Auxiliary Blocks

Event-Analog Signal Multiplier

Block performing a “multiplication” between an events signal and a selection signal. The blocks can be mathematically described as:

\[\begin{split}\begin{aligned} \text{Out}_+ &= f(a_+s - d_+)\text{In}\\ \text{Out}_- &= f(a_-s - d_-)\text{In} \end{aligned}\end{split}\]

where \(f\) is either a Heaviside step function \(H\) or a sigmoid function \(\sigma\) depending on the input-output type, and \(a_{\pm}\) are the slopes and \(d_{\pm}\) the biases of the selection function.

Inputs:

• Ev (boolean) – Input events signal \(\text{Ev}\) such that \(\text{In} = \text{Ev}\).

• s (analog) – Input selection signal \(s\).

Alternative Inputs:

• V (analog) – Input voltage signal \(\text{V}\) such that \(\text{In} = g_{\text{in}\pm}\sigma(a_{\text{in}\pm}\text{V} - d_{\text{in}\pm})\).

• s (analog) – Input selection signal \(s\).

Outputs:

• Ev+ (boolean) – Output positive events signal \(\text{Out}_+\) such that \(f \equiv H\).

• Ev- (boolean) – Output negative events signal \(\text{Out}_-\) such that \(f \equiv H\).

Alternative Outputs:

• V+ (analog) – Output positive voltage signal \(\text{Out}_+\) such that \(f \equiv \sigma\).

• V- (analog) – Output negative voltage signal \(\text{Out}_-\) such that \(f \equiv \sigma\).

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 \(d_{\pm}\) of the selection function. Default value is 0.

• Signal Slopes – The slopes \(a_{\pm}\) 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 \(g_{\text{in}\pm}\) used if voltage input is selected. Default value is 1.

• Input Biases – The input biases \(d_{\text{in}\pm}\) used if voltage input is selected. Default value is 0.

• Input Slopes – The input slopes \(a_{\text{in}\pm}\) used if voltage input is selected. Default value is 1.

Event-Analog Signal Selector

Block performing a “selection” between two incoming events signals using a selection signal. The blocks can be mathematically described as:

\[\begin{aligned} \text{Out} &= f(a_+s - d_+)\text{In}_+ + f(a_-s - d_-)\text{In}_- \end{aligned}\]

where \(f\) is either a Heaviside step function \(H\) or a sigmoid function \(\sigma\) depending on the input-output type, and \(a_{\pm}\) are the slopes and \(d_{\pm}\) the biases of the selection functions.

Inputs:

• Ev+ (boolean) – Input positive events signal \(\text{Ev}_+\) such that \(\text{In}_+ = \text{Ev}_+\).

• Ev- (boolean) – Input negative events signal \(\text{Ev}_-\) such that \(\text{In}_- = \text{Ev}_-\).

• s (analog) – Input selection signal \(s\).

Alternative Inputs:

• V+ (analog) – Input positive voltage signal \(\text{V}_+\) such that \(\text{In}_+ = g_{\text{in}+}\sigma(a_{\text{in}+}\text{V}_+ - d_{\text{in}+})\).

• V- (analog) – Input negative voltage signal \(\text{V}_-\) such that \(\text{In}_- = g_{\text{in}-}\sigma(a_{\text{in}-}\text{V}_- - d_{\text{in}-})\).

• s (analog) – Input selection signal \(s\).

Output:

Ev (boolean) – Output positive events signal \(\text{Out}\) such that \(f \equiv H\).

Alternative Output:

V (analog) – Output positive voltage signal \(\text{Out}\) such that \(f \equiv \sigma\).

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 \(d_{\pm}\) of the selection function. Default value is 0.

• Signal Slopes – The slopes \(a_{\pm}\) 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 \(g_{\text{in}\pm}\) used if voltage input is selected. Default value is 1.

• Input Biases – The input biases \(d_{\text{in}\pm}\) used if voltage input is selected. Default value is 0.

• Input Slopes – The input slopes \(a_{\text{in}\pm}\) used if voltage input is selected. Default value is 1.

Directional Threshold Detector

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 Neuron. The input block can be mathematically described as:

\[\begin{split}\begin{aligned} I &= g\sigma(as - d)\\ \end{aligned}\end{split}\]

where \(g\) is the gain, \(a\) the slope, and \(d\) the bias of the input and \(I\) is the current sent to the internal type III neuron.

