:mod:`Auxiliary Blocks` ======================= .. attribute:: Event-Analog Signal Multiplier .. grid:: 2 .. grid-item:: :columns: 4 :child-align: center .. only:: html .. image:: images/eventmul.png :width: 100% :align: center :alt: Event-Analog Signal Multiplier Block Image .. only:: latex .. image:: images/eventmul.png :width: 50% :align: center :alt: Event-Analog Signal Multiplier Block Image .. grid-item:: :columns: 8 Block performing a "multiplication" between an events signal and a selection signal. The blocks can be mathematically described as: .. math:: \begin{aligned} \text{Out}_+ &= f(a_+s - d_+)\text{In}\\ \text{Out}_- &= f(a_-s - d_-)\text{In} \end{aligned} where :math:`f` is either a Heaviside step function :math:`H` or a sigmoid function :math:`\sigma` depending on the input-output type, and :math:`a_{\pm}` are the slopes and :math:`d_{\pm}` the biases of the selection function. :Inputs: * **Ev** (*boolean*) -- Input events signal :math:`\text{Ev}` such that :math:`\text{In} = \text{Ev}`. * **s** (*analog*) -- Input selection signal :math:`s`. :Alternative Inputs: * **V** (*analog*) -- Input voltage signal :math:`\text{V}` such that :math:`\text{In} = g_{\text{in}\pm}\sigma(a_{\text{in}\pm}\text{V} - d_{\text{in}\pm})`. * **s** (*analog*) -- Input selection signal :math:`s`. :Outputs: * **Ev+** (*boolean*) -- Output positive events signal :math:`\text{Out}_+` such that :math:`f \equiv H`. * **Ev-** (*boolean*) -- Output negative events signal :math:`\text{Out}_-` such that :math:`f \equiv H`. :Alternative Outputs: * **V+** (*analog*) -- Output positive voltage signal :math:`\text{Out}_+` such that :math:`f \equiv \sigma`. * **V-** (*analog*) -- Output negative voltage signal :math:`\text{Out}_-` such that :math:`f \equiv \sigma`. :Parameters: * Differentiate Positive and Negative -- Whether to differentiate positive and negative parameters or set the. Can be set to 'True' or 'False'. Default value is 'False'. * Signal Biases -- The biases :math:`d_{\pm}` of the selection function. Default value is 0. * Signal Slopes -- The slopes :math:`a_{\pm}` of the selection function. Default value is 1. * Input-Output Type -- The exposed input-output channels. Can be set to 'Events' or 'Voltage'. Default value is 'Events'. * Input Conductances -- The input conductances :math:`g_{\text{in}\pm}` used if voltage input is selected. Default value is 1. * Input Biases -- The input biases :math:`d_{\text{in}\pm}` used if voltage input is selected. Default value is 0. * Input Slopes -- The input slopes :math:`a_{\text{in}\pm}` used if voltage input is selected. Default value is 1. .. attribute:: Event-Analog Signal Selector .. grid:: 2 .. grid-item:: :columns: 4 :child-align: center .. only:: html .. image:: images/eventsel.png :width: 100% :align: center :alt: Event-Analog Signal Selector Block Image .. only:: latex .. image:: images/eventsel.png :width: 50% :align: center :alt: Event-Analog Signal Selector Block Image .. grid-item:: :columns: 8 Block performing a "selection" between two incoming events signals using a selection signal. The blocks can be mathematically described as: .. math:: \begin{aligned} \text{Out} &= f(a_+s - d_+)\text{In}_+ + f(a_-s - d_-)\text{In}_- \end{aligned} where :math:`f` is either a Heaviside step function :math:`H` or a sigmoid function :math:`\sigma` depending on the input-output type, and :math:`a_{\pm}` are the slopes and :math:`d_{\pm}` the biases of the selection functions. :Inputs: * **Ev+** (*boolean*) -- Input positive events signal :math:`\text{Ev}_+` such that :math:`\text{In}_+ = \text{Ev}_+`. * **Ev-** (*boolean*) -- Input negative events signal :math:`\text{Ev}_-` such that :math:`\text{In}_- = \text{Ev}_-`. * **s** (*analog*) -- Input selection signal :math:`s`. :Alternative Inputs: * **V+** (*analog*) -- Input positive voltage signal :math:`\text{V}_+` such that :math:`\text{In}_+ = g_{\text{in}+}\sigma(a_{\text{in}+}\text{V}_+ - d_{\text{in}+})`. * **V-** (*analog*) -- Input negative voltage signal :math:`\text{V}_-` such that :math:`\text{In}_- = g_{\text{in}-}\sigma(a_{\text{in}-}\text{V}_- - d_{\text{in}-})`. * **s** (*analog*) -- Input selection signal :math:`s`. :Output: **Ev** (*boolean*) -- Output positive events signal :math:`\text{Out}` such that :math:`f \equiv H`. :Alternative Output: **V** (*analog*) -- Output positive voltage signal :math:`\text{Out}` such that :math:`f \equiv \sigma`. :Parameters: * Differentiate Positive and Negative -- Whether to differentiate positive and negative parameters or set the. Can be set to 'True' or 'False'. Default value is 'False'. * Signal Biases -- The biases :math:`d_{\pm}` of the selection function. Default value is 0. * Signal Slopes -- The slopes :math:`a_{\pm}` of the selection function. Default value is 1. * Input-Output Type -- The exposed input-output channels. Can be set to 'Events' or 'Voltage'. Default value is 'Events'. * Input Conductances -- The input conductances :math:`g_{\text{in}\pm}` used if voltage input is selected. Default value is 1. * Input Biases -- The input biases :math:`d_{\text{in}\pm}` used if voltage input is selected. Default value is 0. * Input Slopes -- The input slopes :math:`a_{\text{in}\pm}` used if voltage input is selected. Default value is 1. .. attribute:: Directional Threshold Detector .. grid:: 2 .. grid-item:: :columns: 4 :child-align: center .. only:: html .. image:: images/threshold.png :width: 100% :align: center :alt: Directional Threshold Detector Block Image .. only:: latex .. image:: images/threshold.png :width: 50% :align: center :alt: Directional Threshold Detector Block Image .. grid-item:: :columns: 8 Block generating an event when the input signal crosses a threshold from a certain direction (above to below or below to above). The block is compose of an input block that generates a current to an internal type III :attr:`Neuron`. The input block can be mathematically described as: .. math:: \begin{aligned} I &= g\sigma(as - d)\\ \end{aligned} where :math:`g` is the gain, :math:`a` the slope, and :math:`d` the bias of the input and :math:`I` is the current sent to the internal type III neuron. :Input: **s** (*analog*) -- Input selection signal :math:`s`. :Output: **Ev** (*boolean*) -- Output positive events signal. See :attr:`Neuron` for details. :Alternative Output: **V** (*analog*) -- Output positive voltage signal. Output is computed from volatage :math:`V_n` of neuron by :math:`\text{V} = g_{\text{out}}\sigma(a_{\text{out}}V_n- - d_{\text{out}})`. See :attr:`Neuron` for details. :Parameters: * Input Gain -- The gain :math:`g`. Default value is -0.5. * Input Bias -- The bias :math:`d`. Default value is 0. * Input Slope -- The slope :math:`a`. Default value is 10. * Timescale -- The timescale :math:`\tau` of the internal neuron. Default value is 0.004. * Output Type -- The exposed output channel. Can be set to 'Events' or 'Voltage'. Default value is 'Events'. * Output Conductance -- The output conductance :math:`g_{\text{out}}` used if voltage output is selected. Default value is 1. * Output Bias -- The output bias :math:`d_{\text{out}}` used if voltage output is selected. Default value is 0. * Output Slope -- The output slope :math:`a_{\text{out}}` used if voltage output is selected. Default value is 1. .. attribute:: Bistable Relay .. grid:: 2 .. grid-item:: :columns: 4 :child-align: center .. only:: html .. image:: images/eventrelay.png :width: 100% :align: center :alt: Bistable Relay Block Image .. only:: latex .. image:: images/eventrelay.png :width: 50% :align: center :alt: Bistable Relay Block Image .. grid-item:: :columns: 8 Block capable of storing the polarity of the last event received. The blocks can be mathematically described as: .. math:: \begin{aligned} \tau\tau_r\dot{v} &= s + g_{+}\text{In}_{+} + g_{-}\text{In}_{-} - v\\ s &= g\sigma(av - d) \end{aligned} where :math:`\tau` is the timescale, :math:`\tau_r` the relative timescale, :math:`g_+` the positive input gain, :math:`g_-` the negative input gain and :math:`g` the gain, :math:`a` the slope, and :math:`d` the bias of the feedback function. :Inputs: * **Ev+** (*boolean*) -- Input positive events signal :math:`\text{Ev}_+` such that :math:`\text{In}_+ = \text{Ev}_+`. * **Ev-** (*boolean*) -- Input negative events signal :math:`\text{Ev}_-` such that :math:`\text{In}_- = \text{Ev}_-`. :Alternative Inputs: * **V+** (*analog*) -- Input positive voltage signal :math:`\text{V}_+` such that :math:`\text{In}_+ = \sigma(a_{\text{in}+}\text{V}_+ - d_{\text{in}+})`. * **V-** (*analog*) -- Input negative voltage signal :math:`\text{V}_-` such that :math:`\text{In}_- = \sigma(a_{\text{in}-}\text{V}_- - d_{\text{in}-})`. :Optional Inputs: * **gsyn_p** (*analog*)-- The gain :math:`g_+` as described in the parameter section. * **gsyn_m** (*analog*)-- The gain :math:`g_-` as described in the parameter section. :Output: * **s** (*analog*) -- Input selection signal :math:`s`. :Parameters: * Feedback Gain -- The gain :math:`g` of the feedback function. Default value is 1. * Feedback Biases -- The biases :math:`d` of the feedback function. Default value is 0. * Feedback Slopes -- The slopes :math:`a` of the feedback function. Default value is 1. * Positive Input Gain -- The positive input gain :math:`g_+`. Default value is 1. * Negative Input Gain -- The negative input gain :math:`g_-`. Default value is 1. * Timescale -- The timescale :math:`\tau`. Default value is 0.004. * Relative Timescale -- The relative timescale :math:`\tau_r`. Default value is 0.01. * Input-Output Type -- The exposed input-output channels. Can be set to 'Events' or 'Voltage'. Default value is 'Events'. * Input Biases -- The input biases :math:`d_{\text{in}\pm}` used if voltage input is selected. Default value is 0. * Input Slopes -- The input slopes :math:`a_{\text{in}\pm}` used if voltage input is selected. Default value is 1. .. attribute:: Noise on Signal .. grid:: 2 .. grid-item:: :columns: 4 :child-align: center .. only:: html .. image:: images/noise.png :width: 100% :align: center :alt: Noise on Signal Block Image .. only:: latex .. image:: images/noise.png :width: 50% :align: center :alt: Noise on Signal Block Image .. grid-item:: :columns: 8 Block adding band-limited white noise to the input signal. The blocks can be mathematically described as: .. math:: \begin{aligned} y &= x + W(t) \end{aligned} where :math:`W(t)` is a band-limited white noise process with zero mean, standard deviation :math:`\sigma`, and a correlation time :math:`\tau\tau_r` with :math:`\tau` the timescale and :math:`\tau_r` the relative timescale. :Input: * **In** (*analog*) -- Input signal :math:`x`. :Output: * **Out** (*analog*) -- Output signal :math:`y`. :Parameters: * Noise Power -- The square of the standard deviation :math:`P = \sigma^2` of the noise. Default value is 1. * Timescale -- The timescale :math:`\tau`. Default value is 0.004. * Relative Timescale -- The relative timescale :math:`\tau_r`. Default value is 1. * Seed -- The seed of the random number generator, a value of -1 specifies a random seed. Default value is -1.