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@INPROCEEDINGS{Helias:202069,
      author       = {Helias, Moritz},
      title        = {{T}heory of individual pairwise correlations in stochastic
                      binary networks},
      reportid     = {FZJ-2015-04358},
      year         = {2015},
      abstract     = {Pairwise correlations between the activities of neurons
                      exhibittime-dependent modulations with respect to behavior
                      [1], influence theinformation-content of population signals
                      [2,3], determine theinteraction of neuronal activity and
                      spike-timing dependent synapticplasticity [4].Correlations
                      averaged over neuron pairs are closely linked tofluctuations
                      of the population activity and are hence readilyaccessible
                      by population-averaged mean-field theory in the large Nlimit
                      [5], but also in finite-sized networks [6].Here we leave the
                      population description and extend the theory ofsecond order
                      correlations in stochastic binary networks [7] toindividual
                      neuron pairs. We show how a systematic truncation of
                      themoment hierarchy that consistently neglects third order
                      cumulantsyields a non-linear system of equations for
                      individual mean activitiesand pairwise covariances, which
                      after linearization, leads to amodified Lyapunov equation.
                      We show that the method of solution,sufficient for the
                      population-averaged case, yields a systematicover-estimation
                      of the spread of individual pairwise covariances,while an
                      adapted method of solution provides quantitative predictions
                      ina balanced random network model down to hundreds of
                      neurons.As a corollary we show how the covariance matrix
                      together with itsslope at zero time lag determine the
                      effective synaptic interactionstrength between neurons only
                      modulo the total synaptic noise level ofthe receiving
                      neuron. The presented theory renders the investigationof
                      distributed pairwise correlations analytically accessible
                      and mayprove useful for network reconstruction as well as to
                      foster ourunderstanding of correlation-sensitive synaptic
                      plasticity inrecurrent networks.Partially supported by the
                      Helmholtz Association: Young investigator'sgroup VH-NG-1028,
                      portfolio theme SMHB, the Jülich Aachen ResearchAlliance
                      (JARA), and 604102 (HBP).[1] Kilavik BE, Roux S,
                      Ponce-Alvarez A, Confais J, Gruen S, et al. (2009) J
                      Neurosci 29: 12653--12663.[2] Zohary E, Shadlen MN, Newsome
                      WT (1994). Nature 370: 140--143.[3] Shamir M, Sompolinsky H
                      (2001). In: Advances in Neural Information Processing
                      Systems. MIT Press, pp. 277--284.[4] Morrison A, Diesmann M
                      and Gerstner W (2008). Biol. Cybern. 98 459--78[5] Renart A,
                      De La Rocha J, Bartho P, Hollender L, Parga N, et al.
                      (2010). Science 327: 587–590.[6] Tetzlaff T, Helias M,
                      Einevoll GT, Diesmann M (2012). PLoS Comput Biol 8(8):
                      e1002596.[7] Ginzburg I, Sompolinsky H (1994). Phys Rev E
                      50: 3171--3191.},
      month         = {Jun},
      date          = {2015-06-02},
      organization  = {Sparks Bernstein Workshop - Beyond
                       Mean-field theory, Goettingen
                       (Germany), 2 Jun 2015 - 5 Jun 2015},
      subtyp        = {Invited},
      cin          = {INM-6 / IAS-6},
      cid          = {I:(DE-Juel1)INM-6-20090406 / I:(DE-Juel1)IAS-6-20130828},
      pnm          = {89574 - Theory, modelling and simulation (POF2-89574) /
                      MSNN - Theory of multi-scale neuronal networks
                      (HGF-SMHB-2014-2018)},
      pid          = {G:(DE-HGF)POF2-89574 / G:(DE-Juel1)HGF-SMHB-2014-2018},
      typ          = {PUB:(DE-HGF)6},
      url          = {https://juser.fz-juelich.de/record/202069},
}