Scale-invariance and diverging length scales are the hallmark of critical systems, the study of which can provide insights into its relation to critical universality classes. In neuroscience, the brain criticality hypothesis has motivated the characterization of cerebral activity using avalanche scaling exponents and long-range temporal correlations. In non-invasive brain recording modalities, the degree of spatial coarse-graining that occurs at the sensor level precludes proper avalanche characterizations, and only the analysis of temporal scale-invariance is possible. Multifractal analysis, which is a higher statistical order extension of the common long-range temporal correlation characterization of scale invariance, has been introduced to extract a full characterization of the temporal scale-invariance of time series. In this contribution, we show that the recently introduced Landau-Ginzburg theory for critical oscillations exhibits multifractal temporal scaling in a neighborhood of its critical point. We compare two approaches used in literature based on observing either the low-frequency fluctuations or the amplitude envelope of the oscillatory process, and show that they correspond to fundamentally different processes. This work provides a currently missing critical modeling basis for interpreting multifractality in electrophysiological brain recordings.
Okay, thanks a lot!
Is your approach related to renormalization?
Hi,
Our approach is not directly related, but there is a link.
Renormalization is concerned with how the model equations change under coarse-graining, and in theory could be applied to this model. However as Pr. Muñoz pointed out yesterday, the fact that we’re working with coupled fields makes this particularly difficult.
Here we investigated simulations of the models for evidence of temporal multifractal scaling: we do not provide theoretical values for the multifractal spectra (which is what you would look for with renormalization), but instead show empirical estimates that describe the temporal multifractal spectra of a spatially coarse-grained finite system.
The link is in the fact that the multifractal scaling functions C_m(j) describe how the higher-order statistics of the time series scale as a function of temporal scale j, and renormalization could give you that information.