iaf_psc_alpha_ps – Current-based leaky integrate-and-fire neuron with alpha-shaped postsynaptic currents using regula falsi method for approximation of threshold crossing
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Description
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.. versionadded:: 2.18
``iaf_psc_alpha_ps`` is the "canonical" implementation of the leaky
integrate-and-fire model neuron with alpha-shaped postsynaptic
currents in the sense of [1]_. This is the most exact implementation
available.
PSCs are normalized to an amplitude of 1pA.
The precise implementation handles neuronal dynamics in a locally
event-based manner with in coarse time grid defined by the minimum
delay in the network, see [1]_. Incoming spikes are applied at the
precise moment of their arrival, while the precise time of outgoing
spikes is determined by a Regula Falsi method to approximate the timing
of a threshold crossing [1]_ [3]_. Return from refractoriness occurs
precisely at spike time plus refractory period.
This implementation is more complex than the plain iaf_psc_alpha
neuron, but achieves much higher precision. In particular, it does not
suffer any binning of spike times to grid points. Depending on your
application, the canonical application may provide superior overall
performance given an accuracy goal; see [1]_ for details. Subthreshold
dynamics are integrated using exact integration between events [2]_.
This model transmits precise spike times to target nodes (on-grid spike
time and offset). If this node is connected to a spike_recorder, the
property "precise_times" of the spike_recorder has to be set to true in
order to record the offsets in addition to the on-grid spike times.
The iaf_psc_alpha_ps neuron accepts connections transmitting
CurrentEvents. These events transmit stepwise-constant currents which
can only change at on-grid times.
.. note::
If `tau_m` is very close to `tau_syn_ex` or `tau_syn_in`, the model
will numerically behave as if `tau_m` is equal to `tau_syn_ex` or
`tau_syn_in`, respectively, to avoid numerical instabilities.
For implementation details see the
`IAF_neurons_singularity <../model_details/IAF_neurons_singularity.ipynb>`_ notebook.
For details about exact subthreshold integration, please see
:doc:`../neurons/exact-integration`.
Parameters
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The following parameters can be set in the status dictionary.
=========== ====== ==========================================================
V_m mV Membrane potential
E_L mV Resting membrane potential
V_min mV Absolute lower value for the membrane potential
C_m pF Capacity of the membrane
tau_m ms Membrane time constant
t_ref ms Duration of refractory period
V_th mV Spike threshold
V_reset mV Reset potential of the membrane
tau_syn_ex ms Rise time of the excitatory synaptic function
tau_syn_in ms Rise time of the inhibitory synaptic function
I_e pA Constant external input current
=========== ====== ==========================================================
References
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.. [1] Morrison A, Straube S, Plesser H E, & Diesmann M (2006) Exact Subthreshold
Integration with Continuous Spike Times in Discrete Time Neural Network
Simulations. To appear in Neural Computation.
.. [2] Rotter S & Diesmann M (1999) Exact simulation of time-invariant linear
systems with applications to neuronal modeling. Biologial Cybernetics
81:381-402.
.. [3] Hanuschkin A, Kunkel S, Helias M, Morrison A & Diesmann M (2010)
A general and efficient method for incorporating exact spike times in
globally time-driven simulations Front Neuroinformatics, 4:113
Sends
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SpikeEvent
Receives
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SpikeEvent, CurrentEvent, DataLoggingRequest
See also
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:doc:`Neuron `, :doc:`Integrate-And-Fire `, :doc:`Current-Based `, :doc:`Precise `