Input:

s (analog) – Input selection signal \(s\).

Output:

Ev (boolean) – Output positive events signal. See Neuron for details.

Alternative Output:

V (analog) – Output positive voltage signal. Output is computed from volatage \(V_n\) of neuron by \(\text{V} = g_{\text{out}}\sigma(a_{\text{out}}V_n- - d_{\text{out}})\). See Neuron for details.

Parameters:

• Input Gain – The gain \(g\). Default value is -0.5.

• Input Bias – The bias \(d\). Default value is 0.

• Input Slope – The slope \(a\). Default value is 10.

• Timescale – The timescale \(\tau\) 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 \(g_{\text{out}}\) used if voltage output is selected. Default value is 1.

• Output Bias – The output bias \(d_{\text{out}}\) used if voltage output is selected. Default value is 0.

• Output Slope – The output slope \(a_{\text{out}}\) used if voltage output is selected. Default value is 1.

Bistable Relay

Block capable of storing the polarity of the last event received. The blocks can be mathematically described as:

\[\begin{split}\begin{aligned} \tau\tau_r\dot{v} &= s + g_{+}\text{In}_{+} + g_{-}\text{In}_{-} - v\\ s &= g\sigma(av - d) \end{aligned}\end{split}\]

where \(\tau\) is the timescale, \(\tau_r\) the relative timescale, \(g_+\) the positive input gain, \(g_-\) the negative input gain and \(g\) the gain, \(a\) the slope, and \(d\) the bias of the feedback function.

Inputs:

• Ev+ (boolean) – Input positive events signal \(\text{Ev}_+\) such that \(\text{In}_+ = \text{Ev}_+\).

• Ev- (boolean) – Input negative events signal \(\text{Ev}_-\) such that \(\text{In}_- = \text{Ev}_-\).

Alternative Inputs:

• V+ (analog) – Input positive voltage signal \(\text{V}_+\) such that \(\text{In}_+ = \sigma(a_{\text{in}+}\text{V}_+ - d_{\text{in}+})\).

• V- (analog) – Input negative voltage signal \(\text{V}_-\) such that \(\text{In}_- = \sigma(a_{\text{in}-}\text{V}_- - d_{\text{in}-})\).

Optional Inputs:

• gsyn_p (analog)– The gain \(g_+\) as described in the parameter section.

• gsyn_m (analog)– The gain \(g_-\) as described in the parameter section.

Output:

• s (analog) – Input selection signal \(s\).

Parameters:

• Feedback Gain – The gain \(g\) of the feedback function. Default value is 1.

• Feedback Biases – The biases \(d\) of the feedback function. Default value is 0.

• Feedback Slopes – The slopes \(a\) of the feedback function. Default value is 1.

• Positive Input Gain – The positive input gain \(g_+\). Default value is 1.

• Negative Input Gain – The negative input gain \(g_-\). Default value is 1.

• Timescale – The timescale \(\tau\). Default value is 0.004.

• Relative Timescale – The relative timescale \(\tau_r\). 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 \(d_{\text{in}\pm}\) used if voltage input is selected. Default value is 0.

• Input Slopes – The input slopes \(a_{\text{in}\pm}\) used if voltage input is selected. Default value is 1.

Noise on Signal

Block adding band-limited white noise to the input signal. The blocks can be mathematically described as:

\[\begin{aligned} y &= x + W(t) \end{aligned}\]

where \(W(t)\) is a band-limited white noise process with zero mean, standard deviation \(\sigma\), and a correlation time \(\tau\tau_r\) with \(\tau\) the timescale and \(\tau_r\) the relative timescale.

Input:

• In (analog) – Input signal \(x\).

Output:

• Out (analog) – Output signal \(y\).

Parameters:

• Noise Power – The square of the standard deviation \(P = \sigma^2\) of the noise. Default value is 1.

• Timescale – The timescale \(\tau\). Default value is 0.004.

• Relative Timescale – The relative timescale \(\tau_r\). Default value is 1.

• Seed – The seed of the random number generator, a value of -1 specifies a random seed. Default value is -1.