Universal temporal characteristics and vanishing of multifractality in Barkhausen avalanches.

Barkhausen effect in ferromagnetic materials provides an excellent area for investigating scaling phenomena found in disordered systems exhibiting crackling noise. The critical dynamics is characterized by random pulses or avalanches with scale-invariant properties, power-law distributions, and universal features. However, the traditional Barkhausen avalanches statistics may not be sufficient to fully characterize the complex temporal correlation of the magnetic domain walls dynamics. Here we focus on the multifractal scenario to quantify the temporal scaling characteristics of Barkhausen avalanches in polycrystalline and amorphous ferromagnetic films with thicknesses from 50 to 1000 nm. We show that the multifractal properties are dependent on film thickness, although they seem to be insensitive to the structural character of the materials. Moreover, we observe for the first time the vanishing of the multifractality in the domain walls dynamics. As the thickness is reduced, the multifractal behavior gives place to a monofractal one over the entire range of time scales. This reorganization in the temporal scaling characteristics of Barkhausen avalanches is understood as a universal restructuring associated to the dimensional crossover, from three- to two-dimensional magnetization dynamics.

Segmentation of time series with long-range fractal correlations.

Segmentation is a standard method of data analysis to identify change-points dividing a nonstationary time series into homogeneous segments. However, for long-range fractal correlated series, most of the segmentation techniques detect spurious change-points which are simply due to the heterogeneities induced by the correlations and not to real nonstationarities. To avoid this oversegmentation, we present a segmentation algorithm which takes as a reference for homogeneity, instead of a random i.i.d. series, a correlated series modeled by a fractional noise with the same degree of correlations as the series to be segmented. We apply our algorithm to artificial series with long-range correlations and show that it systematically detects only the change-points produced by real nonstationarities and not those created by the correlations of the signal. Further, we apply the method to the sequence of the long arm of human chromosome 21, which is known to have long-range fractal correlations. We obtain only three segments that clearly correspond to the three regions of different G + C composition revealed by means of a multi-scale wavelet plot. Similar results have been obtained when segmenting all human chromosome sequences, showing the existence of previously unknown huge compositional superstructures in the human genome.

The suprachiasmatic nucleus functions beyond circadian rhythm generation.

We recently discovered that human activity possesses a complex temporal organization characterized by scale-invariant/self-similar fluctuations from seconds to approximately 4 h-(statistical properties of fluctuations remain the same at different time scales). Here, we show that scale-invariant activity patterns are essentially identical in humans and rats, and exist for up to approximately 24 h: six-times longer than previously reported. Theoretically, such scale-invariant patterns can be produced by a neural network of interacting control nodes-system components with feedback loops-operating at different time scales. However such control nodes have not yet been identified in any neurophysiological model of scale invariance/self-similarity in mammals. Here we demonstrate that the endogenous circadian pacemaker (suprachiasmatic nucleus; SCN), known to modulate locomotor activity with a periodicity of approximately 24 h, also acts as a major neural control node responsible for the generation of scale-invariant locomotor patterns over a broad range of time scales from minutes to at least 24 h (rather than solely at approximately 24 h). Remarkably, we found that SCN lesion in rats completely abolished the scale-invariant locomotor patterns between 4 and 24 h and significantly altered the patterns at time scales <4 h. Identification of the control nodes of a neural network responsible for scale invariance is the critical first step in understanding the neurophysiological origin of scale invariance/self-similarity.

Steady-state visual evoked potentials and phase synchronization in migraine patients.

We investigate phase synchronization in EEG recordings from migraine patients. We use the analytic signal technique, based on the Hilbert transform, and find that migraine brains are characterized by enhanced alpha band phase synchronization in the presence of visual stimuli. Our findings show that migraine patients have an overactive regulatory mechanism that renders them more sensitive to external stimuli.