Journal of Computational Neuroscience

, Volume 22, Issue 1, pp 5–19 | Cite as

Non-parametric detection of temporal order across pairwise measurements of time delays

  • Danko NikolićEmail author


Neuronal synchronization is often associated with small time delays, and these delays can change as a function of stimulus properties. Investigation of time delays can be cumbersome if the activity of a large number of neurons is recorded simultaneously and neuronal synchronization is measured in a pairwise manner (such as the cross-correlation histograms) because the number of pairwise measurements increases quadratically. Here, a non-parametric statistical test is proposed with which one can investigate (i) the consistency of the delays across a large number of pairwise measurements and (ii) the consistency of the changes in the time delays as a function of experimental conditions. The test can be classified as non-parametric because it takes into account only the directions of the delays and thus, does not make assumptions about the distributions and the variances of the measurement errors.


Cross correlation Phase offset Temporal-order code Transitivity Additivity 


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  1. Boneau CA (1960) The effects of violations of assumptions underlying the t-test. Psychol Bull 57:49–64PubMedCrossRefGoogle Scholar
  2. Hopfield JJ (1995) Pattern recognition computation using action potential timing for stimulus representation. Nature 376:33–36PubMedCrossRefGoogle Scholar
  3. König P, Engel AK, Roelfsema PR, Singer W (1995) How precise is neuronal synchronization? Neural Comput 7:469–485PubMedGoogle Scholar
  4. König P (1994) A method for the quantification of synchrony and oscillatory properties of neuronal activity. J Neurosci Methods 54:31–37PubMedCrossRefGoogle Scholar
  5. Mehta MR, Lee AK, Wilson MA (2002) Role of experience and oscillations in transforming a rate code into a temporal code. Nature 417:741–746PubMedCrossRefGoogle Scholar
  6. Moon JW (1968) Topics on tournaments. Holt, Rinehart and Winston, New York, NYGoogle Scholar
  7. Perkel DH, Gerstein GL, Moore GP (1967) Neuronal spike trains and stochastic point processes. II. Simultaneous spike trains. Biophys J 7:419–440PubMedCrossRefGoogle Scholar
  8. Ramsey PH (1980) Exact Type I error rates for robustness of Student’s t test with unequal variances. J Educ Stat 5:337–349CrossRefGoogle Scholar
  9. Roelfsema PR, Engel AK, König P, Singer W (1997) Visuomotor integration is associated with zero time-lag synchronization among cortical areas. Nature 385:157–161PubMedCrossRefGoogle Scholar
  10. Runyon P, Haber A (1980) Fundamental of behavioral statistics. Addison Wesley Publishing Company, Reading, MAGoogle Scholar
  11. Schneider G, Nikolić D (2006) Detection and assessment of near-zero delays in neuronal spiking activity. J Neurosci Methods 152(1–2):97–106PubMedCrossRefGoogle Scholar
  12. Schneider G, Havenith MN, Nikolić D (2006) Spatio-temporal structure in large neuronal networks detected from cross-correlation. Neural Comput 18(10):2387–2413Google Scholar
  13. Van Rullen R, Thorpe SJ (2001) Rate coding versus temporal order coding:What the retinal ganglion cells tell the visual cortex? Neural Comput 13:1255–1283PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  1. 1.Max-Planck-Institute for Brain ResearchFrankfurt am MainGermany
  2. 2.Frankfurt Institute for Advanced StudiesJohann Wolfgang Goethe-UniversityFrankfurtGermany

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