1
|
Abry P, Boniece BC, Didier G, Wendt H. Wavelet eigenvalue regression in high dimensions. STATISTICAL INFERENCE FOR STOCHASTIC PROCESSES 2022. [DOI: 10.1007/s11203-022-09279-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
|
2
|
Lucas CG, Abry P, Wendt H, Didier G. Drowsiness detection from polysomnographic data using multivariate selfsimilarity and eigen-wavelet analysis. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2022; 2022:2949-2952. [PMID: 36085652 DOI: 10.1109/embc48229.2022.9871363] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Because drowsiness is a major cause in vehicle accidents, its automated detection is critical. Scale-free temporal dynamics is known to be typical of physiological and body rhythms. The present work quantifies the benefits of applying a recent and original multivariate selfsimilarity analysis to several modalities of polysomnographic measurements (heart rate, blood pressure, electroencephalogram and respiration), from the MIT-BIH Polysomnographic Database, to better classify drowsiness-related sleep stages. Clinical relevance- This study shows that probing jointly temporal dynamics amongst polysomnographic measurements, with a proposed original multivariate multiscale approach, yields a gain of above 5% in the Area-under-Curve quanti-fying drowsiness-related sleep stage classification performance compared to univariate analysis.
Collapse
|
3
|
Abstract
AbstractIn this paper, we construct operator fractional Lévy motion (ofLm), a broad class of infinitely divisible stochastic processes that are covariance operator self-similar and have wide-sense stationary increments. The ofLm class generalizes the univariate fractional Lévy motion as well as the multivariate operator fractional Brownian motion (ofBm). OfLm can be divided into two types, namely, moving average (maofLm) and real harmonizable (rhofLm), both of which share the covariance structure of ofBm under assumptions. We show that maofLm and rhofLm admit stochastic integral representations in the time and Fourier domains, and establish their distinct small- and large-scale limiting behavior. We also characterize time-reversibility for ofLm through parametric conditions related to its Lévy measure. In particular, we show that, under non-Gaussianity, the parametric conditions for time-reversibility are generally more restrictive than those for the Gaussian case (ofBm).
Collapse
|
4
|
La Rocca D, Wendt H, van Wassenhove V, Ciuciu P, Abry P. Revisiting Functional Connectivity for Infraslow Scale-Free Brain Dynamics Using Complex Wavelets. Front Physiol 2021; 11:578537. [PMID: 33488390 PMCID: PMC7818786 DOI: 10.3389/fphys.2020.578537] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2020] [Accepted: 11/25/2020] [Indexed: 01/18/2023] Open
Abstract
The analysis of human brain functional networks is achieved by computing functional connectivity indices reflecting phase coupling and interactions between remote brain regions. In magneto- and electroencephalography, the most frequently used functional connectivity indices are constructed based on Fourier-based cross-spectral estimation applied to specific fast and band-limited oscillatory regimes. Recently, infraslow arrhythmic fluctuations (below the 1 Hz) were recognized as playing a leading role in spontaneous brain activity. The present work aims to propose to assess functional connectivity from fractal dynamics, thus extending the assessment of functional connectivity to the infraslow arrhythmic or scale-free temporal dynamics of M/EEG-quantified brain activity. Instead of being based on Fourier analysis, new Imaginary Coherence and weighted Phase Lag indices are constructed from complex-wavelet representations. Their performances are first assessed on synthetic data by means of Monte-Carlo simulations, and they are then compared favorably against the classical Fourier-based indices. These new assessments of functional connectivity indices are also applied to MEG data collected on 36 individuals both at rest and during the learning of a visual motion discrimination task. They demonstrate a higher statistical sensitivity, compared to their Fourier counterparts, in capturing significant and relevant functional interactions in the infraslow regime and modulations from rest to task. Notably, the consistent overall increase in functional connectivity assessed from fractal dynamics from rest to task correlated with a change in temporal dynamics as well as with improved performance in task completion, which suggests that the complex-wavelet weighted Phase Lag index is the sole index is able to capture brain plasticity in the infraslow scale-free regime.
Collapse
Affiliation(s)
- Daria La Rocca
- CEA, NeuroSpin, University of Paris-Saclay, Paris, France.,Inria Saclay Île-de-France, Parietal, University of Paris-Saclay, Paris, France
| | - Herwig Wendt
- IRIT, CNRS, University of Toulouse, Toulouse, France
| | - Virginie van Wassenhove
- CEA, NeuroSpin, University of Paris-Saclay, Paris, France.,INSERM U992, Collège de France, University of Paris-Saclay, Paris, France
| | - Philippe Ciuciu
- CEA, NeuroSpin, University of Paris-Saclay, Paris, France.,Inria Saclay Île-de-France, Parietal, University of Paris-Saclay, Paris, France
| | - Patrice Abry
- Univ. Lyon, ENS de Lyon, Univ. Claude Bernard, CNRS, Laboratoire de Physique, Lyon, France
| |
Collapse
|
5
|
Two-step wavelet-based estimation for Gaussian mixed fractional processes. STATISTICAL INFERENCE FOR STOCHASTIC PROCESSES 2018. [DOI: 10.1007/s11203-018-9190-z] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
|