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@ARTICLE{Blundell:851054,
      author       = {Blundell, Inga and Plotnikov, Dimitri and Eppler, Jochen M.
                      and Morrison, Abigail},
      title        = {{A}utomatically {S}electing a {S}uitable {I}ntegration
                      {S}cheme for {S}ystems of {D}ifferential {E}quations in
                      {N}euron {M}odels},
      journal      = {Frontiers in neuroinformatics},
      volume       = {12},
      issn         = {1662-5196},
      address      = {Lausanne},
      publisher    = {Frontiers Research Foundation},
      reportid     = {FZJ-2018-04767},
      pages        = {50},
      year         = {2018},
      abstract     = {On the level of the spiking activity, the
                      integrate-and-fire neuron is one of the most commonly used
                      descriptions of neural activity. A multitude of variants has
                      been proposed to cope with the huge diversity of behaviors
                      observed in biological nerve cells. The main appeal of this
                      class of model is that it can be defined in terms of a
                      hybrid model, where a set of mathematical equations
                      describes the sub-threshold dynamics of the membrane
                      potential and the generation of action potentials is often
                      only added algorithmically without the shape of spikes being
                      part of the equations. In contrast to more detailed
                      biophysical models, this simple description of neuron models
                      allows the routine simulation of large biological neuronal
                      networks on standard hardware widely available in most
                      laboratories these days. The time evolution of the relevant
                      state variables is usually defined by a small set of
                      ordinary differential equations (ODEs). A small number of
                      evolution schemes for the corresponding systems of ODEs are
                      commonly used for many neuron models, and form the basis of
                      the neuron model implementations built into commonly used
                      simulators like Brian, NEST and NEURON. However, an often
                      neglected problem is that the implemented evolution schemes
                      are only rarely selected through a structured process based
                      on numerical criteria. This practice cannot guarantee
                      accurate and stable solutions for the equations and the
                      actual quality of the solution depends largely on the
                      parametrization of the model. In this article, we give an
                      overview of typical equations and state descriptions for the
                      dynamics of the relevant variables in integrate-and-fire
                      models. We then describe a formal mathematical process to
                      automate the design or selection of a suitable evolution
                      scheme for this large class of models. Finally, we present
                      the reference implementation of our symbolic analysis
                      toolbox for ODEs that can guide modelers during the
                      implementation of custom neuron models.},
      cin          = {INM-6 / JSC / JARA-HPC / IAS-6},
      ddc          = {610},
      cid          = {I:(DE-Juel1)INM-6-20090406 / I:(DE-Juel1)JSC-20090406 /
                      $I:(DE-82)080012_20140620$ / I:(DE-Juel1)IAS-6-20130828},
      pnm          = {511 - Computational Science and Mathematical Methods
                      (POF3-511) / 574 - Theory, modelling and simulation
                      (POF3-574) / SMHB - Supercomputing and Modelling for the
                      Human Brain (HGF-SMHB-2013-2017) / HBP SGA1 - Human Brain
                      Project Specific Grant Agreement 1 (720270) / NESTML - A
                      modelling language for spiking neuron and synapse models for
                      NEST (NESTML-20141210) / SLNS - SimLab Neuroscience
                      (Helmholtz-SLNS)},
      pid          = {G:(DE-HGF)POF3-511 / G:(DE-HGF)POF3-574 /
                      G:(DE-Juel1)HGF-SMHB-2013-2017 / G:(EU-Grant)720270 /
                      G:(DE-Juel1)NESTML-20141210 / G:(DE-Juel1)Helmholtz-SLNS},
      typ          = {PUB:(DE-HGF)16},
      pubmed       = {pmid:30349471},
      UT           = {WOS:000446628400001},
      doi          = {10.3389/fninf.2018.00050},
      url          = {https://juser.fz-juelich.de/record/851054},
}