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In this paper we apply symbolic transformations as a visualisation technique for analysing rhythm production. It is shown that qualitative information can be extracted from the experimental data. This approach may provide new insights into the organisation of temporal order by the brain on different levels of description. A simple phenomenological model for the explanation of the observed phenomena is proposed.
We investigate the cognitive control in polyrhythmic hand movements as a model paradigm for bimanual coordination. Using a symbolic coding of the recorded time series, we demonstrate the existence of qualitative transitions induced by experimental manipulation of the tempo. A nonlinear model with delayed feedback control is proposed, which accounts for these dynamical transitions in terms of bifurcations resulting from variation of the external control parameter. Furthermore, it is shown that transitions can also be observed due to fluctuations in the timing control level. We conclude that the complexity of coordinated bimanual movements results from interactions between nonlinear control mechanisms with delayed feedback and stochastic timing components.
We investigate the cognitive control in polyrhythmic hand movements as a model paradigm for bimanual coordination. Using a symbolic coding of the recorded time series, we demonstrate the existence of qualitative transitions induced by experimental manipulation of the tempo. A nonlinear model with delayed feedback control is proposed, which accounts for these dynamical transitions in terms of bifurcations resulting from variation of the external control parameter. Furthermore, it is shown that transitions can also be observed due to fluctuations in the timing control level. We conclude that the complexity of coordinated bimanual movements results from interactions between nonlinear control mechanisms with delayed feedback and stochastic timing components.
Die Produktion von Polyrhythmen ist ein wichtiger experimenteller Zugang für die Untersuchung der menschlichen Motorik. Durch Variation des Tempos (externer Kontrollparameter) bei rhythmischen Bewegungsabläufen können qualitative Übergänge in der Koordinationsdynamik induziert werden. Diese Übergänge lassen sich mit der Methode der symbolischen Dynamik in experimentellen Zeitreihen nachweisen und sind ein wichtiger Hinweis darauf, dass die untersuchten Bewegungsabläufe nichtlinearen Kontrollprozessen unterliegen. Die theoretische Beschreibung bimanueller Rhythmusproduktion mit gekoppelten Differenzengleichungen führt auf ein Modell mit nichtlinearer Fehlerkontrolle. Es ist eine wichtige Eigenschaft der Kontrollprozesse, dass sie mit zeitverzögerter Rückkopplung arbeiten. Neben deterministischen Steuerungsmechanismen ist die Motorik des Menschen ausserdem von Fluktuationen auf zwei Ebenen gekennzeichnet, der kognitiven Kontrollebene und der Ebene der motorischen Systeme. Daher ist die Koordination von Bewegungen das Ergebnis von Wechselwirkungen zwischen nichtlinearen, zeitverzögerten Kontrollprozessen und stochastischen Fluktuationen.
The complex behaviour of cardiorespiratory dynamics is shown to be related to the interaction between several physiological oscillators. This study is based on electrocardiogram and respiratory flow data obtained from 3 different subjects during paced breathing at 10 different pacing cycle lengths ranging from 5 s to 12 s. Two different methods ideally suited for the analysis of synchronization pattern of coupled oscillators are applied: 1. Symbolic dynamics based on symbol coding adapted for the detection of respiratory modulation of cardiac parasympathetic activity discloses two regimes of different synchronization behaviour within the frequency area corresponding to the Arnold tongue of 1:1 frequency-locking between respiratory flow and respiratory heartbeat variation (respiratory sinus arrhythmia). 2. The analysis of the phase shift between respiratory flow and respiratory sinus arrhythmia indicates that synchronization is not a static but a dynamic phenomenon. The observed dependence of the phase shift on respiratory cycle length shows large inter-individual variation. These findings turn out to be further hints for the existence of an additional central oscillator in the frequency range of respiration interacting with the central respiratory oscillator driving mechanical respiration.
