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Biological Cybernetics

, Volume 85, Issue 2, pp 77–87 | Cite as

Mathematical models of eye movements in reading: a possible role for autonomous saccades

  • Ralf Engbert
  • Reinhold Kliegl

Abstract.

 An efficient method for the exact numerical simulation of semi-Markov processes is used to study minimal models of the control of eye movements in reading. When we read a text, typical sequences of fixations form a rather complicated trajectory – almost like a random walk. Mathematical models of eye movement control can account for this behavior using stochastic transition rules between few discrete internal states, which represent combinations of certain stages of lexical access and saccade programs. We show that experimentally observed fixation durations can be explained by residence-time-dependent transition probabilities. Stochastic processes with this property are known as semi-Markov processes. For our numerical simulations we use the minimal process method (Gillespie algorithm), which is an exact and efficient simulation algorithm for this class of stochastic processes. Within this mathematical framework, we study different forms of coupling between eye movements and shifts of covert attention in reading. Our model lends support to the existence of autonomous saccades, i.e., the hypothesis that initiations of saccades are not completely determined by lexical access processes.

Keywords

Random Walk Minimal Model Typical Sequence Fixation Duration Lexical Access 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Ralf Engbert
    • 1
  • Reinhold Kliegl
    • 1
  1. 1. Institut für Psychologie, Universität Potsdam, PF 601553, 14415 Potsdam, GermanyDE

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