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The effect of the noise current on a neuron depends on the switching interval :math:`\delta`.
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For a leaky integrate-and-fire neuron with time constant :math:`\tau_m` and capacitance
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:math:`C_m`, the variance of the membrane potential is given by
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.. math::
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dI = \frac{1}{\tau}(\mu - I)dt + \sigma_{stat} \sqrt{\frac{2}{\tau}} dW
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\Sigma^2 = \frac{\delta \tau_m \sigma^2}{2 C_m^2}
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where:
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- :math:`\mu` is the long-term mean of the process (`mean` parameter).
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- :math:`\tau` is the time constant of the correlation (`tau` parameter).
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- :math:`\sigma_{stat}` is the stationary standard deviation of the process (`std` parameter).
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- :math:`dW` is a Wiener process (Gaussian white noise).
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for :math:`\delta \ll \tau_m`. For details, see the `noise generator notebook
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<../model_details/ou_noise_generator.ipynb>`_.
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The generator integrates this process at a user-defined interval `dt` and delivers the resulting current to its targets. A larger time constant :math:`\tau` results in a more slowly varying noise signal.
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All targets of a noise generator receive different currents, but the currents for all
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targets change at the same points in time. The interval :math:`\delta` between
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changes must be a multiple of the time step.
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All targets of a noise generator receive different, independent noise currents, but the currents for all targets are updated at the same points in time. The interval `dt` between updates must be a multiple of the simulation time step.
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.. admonition:: Recording the generated current
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You can use a :doc:`multimeter <multimeter>` to record the average current sent to all targets for each time step
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if simulating on a single thread; multiple MPI processes with one thread each also work. In this case,
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the recording interval of the multimeter should be equal to the simulation resolution to avoid confusing effects
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due to offset or drift between the recording times of the multimeter and the switching times of the
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noise generator. In multi-threaded mode, recording of noise currents is prohibited for technical reasons.
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You can use a :doc:`multimeter <multimeter>` to record the average current sent to all targets for each time step if simulating on a single thread; multiple MPI processes with one thread each also work. In this case, the recording interval of the multimeter should be equal to the `dt` of the generator to avoid aliasing effects. In multi-threaded mode, recording of noise currents is prohibited for technical reasons.
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.. include:: ../models/stimulation_device.rst
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mean
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The mean value :math:`\mu` of the noise current (pA)
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The mean value :math:`\mu` to which the process reverts (pA).
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std
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The standard deviation :math:`\sigma` of the noise current (pA)
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The stationary standard deviation :math:`\sigma_{stat}` of the process (pA).
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dt
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The interval :math:`\delta` between changes in current (ms; default: 10 * resolution)
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std_mod
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The modulation :math:`\sigma_{\text{mod}}` of the standard deviation of the noise current (pA)
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frequency
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The frequency of the sine modulation (Hz)
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tau
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The correlation time constant :math:`\tau` of the process (ms).
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phase
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The phase of sine modulation (0–360 deg)
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dt
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The interval :math:`\delta` between updates of the noise current (ms).
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