The Critical Point of a Sigmoidal Curve
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Date
2020
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Publisher
Babeș-Bolyai University
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Abstract
Let y(t) be a monotone increasing curve with lim(t ->+/-infinity) y((n))(t) = 0 for all n and let t(n) be the location of the global extremum of the nth derivative y((n))(t). Under certain assumptions on the Fourier and Hilbert transforms of y(t), we prove that the sequence {t(n)} is convergent. This implies in particular a preferred choice of the origin of the time axis and an intrinsic definition of the even and odd components of a sigmoidal function. In the context of phase transitions, the limit point has the interpretation of the critical point of the transition as discussed in previous work [3].
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Keywords
Sigmoidal curve, Critical point, Fourier transform, Hilbert transform
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Citation
1
WoS Q
Scopus Q
Q3
Source
Volume
65
Issue
1
Start Page
77
End Page
91