The fast and the slow of skilled bimanual rhythm production : parallel versus integrated timing
(2000)
Contents: 1 Introduction 2 Experiment 3 Data 4 Symbolic dynamics 4.1 Symbolic dynamics as a tool for data analysis 4.2 2-symbols coding 4.3 3-symbols coding 5 Measures of complexity 5.1 Word statistics 5.2 Shannon entropy 6 Testing for stationarity 6.1 Stationarity 6.2 Time series of cycle durations 6.3 Chi-square test 7 Control parameters in the production of rhythms 8 Analysis of relative phases 9 Discussion 10 Outlook
A dynamical model of saccade generation in reading based on spatially distributed lexical processing
(2002)
We analyse time series from a study on bimanual rhythmic movements in which the speed of performance (the external control parameter) was experimentally manipulated. Using symbolic transformations as a visualization technique we observe qualitative changes in the dynamics of the timing patterns. Such phase transitions are quantitatively described by measures of complexity. Using these results we develop an advanced symbolic coding which enables us to detect important dynamical structures. Furthermore, our analysis raises new questions concerning the modelling of the underlying human cognitive-motor system.
SWIFT explorations
(2003)
Computational models such as E-Z Reader and SWIFT are ideal theoretical tools to test quantitatively our current understanding of eye-movement control in reading. Here we present a mathematical analysis of word skipping in the E-Z Reader model by semianalytic methods, to highlight the differences in current modeling approaches. In E-Z Reader, the word identification system must outperform the oculomotor system to induce word skipping. In SWIFT, there is competition among words to be selected as a saccade target. We conclude that it is the question of competitors in the "game" of word skipping that must be solved in eye movement research
We question the assumption of serial attention shifts and the assumption that saccade programs are initiated or canceled only after stage one of word identification. Evidence: (1) Fixation durations prior to skipped words are not consistently higher compared to those prior to non-skipped words. (2) Attentional modulation of microsaccade rate might occur after early visual processing. Saccades are probably triggered by attentional selection
Computational models such as E-Z Reader and SWIFT are ideal theoretical tools to test quantitatively our current understanding of eye-movement control in reading. Here we present a mathematical analysis of word skipping in the E-Z Reader model by semianalytic methods, to highlight the differences in current modeling approaches. In E-Z Reader, the word identification system must outperform the oculomotor system to induce word skipping. In SWIFT, there is competition among words to be selected as a saccade target. We conclude that it is the question of competitors in the “game” of word skipping that must be solved in eye movement research.
We question the assumption of serial attention shifts and the assumption that saccade programs are initiated or canceled only after stage one of word identification. Evidence: (1) Fixation durations prior to skipped words are not consistently higher compared to those prior to nonskipped words. (2) Attentional modulation of microsaccade rate might occur after early visual processing. Saccades are probably triggered by attentional selection.
During reading, our eyes perform complicated sequences of fixations on words. Stochastic models of eye movement control suggest that this seemingly erratic behaviour can be attributed to noise in the oculomotor system and random fluctuations in lexical processing. Here, we present a qualitative analysis of a recently published dynamical model [Engbert et al., 2002] and propose that deterministic nonlinear control accounts for much of the observed complexity of eye movement patterns during reading. Based on a symbolic coding technique we analyze robust statistical features of simulated fixation sequences
During fixation of a stationary target, small involuntary eye movements exhibit an erratic trajectory-a random walk. Two types of these fixational eye movements are drift and microsaccades (small-amplitude saccades). We investigated fixational eye movements and binocular coordination using a statistical analysis that had previously been applied to human posture control. This random-walk analysis uncovered two different time scales in fixational eye movements and identified specific functions for microsaccades. On a short time scale, microsaccades enhanced perception by increasing fixation errors. On a long time scale, microsaccades reduced fixation errors and binocular disparity (relative to pure drift movements). Thus, our findings clarify the role of oculomotor processes during fixation
We resolve a controversy about reading fixations before word-skipping saccades which were reported as longer or shorter than control fixations in earlier studies. Our statistics are based on resampling of matched sets of fixations before skipped and nonskipped words, drawn from a database of 121,321 single fixations contributed by 230 readers of the Potsdam sentence corpus. Matched fixations originated from single-fixation forward-reading patterns and were equated for their positions within words. Fixations before skipped words were shorter before short or high-frequency words and longer before long or low-frequency words in comparison with control fixations. Reasons for inconsistencies in past research and implications for computational models are discussed
