@article{HempelKoseskaNikoloskietal.2011,
  author    = {Hempel, Sabrina and Koseska, Aneta and Nikoloski, Zoran and Kurths, J{\"u}rgen},
  title     = {Unraveling gene regulatory networks from time-resolved gene expression data - a measures comparison study},
  series = {BMC bioinformatics},
  volume    = {12},
  journal   = {BMC bioinformatics},
  number    = {1},
  publisher = {BioMed Central},
  address   = {London},
  issn      = {1471-2105},
  doi       = {10.1186/1471-2105-12-292},
  pages     = {26},
  year      = {2011},
  abstract  = {Background: Inferring regulatory interactions between genes from transcriptomics time-resolved data, yielding reverse engineered gene regulatory networks, is of paramount importance to systems biology and bioinformatics studies. Accurate methods to address this problem can ultimately provide a deeper insight into the complexity, behavior, and functions of the underlying biological systems. However, the large number of interacting genes coupled with short and often noisy time-resolved read-outs of the system renders the reverse engineering a challenging task. Therefore, the development and assessment of methods which are computationally efficient, robust against noise, applicable to short time series data, and preferably capable of reconstructing the directionality of the regulatory interactions remains a pressing research problem with valuable applications. Results: Here we perform the largest systematic analysis of a set of similarity measures and scoring schemes within the scope of the relevance network approach which are commonly used for gene regulatory network reconstruction from time series data. In addition, we define and analyze several novel measures and schemes which are particularly suitable for short transcriptomics time series. We also compare the considered 21 measures and 6 scoring schemes according to their ability to correctly reconstruct such networks from short time series data by calculating summary statistics based on the corresponding specificity and sensitivity. Our results demonstrate that rank and symbol based measures have the highest performance in inferring regulatory interactions. In addition, the proposed scoring scheme by asymmetric weighting has shown to be valuable in reducing the number of false positive interactions. On the other hand, Granger causality as well as information-theoretic measures, frequently used in inference of regulatory networks, show low performance on the short time series analyzed in this study. Conclusions: Our study is intended to serve as a guide for choosing a particular combination of similarity measures and scoring schemes suitable for reconstruction of gene regulatory networks from short time series data. We show that further improvement of algorithms for reverse engineering can be obtained if one considers measures that are rooted in the study of symbolic dynamics or ranks, in contrast to the application of common similarity measures which do not consider the temporal character of the employed data. Moreover, we establish that the asymmetric weighting scoring scheme together with symbol based measures (for low noise level) and rank based measures (for high noise level) are the most suitable choices.},
  language  = {en}
}
@article{ZhouMotterKurths2006,
  author    = {Zhou, Changsong and Motter, Adilson E. and Kurths, J{\"u}rgen},
  title     = {Universality in the synchronization of weighted random networks},
  doi       = {10.1103/Physrevlett.96.034101},
  year      = {2006},
  abstract  = {Realistic networks display not only a complex topological structure, but also a heterogeneous distribution of weights in the connection strengths. Here we study synchronization in weighted complex networks and show that the synchronizability of random networks with a large minimum degree is determined by two leading parameters: the mean degree and the heterogeneity of the distribution of node's intensity, where the intensity of a node, defined as the total strength of input connections, is a natural combination of topology and weights. Our results provide a possibility for the control of synchronization in complex networks by the manipulation of a few parameters},
  language  = {en}
}
@article{ThielRomanoKurthsetal.2006,
  author    = {Thiel, Marco and Romano, Maria Carmen and Kurths, J{\"u}rgen and Rolfs, Martin and Kliegl, Reinhold},
