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Merge pull request #3275 from jessica-mitchell/minor-doc-fixes
Fix minor issues in docs
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doc/htmldoc/neurons/exact-integration.rst

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@@ -22,9 +22,9 @@ The leaky integrate-and fire model
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In the leaky integrate-and-fire model, the memory problem is solved by adding a "leak" term :math:`\frac{-1}{R}V` (:math:`R` is the resistance and :math:`\tau=RC`) to the membrane potential:
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.. math::
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:label: membrane
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\frac{dV}{dt}=\frac{-1}{\tau}V+\frac{1}{C}I.
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:label: membrane
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This reflects the diffusion of ions that occurs through the membrane when some equilibrium is not reached in the cell.
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doc/htmldoc/synapses/connectivity_concepts.rst

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@@ -69,6 +69,7 @@ Projections are created in NEST with the :py:func:`.Connect` function:
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nest.Connect(pre, post)
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nest.Connect(pre, post, conn_spec)
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nest.Connect(pre, post, conn_spec, syn_spec)
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nest.Connect(pre, post, conn_spec, syn_spec, return_synapsecollection=True)
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In the simplest case, the function just takes the ``NodeCollections`` ``pre`` and ``post``, defining the nodes of
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origin (`sources`) and termination (`targets`) for the connections to be established with the default rule ``all-to-all`` and the synapse model :ref:`static_synapse`.

doc/htmldoc/synapses/index.rst

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.. grid:: 1 1 2 2
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.. grid-item-card:: Managing coonnections
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.. grid-item-card:: Managing coonnections
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* :ref:`connectivity_concepts`
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* :ref:`connection_generator`

