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@ARTICLE{Senk:842906,
      author       = {Senk, Johanna and Korvasová, Karolína and Schuecker,
                      Jannis and Hagen, Espen and Tetzlaff, Tom and Diesmann,
                      Markus and Helias, Moritz},
      title        = {{C}onditions for traveling waves in spiking neural
                      networks},
      reportid     = {FZJ-2018-01079},
      year         = {2018},
      note         = {42 pages, 12 figures},
      abstract     = {Spatiotemporal patterns such as traveling waves are
                      frequently observed in recordings of neural activity. The
                      mechanisms underlying the generation of such patterns are
                      largely unknown. Previous studies have investigated the
                      existence and uniqueness of different types of waves or
                      bumps of activity using neural-field models,
                      phenomenological coarse-grained descriptions of
                      neural-network dynamics. But it remains unclear how these
                      insights can be transferred to more biologically realistic
                      networks of spiking neurons, where individual neurons fire
                      irregularly. Here, we employ mean-field theory to reduce a
                      microscopic model of leaky integrate-and-fire (LIF) neurons
                      with distance-dependent connectivity to an effective
                      neural-field model. In contrast to existing phenomenological
                      descriptions, the dynamics in this neural-field model
                      depends on the mean and the variance in the synaptic input,
                      both determining the amplitude and the temporal structure of
                      the resulting effective coupling kernel. For the
                      neural-field model we derive conditions for the existence of
                      spatial and temporal oscillations and periodic traveling
                      waves using linear stability analysis. We first prove that
                      periodic traveling waves cannot occur in a single
                      homogeneous population of neurons, irrespective of the form
                      of distance dependence of the connection probability.
                      Compatible with the architecture of cortical neural
                      networks, traveling waves emerge in two-population networks
                      of excitatory and inhibitory neurons as a combination of
                      delay-induced temporal oscillations and spatial oscillations
                      due to distance-dependent connectivity profiles. Finally, we
                      demonstrate quantitative agreement between predictions of
                      the analytically tractable neural-field model and numerical
                      simulations of both networks of nonlinear rate-based units
                      and networks of LIF neurons.},
      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          = {571 - Connectivity and Activity (POF3-571) / PhD no Grant -
                      Doktorand ohne besondere Förderung (PHD-NO-GRANT-20170405)
                      / SMHB - Supercomputing and Modelling for the Human Brain
                      (HGF-SMHB-2013-2017) / HBP SGA1 - Human Brain Project
                      Specific Grant Agreement 1 (720270) / DFG project 233510988
                      - Mathematische Modellierung der Entstehung und Suppression
                      pathologischer Aktivitätszustände in den
                      Basalganglien-Kortex-Schleifen (233510988) / ERS Seed Fund
                      (ZUK2) - Exploratory Research Space: Seed Fund (2) als
                      Anschubfinanzierung zur Erforschung neuer
                      interdisziplinärer Ideen (ZUK2-SF)},
      pid          = {G:(DE-HGF)POF3-571 / G:(DE-Juel1)PHD-NO-GRANT-20170405 /
                      G:(DE-Juel1)HGF-SMHB-2013-2017 / G:(EU-Grant)720270 /
                      G:(GEPRIS)233510988 / G:(DE-82)ZUK2-SF},
      typ          = {PUB:(DE-HGF)25},
      eprint       = {1801.06046},
      howpublished = {arXiv:1801.06046},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:1801.06046;\%\%$},
      url          = {https://juser.fz-juelich.de/record/842906},
}