TY - JOUR A1 - Beim Graben, Peter A1 - Atmanspacher, Harald T1 - Complementarity in classical dynamical systems N2 - The concept of complementarity, originally defined for non-commuting observables of quantum systems with states of non-vanishing dispersion, is extended to classical dynamical systems with a partitioned phase space. Interpreting partitions in terms of ensembles of epistemic states (symbols) with corresponding classical observables, it is shown that such observables are complementary to each other with respect to particular partitions unless those partitions are generating. This explains why symbolic descriptions based on an ad hoc partition of an underlying phase space description should generally be expected to be incompatible. Related approaches with different background and different objectives are discussed Y1 - 2006 UR - http://www.springerlink.com/content/101591 U6 - https://doi.org/10.1007/s10701-005-9013-0 SN - 0015-9018 ER - TY - JOUR A1 - Drenhaus, Heiner A1 - Beim Graben, Peter A1 - Saddy, Douglas A1 - Frisch, Stefan T1 - Diagnosis and repair of negative polarity constructions in the light of symbolic resonance analysis N2 - 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. Y1 - 2006 UR - http://www.sciencedirect.com/science/journal/0093934X U6 - https://doi.org/10.1016/j.bandl.2005.05.001 SN - 0093-934X ER - TY - JOUR A1 - Beim Graben, Peter T1 - Symbolic resonance analysis of event-related potentials distinguishes different physiological processes Y1 - 2005 SN - 0898-929X ER - TY - JOUR A1 - Beim Graben, Peter A1 - Frisch, Stefan A1 - Fink, A. A1 - Saddy, Douglas A1 - Kurths, Jürgen T1 - Topographic voltage and coherence mapping of brain potentials by means of the symbolic resonance analysis N2 - 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 Y1 - 2005 SN - 1539-3755 ER - TY - JOUR A1 - Drenhaus, Heiner A1 - Beim Graben, Peter A1 - Saddy, Douglas A1 - Frisch, Stefan T1 - On the processing of negative polarity constructions revealed by the symbolic resonance analysis Y1 - 2005 SN - 0898-929X ER - TY - JOUR A1 - Frisch, Stefan A1 - Beim Graben, Peter T1 - Finding needles in haystacks : Symbolic resonance analysis of event-related potentials unveils different processing demands N2 - Previous ERP studies have found an N400-P600 pattern in sentences in which the number of arguments does not match the number of arguments that the verb can take. In the present study, we elaborate on this question by investigating whether the case of the mismatching object argument in German (accusative/direct object versus dative/ indirect object) affects processing differently. In general, both types of mismatches elicited a biphasic N400 P600 response in the ERP. However, traditional voltage average analysis was unable to reveal differences between the two mismatching conditions, that is, between a mismatching accusative versus dative. Therefore, we employed a recently developed method on ER-P data analysis, the symbolic resonance analysis (SRA), where EEG epochs are symbolically encoded in sequences of three symbols depending on a given parameter, the encoding threshold. We found a larger proportion of threshold crossing events with negative polarity in the N400 time window for a mismatching dative argument compared to a mismatching accusative argument. By contrast, the proportion of threshold crossing events with positive polarity was smaller for dative in the P600 time window. We argue that this difference is due to the phenomenon of "free dative" in German. This result also shows that the SRA provides a useful tool for revealing ERP differences that cannot be discovered using the traditional voltage average analysis. (c) 2005 Elsevier B.V. All rights reserved Y1 - 2005 ER - TY - JOUR A1 - Beim Graben, Peter A1 - Saddy, Douglas A1 - Kurths, Jürgen T1 - Untitled Y1 - 2004 ER - TY - JOUR A1 - Frisch, Stefan A1 - Beim Graben, Peter A1 - Schlesewsky, Matthias T1 - Parallelizing grammatical functions : P600 and P345 reflect different cost of reanalysis N2 - It is well-known from psycholinguistic literature that the human language processing system exhibits preferences when sentence constituents are ambiguous with respect to their grammatical function. Generally, many theories assume that an interpretation towards the subject is preferred in such cases. Later disambiguations which contradict such a preference induce enhanced processing difficulty (i.e. reanalysis) which reflects itself in late positive deflections (P345/P600) in event-related brain potentials (ERPs). In the case of phoric elements such as pronouns, a second strategy is known according to which an ambiguous pronoun preferentially receives the grammatical function that its antecedent has (parallel function strategy). In an ERP study, we show that this strategy can in principle override the general subject preference strategy (known for both pronominal and nonpronominal constituents) and induce an object preference, in case that the pronoun's antecedent is itself an object. Interestingly, the revision of a subject preference leads to a P600 component, whereas the revision of an object preference induces an earlier positivity (P345). In order to show that the latter component is indeed a positivity and not an N400-like negativity in the same time range, we apply an additional analysis based on symbolic dynamics which allows to determine the polarity of an ERP effect on purely methodological grounds. With respect to the two positivities, we argue that the latency differences reflect qualitative differences in the reanalysis processes Y1 - 2004 SN - 0218-1274 ER - TY - JOUR A1 - Beim Graben, Peter A1 - Jurish, B. A1 - Saddy, Douglas A1 - Frisch, Stefan T1 - Language processing by dynamical systems N2 - 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 Y1 - 2004 SN - 0218-1274 ER - TY - JOUR A1 - Beim Graben, Peter A1 - Frisch, Stefan T1 - Is it positive or negative? On determining ERP components N2 - In most experiments using event-related brain potentials (ERPs), there is a straightforward way to define-on theoretical grounds-which of the conditions tested is the experimental condition and which is the control condition. It, however, theoretical assumptions do not give sufficient and unambiguous information to decide this question, then the interpretation of an ERP effect becomes difficult, especially if one takes into account that certain effects can be both a positivity or a negativity on the basis of the morphology of the pattern as well as with respect to peak latency (regard for example, N400 and P345). Exemplified with an ERP experiment on language processing, we present such a critical case and offer a possible solution on the basis of nonlinear data analysis. We show that a generalized polarity histogram, the word statistics of symbolic dynamics, is in principle able to distinguish negative going ERP components from positive ones when an appropriate encoding strategy, the half wave encoding is employed. We propose statistical criteria which allow to determine ERP components on purely methodological grounds Y1 - 2004 SN - 0018-9294 ER -