Cookies Policy
X

This site uses cookies. By continuing to browse the site you are agreeing to our use of cookies.

I accept this policy

Find out more here

Timescale Invariance in the Pacemaker-Accumulator Family of Timing Models

No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
The full text of this article is not currently available.

Brill’s MyBook program is exclusively available on BrillOnline Books and Journals. Students and scholars affiliated with an institution that has purchased a Brill E-Book on the BrillOnline platform automatically have access to the MyBook option for the title(s) acquired by the Library. Brill MyBook is a print-on-demand paperback copy which is sold at a favorably uniform low price.

Access this article

+ Tax (if applicable)
Add to Favorites
You must be logged in to use this functionality

image of Timing & Time Perception

Pacemaker-accumulator (PA) systems have been the most popular kind of timing model in the half-century since their introduction by Treisman (1963). Many alternative timing models have been designed predicated on different assumptions, though the dominant PA model during this period — Gibbon and Church’s Scalar Expectancy Theory (SET) — invokes most of them. As in Treisman, SET’s implementation assumes a fixed-rate clock-pulse generator and encodes durations by storing average pulse counts; unlike Treisman’s model, SET’s decision process invokes Weber’s law of magnitude-comparison to account for timescale-invariant temporal precision in animal behavior. This is one way to deal with the ‘Poisson timing’ issue, in which relative temporal precision increases for longer durations, contrafactually, in a simplified version of Treisman’s model. First, we review the fact that this problem does not afflict Treisman’s model itself due to a key assumption not shared by SET. Second, we develop a contrasting PA model, an extension of Killeen and Fetterman’s Behavioral Theory of Timing that accumulates Poisson pulses up to a fixed criterion level, with pulse rates adapting to time different intervals. Like Treisman’s model, this time-adaptive, opponent Poisson, drift–diffusion model accounts for timescale invariance without first assuming Weber’s law. It also makes new predictions about response times and learning speed and connects interval timing to the popular drift–diffusion model of perceptual decision making. With at least three different routes to timescale invariance, the PA model family can provide a more compelling account of timed behavior than may be generally appreciated.

Affiliations: 1: 1Oberlin College, Department of Neuroscience, 119 Woodland St., Oberlin, OH 44074, USA; 2: 4Princeton University, Princeton Neuroscience Institute, Green Hall, Washington Rd., Princeton, NJ 08540, USA; 3: 5Koç University, College of Social Science & Humanities, Rumelifeneri Yolu, 34450 Sariyer, Istanbul, Turkey; 4: 6Arizona State University, Department of Psychology, P.O. Box 871104, Tempe, AZ 85287-1104, USA

10.1163/22134468-00002018
/content/journals/10.1163/22134468-00002018
dcterms_title,pub_keyword,dcterms_description,pub_author
6
3
Loading
Loading

Full text loading...

/content/journals/10.1163/22134468-00002018
Loading

Data & Media loading...

