The Critical Point of a Sigmoidal Curve

Loading...
Thumbnail Image

Date

2020

Authors

Bilge, Ayşe Hümeyra
Özdemir, Yunus

Journal Title

Journal ISSN

Volume Title

Publisher

Babeș-Bolyai University

Open Access Color

OpenAIRE Downloads

OpenAIRE Views

Research Projects

Organizational Units

Journal Issue

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].

Description

Keywords

Sigmoidal curve, Critical point, Fourier transform, Hilbert transform

Turkish CoHE Thesis Center URL

Fields of Science

Citation

1

WoS Q

Scopus Q

Q3

Source

Volume

65

Issue

1

Start Page

77

End Page

91