TITLE: Symbolic dynamics as a unifying framework for analyzing and modeling language-related brain potentials SPEAKER: Peter beim Graben (School of Psychology and Clinical Language Sciences University of Reading, UK) ABSTRACT: We developed an approach for analyzing event-related brain potentials (ERP) by means of symbolic dynamics and measures of complexity of sliding cylinder sets [1, 2]. By applying these methods to ERP data obtained from different language processing experiments we observed that language-related components such as the P600 or the N400 correspond to decreases or increases of cylinder entropy. In symbolic dynamics theory, any string of finite or infinite length can be mapped onto a real number lying in the unit interval by a g-adic expansion. In the same manner, any bi-infinite sequence is represented by a point in the unit square. By applying this technique, cylinder sets correspond to rectangles in the unit square. On the other hand cylinder sets can be easily interpreted as state descriptions of a deterministic pushdown automaton [3, 4, 5]. We applied two different g-adic expansions to stack and input words of an automaton. This leads to a map of the automaton's (the parser's) states onto rectangles in the unit square. We discuss a simple ambiguous context-free grammar for presenting a toy-model of syntactic reanalysis and processed its output by a pushdown automaton obtaining a list of parsing states. This list has been translated into a sequence of rectangles lying in the unit square by the g-adic expansion algorithm. The processing preferences are represented by a control parameter of the system. We show that applying a wrong processing preference to a certain input string leads to an unwanted invariant set in the parsers dynamics. Then, syntactical 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 [4, 5]. References [1] beim Graben, P., Saddy, J. D., Schlesewsky, M., & J. Kurths (2000). Symbolic dynamics of event-related brain potentials. Physical Review E, 62(4), 5518-5541. [2] beim Graben, P., Frisch, S., Fink, A., Saddy, D. & Kurths, J. (2005). Topographic voltage and coherence mapping of brain potentials by means of the symbolic resonance analysis. Physical Review E, 72, 051916. [3] Moore C. (1990). Unpredictability and undecidability in dynamical systems. Physical Review Letters 64, 2354-2357. [4] beim Graben, P., Jurish, B, Saddy, D. & Frisch, S. (2004). Language processing by dynamical systems. International Journal of Bifurcation and Chaos, 14(2), 599-622. [5] beim Graben, P., Gerth, S. & Vasishth, S. (2008). Towards dynamical system models of event-related brain potentials. Cognitive Neurodynamics, 2(3), 229 255.