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By comparing f d (k) with fD, the false nearest neighbors for all the phase points are verified.
Thus, once the phase space of LF-MDCT coefficients is reconstructed, the relationship between the phase points and MDCT coefficients can be described by a non-linear model.
According to the PSR principle, we can obtain the phase points y5, y6,…, containing the HF-MDCT coefficients, x 7), x 8),….
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When the phase point is on the strong canard, δ = 0. Let δ > 0 when the phase point is in the singular funnel and δ < 0 when the phase point is outside the singular funnel.
Note that when the phase point does not approach the saddle, the model generates bursts with same number of spikes.
Assuming that the phase point x(n) is in the i th element of the partition at time n.
If f d (k) > fD, the phase point y k NN is determined as the false nearest neighbor of the phase point y k, where fD is a threshold value used for verifying whether the nearest neighbor of phase point is false or not.
The path line through the point E intersects with the pulse set at point G, the phase point of the point G in the phase set N is F, and the coordinate is d.
Once the component x 7) within the phase point y5 is determined, we can use a similar method to estimate the component x 8) within phase point y6, and so on.
The number of complete revolutions of the phase point around the spiking manifold, M lc, gives the number of spikes within a burst, see Figures 2 and 6.
If the phase point reaches the edge before the saddle, it falls down to the hyperpolarized branch of M eq to start a new cycle of bursting.
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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