models/iaf_bw_2001.h

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@@ -88,7 +88,7 @@ The membrane potential and synaptic variables evolve according to
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I_\mathrm{NMDA} &= \frac{(V(t) - V_E)}{1+[\mathrm{Mg^{2+}}]\mathrm{exp}(-0.062V(t))/3.57}\sum_{j \in \Gamma_\mathrm{ex}}^{N_E}w_jS_{j,\mathrm{NMDA}}(t) \\[3ex]
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I_\mathrm{GABA} &= (V(t) - V_I)\sum_{j \in \Gamma_\mathrm{in}}^{N_E}w_jS_{j,\mathrm{GABA}}(t) \\[5ex]
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\frac{dS_{j,\mathrm{AMPA}}}{dt} &= -\frac{j,S_{\mathrm{AMPA}}}{\tau_\mathrm{AMPA}}+\sum_{k \in \Delta_j} \delta (t - t_j^k) \\[3ex]
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\frac{dS_{j,\mathrm{GABA}}}{dt} &= -\frac{S_{j,\mathrm{GABA}}}{\tau_\mathrm{GABA}} + \sum_{k \in \Delta_j} \delta (t - t_j^k) \\[3ex]
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\frac{dS_{j,\mathrm{GABA}}}{dt} &= -\frac{S_{j,\mathrm{GABA}}}{\tau_\mathrm{GABA}} + \sum_{k \in \Delta_j} \delta (t - t_j^k) \\[3ex]
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\frac{dS_{j,\mathrm{NMDA}}}{dt} &= -\frac{S_{j,\mathrm{NMDA}}}{\tau_\mathrm{NMDA,decay}} + \sum_{k \in \Delta_j} (k_0 + k_1 S(t)) \delta (t - t_j^k) \\[3ex]
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where :math:`\Gamma_\mathrm{ex}` and :math:`\Gamma_\mathrm{in}` are index sets for presynaptic excitatory and inhibitory neurons respectively, and :math:`\Delta_j` is an index set for the spike times of neuron :math:`j`.
@@ -105,6 +105,8 @@ The specification of this model differs slightly from the one in [1]_. The param
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:math:`g_\mathrm{GABA}`, and :math:`g_\mathrm{NMDA}` have been absorbed into the respective synaptic weights.
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Additionally, the synapses from the external population are not separated from the recurrent AMPA-synapses.
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See also [2]_ and [3]_.
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For more implementation details and a comparison to the exact version, see:
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- `Brunel_Wang_2001_Model_Approximation <../model_details/Brunel_Wang_2001_Model_Approximation.ipynb>`_
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**Parameter** **Default** **Math equivalent** **Description**
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=================== ================== ================================= ========================================================================
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``E_L`` -70.0 mV :math:`E_\mathrm{L}` Leak reversal potential
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``E_ex`` 0.0 mV :math:`E_\mathrm{ex}` Excitatory reversal potential
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``E_in`` -70.0 mV :math:`E_\mathrm{in}` Inhibitory reversal potential
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``V_th`` -55.0 mV :math:`V_\mathrm{th}` Spike threshold
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``E_ex`` 0.0 mV :math:`E_\mathrm{ex}` Excitatory reversal potential
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``E_in`` -70.0 mV :math:`E_\mathrm{in}` Inhibitory reversal potential
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``V_th`` -55.0 mV :math:`V_\mathrm{th}` Spike threshold
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``V_reset`` -60.0 mV :math:`V_\mathrm{reset}` Reset potential of the membrane
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``C_m`` 250.0 pF :math:`C_\mathrm{m}` Capacitance of the membrane
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``g_L`` 25.0 nS :math:`g_\mathrm{L}` Leak conductance
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``t_ref`` 2.0 ms :math:`t_\mathrm{ref}` Duration of refractory period
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``C_m`` 250.0 pF :math:`C_\mathrm{m}` Capacitance of the membrane
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``g_L`` 25.0 nS :math:`g_\mathrm{L}` Leak conductance
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``t_ref`` 2.0 ms :math:`t_\mathrm{ref}` Duration of refractory period
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``tau_AMPA`` 2.0 ms :math:`\tau_\mathrm{AMPA}` Time constant of AMPA synapse
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``tau_GABA`` 5.0 ms :math:`\tau_\mathrm{GABA}` Time constant of GABA synapse
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``tau_rise_NMDA`` 2.0 ms :math:`\tau_\mathrm{NMDA,rise}` Rise time constant of NMDA synapse
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``tau_rise_NMDA`` 2.0 ms :math:`\tau_\mathrm{NMDA,rise}` Rise time constant of NMDA synapse
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``tau_decay_NMDA`` 100.0 ms :math:`\tau_\mathrm{NMDA,decay}` Decay time constant of NMDA synapse
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``alpha`` 0.5 ms^{-1} :math:`\alpha` Rise-time coupling strength for NMDA synapse
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``conc_Mg2`` 1.0 mM :math:`[\mathrm{Mg}^+]` Extracellular magnesium concentration
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**State variable** **Initial value** **Math equivalent** **Description**
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================== ================= ========================== =================================
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``V_m`` -70 mV :math:`V_{\mathrm{m}}` Membrane potential
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``s_AMPA`` 0 :math:`s_\mathrm{AMPA}` AMPA gating variable
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``s_GABA`` 0 :math:`s_\mathrm{GABA}` GABA gating variable
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``s_NMDA`` 0 :math:`s_\mathrm{NMDA}` NMDA gating variable
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``s_AMPA`` 0 :math:`s_\mathrm{AMPA}` AMPA gating variable
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``s_GABA`` 0 :math:`s_\mathrm{GABA}` GABA gating variable
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``s_NMDA`` 0 :math:`s_\mathrm{NMDA}` NMDA gating variable
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``I_NMDA`` 0 pA :math:`I_\mathrm{NMDA}` NMDA current
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``I_AMPA`` 0 pA :math:`I_\mathrm{AMPA}` AMPA current
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``I_GABA`` 0 pA :math:`I_\mathrm{GABA}` GABA current
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References
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++++++++++
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.. [1] Wang, X.-J. (1999). Synaptic Basis of Cortical Persistent Activity: The Importance of NMDA Receptors to Working Memory. Journal of Neuroscience, 19(21), 9587–9603. https://doi.org/10.1523/JNEUROSCI.19-21-09587.1999
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.. [2] Brunel, N., & Wang, X.-J. (2001). Effects of Neuromodulation in a Cortical Network Model of Object Working Memory Dominated by Recurrent Inhibition. Journal of Computational Neuroscience, 11(1), 63–85. https://doi.org/10.1023/A:1011204814320
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.. [1] Wang, X.-J. (1999). Synaptic Basis of Cortical Persistent Activity: The
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Importance of NMDA Receptors to Working Memory. Journal of Neuroscience,
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19(21), 9587–9603. https://doi.org/10.1523/JNEUROSCI.19-21-09587.1999
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.. [2] Brunel, N., & Wang, X.-J. (2001). Effects of Neuromodulation in a Cortical
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Network Model of Object Working Memory Dominated by Recurrent Inhibition.
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Journal of Computational Neuroscience, 11(1), 63–85. https://doi.org/10.1023/A:1011204814320
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.. [3] Wang, X. J. (2002). Probabilistic decision making by slow reverberation in
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cortical circuits. Neuron, 36(5), 955-968. https://doi.org/10.1016/S0896-6273(02)01092-9
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models/iaf_bw_2001_exact.h