1. Ahrens M. B. , Sahani M. ( 2008). "Observers exploit stochastic models of sensory change to help judge the passage of time". Curr. Biol., Vol 21, 17.
2. Allan L. G. , Gibbon J. ( 1991). "Human bisection at the geometric mean". Learn. Motiv., Vol 22, 3958. http://dx.doi.org/10.1016/0023-9690(91)90016-2
3. Almeida R. , Ledberg A. ( 2010). "A biologically plausible model of time-scale invariant interval timing". J. Comput. Neurosci., Vol 28, 155175. http://dx.doi.org/10.1007/s10827-009-0197-8
4. Balci F. , Freestone D. , Simen P. , deSouza L. , Cohen J. D. , Holmes P. ( 2011). "Optimal temporal risk assessment". Front. Neurosci., Vol 5, 56.
5. Balci F. , Gallistel C. R. , Allen B. D. , Frank K. M. , Gibson J. M. , Brunner D. ( 2009). "Acquisition of peak responding: What is learned?" Behav. Process., Vol 80, 6775. http://dx.doi.org/10.1016/j.beproc.2008.09.010
6. Balsam P. D. , Drew M. R. , Gallistel C. R. ( 2010). "Time and associative learning". Comp. Cogn. Behav. Rev., Vol 5, 122. http://dx.doi.org/10.3819/ccbr.2010.50001
7. Bizo L. A. , Chu J. Y. M. , Sanabria F. , Killeen P. R. ( 2006). "The failure of Weber’s law in time perception and production". Behav. Process., Vol 71, 201210. http://dx.doi.org/10.1016/j.beproc.2005.11.006
8. Brown S. , Heathcote A. ( 2008). "The simplest complete model of choice response time: Linear ballistic accumulation". Cognit. Psychol., Vol 57, 153178. http://dx.doi.org/10.1016/j.cogpsych.2007.12.002
9. Catania A. C. ( 1970). "Reinforcement schedules and psychophysical judgments: A study of some temporal properties of behavior". In Schoenfeld W. N. (Ed.), The theory of reinforcement schedules(pp.  142). New York, NY: Appleton-Century-Crofts.
10. Chhikara R. S. , Folks L. ( 1989). The inverse Gaussian distribution: theory, methodology, and applications, Vol Vol. 95. Boca Raton, FL: CRC.
11. Church R. M. , Deluty M. Z. ( 1977). "Bisection of temporal intervals". J. Exp. Psychol., Vol 3, 216228.
12. Church R. M. , Lacourse D. M. , Crystal J. D. ( 1998). "Temporal search as a function of the variability of interfood intervals". J. Exp. Psychol. Anim. Behav. Process., Vol 24, 291315. http://dx.doi.org/10.1037/0097-7403.24.3.291
13. Church R. M. , Meck W. H. , Gibbon J. ( 1994). "Application of scalar timing theory to individual trials". J. Exp. Psychol. Anim. Behav. Process., Vol 20, 135155. http://dx.doi.org/10.1037/0097-7403.20.2.135
14. Einstein A. ( 1905). "Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen". Ann. Phys., Vol 17, 549560. http://dx.doi.org/10.1002/andp.19053220806
15. Feller W. ( 1968). An introduction to probability theory and its applications( 3rd ed.). New York, NY: Wiley.
16. Gallistel C. R. , Gibbon J. ( 2000). "Time, rate and conditioning". Psychol. Rev., Vol 107, 289344. http://dx.doi.org/10.1037/0033-295X.107.2.289
17. Gallistel C. R. , King A. , McDonald R. ( 2004). "Sources of variability and systematic error in mouse timing behavior". J. Exp. Psychol. Anim. Behav. Process., Vol 30, 316. http://dx.doi.org/10.1037/0097-7403.30.1.3
18. Gardiner C. W. ( 2004). Handbook of stochastic methods( 3rd ed.). New York, NY: Springer-Verlag. http://dx.doi.org/10.1007/978-3-662-05389-8
19. Gibbon J. ( 1977). "Scalar expectancy theory and Weber’s law in animal timing". Psychol. Rev., Vol 84, 279325. http://dx.doi.org/10.1037/0033-295X.84.3.279
20. Gibbon J. ( 1992). "Ubiquity of scalar timing with a Poisson clock". J. Math. Psychol., Vol 35, 283293. http://dx.doi.org/10.1016/0022-2496(92)90041-5
21. Gibbon J. , Church R. M. ( 1984). "Sources of variance in an information processing theory of timing". In Roitblat H. L. , Bever T. G. , Terrace H. S. (Eds.), Animal cognition(pp.  465488). Hillsdale, NJ: Lawrence Erlbaum Associates.
22. Gibbon J. , Church R. M. ( 1990). "Representation of time". Cognition, Vol 37, 2354. http://dx.doi.org/10.1016/0010-0277(90)90017-E
