@misc{ThielRomanoKurthsetal.2006,
  author    = {Thiel, Marco and Romano, Maria Carmen and Kurths, J{\"u}rgen and Rolfs, Martin and Kliegl, Reinhold},
  title     = {Generating Surrogates from Recurrences},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-56906},
  year      = {2006},
  abstract  = {In this paper we present an approach to recover the dynamics from recurrences of a system and then generate (multivariate) twin surrogate (TS) trajectories. In contrast to other approaches, such as the linear-like surrogates, this technique produces surrogates which correspond to an independent copy of the underlying system, i. e. they induce a trajectory of the underlying system visiting the attractor in a different way. We show that these surrogates are well suited to test for complex synchronization, which makes it possible to systematically assess the reliability of synchronization analyses. We then apply the TS to study binocular fixational movements and find strong indications that the fixational movements of the left and right eye are phase synchronized. This result indicates that there might be one centre only in the brain that produces the fixational movements in both eyes or a close link between two centres.},
  language  = {en}
}
@phdthesis{Pazienti2007,
  author    = {Pazienti, Antonio},
  title     = {Manipulations of spike trains and their impact on synchrony analysis},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-17447},
  school      = {Universit{\"a}t Potsdam},
  year      = {2007},
  abstract  = {The interaction between neuronal cells can be identified as the computing mechanism of the brain. Neurons are complex cells that do not operate in isolation, but they are organized in a highly connected network structure. There is experimental evidence that groups of neurons dynamically synchronize their activity and process brain functions at all levels of complexity. A fundamental step to prove this hypothesis is to analyze large sets of single neurons recorded in parallel. Techniques to obtain these data are meanwhile available, but advancements are needed in the pre-processing of the large volumes of acquired data and in data analysis techniques. Major issues include extracting the signal of single neurons from the noisy recordings (referred to as spike sorting) and assessing the significance of the synchrony. This dissertation addresses these issues with two complementary strategies, both founded on the manipulation of point processes under rigorous analytical control. On the one hand I modeled the effect of spike sorting errors on correlated spike trains by corrupting them with realistic failures, and studied the corresponding impact on correlation analysis. The results show that correlations between multiple parallel spike trains are severely affected by spike sorting, especially by erroneously missing spikes. When this happens sorting strategies characterized by classifying only good'' spikes (conservative strategies) lead to less accurate results than tolerant'' strategies. On the other hand, I investigated the effectiveness of methods for assessing significance that create surrogate data by displacing spikes around their original position (referred to as dithering). I provide analytical expressions of the probability of coincidence detection after dithering. The effectiveness of spike dithering in creating surrogate data strongly depends on the dithering method and on the method of counting coincidences. Closed-form expressions and bounds are derived for the case where the dither equals the allowed coincidence interval. This work provides new insights into the methodologies of identifying synchrony in large-scale neuronal recordings, and of assessing its significance.},
  language  = {en}
}