stdp_nn_pre_centered_synapse – Synapse type for spike-timing dependent plasticity with presynaptic-centered nearest-neighbour spike pairing scheme
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Description
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``stdp_nn_pre_centered_synapse`` is a connector to create synapses with spike
time dependent plasticity with the ``presynaptic``-centered nearest-neighbour
spike pairing scheme, as described in [1]_.

Each presynaptic spike is taken into account in the STDP weight change rule
with the nearest preceding postsynaptic one and the nearest succeeding
postsynaptic one (instead of pairing with all spikes, like in ``stdp_synapse``).
So, when a presynaptic spike occurs, it is accounted in the depression rule
with the nearest preceding postsynaptic one; and when a postsynaptic spike
occurs, it is accounted in the facilitation rule with all preceding
presynaptic spikes that were not earlier than the previous postsynaptic
spike. For a clear illustration of this scheme see fig. 7B in [2]_.

The pairs exactly coinciding (so that ``presynaptic_spike == postsynaptic_spike
+ dendritic_delay``), leading to zero ``delta_t``, are discarded. In this case the
concerned pre/postsynaptic spike is paired with the second latest preceding
post/presynaptic one (for example, ``pre=={10 ms; 20 ms}`` and ``post=={20 ms}`` will
result in a potentiation pair 20-to-10).

The implementation involves two additional variables - presynaptic and
postsynaptic traces [2]_. The presynaptic trace decays exponentially over
time with the time constant ``tau_plus``, increases by 1 on a pre-spike
occurrence, and is reset to 0 on a post-spike occurrence. The postsynaptic
trace (implemented on the postsynaptic neuron side) decays with the time
constant ``tau_minus`` and increases to 1 on a post-spike occurrence.

.. warning::

   This synaptic plasticity rule does not take
   :ref:`precise spike timing <sim_precise_spike_times>` into
   account. When calculating the weight update, the precise spike time part
   of the timestamp is ignored.

Parameters
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========= =======  ======================================================
 tau_plus  ms      Time constant of STDP window, potentiation
                   (tau_minus defined in postsynaptic neuron)
 lambda    real    Step size
 alpha     real    Asymmetry parameter (scales depressing increments as
                   alpha*lambda)
 mu_plus   real    Weight dependence exponent, potentiation
 mu_minus  real    Weight dependence exponent, depression
 Wmax      real    Maximum allowed weight
========= =======  ======================================================

Transmits
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SpikeEvent

References
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.. [1] Izhikevich E. M., Desai N. S. (2003) Relating STDP to BCM,
       Neural Comput. 15, 1511--1523

.. [2] Morrison A., Diesmann M., and Gerstner W. (2008) Phenomenological
       models of synaptic plasticity based on spike timing,
       Biol. Cybern. 98, 459--478

See also
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:doc:`Synapse <index_synapse>`, :doc:`Spike-Timing-Dependent Plasticity <index_spike-timing-dependent plasticity>`