23. Gibbon J. , Church R. M. , Meck W. H. ( 1984). "Scalar timing in memory". In Gibbon J. , Allan L. G. (Eds.), Annals of the New York Academy of Sciences: timing and time perception, Vol Vol. 423(pp.  5277). New York, NY: New York Academy of Sciences.
24. Gibbon J. , Malapani C. , Dale C. , Gallistel C. R. ( 1997). "Toward a neurobiology of temporal cognition: Advances and challenges". Curr. Opin. Neurobiol., Vol 7, 170184. http://dx.doi.org/10.1016/S0959-4388(97)80005-0
25. Gold J. I. , Shadlen M. N. ( 2007). "The neural basis of decision making". Annu. Rev. Neurosci., Vol 30, 535574. http://dx.doi.org/10.1146/annurev.neuro.29.051605.113038
26. Gooch C. M. , Wiener M. , Hamilton A. C. , Coslett H. B. ( 2011). "Temporal discrimination of sub- and suprasecond time intervals: A voxel-based lesion mapping analysis". Front. Integr. Neurosci., Vol 5, 59. http://dx.doi.org/10.3389/fnint.2011.00059
27. Grossberg S. , Schmajuk N. A. ( 1989). "Neural dynamics of adaptive timing and temporal discrimination during associative learning". Neural Netw., Vol 2, 79102. http://dx.doi.org/10.1016/0893-6080(89)90026-9
28. Guilhardi P. , Yi L. , Church R. M. ( 2007). "A modular theory of learning and performance". Psychon. Bull. Rev., Vol 14, 543559. http://dx.doi.org/10.3758/BF03196805
29. Haß J. , Blaschke S. , Rammsayer T. , Herrmann J. M. ( 2008). "A neurocomputational model for optimal temporal processing". J. Comput. Neurosci., Vol 25, 449464. http://dx.doi.org/10.1007/s10827-008-0088-4
30. Higham D. J. ( 2001). "An algorithmic introduction to numerical simulation of stochastic differential equations". Soc. Ind. Appl. Math. Rev., Vol 43, 525546.
31. Jozefowiez J. , Staddon J. E. R. , Cerutti D. T. ( 2009). "The behavioral economics of choice and interval timing". Psychol. Rev., Vol 116, 519539. http://dx.doi.org/10.1037/a0016171
32. Karmarkar U. R. , Buonomano D. V. ( 2007). "Timing in the absence of clocks: Encoding time in neural network states". Neuron, Vol 53, 427438. http://dx.doi.org/10.1016/j.neuron.2007.01.006
33. Killeen P. R. ( 2013). "Absent without leave: A neuroenergetic theory of mind wandering". Front. Psychol., Vol 4, 373. http://dx.doi.org/10.3389/fpsyg.2013.00373
34. Killeen P. R. , Fetterman J. G. ( 1988). "A behavioral theory of timing". Psychol. Rev., Vol 95, 274295. http://dx.doi.org/10.1037/0033-295X.95.2.274
35. Killeen P. R. , Fetterman J. G. , Bizo L. A. ( 1997). "Time’s causes". In Bradshaw C. M. , Szabadi E. (Eds.), Time and behaviour: psychological and neurobehavioural analyses(pp.  79131). Amsterdam: Elsevier Science Publishers. http://dx.doi.org/10.1016/S0166-4115(97)80055-6
36. Killeen P. R. , Weiss N. A. ( 1987). "Optimal timing and the Weber function". Psychol. Rev., Vol 94, 455468. http://dx.doi.org/10.1037/0033-295X.94.4.455
37. Laming D. R. J. ( 1968). Information theory of choice reaction time. New York, NY: Wiley.
38. Link S. W. ( 1992). The wave theory of difference and similarity. Hillsdale, NJ: Lawrence Erlbaum Associates.
39. Luce R. D. ( 1986). Response times: their role in Inferring Elementary Mental Organization. New York NY: Oxford University Press.
40. Ludvig E. A. , Sutton R. S. , Kehoe E. J. ( 2008). "Stimulus representation and the timing of reward-prediction errors". Neural Comput., Vol 20, 30343054. http://dx.doi.org/10.1162/neco.2008.11-07-654
41. Luzardo A. , Ludvig E. A. , Rivest F. ( 2013). "An adaptive drift–diffusion model of interval timing dynamics". Behav. Process., Vol 95, 9099. http://dx.doi.org/10.1016/j.beproc.2013.02.003
42. Machado A. ( 1997). "Learning the temporal dynamics of behavior". Psychol. Rev., Vol 104, 241265. http://dx.doi.org/10.1037/0033-295X.104.2.241
43. Matell M. , Meck W. H. ( 2004). "Cortico-striatal circuits and interval timing: Coincidence detection of oscillatory processes". Cogn. Brain Res., Vol 21, 139170. http://dx.doi.org/10.1016/j.cogbrainres.2004.06.012
