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Depending on the relative timings of the presynaptic input at time tpre and the postsynaptic excitation at time tpost, the synapse is strengthened (delta_t = t post) - t(pre) > 0) or weakened (delta_t < 0).
So the question then is what can we say about h(t), the impulse response in order to guarantee, let's say, that the output depends only on the input at time t.
Feedforward inhibition is modeled by assuming that for each excitatory input at time (t_{n}) there will be a corresponding inhibitory input at time (t_{n} + d), where d represents the feedforward delay.
It got so bad that Blizzard created a keyfob (and mobile app equivalents) that generates a unique password that you'd input at time of login.
Consider the input at time t with a set of parameters: Input ( t ) = { x 1 ( t ), x 2 ( t ), x 3 ( t ), …, x N ( t ) }.
where denotes the STFT of the th microphone input at time and frequency, and the superscript denotes the transpose of a vector or a matrix.
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In other words, impulsive inputs at time 0 can be used to set up arbitrary initial conditions.
The channel is assumed to be memoryless; that is, the channel outputs at time depend only on channel inputs at time.
where is the neural state vector;,, are the interconnection matrices representing the weighting coefficients of the neurons; are activation functions; are transmission delays; denotes the external inputs at time.
The functions G i contain all information about the internal wiring of the network (who influences whom) as well as the logic of each gene's regulation (given the configuration of all of gene i's inputs at time t, whether gene i will be on or off at t + 1).
In general, a length FIR filter is fully ''warmed up" after samples of input; that is, for an input starting at time, by time, all internal state delays of the filter contain delayed input samples instead of their initial zeros.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com