Browsing by Author "Özdemir, Yunus"
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The critical point of a sigmoidal curve
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 ...

Determining the critical point of a sigmoidal curve via its fourier transform
Authors:Bilge, Ayşe Hümeyra; Özdemir, Yunus
Publisher and Date:(Institute of Physics Publishing, 2016)A sigmoidal curve y(t) is a monotone increasing curve such that all derivatives vanish at infinity. Let tn be the point where the nth derivative of y(t) reaches its global extremum. In the previous work on solgel transition modelled by the SusceptibleInfected Recovered (SIR) system, we observed that the sequence {tn } seemed to converge to a point that agrees qualitatively with the location of the gel point [2]. In the present work we outline a proof that for sigmoidal curves satisfying fairly ...

The Fourier Transform of the First Derivative of the Generalized Logistic Growth Curve
Authors:Bilge, Ayşe Hümeyra; Özdemir, Yunus
Publisher and Date:(International journal of advances in engineering and pure sciences (Online), 2020)The “generalized logistic growth curve” or the “5point sigmoid” is a typical example for sigmoidal curves without symmetry and it is commonly used for nonlinear regression. The “critical point” of a sigmoidal curve is defined as the limit, if it exists, of the points where its derivatives reach their absolute extreme values. The existence and the location of the critical point of a sigmoidal curve is expressed in terms of its Fourier transform. In this work, we obtain the Fourier transform of ...