# -*- coding: utf-8 -*-
from typing import Union, Dict, Callable, Optional
from brainpy._src.connect import TwoEndConnector
from brainpy._src.dyn import synapses
from brainpy._src.dynold.synouts import CUBA
from brainpy._src.dynold.synapses import _TwoEndConnAlignPre
from brainpy._src.dynsys import Sequential
from brainpy._src.dyn.base import NeuDyn
from brainpy._src.initialize import Initializer
from brainpy._src.mixin import ParamDesc
from brainpy.types import ArrayType
__all__ = [
'STP'
]
class _STPModel(Sequential, ParamDesc):
def __init__(self, size, keep_size, tau, U, tau_f, tau_d, mode=None, method='exp_euler'):
stp = synapses.STP(size, keep_size, U=U, tau_f=tau_f, tau_d=tau_d, method=method, mode=mode)
exp = synapses.Expon(size, keep_size, tau=tau, method=method, mode=mode)
super().__init__(stp, exp)
[docs]
class STP(_TwoEndConnAlignPre):
r"""Short-term plasticity model.
**Model Descriptions**
Short-term plasticity (STP) [1]_ [2]_ [3]_, also called dynamical synapses,
refers to the changes of synaptic strengths over time in a way that reflects
the history of presynaptic activity. Two types of STP, with opposite effects
on synaptic efficacy, have been observed in experiments. They are known as
Short-Term Depression (STD) and Short-Term Facilitation (STF).
In the model proposed by Tsodyks and Markram [4]_ [5]_, the STD effect is
modeled by a normalized variable :math:`x (0 \le x \le 1)`, denoting the fraction
of resources that remain available after neurotransmitter depletion.
The STF effect is modeled by a utilization parameter :math:`u`, representing
the fraction of available resources ready for use (release probability).
Following a spike,
- (i) :math:`u` increases due to spike-induced calcium influx to the presynaptic
terminal, after which
- (ii) a fraction :math:`u` of available resources is consumed to produce the
post-synaptic current.
Between spikes, :math:`u` decays back to zero with time constant :math:`\tau_f`
and :math:`x` recovers to 1 with time constant :math:`\tau_d`.
In summary, the dynamics of STP is given by
.. math::
\begin{aligned}
\frac{du}{dt} & = -\frac{u}{\tau_f}+U(1-u^-)\delta(t-t_{sp}),\nonumber \\
\frac{dx}{dt} & = \frac{1-x}{\tau_d}-u^+x^-\delta(t-t_{sp}), \\
\frac{dI}{dt} & = -\frac{I}{\tau_s} + Au^+x^-\delta(t-t_{sp}),
\end{aligned}
where :math:`t_{sp}` denotes the spike time and :math:`U` is the increment
of :math:`u` produced by a spike. :math:`u^-, x^-` are the corresponding
variables just before the arrival of the spike, and :math:`u^+`
refers to the moment just after the spike. The synaptic current generated
at the synapse by the spike arriving at :math:`t_{sp}` is then given by
.. math::
\Delta I(t_{spike}) = Au^+x^-
where :math:`A` denotes the response amplitude that would be produced
by total release of all the neurotransmitter (:math:`u=x=1`), called
absolute synaptic efficacy of the connections.
**Model Examples**
- `STP for Working Memory Capacity <https://brainpy-examples.readthedocs.io/en/latest/working_memory/Mi_2017_working_memory_capacity.html>`_
**STD**
>>> import brainpy as bp
>>> import matplotlib.pyplot as plt
>>>
>>> neu1 = bp.neurons.LIF(1)
>>> neu2 = bp.neurons.LIF(1)
>>> syn1 = bp.synapses.STP(neu1, neu2, bp.connect.All2All(), U=0.2, tau_d=150., tau_f=2.)
>>> net = bp.Network(pre=neu1, syn=syn1, post=neu2)
>>>
>>> runner = bp.DSRunner(net, inputs=[('pre.input', 28.)], monitors=['syn.I', 'syn.u', 'syn.x'])
>>> runner.run(150.)
