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Di Bernardino E, León J, Tchumatchenko T. Cross-correlations and joint gaussianity in multivariate level crossing models. J Math Neurosci. 2014;4(1):22doi: 10.1186/2190-8567-4-22.
Di Bernardino, E., León, J., & Tchumatchenko, T. (2014). Cross-correlations and joint gaussianity in multivariate level crossing models. Journal of mathematical neuroscience, 4(1), 22. https://doi.org/10.1186/2190-8567-4-22
Di Bernardino, Elena, et al. "Cross-correlations and joint gaussianity in multivariate level crossing models." Journal of mathematical neuroscience vol. 4,1 (2014): 22. doi: https://doi.org/10.1186/2190-8567-4-22
Di Bernardino E, León J, Tchumatchenko T. Cross-correlations and joint gaussianity in multivariate level crossing models. J Math Neurosci. 2014 Apr 17;4(1):22. doi: 10.1186/2190-8567-4-22. PMID: 24742344; PMCID: PMC3990273.
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J Math Neurosci. 2014 Apr 17;4(1):22. doi: 10.1186/2190-8567-4-22.

Cross-correlations and joint gaussianity in multivariate level crossing models.

Journal of mathematical neuroscience

Elena Di Bernardino, José León, Tatjana Tchumatchenko

Affiliations

  1. Max Planck Institute for Brain Research, Max-von-Laue-Str 4, 60438, Frankfurt am Main, Germany. [email protected].

PMID: 24742344 PMCID: PMC3990273 DOI: 10.1186/2190-8567-4-22

Abstract

A variety of phenomena in physical and biological sciences can be mathematically understood by considering the statistical properties of level crossings of random Gaussian processes. Notably, a growing number of these phenomena demand a consideration of correlated level crossings emerging from multiple correlated processes. While many theoretical results have been obtained in the last decades for individual Gaussian level-crossing processes, few results are available for multivariate, jointly correlated threshold crossings. Here, we address bivariate upward crossing processes and derive the corresponding bivariate Central Limit Theorem as well as provide closed-form expressions for their joint level-crossing correlations.

References

  1. Science. 2010 Jan 29;327(5965):587-90 - PubMed
  2. Science. 2010 Jan 29;327(5965):584-7 - PubMed
  3. J Neurosci. 2009 Aug 19;29(33):10234-53 - PubMed
  4. Nat Rev Neurosci. 2003 Sep;4(9):739-51 - PubMed
  5. Nat Neurosci. 2008 Jul;11(7):749-51 - PubMed
  6. Biol Cybern. 2006 Aug;95(2):97-112 - PubMed
  7. J Neurophysiol. 2001 Nov;86(5):2266-75 - PubMed
  8. Biol Cybern. 2006 Jul;95(1):1-19 - PubMed
  9. Neuron. 1999 Feb;22(2):361-74 - PubMed
  10. Front Comput Neurosci. 2010 Apr 08;4:1 - PubMed
  11. PLoS Comput Biol. 2011 May;7(5):e1002059 - PubMed
  12. Neural Comput. 2009 Aug;21(8):2269-308 - PubMed
  13. Nature. 1994 Jul 14;370(6485):140-3 - PubMed
  14. Phys Rev Lett. 2010 Feb 5;104(5):058102 - PubMed
  15. Neural Comput. 2002 Sep;14(9):2057-110 - PubMed
  16. Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Sep;80(3 Pt 1):031909 - PubMed
  17. Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Oct;84(4 Pt 1):041919 - PubMed
  18. Neural Comput. 2008 Sep;20(9):2133-84 - PubMed
  19. Phys Rev Lett. 2008 Mar 14;100(10):108102 - PubMed
  20. Nature. 2007 Aug 16;448(7155):802-6 - PubMed
  21. Biol Cybern. 2007 Dec;97(5-6):337-9 - PubMed

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