@article{BeimGrabenJurishSaddyetal.2004,
  author    = {Beim Graben, Peter and Jurish, B. and Saddy, Douglas and Frisch, Stefan},
  title     = {Language processing by dynamical systems},
  issn      = {0218-1274},
  year      = {2004},
  abstract  = {We describe a part of the stimulus sentences of a German language processing ERP experiment using a context- free grammar and represent different processing preferences by its unambiguous partitions. The processing is modeled by deterministic pushdown automata. Using a theorem proven by Moore, we map these automata onto discrete time dynamical systems acting at the unit square, where the processing preferences are represented by a control parameter. The actual states of the automata are rectangles lying in the unit square that can be interpreted as cylinder sets in the context of symbolic dynamics theory. We show that applying a wrong processing preference to a certain input string leads to an unwanted invariant set in the parsers dynamics. Then, syntactic reanalysis and repair can be modeled by a switching of the control parameter - in analogy to phase transitions observed in brain dynamics. We argue that ERP components are indicators of these bifurcations and propose an ERP-like measure of the parsing model},
  language  = {en}
}
@article{BeimGrabenSaddyKurths2004,
  author    = {Beim Graben, Peter and Saddy, Douglas and Kurths, J{\"u}rgen},
  title     = {Untitled},
  year      = {2004},
  language  = {de}
}
@article{BeimGrabenFrischFinketal.2005,
  author    = {Beim Graben, Peter and Frisch, Stefan and Fink, A. and Saddy, Douglas and Kurths, J{\"u}rgen},
  title     = {Topographic voltage and coherence mapping of brain potentials by means of the symbolic resonance analysis},
  issn      = {1539-3755},
  year      = {2005},
  abstract  = {We apply the recently developed symbolic resonance analysis to electroencephalographic measurements of event- related brain potentials (ERPs) in a language processing experiment by using a three-symbol static encoding with varying thresholds for analyzing the ERP epochs, followed by a spin-flip transformation as a nonlinear filter. We compute an estimator of the signal-to-noise ratio (SNR) for the symbolic dynamics measuring the coherence of threshold-crossing events. Hence, we utilize the inherent noise of the EEG for sweeping the underlying ERP components beyond the encoding thresholds. Plotting the SNR computed within the time window of a particular ERP component (the N400) against the encoding thresholds, we find different resonance curves for the experimental conditions. The maximal differences of the SNR lead to the estimation of optimal encoding thresholds. We show that topographic brain maps of the optimal threshold voltages and of their associated coherence differences are able to dissociate the underlying physiological processes, while corresponding maps gained from the customary voltage averaging technique are unable to do so},
  language  = {en}
}
@article{BrehmJurishSaddy2005,
  author    = {Brehm-Jurish, Eva Ute and Saddy, Douglas},
  title     = {On cohesion and coherence in text processing : two ERP studies},
  issn      = {0898-929X},
  year      = {2005},
  language  = {en}
}
@article{DrenhausBeimGrabenSaddyetal.2005,
  author    = {Drenhaus, Heiner and Beim Graben, Peter and Saddy, Douglas and Frisch, Stefan},
  title     = {On the processing of negative polarity constructions revealed by the symbolic resonance analysis},
  issn      = {0898-929X},
  year      = {2005},
  language  = {en}
}
@article{DrenhausBeimGrabenSaddyetal.2006,
  author    = {Drenhaus, Heiner and Beim Graben, Peter and Saddy, Douglas and Frisch, Stefan},
  title     = {Diagnosis and repair of negative polarity constructions in the light of symbolic resonance analysis},
  issn      = {0093-934X},
  doi       = {10.1016/j.bandl.2005.05.001},
  year      = {2006},
  abstract  = {in a post hoc analysis, we investigate differences in event-related potentials of two studies (Drenhaus et al., 2004, to appear; Saddy et al., 2004) by using the symbolic resonance analysis (Beim Graben \& Kurths, 2003). The studies under discussion, examined the failure to license a negative polarity item (NPI) in German: Saddy et al. (2004a) reported an N400 component when the NPI was not accurately licensed by negation; Drenhaus et al. (2004, to appear) considered additionally the influence of constituency of the licensor in NPI constructions. A biphasic N400-P600 response was found for the two induced violations (the lack of licensor and the inaccessibility of negation in a relative clause). The symbolic resonance analysis (SRA) revealed an effect in the P600 time window for the data in Saddy et al., which was not found by using the averaging technique. The SRA of the ERPs in Drenhaus et al., showed that the P600 components are distinguishable concerning the amplitude and latency. It was smaller and earlier in the condition where the licensor is inaccessible, compared to the condition without negation in the string. Our findings suggest that the failure in licensing NPIs is not exclusively related to semantic integration costs (N400). The elicited P600 components reflect differences in syntactic processing. Our results confirm and replicate the effects of the traditional voltage average analysis and show that the SRA is a useful tool to reveal and pull apart ERP differences which are not evident using the traditional voltage average analysis.},
  language  = {en}
}