Abstract
Long-range dependence is a characteristic property of successively produced time intervals, such as in un-paced or continuation tapping. We hypothesise in the present paper that serial dependence in such tasks could be related to a closed-loop regulation process, in which the current interval is determined by preceding ones. As a consequence, the quality of sensory feedback is likely to affect serial dependence. An experiment with human participants shows that diminished sensory information tends to increase the Hurst exponent for short inter-onset intervals and tends to decrease it for long intervals. A simulation shows that a simple auto-regressive model, whose order depends on the ratio between the inter-onset interval and an assumed temporal integration span, is able to account for most of our empirical results, including the duration specificity of long-range correlation.
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Notes
The experimental system incorporates a delay from obstructing the light beam to the corresponding MIDI message being sent of less than 3 ms, from start of the MIDI message to the start of the sound of ~4.5 ms, and in the operation of the program of less than 1 ms. The MIDI asynchronous communication clock frequency of 31.25 kHz leads to a estimated minimum temporal variability of 32 µs. The trigger and sound devices have similar clock frequencies and hence also temporal variability in the same range.
References
Bak P (1997) How nature works. Oxford University Press, Oxford
Balasubramaniam R, Wing AM, Daffertshofer A (2004) Keeping with the beat: movement trajectories contribute to movement timing. Exp Brain Res 159:129–134
Billon M, Semjen A, Cole J, Gauthier G (1996) The role of sensory information in the production of periodic finger-tapping sequences. Exp Brain Res 110:117–130
Block RA, Zakay D (2006) Prospective remembering involves time estimation. In: Glicksohn J, Myslobodsky MS (eds) Timing the future. The case for a time-based prospective memory. World Scientific Printers, London, pp 25–49
Chen Y, Repp BH, Patel AD (2002) Spectral decomposition of variability in synchronization and continuation tapping: comparisons between auditory and visual pacing and feedback conditions. Hum Mov Sci 21:515–532
Collins JJ, De Luca CJ (1993) Open-loop and closed-loop control of posture: a random-walk analysis of center-of-pressure trajectories. Exp Brain Res 95:308–318
Delignières D, Lemoine L, Torre K (2004) Time intervals production in tapping and oscillatory motion. Hum Mov Sci 23:87–103
Delignières D, Torre K, Lemoine L (2008) Fractal models for event-based and dynamical timers. Acta Psychol 127:382–397
Drewing K, Hennings M, Aschersleben G (2002) The contribution of tactile reafference to temporal regularity during bimanual finger tapping. Psychol Res 66:60–70
Einstein A (1905) Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen. Annu Phys 322:549–560
Finney SA, Warren WH (2002) Delayed auditory feedback and rhythmic tapping: evidence for a critical interval shift. Percept Psychophys 64:896–908
Fraisse P (1980) Les synchronizations sensori-motrices aux rhythmes. In: Requin JE (ed) Anticipation et Comportement. Editions de C.N.R.S., Paris, pp 233–257
Fraisse P (1984) Perception and estimation of time. Annu Rev 35:1–36
Fraisse P, Voillaume C (1971) Les repéres du sujet dans la synchronisation et dans la pseudo-synchronisation. Psych Franc 71:359–369
Fraisse P, Oléron G, Paillard J (1958) Sur le repéres sensoriels qui permettent de controler les mouvements d’accompagnements de stimuli périodiques. Ann Psychol 58:321–338
Gibbon J (1977) Scalar expectancy theory and Weber’s law in animal timing. Psychol Rev 84:279–325
Gibbon J, Malapani C, Dale CL, Gallistel CR (1997) Toward a neurobiology of temporal cognition: advances and challenges. Curr Opin Neurobiol 7:170–184
Gilden DL (1997) Fluctuations in the time required for elementary decisions. Psychol Sci 8:296–301
Gilden DL (2001) Cognitive emissions of 1/f noise. Psychol Rev 108:33–56
Gilden DL, Thornton T, Mallon MW (1995) 1/f noise in human cognition. Science 267:1837–1839
Grondin S, Meilleur-Wells G, Oullette C, Macar F (1998) Sensory effects on jugdments of short time-intervals. Psychol Res 61:261–268
Halpern AR, Darwin CL (1982) Duration discrimination in a series of rhythmic events. Percept Psychophys 31:86–89
James W (1890) The principles of psychology, vol 1. Holt, New York
Kolers PA, Brewster JM (1985) Rhythms and responses. J Exp Psychol Hum Percept Perform 11:150–167
Lemoine L, Torre K, Delignières D (2006) Testing for the presence of 1/f noise in continuation tapping data. Can J Exp Psychol 60:247–257