44. Meck W. H. ( 1996). "Neuropharmacology of timing and time perception". Cogn. Brain Res., Vol 3, 227242. http://dx.doi.org/10.1016/0926-6410(96)00009-2
45. Meck W. H. ( 2006). "Neuroanatomical localization of an internal clock: A functional link between mesolimbic, nigrostriatal, and mesocortical dopaminergic systems". Brain Res., Vol 1109, 93107. http://dx.doi.org/10.1016/j.brainres.2006.06.031
46. Miall R. C. ( 1989). "The storage of time intervals using oscillating neurons". Neural Comput., Vol 1, 359371. http://dx.doi.org/10.1162/neco.1989.1.3.359
47. Ratcliff R. ( 1978). "A theory of memory retrieval". Psychol. Rev., Vol 85, 59108. http://dx.doi.org/10.1037/0033-295X.85.2.59
48. Ratcliff R. ( 1985). "Theoretical interpretations of the speed and accuracy of positive and negative responses". Psychol. Rev., Vol 92, 212225. http://dx.doi.org/10.1037/0033-295X.92.2.212
49. Ratcliff R. , Cherian A. , Segraves M. A. ( 2003). "A comparison of macaque behavior and superior colliculus neuronal activity to predictions from models of two choice decisions". J. Neurophysiol., Vol 90, 13921407. http://dx.doi.org/10.1152/jn.01049.2002
50. Ratcliff R. , Rouder J. N. ( 1998). "Modeling response times for two-choice decisions". Psychol. Sci., Vol 9, 347356. http://dx.doi.org/10.1111/1467-9280.00067
51. Ratcliff R. , Rouder J. N. ( 2000). "A diffusion model account of masking in two-choice letter identification". J. Exp. Psychol. Hum. Percept. Perform., Vol 26, 127140. http://dx.doi.org/10.1037/0096-1523.26.1.127
52. Ratcliff R. , Smith P. L. ( 2010). "Perceptual discrimination in static and dynamic noise: The temporal relation between perceptual encoding and decision making". J. Exp. Psychol. Gen., Vol 139, 7094. http://dx.doi.org/10.1037/a0018128
53. Rivest F. , Bengio Y. ( 2011). Adaptive drift–diffusion process to learn time intervals. .
54. Roberts S. ( 1981). "Isolation of an internal clock". J. Exp. Psychol. Anim. Behav. Process., Vol 7, 242268. http://dx.doi.org/10.1037/0097-7403.7.3.242
55. Schrödinger E. ( 1915). "Zur Theorie der Fall und Steigversuche an Teilchen mit Brownscher Bewegung". Phys. Z., Vol 16, 289295.
56. Seung H. S. ( 1996). "How the brain keeps the eyes still". Proc. Natl Acad. Sci. U.S.A., Vol 93, 1333913344. http://dx.doi.org/10.1073/pnas.93.23.13339
57. Shankar K. , Howard M. ( 2012). "A scale-invariant internal representation of time". Neural Comput., Vol 24, 134193. http://dx.doi.org/10.1162/NECO_a_00212
58. Simen P. , Balci F. , deSouza L. , Cohen J. D. , Holmes P. ( 2011a). "Interval timing by long-range temporal integration". Front. Integr. Neurosci., Vol 5, 28. http://dx.doi.org/10.3389/fnint.2011.00028
59. Simen P. , Balci F. , deSouza L. , Cohen J. D. , Holmes P. ( 2011b). "A model of interval timing by neural integration". J. Neurosci., Vol 31, 92389253. http://dx.doi.org/10.1523/JNEUROSCI.3121-10.2011
60. Smith P. L. , Ratcliff R. ( 2004). "Psychology and neurobiology of simple decisions". Trends Neurosci., Vol 27, 161168. http://dx.doi.org/10.1016/j.tins.2004.01.006
61. Smoluchowsky M. V. ( 1915). "Notiz über die Berechning der Brownschen Molkularbewegung bei des Ehrenhaft-millikanchen Versuchsanordnung". Phys. Z., Vol 16, 318321.
62. Staddon J. E. R. ( 2001). The new behaviorism. Philadelphia, PA: Psychology Press.
63. Staddon J. E. R. , Chelaru I. M. , Higa J. J. ( 2002). "A tuned-trace theory of interval-timing dynamics". J. Exp. Anal. Behav., Vol 77, 105124. http://dx.doi.org/10.1901/jeab.2002.77-105
64. Staddon J. E. R. , Higa J. J. ( 1996). "Multiple time scales in simple habituation". Psychol. Rev., Vol 103, 720733. http://dx.doi.org/10.1037/0033-295X.103.4.720
65. Staddon J. E. R. , Higa J. J. ( 1999a). "Time and memory: Towards a pacemaker-free theory of interval timing". J. Exp. Anal. Behav., Vol 71, 215251. http://dx.doi.org/10.1901/jeab.1999.71-215