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I_\mathrm{NMDA} &= \frac{(V(t) - V_E)}{1+[\mathrm{Mg^{2+}}]\mathrm{exp}(-0.062V(t))/3.57}\sum_{j \in
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\Gamma_\mathrm{ex}}^{N_E}w_jS_{j,\mathrm{NMDA}}(t) \\[3ex]
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I_\mathrm{GABA} &= (V(t) - V_I)\sum_{j \in \Gamma_\mathrm{in}}^{N_E}w_jS_{j,\mathrm{GABA}}(t) \\[5ex]
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\frac{dS_{j,\mathrm{AMPA}}}{dt} &=-\frac{j,S_{\mathrm{AMPA}}}{\tau_\mathrm{AMPA}}+\sum_{k \in \Delta_j} \delta (t - t_j^k) \\[3ex]
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\frac{dS_{j,\mathrm{AMPA}}}{dt} &=-\frac{j,S_{\mathrm{AMPA}}}{\tau_\mathrm{AMPA}}+\sum_{k \in \Delta_j} \delta (t - t_j^k) \\[3ex]
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\frac{dS_{j,\mathrm{GABA}}}{dt} &= -\frac{S_{j,\mathrm{GABA}}}{\tau_\mathrm{GABA}} + \sum_{k \in \Delta_j} \delta (t - t_j^k) \\[3ex]
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\frac{dS_{j,\mathrm{NMDA}}}{dt} &= -\frac{S_{j,\mathrm{NMDA}}}{\tau_\mathrm{NMDA,decay}}+ \alpha x_j (1 - S_{j,\mathrm{NMDA}})\\[3ex]
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\frac{dx_j}{dt} &= -\frac{x_j}{\tau_\mathrm{NMDA,rise}} + \sum_{k \in \Delta_j} \delta (t - t_j^k)
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Additionally, the synapses from the external population is not separated from the recurrent AMPA-synapses.
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This model is slow to simulate when there are many neurons with NMDA-synapses, since each post-synaptic neuron simulates each pre-synaptic connection explicitly. The model :doc:`iaf_bw_2001 </models/iaf_bw_2001>` is an approximation to this model which is significantly faster.
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See also [2]_, [3]_
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Parameters
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**Parameter** **Default** **Math equivalent** **Description**
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=================== ================== ================================= ========================================================================
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``E_L`` -70.0 mV :math:`E_\mathrm{L}` Leak reversal potential
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``E_ex`` 0.0 mV :math:`E_\mathrm{ex}` Excitatory reversal potential
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``E_in`` -70.0 mV :math:`E_\mathrm{in}` Inhibitory reversal potential
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``V_th`` -55.0 mV :math:`V_\mathrm{th}` Spike threshold
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``E_ex`` 0.0 mV :math:`E_\mathrm{ex}` Excitatory reversal potential
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``E_in`` -70.0 mV :math:`E_\mathrm{in}` Inhibitory reversal potential
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``V_th`` -55.0 mV :math:`V_\mathrm{th}` Spike threshold
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``V_reset`` -60.0 mV :math:`V_\mathrm{reset}` Reset potential of the membrane
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``C_m`` 250.0 pF :math:`C_\mathrm{m}` Capacitance of the membrane
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``g_L`` 25.0 nS :math:`g_\mathrm{L}` Leak conductance
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``t_ref`` 2.0 ms :math:`t_\mathrm{ref}` Duration of refractory period
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``C_m`` 250.0 pF :math:`C_\mathrm{m}` Capacitance of the membrane
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``g_L`` 25.0 nS :math:`g_\mathrm{L}` Leak conductance
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``t_ref`` 2.0 ms :math:`t_\mathrm{ref}` Duration of refractory period
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``tau_AMPA`` 2.0 ms :math:`\tau_\mathrm{AMPA}` Time constant of AMPA synapse
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``tau_GABA`` 5.0 ms :math:`\tau_\mathrm{GABA}` Time constant of GABA synapse
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``tau_rise_NMDA`` 2.0 ms :math:`\tau_\mathrm{NMDA,rise}` Rise time constant of NMDA synapse
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``tau_rise_NMDA`` 2.0 ms :math:`\tau_\mathrm{NMDA,rise}` Rise time constant of NMDA synapse
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``tau_decay_NMDA`` 100.0 ms :math:`\tau_\mathrm{NMDA,decay}` Decay time constant of NMDA synapse
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``alpha`` 0.5 ms^{-1} :math:`\alpha` Rise-time coupling strength for NMDA synapse
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``conc_Mg2`` 1.0 mM :math:`[\mathrm{Mg}^+]` Extracellular magnesium concentration
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**State variable** **Initial value** **Math equivalent** **Description**
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================== ================= ========================== =================================
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``V_m`` -70 mV :math:`V_{\mathrm{m}}` Membrane potential
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``s_AMPA`` 0 :math:`s_\mathrm{AMPA}` AMPA gating variable
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``s_GABA`` 0 :math:`s_\mathrm{GABA}` GABA gating variable
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``s_NMDA`` 0 :math:`s_\mathrm{NMDA}` NMDA gating variable
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``s_AMPA`` 0 :math:`s_\mathrm{AMPA}` AMPA gating variable
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``s_GABA`` 0 :math:`s_\mathrm{GABA}` GABA gating variable
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``s_NMDA`` 0 :math:`s_\mathrm{NMDA}` NMDA gating variable
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``I_NMDA`` 0 pA :math:`I_\mathrm{NMDA}` NMDA current
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``I_AMPA`` 0 pA :math:`I_\mathrm{AMPA}` AMPA current
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``I_GABA`` 0 pA :math:`I_\mathrm{GABA}` GABA current

