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@ARTICLE{Krishnan:842507,
      author       = {Krishnan, Jeyashree and Mana, PierGianLuca and Helias,
                      Moritz and Diesmann, Markus and Di Napoli, Edoardo},
      title        = {{P}erfect {D}etection of {S}pikes in the {L}inear
                      {S}ub-threshold {D}ynamics of {P}oint {N}eurons},
      journal      = {Frontiers in neuroinformatics},
      volume       = {11},
      issn         = {1662-5196},
      address      = {Lausanne},
      publisher    = {Frontiers Research Foundation},
      reportid     = {FZJ-2018-00732},
      pages        = {75},
      year         = {2018},
      abstract     = {Spiking neuronal networks are usually simulated with three
                      main simulation schemes: the classical time-driven and
                      event-driven schemes, and the more recent hybrid scheme. All
                      three schemes evolve the state of a neuron through a series
                      of checkpoints: equally spaced in the first scheme and
                      determined neuron-wise by spike events in the latter two.
                      The time-driven and the hybrid scheme determine whether the
                      membrane potential of a neuron crosses a threshold at the
                      end of of the time interval between consecutive checkpoints.
                      Threshold crossing can, however, occur within the interval
                      even if this test is negative. Spikes can therefore be
                      missed. The present work derives, implements, and benchmarks
                      a method for perfect retrospective spike detection. This
                      method can be applied to neuron models with affine or linear
                      subthreshold dynamics. The idea behind the method is to
                      propagate the threshold with a time-inverted dynamics,
                      testing whether the threshold crosses the neuron state to be
                      evolved, rather than vice versa. Algebraically this
                      translates into a set of inequalities necessary and
                      sufficient for threshold crossing. This test is slower than
                      the imperfect one, but faster than an alternative perfect
                      tests based on bisection or root-finding methods. Comparison
                      confirms earlier results that the imperfect test rarely
                      misses spikes (less than a fraction $1/10^8$ of missed
                      spikes) in biologically relevant settings. This study offers
                      an alternative geometric point of view on neuronal
                      dynamics.},
      cin          = {IAS-6 / INM-6 / INM-10 / JSC},
      ddc          = {610},
      cid          = {I:(DE-Juel1)IAS-6-20130828 / I:(DE-Juel1)INM-6-20090406 /
                      I:(DE-Juel1)INM-10-20170113 / I:(DE-Juel1)JSC-20090406},
      pnm          = {511 - Computational Science and Mathematical Methods
                      (POF3-511) / 574 - Theory, modelling and simulation
                      (POF3-574) / HBP SGA1 - Human Brain Project Specific Grant
                      Agreement 1 (720270) / MSNN - Theory of multi-scale neuronal
                      networks (HGF-SMHB-2014-2018) / SMHB - Supercomputing and
                      Modelling for the Human Brain (HGF-SMHB-2013-2017) /
                      Simulation and Data Laboratory Quantum Materials (SDLQM)
                      (SDLQM)},
      pid          = {G:(DE-HGF)POF3-511 / G:(DE-HGF)POF3-574 /
                      G:(EU-Grant)720270 / G:(DE-Juel1)HGF-SMHB-2014-2018 /
                      G:(DE-Juel1)HGF-SMHB-2013-2017 / G:(DE-Juel1)SDLQM},
      typ          = {PUB:(DE-HGF)16},
      eprint       = {1706.05702},
      howpublished = {arXiv:1706.05702},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:1706.05702;\%\%$},
      UT           = {WOS:000419441000001},
      pubmed       = {pmid:29379430},
      doi          = {10.3389/fninf.2017.00075},
      url          = {https://juser.fz-juelich.de/record/842507},
}