Abstract
The scale-free concept formalizes the intuition that, in many systems, the analysis of temporal dynamics cannot be grounded on specific and characteristic time scales. The scale-free paradigm has permitted the relevant analysis of numerous applications, very different in nature, ranging from natural phenomena (hydrodynamic turbulence, geophysics, body rythms, brain activity,. . . ) to human activities (Internet traffic, population, finance, art,. . . ).Yet, most successes of scale-free analysis were obtained in contexts where data are univariate, homogeneous along time (a single stationary time series), and well-characterized by simple-shape local singularities. For such situations, scale-free dynamics translate into global or local power laws, which significantly eases practical analyses. Numerous recent real-world applications (macroscopic spontaneous brain dynamics, the central application in this project, being one paradigm example), however, naturally entail large multivariate data (many signals), whose properties vary along time (non-stationarity) and across components (non-homogeneity), with potentially complex temporal dynamics, thus intricate local singular behaviors.
These three issues call into question the intuitive and founding identification of scale-free to power laws, and thus make uneasy multivariate scale-free and multifractal analyses, precluding the use of univariate methodologies. This explains why the concept of scale-free dynamics is barely used and with limited successes in such settings and highlights the overriding need for a systematic methodological study of multivariate scale-free and multifractal dynamics.
The Core Theme of MULTIFRACS consists in :
- laying the theoretical foundations of a practical robust statistical signal processing framework for multivari- ate non homogeneous scale-free and multifractal analyses, suited to varied types of rich singularities, as well as in
- performing accurate analyses of scale-free dynamics in spontaneous and task-related macroscopic brain ac- tivity, to assess their natures, functional roles and relevance, and their relations to behavioral performance in a timing estimation task using multimodal functional imaging techniques.
This overarching objective is organized into 4 Challenges:
1. Multivariate scale-free and multifractal analysis,
2. Second generation of local singularity indices,
3. Scale-free dynamics, non-stationarity and non-homogeneity,
4. Multivariate scale-free temporal dynamics analysis in macroscopic brain activity.
To reach such ambitious goals, a solid multidisciplinary consortium has been assembled, spanning large scien- tific expertises within each field (statistical signal processing, mathematics, neurosciences), combined with a long- standing experience of the pitfalls and stakes in conducting actual fruitful interdisciplinary research, and relying on international research collaborative networks. Interactions between methodology and application will constitute a leading thread, sustained by the construction of a public website, with codes, tutorial demos and publications. An application gallery will be customized to the specificities of scale-free functional neuroimaging data, to match stan- dard reference procedures of the field. This website will also serve for dissemination of the project achievements to other scientific fields. Specific efforts will also be devoted to scientific mediation towards society, citizens, and general public audiences.
Beyond methodological developments in multivariate scale-free analysis, also of interest to other scientific com- munities, MULTIFRACS targets significant societal impact by addressing fundamental issues in neurosciences such as the extent to which scale-free brain dynamics can account for power-laws and scaling in psychology; and by opening up perspectives for early detection and characterization of neurodegenerative diseases (e.g., Alzheimer) or neurological disorders (e.g., epilepsy, drug addictions).