66. Staddon J. E. R. , Higa J. J. ( 1999b). "The choose-short effect and trace models of timing". J. Exp. Anal. Behav., Vol 72, 473478. http://dx.doi.org/10.1901/jeab.1999.72-473
67. Stone M. ( 1960). "Models for choice reaction time". Psychometrika, Vol 25, 251260. http://dx.doi.org/10.1007/BF02289729
68. Telfeian A. E. , Connors B. W. ( 1998). "Layer-specific pathways for the horizontal propagation of epileptiform discharges in neocortex". Epilepsia, Vol 39, 700708. http://dx.doi.org/10.1111/j.1528-1157.1998.tb01154.x
69. Treisman M. ( 1963). "Temporal discrimination and the indifference interval: Implications for a model of the ‘internal clock’". Psychol. Monogr., Vol 77, 131. http://dx.doi.org/10.1037/h0093864
70. Treisman M. ( 1964). "Noise and Weber’s Law: The discrimination of brightness and other dimensions". Psychol. Rev., Vol 71, 314330. http://dx.doi.org/10.1037/h0042445
71. Treisman M. ( 1966). "A statistical decision model for sensory discrimination which predicts Weber’s law and other sensory laws: Some results of a computer simulation". Percept. Psychophys., Vol 1, 203230. http://dx.doi.org/10.3758/BF03215786
72. Treisman M. ( 1984). "Temporal rhythms and cerebral rhythms". In Gibbon J. , Allan L. (Eds.), Annals of the New York Academy of Sciences: timing and time perception, Vol Vol. 423(pp.  542565). New York, NY: New York Academy of Sciences.
73. Treisman M. , Cook N. , Naish P. L. N. , MacCrone J. K. ( 1992). "The internal clock: Electroencephalographic evidence for oscillatory processes underlying time perception". Q. J. Exp. Psychol. A, Vol 47, 241289. http://dx.doi.org/10.1080/14640749408401112
74. Treisman M. , Faulkner A. , Naish P. L. N. , Brogan D. ( 1990). "The internal clock: Evidence for a temporal oscillator underlying time perception with some estimates of its characteristic frequency". Perception, Vol 19, 705743. http://dx.doi.org/10.1068/p190705
75. Tuerlinckx F. ( 2004). "The efficient computation of the cumulative distribution and probability density functions in the diffusion model". Behav. Res. Methods Instrum. Comput., Vol 36, 702716. http://dx.doi.org/10.3758/BF03206552
76. Usher M. , McClelland J. L. ( 2001). "The time course of perceptual choice: The leaky, competing accumulator model". Psychol. Rev., Vol 108, 550592. http://dx.doi.org/10.1037/0033-295X.108.3.550
77. Uttal W. R. ( 2008). Distributed neural systems: beyond the new phrenology. Cambridge, MA: Sloan Educational Publishing.
78. Wackermann J. , Ehm W. ( 2006). "The dual klepsydra model of internal time representation and time reproduction". J. Theor. Biol., Vol 239, 482493. http://dx.doi.org/10.1016/j.jtbi.2005.08.024
79. Wald A. ( 1947). Sequential analysis. New York, NY: Dover.
80. Wald A. , Wolfowitz J. ( 1948). "Optimum character of the sequential probability ratio test". Ann. Math. Stat., Vol 19, 326339. http://dx.doi.org/10.1214/aoms/1177730197
81. Wang X. J. ( 2002). "Probabilistic decision making by slow reverberation in cortical circuits". Neuron, Vol 36, 955968. http://dx.doi.org/10.1016/S0896-6273(02)01092-9
82. Wearden J. H. , Bray S. ( 2001). "Scalar timing without reference memory? Episodic temporal generalization and bisection in humans". Q. J. Exp. Psychol. B, Vol 54, 289309. http://dx.doi.org/10.1080/02724990042000173
http://brill.metastore.ingenta.com/content/journals/10.1163/22134468-00002018
Loading

Article metrics loading...

/content/journals/10.1163/22134468-00002018
2013-01-01
2016-12-08

Sign-in

Can't access your account?
  • Tools

  • Add to Favorites
  • Printable version
  • Email this page
  • Subscribe to ToC alert
  • Get permissions
  • Recommend to your library

    You must fill out fields marked with: *

    Librarian details
    Your details
    Why are you recommending this title?
    Select reason:
     
    Timing & Time Perception — Recommend this title to your library
  • Export citations
  • Key

  • Full access
  • Open Access
  • Partial/No accessInformation