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@INPROCEEDINGS{Rostami:189185,
      author       = {Rostami, Vahid and Ito, Junji and Torre, Emiliano and
                      Quaglio, Pietro and Helias, Moritz and Grün, Sonja},
      title        = {{I}ndications of {H}igher-{O}rder {C}orrelations in a
                      {P}airwise {P}opulation {M}easure},
      reportid     = {FZJ-2015-02379},
      year         = {2015},
      abstract     = {The Unitary Event (UE) analysis method was designed to
                      detect excess spike synchrony in parallel spike trains as an
                      indicator of assembly activity [1]. The application of the
                      method to simultaneous recordings from cortical neurons
                      provided evidence for occurrence of excess synchrony related
                      to behavior [2]. However, the UE analysis does not scale to
                      arbitrary cell assemblies in massively parallel spike trains
                      (MPST, e.g. 100 or more neurons) due to the combinatorial
                      explosion of occurring spike patterns, and thus the
                      consequent massive multiple testing problem.Here we present
                      an extended UE analysis that is applicable to MPST with
                      acceptable computational effort. It provides indications of
                      the presence of higher-order synchrony (HOS) in a time
                      dependent manner. The extension is based on a population
                      measure derived from pairwise measures, namely the sum of
                      the empirical pairwise coincidences from all neuron pairs
                      nemppop and the expected number of coincidences nexppop. The
                      latter is calculated for all neuron pairs on the basis of
                      their firing rates under assumption of mutual independence.
                      The significance of the nemppop given nexppop is derived by
                      the p-value ppop, and accordingly the surprise
                      Spop=log(1-ppop)/ppop. Given recordings from multiple
                      trials, we define the Fano factor FFpop as the variance of
                      Spop across trials divided by its mean. For calibration of
                      the measures, we use a compound Poisson process (CPP) [3] to
                      model parallel spike trains that possess a) an arbitrary
                      order of HOS, b) a specific average pairwise correlation,
                      and c) a given firing rate distribution across the neurons.
                      We find that the average pairwise correlation is reflected
                      by the mean of Spop across trials, whereas the order of the
                      synchrony by FFpop. As the measures provide reliable
                      statistics on a short time scale (~100 ms), we use them to
                      track the temporal changes in correlation order and average
                      pairwise correlation (Figure). Furthermore, our measures
                      show robustness against the heterogeneity of experimental
                      data, in particular non-homogeneous firing rates across
                      neurons and trials, and non-stationary firing rates in
                      time.Our method thus suggests a way to detect temporal
                      variation of the correlation order and the average pairwise
                      correlation in MPST. We currently work on a comparison of
                      our analysis to existing methods such as CuBIC [3], which
                      infers the lower bound of the order of synchrony, in terms
                      of reliability with respect to the amount of available
                      data.},
      month         = {Mar},
      date          = {2015-03-17},
      organization  = {NWG, Goettingen (Germany), 17 Mar 2015
                       - 21 Mar 2015},
      subtyp        = {Other},
      cin          = {INM-6 / IAS-6},
      cid          = {I:(DE-Juel1)INM-6-20090406 / I:(DE-Juel1)IAS-6-20130828},
      pnm          = {571 - Connectivity and Activity (POF3-571) / Helmholtz
                      Young Investigators Group (HGF-YoungInvestigatorsGroup) /
                      SMHB - Supercomputing and Modelling for the Human Brain
                      (HGF-SMHB-2013-2017) / HBP - The Human Brain Project
                      (604102) / BRAINSCALES - Brain-inspired multiscale
                      computation in neuromorphic hybrid systems (269921)},
      pid          = {G:(DE-HGF)POF3-571 / G:(DE-HGF)HGF-YoungInvestigatorsGroup
                      / G:(DE-Juel1)HGF-SMHB-2013-2017 / G:(EU-Grant)604102 /
                      G:(EU-Grant)269921},
      typ          = {PUB:(DE-HGF)24},
      url          = {https://juser.fz-juelich.de/record/189185},
}