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@INPROCEEDINGS{Essink:885770,
      author       = {Essink, Simon and Helin, Runar and Shimoura, Renan and
                      Senk, Johanna and Tetzlaff, Tom and van Albada, Sacha and
                      Helias, Moritz and Grün, Sonja and Plesser, Hans Ekkehard
                      and Diesmann, Markus},
      title        = {{U}ltra-high frequency spectrum of neuronal activity},
      reportid     = {FZJ-2020-04078},
      year         = {2020},
      abstract     = {The activity of spiking network models exhibits fast
                      oscillations (>200 Hz), caused by inhibition-dominated
                      excitatory-inhibitory loops [1, 2]. As correlations between
                      pairs of neurons are weak in nature and models, fast
                      oscillations have so far received little attention.Today’s
                      models of cortical networks with natural numbers of neurons
                      and synapses [3] remove any uncertainty about down-scaling
                      artifacts [4]. Fast oscillations here arise as vertical
                      stripes in raster diagrams. We discuss experimental
                      detectability of oscillations, ask whether they are an
                      artifact of simplified models, and identify adaptations to
                      control them.The population rate spectrum decomposes into
                      single-neuron power spectra (∼N) and cross-spectra of
                      pairs of neurons (∼N2) [5,6]. For low numbers of neurons
                      (100) and weak correlations, the single-neuron spectra
                      dominate the compound spectrum. Coherent oscillations in the
                      population activity may thus go unnoticed in experimental
                      spike recordings. Population measures obtained from large
                      neuron ensembles (e.g., LFP), however, should show a
                      pronounced peak.Cortical network models allow an
                      investigation from different angles. We rule out artifacts
                      of time-discrete simulation and investigate the effect of
                      distributed synaptic delays: exponential distributions
                      decrease the oscillation amplitude, expected by their
                      equivalence to low-pass filtering [7], whereas truncated
                      Gaussian distributions are ineffective.Surprisingly, a model
                      of V1 [8], with the same architecture, but fewer synapses
                      per neuron, does not exhibit fast oscillations. Mean-field
                      theory shows that loops within each inhibitory population
                      cause fast oscillations. Peak frequency and amplitude are
                      determined by eigenvalues of the effective connectivity
                      matrix approaching instability [9]. Reducing the connection
                      density decreases the eigenvalues, increasing their distance
                      to instability; we thus expect weaker oscillations.Counter
                      to expectation and simulation, mean-field theory predicts an
                      increase, explained by an overestimation of the transfer
                      function at high frequencies [10]: the initial network
                      appears to be linearly unstable, with |λ|>1; reduced
                      connectivity seemingly destabilizes the system. A
                      semi-analytical correction restores qualitative agreement
                      with simulation.The work points at the importance of models
                      with realistic cell densities and connectivity, and
                      illustrates the productive interplay of simulation-driven
                      and analytical approaches.References 1. Brunel, N. Dynamics
                      of sparsely connected networks of excitatory and inhibitory
                      spiking neurons. JComputNeurosci 8, 183–208 (2000).,
                      10.1371/journal.pcbi.1006359 2. Brunel, N. $\&$ Wang, X.-J.
                      What Determines the Frequency of Fast Network Oscillations
                      With Irregular Neural Discharges? I. Synaptic Dynamics and
                      Excitation-Inhibition Balance. JNeurophysiol 90, 415–430
                      (2003)., 10.1152/jn.01095.2002 3. Potjans, T. C. $\&$
                      Diesmann, M. The Cell-Type Specific Cortical Microcircuit:
                      Relating Structure and Activity in a Full-Scale Spiking
                      Network Model. CerebCortex 24, 785–806 (2014).,
                      10.1093/cercor/bhs358 4. van Albada, S. J., Helias, M. $\&$
                      Diesmann, M. Scalability of asynchronous networks is limited
                      by one-to-one mapping between effective connectivity and
                      correlations. ploscb 11, e1004490 (2015).,
                      10.1371/journal.pcbi.1004490 5. Harris, K. D., $\&$ Thiele,
                      A. Cortical state and attention. Nature Reviews
                      Neuroscience, 12(9), 509-523 (2011)., 10.1038/nrn3084 6.
                      Tetzlaff, T., Helias, M., Einevoll, G. T., $\&$ Diesmann, M.
                      Decorrelation of neural-network activity by inhibitory
                      feedback. PLoS Comput Biol, 8(8), e1002596 (2012).,
                      10.1371/journal.pcbi.1002596 7. Mattia, M., Biggio, M.,
                      Galluzzi, A. $\&$ Storace, M. Dimensional reduction in
                      networks of non-Markovian spiking neurons: Equivalence of
                      synaptic filtering and heterogeneous propagation delays.
                      PLoS Comput Biol 15, e1007404 (2019).,
                      10.1371/journal.pcbi.1007404 8. Schmidt, M. et al. A
                      multi-scale layer-resolved spiking network model of
                      resting-state dynamics in macaque visual cortical areas.
                      ploscb 14, e1006359 (2018)., 10.1023/a:1008925309027 9. Bos,
                      H., Diesmann, M. $\&$ Helias, M. Identifying Anatomical
                      Origins of Coexisting Oscillations in the Cortical
                      Microcircuit. ploscb 12, e1005132 (2016).,
                      10.1371/journal.pcbi.1005132 10. Schuecker, J., Diesmann, M.
                      $\&$ Helias, M. Modulated escape from a metastable state
                      driven by colored noise. Phys. Rev. E (2015).,
                      10.1103/PhysRevE.92.052119},
      month         = {Sep},
      date          = {2020-09-29},
      organization  = {Bernstein Konferenz 2020, online
                       (Germany), 29 Sep 2020 - 1 Oct 2020},
      subtyp        = {Other},
      cin          = {INM-6 / IAS-6 / INM-10},
      cid          = {I:(DE-Juel1)INM-6-20090406 / I:(DE-Juel1)IAS-6-20130828 /
                      I:(DE-Juel1)INM-10-20170113},
      pnm          = {574 - Theory, modelling and simulation (POF3-574) / 571 -
                      Connectivity and Activity (POF3-571) / HBP SGA3 - Human
                      Brain Project Specific Grant Agreement 3 (945539) / GRK 2416
                      - GRK 2416: MultiSenses-MultiScales: Neue Ansätze zur
                      Aufklärung neuronaler multisensorischer Integration
                      (368482240) / Advanced Computing Architectures
                      $(aca_20190115)$ / HBP SGA2 - Human Brain Project Specific
                      Grant Agreement 2 (785907)},
      pid          = {G:(DE-HGF)POF3-574 / G:(DE-HGF)POF3-571 /
                      G:(EU-Grant)945539 / G:(GEPRIS)368482240 /
                      $G:(DE-Juel1)aca_20190115$ / G:(EU-Grant)785907},
      typ          = {PUB:(DE-HGF)24},
      doi          = {10.12751/NNCN.BC2020.0080},
      url          = {https://juser.fz-juelich.de/record/885770},
}