@article{SchinkelMarwanKurths2009,
  author    = {Schinkel, Stefan and Marwan, Norbert and Kurths, J{\"u}rgen},
  title     = {Brain signal analysis based on recurrences},
  issn      = {0928-4257},
  doi       = {10.1016/j.jphysparis.2009.05.007},
  year      = {2009},
  abstract  = {The EEG is one of the most commonly used tools in brain research. Though of high relevance in research, the data obtained is very noisy and nonstationary. In the present article we investigate the applicability of a nonlinear data analysis method, the recurrence quantification analysis (RQA), to Such data. The method solely rests on the natural property of recurrence which is a phenomenon inherent to complex systems, such as the brain. We show that this method is indeed suitable for the analysis of EEG data and that it might improve contemporary EEG analysis.},
  language  = {en}
}
@article{MarwanKurths2009,
  author    = {Marwan, Norbert and Kurths, J{\"u}rgen},
  title     = {Comment on "Stochastic analysis of recurrence plots with applications to the detection of deterministic signals" by Rohde et al. : [Physica D 237 (2008) 619-629]},
  issn      = {0167-2789},
  doi       = {10.1016/j.physd.2009.04.018},
  year      = {2009},
  abstract  = {In the recent article "Stochastic analysis of recurrence plots with applications to the detection of deterministic signals" (Physica D 237 (2008) 619-629), Rohde et al. stated that the performance of RQA in order to detect deterministic signals would be below traditional and well-known detectors. However, we have concerns about such a general statement. Based on our own studies we cannot confirm their conclusions. Our findings suggest that the measures of complexity provided by RQA are useful detectors outperforming well-known traditional detectors, in particular for the detection of signals of complex systems, with phase differences or signals modified due to the measurement process.},
  language  = {en}
}
@article{DongesZouMarwanetal.2009,
  author    = {Donges, Jonathan Friedemann and Zou, Yong and Marwan, Norbert and Kurths, J{\"u}rgen},
  title     = {Complex networks in climate dynamics : comparing linear and nonlinear network construction methods},
  issn      = {1951-6355},
  doi       = {10.1140/epjst/e2009-01098-2},
  year      = {2009},
  abstract  = {Complex network theory provides a powerful framework to statistically investigate the topology of local and non- local statistical interrelationships, i.e. teleconnections, in the climate system. Climate networks constructed from the same global climatological data set using the linear Pearson correlation coefficient or the nonlinear mutual information as a measure of dynamical similarity between regions, are compared systematically on local, mesoscopic and global topological scales. A high degree of similarity is observed on the local and mesoscopic topological scales for surface air temperature fields taken from AOGCM and reanalysis data sets. We find larger differences on the global scale, particularly in the betweenness centrality field. The global scale view on climate networks obtained using mutual information offers promising new perspectives for detecting network structures based on nonlinear physical processes in the climate system.},
  language  = {en}
}
@article{SchinkelMarwanDimigenetal.2009,
  author    = {Schinkel, Stefan and Marwan, Norbert and Dimigen, Olaf and Kurths, J{\"u}rgen},
  title     = {Confidence bounds of recurrence-based complexity measures},
  issn      = {0375-9601},
  doi       = {10.1016/j.physleta.2009.04.045},
  year      = {2009},
  abstract  = {In the recent past, recurrence quantification analysis (RQA) has gained an increasing interest in various research areas. The complexity measures the RQA provides have been useful in describing and analysing a broad range of data. It is known to be rather robust to noise and nonstationarities. Yet, one key question in empirical research concerns the confidence bounds of measured data. In the present Letter we suggest a method for estimating the confidence bounds of recurrence-based complexity measures. We study the applicability of the suggested method with model and real- life data.},
  language  = {en}
}
@article{ZolotovaPonyavinMarwanetal.2009,
  author    = {Zolotova, Nadezhda V. and Ponyavin, Dmitri I. and Marwan, Norbert and Kurths, J{\"u}rgen},
  title     = {Long-term asymmetry in the wings of the butterfly diagram},
  issn      = {0004-6361},
  doi       = {10.1051/0004-6361/200811430},
  year      = {2009},
  abstract  = {Aims. Sunspot distribution in the northern and southern solar hemispheres exibit striking synchronous behaviour on the scale of a Schwabe cycle. However, sometimes the bilateral symmetry of the Butterfly diagram relative to the solar equatorial plane breaks down. The investigation of this phenomenon is important to explaining the almost-periodic behaviour of solar cycles. Methods. We use cross-recurrence plots for the study of the time-varying phase asymmetry of the northern and southern hemisphere and compare our results with the latitudinal distribution of the sunspots. Results. We observe a long-term persistence of phase leading in one of the hemispheres, which lasts almost 4 solar cycles and probably corresponds to the Gleissberg cycle. Long-term variations in the hemispheric-leading do not demonstrate clear periodicity but are strongly anti-correlated with the long-term variations in the magnetic equator.},
  language  = {en}
}
@article{MarwanKurthsThomsenetal.2009,
  author    = {Marwan, Norbert and Kurths, J{\"u}rgen and Thomsen, Jesper Skovhus and Felsenberg, Dieter and Saparin, Peter},
  title     = {Three-dimensional quantification of structures in trabecular bone using measures of complexity},
  issn      = {1539-3755},
  doi       = {10.1103/Physreve.79.021903},
  year      = {2009},
  abstract  = {The study of pathological changes of bone is an important task in diagnostic procedures of patients with metabolic bone diseases such as osteoporosis as well as in monitoring the health state of astronauts during long-term space flights. The recent availability of high-resolution three-dimensional (3D) imaging of bone challenges the development of data analysis techniques able to assess changes of the 3D microarchitecture of trabecular bone. We introduce an approach based on spatial geometrical properties and define structural measures of complexity for 3D image analysis. These measures evaluate different aspects of organization and complexity of 3D structures, such as complexity of its surface or shape variability. We apply these measures to 3D data acquired by high-resolution microcomputed tomography (mu CT) from human proximal tibiae and lumbar vertebrae at different stages of osteoporotic bone loss. The outcome is compared to the results of conventional static histomorphometry and exhibits clear relationships between the analyzed geometrical features of trabecular bone and loss of bone density, but also indicate that the measures reveal additional information about the structural composition of bone, which were not revealed by the static histomorphometry. Finally, we have studied the dependency of the developed measures of complexity on the spatial resolution of the mu CT data sets.},
  language  = {en}
}