Federico Sanabria

1
Accounting for Cyclic Responding in Timing using
Binary Counting

• Federico Sanabria Peter R. Killeen
• Department of Psychology
• Arizona State University
• May 28th, 2006
• 32nd Annual ABA Convention
• Atlanta, GA

• Acknowledgments
• For enriching discussions Lewis Bizo, Espen
  Johansen, and Ricardo Pellón.
• For data production and pre-analysis Heather
  Adams, Michelle Barker, Cindy Bazua, Weihua Chen,
  Kayla Cranston, Courtney Ficks, Michelle Gaza,
  Paul Jellison, Kweku Osafo-Acquaah, and Hyewon
  Rhieu.
• For funding NSF IBN 023682.

2
Temporal Generalization Gradients

• Method Peak Procedure
• Training Trials Fixed Interval F
• Probe Trials Unsignaled extinction trials with
  duration P
• Results (in Probe Trials)
• Responses congregate around F
• Dispersion proportional to F (Webers Law)
• However

3
Response Resurgence
Asgari et al. (2006)
Colombo et al. (2001)
Bayley et al. (1998)
Rodríguez-Gironés Kacelnik (1999)
Nevin Grace (1999)
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Mean Response Rates
F, P
B wF N(F ,?F) (1 - wF) N (P F ,?PF)
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Scalar Invariance of Rate Model
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Within-Trial Rate Patterns

• Bitonic Trials Break1-Run-Break2
• Tritonic Trials Break1-Run1-Break2-Run2

(Church, Meck Gibbon, 1994)
Stop
Resurgence
Start
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Start and Resurgence
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Resurgence Times
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Timing Model

• General Framework (Clock)

Pacemaker
Counter
?
Memory
Comparator
F PF
Roberts (1981) Internal Clock
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Stochastic Binary Counter
Time Bit 0 Bit 1 Bit 2 Bit 3 Bit
4 0 0 0 0 0 0 1 1 0 0 0 0 2 0 1 0 0 0 3 1 1 0 0 0
4 0 0 1 0 0 15 1 1 1 1 0 3
0 0 1 1 1 1 0 0 0 0 0 0
Reinforcement
Killeen Taylors (2000) Theory of Stochastic
Counters (TSC)
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Stochastic Binary Counter
Time Bit 0 Bit 1 Bit 2 Bit 3 Bit
4 0 0 0 0 0 0 1 1 0 0 0 0 2 0 1 0 0 0 3 1 1 0 0 0
4 0 0 1 0 0 15 1 1 1 1 0 3
0 0 1 1 1 1 -1 1 1 1 1
Reinforcement
Memory
Killeen Taylors (2000) Theory of Stochastic
Counters (TSC)
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Stochastic Binary Counter
Time Bit 0 Bit 1 Bit 2 Bit 3 Bit
4 0 0 0 0 0 0 1 1 0 0 0 0 2 0 1 0 0 0 3 1 1 0 0 0
4 0 0 1 0 0 15 1 1 1 1 0 ? ? ?
? ? -.04 -.01 -.04 0 .34 -.04 -.01
-.04 0 0
Memory
Comparator
-.09
Killeen Taylors (2000) Theory of Stochastic
Counters (TSC)
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SBC Simulation
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Conclusions

• Response Resurgence
• Is controlled by forthcoming reinforcement
• Appears despite salient forthcoming stimuli
  signaling FI
• These stimuli, however, effectively restart the
  clock
• Stochastic Binary Counter
• A conditionable and fallible binary counter that
  is reset after reinforcement may simulate the
  probability distribution of run initiations.
• The SBC does not exclude models originated from
  alternate theories (e.g., Packet Theory) it
  specifies a plausible source of variability in
  performance without invoking Gaussian filters.

15
THANK YOU
16
What Generates the Gaussian Distributions?
Probability of Start or Resurge

• ISI Counter

Encode Only?

IRI Counter
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What Generates the Gaussian Distributions?

• Two-Counter Model

ISI Counter
FI Onset

Pacemaker
IRI Counter
Memory
Comparator
F
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Conclusions

• Response resurgence
• Is controlled by forthcoming reinforcement
• Appears despite salient forthcoming stimuli
  signaling FI
• These stimuli, however, effectively restart the
  clock
• Two-Counter Model
• Appears to be necessary to encode P F interval
  while performing according to F .

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Conclusions

• Stochastic Binary Counter
• Two SBCs (IRI for encoding, IRIISI for
  performance) with otherwise identical
  characteristics, appears to account for the data.
• It does not exclude models originated from
  alternate theories (e.g., Packet Theory), but
  specify a plausible source of variability in
  performance without invoking Gaussian filters.