models/iaf_psc_exp.h

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will numerically behave as if ``tau_m`` is equal to ``tau_syn_ex`` or
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``tau_syn_in``, respectively, to avoid numerical instabilities.
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NEST uses exact integration [2]_, [3]_ to integrate subthreshold membrane dynamics
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with maximum precision.
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For implementation details see the
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`IAF Integration Singularity notebook <../model_details/IAF_Integration_Singularity.ipynb>`_.
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pynest/examples/one_neuron_with_noise.py

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###############################################################################
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# Third, the Poisson generator is configured using ``SetStatus``, which expects
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# a list of node handles and a list of parameter dictionaries. We set the
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# Poisson generators to 8,000 Hz and 15,000 Hz, respectively. Note that we do
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# Poisson generators to 80,000 Hz and 15,000 Hz, respectively. Note that we do
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# not need to set parameters for the neuron and the voltmeter, since they have
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# satisfactory defaults.
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pynest/examples/wang_decision_making.py

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References
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~~~~~~~~~~
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.. [1] Wang X-J (2002). Probabilistic Decision Making by Slow Reverberation in
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Cortical Circuits. Neuron, Volume 36, Issue 5, Pages 955-968.
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https://doi.org/10.1016/S0896-6273(02)01092-9.
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Cortical Circuits. Neuron, Volume 36, Issue 5, Pages 955-968.
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https://doi.org/10.1016/S0896-6273(02)01092-9.
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"""
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