Wavelets: Algorithms &amp; Applications.

Lei, Junjiang; Meyer, Yves; Ryan, Robert D.

doi:10.2307/2153305

Cited by 12 publications

(5 citation statements)

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“…Directly from the CWT scalogram we can find, for a given logistic wave, such values of the parameters b and a so that the value of the Index ( 16) at the point with coordinates (b, a) is maximal. By (15) we have…”

Section: Logistic Waveletsmentioning

confidence: 99%

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A Generalized Logistic Function and Its Applications

Rza̧dkowski

Sobczak

2020

Foundations of Management

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Section: Logistic Waveletsmentioning

confidence: 99%

“…Let us now recall some general facts about wavelet theory (cf. [3,15,16]) which we will use later. A wavelet or mother wavelet ( Daubechies [3], p.24 ) is an integrable function ψ ∈ L 1 (R) with the following admissibility condition:…”

Section: Wavelets and Logistic Wavelets 21 Waveletsmentioning

confidence: 99%

A Generalized Logistic Function and Its Applications

Rza̧dkowski

Sobczak

2020

Foundations of Management

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“…Multiresolution analysis (Meyer 1993a(Meyer , 1993b) is a mathematical approach that assumes the approximation of a signal f(t) by a series of quite simple functions φ m, k (t) and ψ j, k (t):…”

Section: Multiresolution Analysismentioning

confidence: 99%

“…The functions φ(t) and ψ(t) are selected in such a way that they can fully be represented by their values at rescaling with the factor 2 j , i.e., at the transition to another level of resolution. For the simplest, the Haar wavelet, the approximation of f(t) by φ(t) is interpreted as the histogram approach (a representation of the signal by averaged mean values within some time intervals) while the wavelets ψ(t) add details to this approximation on smaller levels of resolution (Meyer 1993a, Addison 2002. Transition from the level j to j + 1 is equivalent to a changing of t by 2t.…”

Section: Multiresolution Analysismentioning

confidence: 99%

“…Aiming to characterize how the adrenodependent relaxation of cerebral veins contributes to the development of ICH in newborns we apply here the multiresolution analysis based on the discrete wavelet-transform (DWT) (Meyer 1993a, 1993b, Daubechies 1992, Addison 2002. This mathematical tool is widely used in many scientific and technical applications if one requires quantifying multiscale dynamics of time-varying systems.…”

Section: Introductionmentioning

confidence: 99%

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Multiresolution analysis of pathological changes in cerebral venous dynamics in newborn mice with intracranial hemorrhage: adrenorelated vasorelaxation

Павлов

Semyachkina-Glushkovskaya

Zhang

et al. 2014

Physiol. Meas.

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Intracranial hemorrhage (ICH) is the major problem of modern neonatal intensive care. Abnormalities of cerebral venous blood flow (CVBF) can play a crucial role in the development of ICH in infants. The mechanisms underlying these pathological processes remain unclear; however it has been established that the activation of the adrenorelated vasorelaxation can be an important reason. Aiming to reach a better understanding of how the adrenodependent relaxation of cerebral veins contributes to the development of ICH in newborns, we study here the effects of pharmacological stimulation of adrenorelated dilation of the sagittal sinus by isoproterenol on the cerebral venous hemodynamics. Our study is performed in newborn mice at different stages of ICH using the laser speckle contrast imaging and wavelet analysis of the vascular dynamics of CVBF. We show that the dilation of the sagittal sinus with the decreased velocity of blood flow presides to the stress-induced ICH in newborn mice. These morphofunctional vascular changes are accompanied by an increased variance of the wavelet-coefficients in the areas of endothelial and non-endothelial (KATP-channels activity of vascular muscle) sympathetic components of the CVBF variability. Changes in the cerebral venous hemodynamics at the latent stage of ICH are associated with a high responsiveness of the sagittal sinus to isoproterenol quantifying by wavelet-coefficients related to a very slow region of the frequency domain. The obtained results certify that a high activation of the adrenergic-related vasodilatory responses to severe stress in newborn mice can be one of the important mechanisms underlying the development of ICH. Thus, the venous insufficiency with the decreased blood outflow from the brain associated with changes in the endothelial and the sympathetic components of CVBF-variability can be treated as prognostic criteria for the risk of ICH during the first days after birth.

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