Beacons in dense Wi-Fi networks: How to befriend with neighbors in the 5G world?
We present a novel method for the extraction of neuronal components showing cross-frequency phase synchronization.
In general the method can be applied for the detection of phase interactions between components with frequencies f1 and f2, where f2 ≈ rf1 and r is some integer. We refer to the method as cross-frequency decomposition (CFD), which consists of the following steps: (a) extraction of f1-oscillations with the spatio-spectral decomposition algorithm (SSD); (b) frequency modification of the f1-oscillations obtained with SSD; and (c) finding f2-oscillations synchronous with f1-oscillations using least-squares estimation.
Our simulations showed that CFD was capable of recovering interacting components even when the signal-to-noise ratio was as low as 0.01. An application of CFD to the real EEG data demonstrated that cross-frequency phase synchronization between alpha and beta oscillations can originate from the same or remote neuronal populations.
CFD allows a compact representation of the sets of interacting components. The application of CFD to EEG data allows differentiating cross-frequency synchronization arising due to genuine neurophysiological interactions from interactions occurring due to quasi-sinusoidal waveform of neuronal oscillations.
CFD is a method capable of extracting cross-frequency coupled neuronal oscillations even in the presence of strong noise.
Copyright © 2011 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.
We consider a minimal action of a finitely generated semigroup by homeomorphisms of the circle, and show that the collection of translation numbers of individual elements completely determines the set of generators (up to a common continuous change of coordinates). One of the main tools used in the proof is the synchronization properties of random dynamics of circle homeomorphisms: Antonov’s theorem and its corollaries.