Patrice Abry

Log Wavelet Leaders Cumulant Based Multifractal Analysis of EVI fMRI Time Series: Evidence of Scaling in Ongoing and Evoked Brain Activity

Classical within-subject analysis in functional magnetic resonance imaging (fMRI) relies on a detection step to localize which parts of the brain are activated by a given stimulus type. This is usually achieved using model-based approaches. Here, we propose an alternative exploratory analysis. The originality of this contribution is twofold. First, we propose a synthetic, consistent, and comparative overview of the various stochastic processes and estimation procedures used to model and analyze scale invariance. Notably, it is explained how multifractal models are more versatile to adjust the scaling properties of fMRI data but require more elaborated analysis procedures. Second, we bring evidence of the existence of actual scaling in fMRI time series that are clearly disentangled from putative superimposed nonstationarities. By nature, scaling analysis requires the use of long enough signals with high frequency sampling rate. To this end, we make use of a localized 3-D echo volume imaging (EVI) technique, which has recently emerged in fMRI because it allows very fast acquisitions of successive brain volumes. High temporal resolution EVI fMRI data have been acquired both in resting state and during a slow event-related visual paradigm. A voxel-based systematic multifractal analysis has been performed over both kinds of data. Combining multifractal attribute estimates together with paired statistical tests, we observe significant scaling parameter changes between ongoing and evoked brain activity, which clearly validate an increase in long memory and suggest a global multifractality decrease effect under activation.

Intermittency and coherent structures in a swirling flow: A wavelet analysis of joint pressure and velocity measurements

This work is a contribution to the analysis of intermittency in turbulence, and more precisely of its relation with the existence of coherent structures in the flow. We perform joint in time and space measurements of velocity and pressure in a swirling flow. We detect strong pressure drops on the pressure time series, and study the statistics of the interarrivals of the drops. We then perform a statistical analysis of the pressure and velocity signals, conditioned to the list of detected pressure drops. This allows us to show that the detected drops can be associated with the existence of coherent structures in the flow, whose time patterns, in pressure and velocity, can be deeply connected to these of a filamentary vortex. The wavelet transform allows us to separate the velocity signal into a background phase and a filament phase. We analyze intermittency in terms of log-infinitely divisible cascade models. To do so we rewrite the structure functions, the extended self-similarity ansatz and the log-infin...