Theory in Biosciences

, Volume 122, Issue 1, pp 5–18 | Cite as

Spatial and temporal stochastic interaction in neuronal assemblies

  • Thomas Wennekers
  • Nihat Ay


The observation of various types of spatio-temporal correlations in spike-patterns of multiple cortical neurons has shifted attention from rate coding paradigms to computational processes based on the precise timing of spikes in neuronal ensembles. In the present work we develop the notion of “spatial” and “temporal interaction” which provides measures for statistical dependences in coupled stochastic processes like multiple unit spike trains. We show that the classical Willshaw network and Abeles’ synfire chain model both reveal a moderate spatial interaction, but only the synfire chain model reveals a positive temporal interaction, too. Systems that maximize temporal interaction are shown to be almost deterministic globally, but posses almost unpredictable firing behavior on the single unit level.

Key words

Spatio-temporal spike patterns Gamma-oscillations Synfire chains Information geometry Temporal Information maximization 


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  1. Abeles, M. (1991) Corticonics: Neural circuits of the cerebral cortex. Cambridge University Press, Cambridge UK.Google Scholar
  2. Aertsen, A. M. H. J.; Gerstein, G. L.; Habib, M. K. and Palm, G. (1989) Dynamics of Neuronal Firing Correlation: Modulation of “Effective Connectivity”. J. Neurophysiol. 61: 900–917.PubMedGoogle Scholar
  3. Amari, S.-I. (2001) Information Geometry on Hierarchy of Probability Distributions. IEEE Trans. Information Theory 47: 1701–1711.CrossRefGoogle Scholar
  4. Amit, D. J. (1995) The Hebbian Paradigm Reintegrated: Local Reverberations as Internal Representations. Beh. Brain Sci. 18: 617–657.CrossRefGoogle Scholar
  5. Ay, N. (2002a) An Information-Geometric Approach to a Theory of Pragmatic Structuring. Annals of Probability 30: 416–436.CrossRefGoogle Scholar
  6. Ay, N. (2002b) Locality of Global Stochastic Interaction in Directed Acyclic Networks. Neural Comput. 14: 2959–2980.PubMedCrossRefGoogle Scholar
  7. Ay, N. (2003) Information Geometry on Complexity and Stochastic Interaction. IEEE Trans. Information Theory, submitted.Google Scholar
  8. Ay, N.; Wennekers, T. (2003) Dynamical Properties of Strongly Interacting Markov Chains. Neural Networks, submitted.Google Scholar
  9. Bliss, T. V. P. and Collingridge, G. L. (1993) A synaptic model of memory: long-term potentiation in the hippocampus. Nature 361: 31–39.PubMedCrossRefGoogle Scholar
  10. Cover, T. M. and Thomas, J. A. (1991) Elements of Information Theory. Wiley Series in Telecommunications. New York: Wiley-Interscience.Google Scholar
  11. Dayan, P. and Abbott, L. F. (2001) Theoretical Neuroscience. MIT-Press, Cambridge, MA.Google Scholar
  12. Eckhorn, R. (1999) Neural mechanisms of scene segmentation: Recordings from the visual cortex suggest basic circuits for linking field models. IEEE Trans. Neural Networks 10: 464–479.CrossRefGoogle Scholar
  13. Fuster, J. M. (1994) Memory in the cerebral cortex. MIT Press, Cambridge.Google Scholar
  14. Grün, S.; Diesmann, M. and Aertsen, A. (2002) Unitary events in multiple single-neuron spiking activity: I. Detection and significance. Neural Comput. 14: 43–80. II. Nonstationary data. Neural Comput. 14: 81–119.PubMedCrossRefGoogle Scholar
  15. Hebb, D. O. (1949) The organization of behavior. Wiley, New York.Google Scholar
  16. Linsker, R. (1988) Self-organization in a perceptual network. IEEE Computer 21, 105–117.Google Scholar
  17. Martignon, L.; von Hasseln, H.; Grün, S.; Aertsen, A. and Palm, G. (1995) Detecting higher-order interactions among the spiking events in a group of neurons. Biol. Cybern. 73: 69–81.PubMedGoogle Scholar
  18. Nakahara, H. and Amari, S. (2002) Information geometric measure for neural spike trains. Neural Comput. 14: 2269–2316.PubMedCrossRefGoogle Scholar
  19. Nicolelis, M. A. L., and De Schutter, E. (2001) Special Issue on Multiple Electrode Recordings. J. Neurosci. Meth. 94(1): 3–154.Google Scholar
  20. Palm, G. (1982) Neural Assemblies. An Alternative Approach to Artificial Intelligence, Springer Verlag, Berlin.Google Scholar
  21. Rieke, F., Warland, D., Ruyter van Steveninck, R. and Bialek W. (1998) Spikes: Exploring the Neural Code. MIT Press, Cambridge.Google Scholar
  22. Singer, W. and Gray, C. M. (1995) Visual feature integration and the temporal correlation hypotheses. Ann. Rev. Neurosci. 18: 555–586.PubMedCrossRefGoogle Scholar
  23. Tononi, G.; Sporns, O. and Edelman, G. M. (1994) A measure for brain complexity: Relating functional segregation and integration in the nervous system. Proc. Natl. Acad. Sci. 91: 5033–5037.PubMedCrossRefGoogle Scholar
  24. Wennekers, T. and Ay, N. (2002) Temporal Infomax on Markov Chains with Input Leads to Finite State Automata. Neurocomputing, in press.Google Scholar
  25. Willshaw, D. J.; Buneman, O. P. and Longuet-Higgins, H. C. (1969) Non-holographic associative memory. Nature 222: 960–962.PubMedCrossRefGoogle Scholar

Copyright information

© Urban & Fischer Verlag 2003

Authors and Affiliations

  1. 1.Max-Planck-Institute for Mathematics in the SciencesLeipzigGermany

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