## Abstract We study geometric rigidity of a class of fractals, which is slightly larger than the collection of selfβconformal sets. Namely, using a new method, we shall prove that a set of this class is contained in a smooth submanifold or is totally spread out. (Β© 2006 WILEYβVCH Verlag GmbH & Co.
Fractal rigidity in migraine
β Scribed by Miroslaw Latka; Marta Glaubic-Latka; Dariusz Latka; Bruce J. West
- Publisher
- Elsevier Science
- Year
- 2004
- Tongue
- English
- Weight
- 107 KB
- Volume
- 20
- Category
- Article
- ISSN
- 0960-0779
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β¦ Synopsis
We study the middle cerebral artery blood flow velocity in humans using transcranial Doppler ultrasonography. Scaling properties of time series of the axial flow velocity averaged over a cardiac beat interval may be characterized by two exponents. The short-time scaling exponent (STSE) determines the statistical properties of fluctuations of blood flow velocities in short-time intervals while the Hurst exponent describes the long-term fractal properties. In many migraineurs the value of the STSE is significantly reduced and may approach that of the Hurst exponent. This change in dynamical properties reflects the significant loss of short-term adaptability and the overall hyperexcitability of underlying cerebral blood flow control system. We call this effect fractal rigidity.
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