Lewis PA, Miall RC (2006) Remembering the time: a continuous clock. Trends Cogn Sci 10:401–406
Madison G (2001a) Functional modelling of the human timing mechanism. PhD thesis, Uppsala University Library, Uppsala
Madison G (2001b) Variability in isochronous tapping: higher-order dependencies as a function of inter tap interval. J Exp Psychol Hum Percept Perform 27:411–422
Madison G (2004a) Detection of linear temporal drift in sound sequences: principles and empirical evaluation. Acta Psychol 117:95–118
Madison G (2004b) Fractal modeling of human isochronous serial interval production. Biol Cybern 90:105–112
Madison G (2006) Duration specificity in the long-range correlation of human serial interval production. Physica D 216:301–306
Madison G, Merker B (2004) Human sensorimotor tracking of continuous subliminal deviations from isochrony. Neurosci Lett 370:69–73
Madison G, Forsman L, Blom Ö, Karabanov A, Ullén F (2008) Correlations between general intelligence and components of serial timing variability. Intelligence. doi:10.1016/j.intell.2008.07.006
Mandelbrot BB, van Ness JW (1968) Fractional Brownian motions, fractional noises and applications. SIAM Rev 10:422–437
Mauk MD, Buonomano DV (2004) The neural basis of temporal processing. Annu Rev Neurosci 27:307–340
Michon JA (1978) The making of the present. A tutorial review. In: Requin JE (ed) Attention and performance. Erlbaum, Hillsdale, pp 89–111
Peng C-K, Buldyrev V, Havlin S, Simons M, Stanley HE, Goldberger AL (1994) Mosaic organization of DNA nucleotides. Phys Rev E 49:1685–1689
Pfordresher PQ (2003) Auditory feedback in music performance: evidence for a dissociation of sequencing and timing. J Exp Psychol Hum Percept Perform 29:949–964
Pöppel E (1997) A hierarchical model of temporal perception. Trends Cogn Sci 1:56–61
Pressing J (1998) Error correction processes in temporal pattern production. J Math Psychol 42:63–101
Repp BH (2005) Sensorimotor synchronization: a review of the tapping literature. Psychon Bull Rev 12:969–992
Riecker A, Wildgruber D, Mathiak K, Grodd W, Ackermann H (2003) Parametric analysis of rate-dependent hemodynamic response functions of cortical and subcortical brain structures during auditorily cued finger tapping: a fMRI study. Neuroimage 18:731–739
Staddon JER (2005) Interval timing: memory, not a clock. Trends Cogn Sci 9:312–314
Staddon JER, Chelaru IM, Higa JJ (2002) Habituation, memory and the brain: the dynamics of interval timing. Behav Processes 57:71–88
Stenneken P, Prinz W, Cole J, Paillard J, Aschersleben G (2006) The effect of sensory feedback on the timing of movements: evidence from deafferented patients. Brain Res 1084:123–131
Stevens LT (1886) On the time-sense. Mind 11:393–404
Thaut MH, Tian B, Azimi-Sadjadi MR (1998) Rhythmic finger tapping to cosine-wave modulated metronome sequences: evidence of subliminal entrainment. Hum Mov Sci 17:839–863
Torre K, Delignières D, Lemoine L (2007a) 1/f(beta) fluctuations in bimanual coordination: an additional challenge for modeling. Exp Brain Res 183(2):225–234
Torre K, Delignières D, Lemoine L (2007b) Detection of long-range dependence and estimation of fractal exponents through ARFIMA modelling. Br J Math Stat Psychol 60(1):85–106
van Orden GC, Holden JG, Turvey MT (2005) Human cognition and 1/f scaling. J Exp Psychol Gen 134:117–123
Vorberg D, Wing AM (1996) Modeling variability and dependence in timing. In: Heuer H, Keele SW (eds) Handbook of perception and action, vol 2: Motor skills. Academic Press, New York, pp 181–262
Wagenmakers E-J, Farrell S, Ratcliff R (2004) Estimation and interpretation of 1/f(alpha) noise in human cognition. Psychon Bull Rev 11(4):579–615
Wearden JH (1999) “Beyond the fields we know…”: exploring and developing scalar timing theory. Behav Process 45:3–21
Wing AM (1977) Perturbations of auditory feedback delay and the timing of movement. J Exp Psychol Hum Percept Perform 3:175–186
Wing AM, Kristofferson A (1973) Response delays and the timing of discrete motor responses. Percept Psychophys 14:5–12
Yamada N (1995) Nature of variability in rhythmical movement. Hum Mov Sci 14:371–384
Acknowledgment
Part of this work was supported by grant RJ 2002:0791 from the Bank of Sweden Tercentenary Foundation to Dr. Madison.
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Madison, G., Delignières, D. Auditory feedback affects the long-range correlation of isochronous serial interval production: support for a closed-loop or memory model of timing. Exp Brain Res 193, 519–527 (2009). https://doi.org/10.1007/s00221-008-1652-x
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DOI: https://doi.org/10.1007/s00221-008-1652-x