Nicolas B. Garnier
Chargé de Recherche, CNRS
Information Theory
This long-running project aims at applying Information Theory to the study of physical systems, especially those labeled as "complex", but more generally non-linear systems where statistical approach is one of the few tools that are expected to be relevant, once linear approaches have been ruled out.
In this respect, I believe a rethinking of original ideas and concepts is worth exploring, as are connexions and similarities with other, a priori distinct, ideas and concepts.
Amongst several goals are the description in Information Theoretical terms of multi-scale systems, and the exploration of causality relations.
- In fluid turbulence: in collaboration with Stéphane Roux, and Carlos Granero-Belichon, we propose a new perspective on turbulence:
- using the Shannon entropy rate, we propose a coherent description of homogeneous turbulence within the K41 (monofractal) viewpoint. An arXiv preprint is available (published in EuroPhysics Letters).
- using the Kullback-Leibler divergence, we propose an efficient measure of intermittency, and hence probe the K62 (multifractal) viewpoint. An arXiv preprint is available (published in Physical Review E).
- we gradually enhanced this approach by refining the tools, to probe and quantify efficiently non-stationarity and intermittency.
- In signal processing / inforation processing: we explore how information theory quantities can be used to probe high-order dependencies, i.e., beyond mere two-point correlations. We also tackled how to analyze non-stationary processes.
- first, we proposed a performant estimator of the entropy rate, using its close relation to auto-mutual information (GRETSI 2017), and then we used it as a building block of other tools.
- arXiv preprint describing tools to assess refined dependencies of any order in signal temporal dynamics,
and giving an illustration of how auto-mutual nformation permits to discriminate between several different non Gaussian processes, having exactly the same marginal distribution and covariance function.
- arXiv preprint describing how to directly measure some properties of a non-stationary signal (with stationary increments) by using an extended ergodic asumption, and using global statistics.
- arXiv preprint describing how the subtle differences between the entropy rate of a signal on one hand and the entropy of the increments of this signal on the other hand, can be exploited to quantify the non-statinoarity of the signal, or equivalently the roughness of ts time evolution.
- In fetal medecine: we aim at providing tools to "measure" the well-being of the fetus, using recordings of its heart rate.
More precisely, the goal is to detect as early as possible fetal acidosis or fetal cardiovascular decompensation.
In collaboration with Stéphane Roux, Patrice Abry and Muriel Doret, we proposed new tools to analyse fetal heart rate (FHR). Compared to previous approaches (the most successful of these approaches were based on Approximate entropy and Sample entropy), our analysis showed that entropy rate and mutual information might better predict abnormal heart behaviors leading to acidosis.
- Two articles were presented at the Annual International Conference of the IEEE Engineering in Medicine and Biology Society,
in 2014 and
in 2017.
- A larger article, including a description of our viewpoint, was published in a special issue entitled "Entropy and cardiac Physics II" of the journal "Entropy" (2017).
In collaboration with Martin G. Frasch, we extended this study to early detect cardiovascular decompensation:
- An open-access article (Frontiers in Pediatrics, Neonatalogy) shows how to measure a distance from the "healthy" fetus state.
Synchronization
- How do globally coupled Stuart-Landau oscillators synchronize? In collaboration with Chaoqing Wang, we studied how adding a new freedom degree to oscillators (considering also the radius instead of the phase alone as in the Kuramoto model) can lead to a sub-critical transition to synchronization.
An arXiv preprint is available.
- One (out of many possible) application of synchronization in Biology is to explain physiological properties of cell assemblies. Besides the uterus, detailed below, is the cochlea, of which one may explain the very sensitive selectivity with an ad-hoc model.
An arXiv preprint is available.
Modeling the uterus
- arXiv preprint reporting the effect of increased coupling between cells over maturation of the uterus.
This work in collaboration with Jinshan Xu, Alain Pumir, Rajeev Singh and Sitabhra Sinha has been published in Phys. Rev. Lett., and has received some advertisement : in APS Physics and in Physics World.
- arXiv preprint reporting multistability in a system of coupled Fitzhugh-Nagumo equations. In itself, this work is an exploration of the effects of spatial correlations on bifurcations, via a local mean-field approach. This application of statistical physics may be of interest to the study and description of biological systems like the uterus.
- arXiv preprint studying the role of cellular coupling in the spontaneous generation of electrical activity in uterine tissue. This work presents a physiological model involving more than 20 variables, and more than 120 parameters.
This work in collaboration with Jinshan Xu, Alain Pumir, Rajeev Singh, Shakti N. Menon and Sitabhra Sinha has been published in PloS One.
- arXiv preprint studying the influence of cells densities gradients (and hence coupling gradients) in such systems, and how these gradients may influence the direction of propagation of activity.
Collective Free Improvisation (model and experiments)
- With Clément Canonne, we proposed a model for collective free improvisation,
using complex systems to describe the organisation of an improvisation piece in coherent and non-coherent sequences.
- We also performed experiments (recording Collective Free Improvisations under some specific protocol) in order to decipher the relations between individual decisions taken by the musicians and the global structure of the musical piece.
This work has been published in Journal of New Music Research.
Fluctuations in systems out of (or even far from) equilibrium / stochastic thermodynamics
-
An introduction to this topic (pdf slides) that I gave at the
GDR Phenix
meeting on November 30th 2006.
- Experimental measurements of the fluctuations of the work W given to
and the heat Q dissipated by an harmonic oscillator in contact with a thermostat,
together with an analytical derivation of the the probability density function of W and Q.
Fluctuation Theorems for those two quantities are studied :
- arXiv preprint for the work W (letter).
- arXiv preprint for the heat Q (letter).
- arXiv preprint of a full report on fluctuations of W and Q,
with a formulation of the first principle, the study of transient evolutions and steady
states (with a linear or sinusoidal time-prescription of the driving), and the definition
of the distance from equilibrium.
- arXiv preprint Fluctuations in a resistor :
Fluctuation Dissipation Theorem (FDT) and Fluctuation Theorems (FT) for work and heat
have been tested on a model electrical system.
- arXiv preprint presenting a novel
method (from Pierre Gaspard)
to measure entropy production from time series, and how this has been exploited on our experimental data.
- arXiv preprint presenting experimental measurements
of extreme fluctuations of large negative amplitude in two turbulent flows, and how those
fluctuations verify the Fluctuation Theorem.
Fluid turbulence
- Related with the stochastic thermodynamics approach above, an arXiv preprint reporting a measure of effective temperature of Turbulence, with Antoine Naert.
- With C. Granero and S. Roux, we applied analog forecasting methods to turbulent velocity time series, which allows a characterization of intermittency based on predictability via innovation. A short summary using experimental data is in this HAL preprint and a longer article also using shell model data in this HAL preprint.
- Related to the information theory approach above, we show how to detect the
anisotropy in a turbulent channel flow in this HAL preprint, where we reported that scaling properties depend on the direction of analysis.
- see also the "Information Theory" section above.
Instabilities in spatially extended systems
- arXiv preprint reporting how to quantify the asymetry oof convective rolls in the marine atmospheric boundary layer, with former PhD student C. Granero.
- see also the "Previous Research Topics" section below.
See this separate page for a short description.
In the (very short!) description of research topics above are given sorted links to open-access pre-prints (ArXiv or HAL) or open-access journals websites).
A chronological (but incomplete) list of my pre-prints is available on ArXiv.
Published versions are listed and linked on a separate page.
Positions
Diplomas
|
Last update: February 10th, 2025.
|
|
