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fact, this stationary value represents a stable fixed point: let us rewrite Eq. (40) as the gradient dynamics of an overdamped motion, (Formula presented) with (Formula presented) The integral (Formula presented) is a monotonically increasing function that scales faster than (Formula presented) Therefore, the gradient dynamics has a unique and globally stable fixed point
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In fact, this stationary value represents a stable fixed point: let us rewrite Eq. (40) as the gradient dynamics of an overdamped motion, (Formula presented) with (Formula presented) The integral (Formula presented) is a monotonically increasing function that scales faster than (Formula presented) Therefore, the gradient dynamics has a unique and globally stable fixed point.
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Note that Eq. (53) is solved by Gaussian time-dependent probability densities whose BGS entropies can be expressed in terms of their variances. The BGS entropies, in turn, can be related by Fitts law to neural processing times
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Note that Eq. (53) is solved by Gaussian time-dependent probability densities whose BGS entropies can be expressed in terms of their variances. The BGS entropies, in turn, can be related by Fitts law to neural processing times.
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We have (Formula presented) with (Formula presented) and (Formula presented) for all (Formula presented) Since (Formula presented) for (Formula presented) we find that (Formula presented) and (Formula presented) Consequently, the Lindeberg condition holds for (Formula presented) Roughly speaking, if we can neglect the asymptotic parts of (Formula presented) then we can also neglect the asymptotic parts of the corresponding squeezed normalized probability density (Formula presented) with (Formula presented) e.g., consider (Formula presented)
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We have (Formula presented) with (Formula presented) and (Formula presented) for all (Formula presented) Since (Formula presented) for (Formula presented) we find that (Formula presented) and (Formula presented) Consequently, the Lindeberg condition holds for (Formula presented) Roughly speaking, if we can neglect the asymptotic parts of (Formula presented) then we can also neglect the asymptotic parts of the corresponding squeezed normalized probability density (Formula presented) with (Formula presented) e.g., consider (Formula presented)
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