>>>
>>>
>>> # plot
>>> fig, gs = bp.visualize.get_figure(2, 1, 3, 7)
>>>
>>> fig.add_subplot(gs[0, 0])
>>> plt.plot(runner.mon.ts, runner.mon['syn.u'][:, 0], label='u')
>>> plt.plot(runner.mon.ts, runner.mon['syn.x'][:, 0], label='x')
>>> plt.legend()
>>>
>>> fig.add_subplot(gs[1, 0])
>>> plt.plot(runner.mon.ts, runner.mon['syn.I'][:, 0], label='I')
>>> plt.legend()
>>>
>>> plt.xlabel('Time (ms)')
>>> plt.show()
**STF**
>>> import brainpy as bp
>>> import matplotlib.pyplot as plt
>>>
>>> neu1 = bp.neurons.LIF(1)
>>> neu2 = bp.neurons.LIF(1)
>>> syn1 = bp.neurons.STP(neu1, neu2, bp.connect.All2All(), U=0.1, tau_d=10, tau_f=100.)
>>> net = bp.Network(pre=neu1, syn=syn1, post=neu2)
>>>
>>> runner = bp.DSRunner(net, inputs=[('pre.input', 28.)], monitors=['syn.I', 'syn.u', 'syn.x'])
>>> runner.run(150.)
>>>
>>>
>>> # plot
>>> fig, gs = bp.visualize.get_figure(2, 1, 3, 7)
>>>
>>> fig.add_subplot(gs[0, 0])
>>> plt.plot(runner.mon.ts, runner.mon['syn.u'][:, 0], label='u')
>>> plt.plot(runner.mon.ts, runner.mon['syn.x'][:, 0], label='x')
>>> plt.legend()
>>>
>>> fig.add_subplot(gs[1, 0])
>>> plt.plot(runner.mon.ts, runner.mon['syn.I'][:, 0], label='I')
>>> plt.legend()
>>>
>>> plt.xlabel('Time (ms)')
>>> plt.show()
**Model Parameters**
============= ============== ======== ===========================================
**Parameter** **Init Value** **Unit** **Explanation**
------------- -------------- -------- -------------------------------------------
tau_d 200 ms Time constant of short-term depression.
tau_f 1500 ms Time constant of short-term facilitation.
U .15 \ The increment of :math:`u` produced by a spike.
A 1 \ The response amplitude that would be produced by total release of all the neurotransmitter
delay 0 ms The decay time of the current :math:`I` output onto the post-synaptic neuron groups.
============= ============== ======== ===========================================
**Model Variables**
=============== ================== =====================================================================
**Member name** **Initial values** **Explanation**
--------------- ------------------ ---------------------------------------------------------------------
u 0 Release probability of the neurotransmitters.
x 1 A Normalized variable denoting the fraction of remain neurotransmitters.
I 0 Synapse current output onto the post-synaptic neurons.
=============== ================== =====================================================================
**References**
.. [1] Stevens, Charles F., and Yanyan Wang. "Facilitation and depression
at single central synapses." Neuron 14, no. 4 (1995): 795-802.
.. [2] Abbott, Larry F., J. A. Varela, Kamal Sen, and S. B. Nelson. "Synaptic
depression and cortical gain control." Science 275, no. 5297 (1997): 221-224.
.. [3] Abbott, L. F., and Wade G. Regehr. "Synaptic computation."
Nature 431, no. 7010 (2004): 796-803.
.. [4] Tsodyks, Misha, Klaus Pawelzik, and Henry Markram. "Neural networks
with dynamic synapses." Neural computation 10.4 (1998): 821-835.
.. [5] Tsodyks, Misha, and Si Wu. "Short-term synaptic plasticity."
Scholarpedia 8, no. 10 (2013): 3153.
"""
[docs]
def __init__(
self,
pre: NeuDyn,
post: NeuDyn,
conn: Union[TwoEndConnector, ArrayType, Dict[str, ArrayType]],
U: Union[float, ArrayType] = 0.15,
tau_f: Union[float, ArrayType] = 1500.,
tau_d: Union[float, ArrayType] = 200.,
tau: Union[float, ArrayType] = 8.,
A: Union[float, ArrayType] = 1.,
delay_step: Union[int, ArrayType, Initializer, Callable] = None,
method: str = 'exp_auto',
name: Optional[str] = None
):
# parameters
self.tau_d = tau_d
self.tau_f = tau_f
self.tau = tau
self.U = U
self.A = A
syn = _STPModel(pre.size,
pre.keep_size,
tau,
U,
tau_f,
tau_d,
method=method)
super().__init__(pre=pre,
post=post,
syn=syn,
conn=conn,
g_max=A,
output=CUBA(),
comp_method='sparse',
delay_step=delay_step,
name=name)
# variables
self.x = self.syn[0].x
self.u = self.syn[0].u
self.I = self.syn[1].g
