recent reports on small-world topologies of interaction networks derived from the dynamics of spatially extended systems that are investigated in diverse scientific fields such as neurosciences, geophysics, or meteorology. With numerical simulations that mimic typical experimental situations, we have identified an important constraint when characterizing such networks: indications of a small-world topology can be expected solely due to the spatial sampling of the system along with the commonly used time series analysis based approaches to network characterization.},
  language  = {en}
}
@incollection{Bialonski2016,
  author    = {Bialonski, Stephan},
  title     = {Are interaction clusters in epileptic networks predictive of seizures?},
  series = {Epilepsy: The Intersection of Neurosciences, Biology, Mathematics, Engineering, and Physics},
  booktitle = {Epilepsy: The Intersection of Neurosciences, Biology, Mathematics, Engineering, and Physics},
  publisher = {CRC Press},
  isbn      = {978-143983886-0},
  pages     = {349 -- 355},
  year      = {2016},
  language  = {en}
}
@article{BialonskiWendlerLehnertz2011,
  author    = {Bialonski, Stephan and Wendler, Martin and Lehnertz, Klaus},
  title     = {Unraveling spurious properties of interaction networks with tailored random networks},
  series = {Plos one},
  volume    = {6},
  journal   = {Plos one},
  number    = {8},
  publisher = {Plos},
  address   = {San Francisco},
  doi       = {10.1371/journal.pone.0022826},
  pages     = {e22826},
  year      = {2011},
  abstract  = {We investigate interaction networks that we derive from multivariate time series with methods frequently employed in diverse scientific fields such as biology, quantitative finance, physics, earth and climate sciences, and the neurosciences. Mimicking experimental situations, we generate time series with finite length and varying frequency content but from independent stochastic processes. Using the correlation coefficient and the maximum cross-correlation, we estimate interdependencies between these time series. With clustering coefficient and average shortest path length, we observe unweighted interaction networks, derived via thresholding the values of interdependence, to possess non-trivial topologies as compared to Erd{\"o}s-R{\´e}nyi networks, which would indicate small-world characteristics. These topologies reflect the mostly unavoidable finiteness of the data, which limits the reliability of typically used estimators of signal interdependence. We propose random networks that are tailored to the way interaction networks are derived from empirical data. Through an exemplary investigation of multichannel electroencephalographic recordings of epileptic seizures - known for their complex spatial and temporal dynamics - we show that such random networks help to distinguish network properties of interdependence structures related to seizure dynamics from those spuriously induced by the applied methods of analysis.},
  language  = {en}
}
@book{Bialonski2012,
  author    = {Bialonski, Stephan},
  title     = {Inferring complex networks from time series of dynamical systems: Pitfalls, misinterpretations, and possible solutions},
  publisher = {Universit{\"a}ts- und Landesbibliothek Bonn},
  address   = {Bonn},
  pages     = {Online-Ausgabe (III, 135 S. : Ill., graph. Darst.)},
  year      = {2012},
  language  = {en}
}
@incollection{BialonskiLehnertz2013,
  author    = {Bialonski, Stephan and Lehnertz, Klaus},
  title     = {From time series to complex networks: an overview},
  series = {Recent Advances in Predicting and Preventing Epileptic Seizures: Proceedings of the 5th International Workshop on Seizure Prediction},
  booktitle = {Recent Advances in Predicting and Preventing Epileptic Seizures: Proceedings of the 5th International Workshop on Seizure Prediction},
  isbn      = {978-981-4525-36-7},
  doi       = {10.1142/9789814525350_0010},
  pages     = {132 -- 147},
  year      = {2013},
  abstract  = {The network approach towards the analysis of the dynamics of complex systems has been successfully applied in a multitude of studies in the neurosciences and has yielded fascinating insights. With this approach, a complex system is considered to be composed of different constituents which interact with each other. Interaction structures can be compactly represented in interaction networks. In this contribution, we present a brief overview about how interaction networks are derived from multivariate time series, about basic network characteristics, and about challenges associated with this analysis approach.},
  language  = {en}
}
@article{BialonskiLehnertz2013,
  author    = {Bialonski, Stephan and Lehnertz, Klaus},
  title     = {Assortative mixing in functional brain networks during epileptic seizures},
  series = {Chaos: An Interdisciplinary Journal of Nonlinear Science},
  volume    = {23},
  journal   = {Chaos: An Interdisciplinary Journal of Nonlinear Science},
  number    = {3},
  doi       = {10.1063/1.4821915},
  pages     = {033139},
  year      = {2013},
  language  = {en}
}