Fixational eye movements occur involuntarily during visual fixation of stationary scenes. The fastest components of these miniature eye movements are microsaccades, which can be observed about once per second. Recent studies demonstrated that microsaccades are linked to covert shifts of visual attention. Here, we generalized this finding in two ways. First, we used peripheral cues, rather than the centrally presented cues of earlier studies. Second, we spatially cued attention in vision and audition to visual and auditory targets. An analysis of microsaccade responses revealed an equivalent impact of visual and auditory cues on microsaccade-rate signature (i.e. an initial inhibition followed by an overshoot and a final return to the pre-cue baseline rate). With visual cues or visual targets, microsaccades were briefly aligned with cue direction and then opposite to cue direction during the overshoot epoch, probably as a result of an inhibition of an automatic saccade to the peripheral cue. With left auditory cues and auditory targets microsaccades oriented in cue direction. We argue that microsaccades can be used to study crossmodal integration of sensory information and to map the time course of saccade preparation during covert shifts of visual and auditory attention
Eye movements during fixation of a stationary target prevent the adaptation of the visual system to continuous illumination and inhibit fading of the image. These random, involuntary, small movements are restricted at long time scales so as to keep the target at the center of the field of view. Here we use detrended fluctuation analysis in order to study the properties of fixational eye movements at different time scales. Results show different scaling behavior between horizontal and vertical movements. When the small ballistic movements, i.e., microsaccades, are removed, the scaling exponents in both planes become similar. Our findings suggest that microsaccades enhance the persistence at short time scales mostly in the horizontal component and much less in the vertical component. This difference may be due to the need for continuously moving the eyes in the horizontal plane, in order to match the stereoscopic image for different viewing distances
We compared effects of covert spatial-attention shifts induced with exogenous or endogenous cues on microsaccade rate and direction. Separate and dissociated effects were obtained in rate and direction measures. Display changes caused microsaccade rate inhibition, followed by sustained rate enhancement. Effects on microsaccade direction were differentially tied to cue class (exogenous vs. endogenous) and type (neutral vs. directional). For endogenous cues, direction effects were weak and occurred late. Exogenous cues caused a fast direction bias towards the cue (i.e., early automatic triggering of saccade programs), followed by a shift in the opposite direction (i.e, controlled inhibition of cue-directed saccades, leading to a 'leakage' of microsaccades in the opposite direction). (C) 2004 Elsevier Ltd. All rights reserved
Mathematical models have become an important tool for understanding the control of eye movements during reading. Main goals of the development of the SWIFT model (Engbert, Longtin, & Kliegl, 2002)were to investigate the possibility of spatially distributed processing and to implement a general mechanism for all types of eye movements we observe in reading experiments. Here, we present an advanced version of SWIFT which integrates properties of the oculomotor system and effects of word recognition to explain many of the experimental phenomena faced in reading research. We propose new procedures for the estimation of model parameters and for the test of the model’s performance. A mathematical analysis of the dynamics of the SWIFT model is presented. Finally, within this framework, we present an analysis of the transition from parallel to serial processing.
Fixational eye movements occur involuntarily during visual fixation of stationary scenes. The fastest components of these miniature eye movements are microsaccades, which can be observed about once per second. Recent studies demonstrated that microsaccades are linked to covert shifts of visual attention [e.g., Engbert & Kliegl (2003), Vision Res 43:1035-1045]. Here,we generalized this finding in two ways. First, we used peripheral cues, rather than the centrally presented cues of earlier studies. Second, we spatially cued attention in vision and audition to visual and auditory targets. An analysis of microsaccade responses revealed an equivalent impact of visual and auditory cues on microsaccade-rate signature (i.e., an initial inhibition followed by an overshoot and a final return to the pre-cue baseline rate). With visual cues or visual targets,microsaccades were briefly aligned with cue direction and then opposite to cue direction during the overshoot epoch, probably as a result of an inhibition of an automatic saccade to the peripheral cue. With left auditory cues and auditory targets microsaccades oriented in cue direction. Thus, microsaccades can be used to study crossmodal integration of sensory information and to map the time course of saccade preparation during covert shifts of visual and auditory attention.
