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With both the linear and saturating activation functions, the critical regime can only be reached exactly in the absence of external input.
Without loss of generality, suppose that the fixed point in the absence of external input is given by (widehat {u}_{1}>0) and (widehat {u}_{2}<0).
To show that the frequency content of the stimulus is not always of central importance, we aimed at studying STR in an idealized and simplified model in situation (ii), quiescence in the absence of external input.
a With w = α the eigenvalue decreases with lower levels of external input h, with the system reaching the critical regime in the absence of external input ( λ = 0 i.e. R 0 = 1, the case studied in the companion paper).
However, in the absence of external input, the equilibrium activity bump drifts over the megamap [10], so it is important to choose (textbf{x}_{k}) to be a location from which activity bumps do not drift.
It is also important to contrast two different situations under which STR can occur: (i) in neurons that are spontaneously spiking, and (ii) in neurons that are quiescent in the absence of external input.
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To minimize the influence of IRP and intrinsic frequencies on model neurons that are quiescent in the absence of external inputs, we use specifically generated input signals that only trigger spike trains with relatively long ISIs.
The empirical evidence described in this article concurs with several earlier publications highlighting Fulani self-governance systems that arise in the absence of external inputs from the state (Riesman [1977]; Azarya [1996]; de Bruijn [1997]).
We define a phase variable θ along the limit cycle so that (theta(t) = theta(mathbf{X}_{0}(t))), θ has a constant angular velocity ω, and its range is ([0,1)). This means that in the absence of external inputs we will have dot{theta}_{i}(t) = omega_{i}. (4) In the first part of the results section we work with systems where all the oscillators have the same angular frequency ω.
The results for neurons that are quiescent in the absence of an external input suggest a number of other future directions for investigation.
Subsequently to such circuit formation, in absence of any external input, spontaneous build up and reverberation of noise within their potentiated synapses occurs.
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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