  title     = {Twin surrogates to test for complex synchronisation},
  doi       = {10.1209/epl/i2006-10147-0},
  year      = {2006},
  abstract  = {We present an approach to generate (multivariate) twin surrogates (TS) based on recurrence properties. This technique generates surrogates which correspond to an independent copy of the underlying system, i.e. they induce a trajectory of the underlying system starting at different initial conditions. We show that these surrogates are well suited to test for complex synchronisation and exemplify this for the paradigmatic system of Rossler oscillators. The proposed test enables to assess the statistical relevance of a synchronisation analysis from passive experiments which are typical in natural systems},
  language  = {en}
}
@article{ZhangHuHuetal.2002,
  author    = {Zhang, H. and Hu, B. and Hu, G. and Ouyang, Q. and Kurths, J{\"u}rgen},
  title     = {Turbulence control by developing a spiral wave with a periodic signal injection in the complex Ginzburg-Laundau equation},
  year      = {2002},
  language  = {en}
}
@article{HeuerSchultheissHodgsonetal.1999,
  author    = {Heuer, Axel and Schultheiss, J. and Hodgson, N. and Kurths, J{\"u}rgen and Menzel, Ralf and Raab, Volker},
  title     = {Transverse effects in phase conjugate laser mirrors based on stimulated brillouin scattering},
  year      = {1999},
  language  = {en}
}
@article{HassanKurths2001,
  author    = {Hassan, M. K. and Kurths, J{\"u}rgen},
  title     = {Transition from random to ordered fractals in fragmentation of particles in an open system},
  year      = {2001},
  language  = {en}
}
@article{PopovychMaistrenkoMosekildeetal.2001,
  author    = {Popovych, Orest and Maistrenko, Yu and Mosekilde, Erik and Pikovskij, Arkadij and Kurths, J{\"u}rgen},
  title     = {Transcritical riddling in a system of coupled maps},
  year      = {2001},
  abstract  = {The transition from fully synchronized behavior to two-cluster dynamics is investigated for a system of N globally coupled chaotic oscillators by means of a model of two coupled logistic maps. An uneven distribution of oscillators between the two clusters causes an asymmetry to arise in the coupling of the model system. While the transverse period-doubling bifurcation remains essentially unaffected by this asymmetry, the transverse pitchfork bifurcation is turned into a saddle-node bifurcation followed by a transcritical riddling bifurcation in which a periodic orbit embedded in the synchronized chaotic state loses its transverse stability. We show that the transcritical riddling transition is always hard. For this, we study the sequence of bifurcations that the asynchronous point cycles produced in the saddle-node bifurcation undergo, and show how the manifolds of these cycles control the magnitude of asynchronous bursts. In the case where the system involves two subpopulations of oscillators with a small mismatch of the parameters, the transcritical riddling will be replaced by two subsequent saddle-node bifurcations, or the saddle cycle involved in the transverse destabilization of the synchronized chaotic state may smoothly shift away from the synchronization manifold. In this way, the transcritical riddling bifurcation is substituted by a symmetry-breaking bifurcation, which is accompanied by the destruction of a thin invariant region around the symmetrical chaotic state.},
  language  = {en}
}
@article{PopovychMaistrenkoMosekildeetal.2000,
  author    = {Popovych, Orest and Maistrenko, Yu and Mosekilde, Erik and Pikovskij, Arkadij and Kurths, J{\"u}rgen},
  title     = {Transcritical loss of synchronization in coupled chaotic systems},
  year      = {2000},
  language  = {en}
}
@article{WittFeudelGebogietal.1998,
  author    = {Witt, Annette and Feudel, Fred and Gebogi, C. and Kurths, J{\"u}rgen and Braun, Robert},
  title     = {Tracer dynamics in a flow of driven vortices},
  series = {Preprint NLD},
  volume    = {51},
  journal   = {Preprint NLD},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1432-2935},
  pages     = {8 S. : graph. Darst.},
  year      = {1998},
  language  = {en}
}
@article{BraunFeudelGebogietal.1999,
  author    = {Braun, Robert and Feudel, Fred and Gebogi, C. and Kurths, J{\"u}rgen and Witt, Annette},
  title     = {Tracer dynamics in a flow of driven vortices},
  year      = {1999},
  language  = {en}
}