Refixation probability during reading is lowest near the word center, suggestive of an optimal viewing position (OVP). Counter-intuitively, fixation durations are largest at the OVP, a result called the inverted optimal viewing position (IOVP) effect [Vitu, McConkie, Kerr, & O'Regan, (2001). Vision Research 41, 3513-3533]. Current models of eye-movement control in reading fail to reproduce the IOVP effect. We propose a simple mechanism for generating this effect based on error-correction of mislocated fixations due to saccadic errors, First, we propose an algorithm for estimating proportions of mislocated fixations from experimental data yielding a higher probability for mislocated fixations near word boundaries. Second, we assume that mislocated fixations trigger an immediate start of a new saccade program causing a decrease of associated durations. Thus, the IOVP effect could emerge as a result of a coupling between cognitive and oculomotor processes. (c) 2005 Elsevier Ltd. All rights reserved
Mathematical, models,have become an important tool for understanding the control of eye movements during reading. Main goals of the development of the SWIFT model (R. Engbert, A. Longtin, & R. Kliegl, 2002) were to investigate the possibility of spatially distributed processing and to implement a general mechanism for all types of eye movements observed in reading experiments. The authors present an advanced version of SWIFT that integrates properties of the oculomotor system and effects of word recognition to explain many of the experimental phenomena faced in reading research. They propose new procedures for the estimation of model parameters and for the test of the model's performance. They also present a mathematical analysis of the dynamics of the SWIFT model. Finally, within this framework, they present an analysis of the transition from parallel to serial processing
Even during visual fixation of a stationary target, our eyes perform rather erratic miniature movements, which represent a random walk. These "fixational" eye movements counteract perceptual fading, a consequence of fast adaptation of the retinal receptor systems to constant input. The most important contribution to fixational eye movements is produced by microsaccades; however, a specific function of microsaccades only recently has been found. Here we show that the occurrence of microsaccades is correlated with low retinal image slip approximate to 200 ms before microsaccade onset. This result suggests that microsaccades are triggered dynamically, in contrast to the current view that microsaccades are randomly distributed in time characterized by their rate-of-occurrence of 1 to 2 per second. As a result of the dynamic triggering mechanism, individual microsaccade rate can be predicted by the fractal dimension of trajectories. Finally, we propose a minimal computational model for the dynamic triggering of microsaccades
Reading requires the orchestration of visual, attentional, language-related, and oculomotor processing constraints. This study replicates previous effects of frequency, predictability, and length of fixated words on fixation durations in natural reading and demonstrates new effects of these variables related to previous and next words. Results are based on fixation durations recorded from 222 persons, each reading 144 sentences. Such evidence for distributed processing of words across fixation durations challenges psycholinguistic immediacy-of-processing and eye- mind assumptions. Most of the time the mind processes several words in parallel at different perceptual and cognitive levels. Eye movements can help to unravel these processes
Microsaccades are miniature eye movements produced involuntarily during visual fixation of stationary objects. Since their first description more than 40 years ago, the role of microsaccades in vision has been controversial. In this issue, Martinez-Conde and colleagues present a solution to the long-standing research problem connecting this basic oculomotor function to visual perception, by showing that microsaccades may control peripheral vision during visual fixation by inducing flips in bistable peripheral percepts in head-unrestrained viewing. Their study provides new insight into the functional connectivity between oculomotor function and visual perception
Current advances in SWIFT
(2006)
Models of eye movement control are very useful for gaining insights into the intricate connections of different cognitive and oculomotor subsystems involved in reading. The SWIFT model (Engbert, Longtin, & Kliegl (2002). Vision Research, 42, 621 - 636) proposed a unified mechanism to account for all types of eye movement patterns that might be observed in reading behavior. The model is based on the notion of spatially distributed, or parallel, processing of words in a sentence. We present a refined version of SWIFT introducing a letter-based approach that proposes a processing gradient in the shape of a smooth function. We show that SWIFT extents its capabilities by accounting for distributions of landing positions.