@article{RomanoThielKurthsetal.2009, author = {Romano, Maria Carmen and Thiel, Marco and Kurths, J{\"u}rgen and Mergenthaler, Konstantin and Engbert, Ralf}, title = {Hypothesis test for synchronization : twin surrogates revisited}, issn = {1054-1500}, doi = {10.1063/1.3072784}, year = {2009}, abstract = {The method of twin surrogates has been introduced to test for phase synchronization of complex systems in the case of passive experiments. In this paper we derive new analytical expressions for the number of twins depending on the size of the neighborhood, as well as on the length of the trajectory. This allows us to determine the optimal parameters for the generation of twin surrogates. Furthermore, we determine the quality of the twin surrogates with respect to several linear and nonlinear statistics depending on the parameters of the method. In the second part of the paper we perform a hypothesis test for phase synchronization in the case of experimental data from fixational eye movements. These miniature eye movements have been shown to play a central role in neural information processing underlying the perception of static visual scenes. The high number of data sets (21 subjects and 30 trials per person) allows us to compare the generated twin surrogates with the "natural" surrogates that correspond to the different trials. We show that the generated twin surrogates reproduce very well all linear and nonlinear characteristics of the underlying experimental system. The synchronization analysis of fixational eye movements by means of twin surrogates reveals that the synchronization between the left and right eye is significant, indicating that either the centers in the brain stem generating fixational eye movements are closely linked, or, alternatively that there is only one center controlling both eyes.}, language = {en} } @article{SafdariCherstvyChechkinetal.2015, author = {Safdari, Hadiseh and Cherstvy, Andrey G. and Chechkin, Aleksei V. and Thiel, Felix and Sokolov, Igor M. and Metzler, Ralf}, title = {Quantifying the non-ergodicity of scaled Brownian motion}, series = {Journal of physics : A, Mathematical and theoretical}, volume = {48}, journal = {Journal of physics : A, Mathematical and theoretical}, number = {37}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1751-8113}, doi = {10.1088/1751-8113/48/37/375002}, pages = {18}, year = {2015}, abstract = {We examine the non-ergodic properties of scaled Brownian motion (SBM), a non-stationary stochastic process with a time dependent diffusivity of the form D(t) similar or equal to t(alpha-1). We compute the ergodicity breaking parameter EB in the entire range of scaling exponents a, both analytically and via extensive computer simulations of the stochastic Langevin equation. We demonstrate that in the limit of long trajectory lengths T and short lag times Delta the EB parameter as function of the scaling exponent a has no divergence at alpha - 1/2 and present the asymptotes for EB in different limits. We generalize the analytical and simulations results for the time averaged and ergodic properties of SBM in the presence of ageing, that is, when the observation of the system starts only a finite time span after its initiation. The approach developed here for the calculation of the higher time averaged moments of the particle displacement can be applied to derive the ergodic properties of other stochastic processes such as fractional Brownian motion.}, language = {en} } @article{AgneNaylorPreicketal.2022, author = {Agne, Stefanie and Naylor, Gavin J. P. and Preick, Michaela and Yang, Lei and Thiel, Ralf and Weigmann, Simon and Paijmans, Johanna L. A. and Barlow, Axel and Hofreiter, Michael and Straube, Nicolas}, title = {Taxonomic identification of two poorly known lantern shark species based on mitochondrial DNA from wet-collection paratypes}, series = {Frontiers in Ecology and Evolution}, volume = {10}, journal = {Frontiers in Ecology and Evolution}, publisher = {Frontiers Media}, address = {Lausanne}, issn = {2296-701X}, doi = {10.3389/fevo.2022.910009}, pages = {10}, year = {2022}, abstract = {Etmopteridae (lantern sharks) is the most species-rich family of sharks, comprising more than 50 species. Many species are described from few individuals, and re-collection of specimens is often hindered by the remoteness of their sampling sites. For taxonomic studies, comparative morphological analysis of type specimens housed in natural history collections has been the main source of evidence. In contrast, DNA sequence information has rarely been used. Most lantern shark collection specimens, including the types, were formalin fixed before long-term storage in ethanol solutions. The DNA damage caused by both fixation and preservation of specimens has excluded these specimens from DNA sequence-based phylogenetic analyses so far. However, recent advances in the field of ancient DNA have allowed recovery of wet-collection specimen DNA sequence data. Here we analyse archival mitochondrial DNA sequences, obtained using ancient DNA approaches, of two wet-collection lantern shark paratype specimens, namely Etmopterus litvinovi and E. pycnolepis, for which the type series represent the only known individuals. Target capture of mitochondrial markers from single-stranded DNA libraries allows for phylogenetic placement of both species. Our results suggest synonymy of E. benchleyi with E. litvinovi but support the species status of E. pycnolepis. This revised taxonomy is helpful for future conservation and management efforts, as our results indicate a larger distribution range of E. litvinovi. This study further demonstrates the importance of wet-collection type specimens as genetic resource for taxonomic research.}, language = {en} } @article{RomanoThielKurthsetal.2006, author = {Romano, Maria Carmen and Thiel, Marco and Kurths, J{\"u}rgen and Rolfs, Martin and Engbert, Ralf and Kliegl, Reinhold}, title = {Synchronization Analysis and Recurrence in Complex Systems}, isbn = {978-3-527-40623-4}, year = {2006}, language = {en} }