Laboratoire de Physique de l'ENS de Lyon

Empirical mode decomposition (EMD) has recently been pioneered by Huang et al. for adaptively representing nonstationary signals as sums of zero-mean amplitude modulation frequency modulation components. In order to better understand the way EMD behaves in stochastic situations involving broadband noise, we report here on numerical experiments based on fractional Gaussian noise. In such a case, it turns out that EMD acts essentially as a dyadic filter bank resembling those involved in wavelet decompositions. It is also pointed out that the hierarchy of the extracted modes may be similarly exploited for getting access to the Hurst exponent.

Huang’s data-driven technique of Empirical Mode Decomposition (EMD) is presented, and issues re-lated to its effective implementation are discussed. A number of algorithmic variations, including new stopping criteria and an on-line version of the al-gorithm, are proposed. Numerical simulations are used for empirically assessing performance elements related to tone identification and separation. The obtained results support an interpretation of the method in terms of adaptive constant-Q filter banks. 1

The physics of one-dimensional interacting bosonic systems is reviewed. Beginning with results from exactly solvable models and computational approaches, the concept of bosonic Tomonaga-Luttinger liquids relevant for one-dimensional Bose fluids is introduced, and compared with Bose-Einstein condensates existing in dimensions higher than one. The effects of various perturbations on the Tomonaga-Luttinger liquid state are discussed as well as extensions to multicomponent and out of equilibrium situations. Finally, the experimental systems that can be described in terms of models of interacting bosons in one dimension are discussed.

A wavelet-based tool for the analysis of long-range dependence and a related semi-parametric estimator of the Hurst parameter is introduced. The estimator is shown to be unbiased under very general conditions, and efficient under Gaussian assumptions. It can be implemented very efficiently allowing the direct analysis of very large data sets, and is highly robust against the presence of deterministic trends, as well as allowing their detection and identification. Statistical, computational, and numerical comparisons are made against traditional estimators including that of Whittle. The estimator is used to perform a thorough analysis of the long-range dependence in Ethernet traffic traces. New features are found with important implications for the choice of valid models for performance evaluation. A study of mono versus multifractality is also performed, and a preliminary study of the stationarity with respect to the Hurst parameter and deterministic trends.

BACKGROUND: Little quantitative information is available on the mixing patterns of children in school environments. Describing and understanding contacts between children at school would help quantify the transmission opportunities of respiratory infections and identify situations within schools where the risk of transmission is higher. We report on measurements carried out in a French school (6-12 years children), where we collected data on the time-resolved face-to-face proximity of children and teachers using a proximity-sensing infrastructure based on radio frequency identification devices. METHODS AND FINDINGS: Data on face-to-face interactions were collected on Thursday, October 1(st) and Friday, October 2(nd) 2009. We recorded 77,602 contact events between 242 individuals (232 children and 10 teachers). In this setting, each child has on average 323 contacts per day with 47 other children, leading to an average daily interaction time of 176 minutes. Most contacts are brief, but long contacts are also observed. Contacts occur mostly within each class, and each child spends on average three times more time in contact with classmates than with children of other classes. We describe the temporal evolution of the contact network and the trajectories followed by the children in the school, which constrain the contact patterns. We determine an exposure matrix aimed at informing mathematical models. This matrix exhibits a class and age structure which is very different from the homogeneous mixing hypothesis. CONCLUSIONS: We report on important properties of the contact patterns between school children that are relevant for modeling the propagation of diseases and for evaluating control measures. We discuss public health implications related to the management of schools in case of epidemics and pandemics. Our results can help define a prioritization of control measures based on preventive measures, case isolation, classes and school closures, that could reduce the disruption to education during epidemics.

BACKGROUND: Digital networks, mobile devices, and the possibility of mining the ever-increasing amount of digital traces that we leave behind in our daily activities are changing the way we can approach the study of human and social interactions. Large-scale datasets, however, are mostly available for collective and statistical behaviors, at coarse granularities, while high-resolution data on person-to-person interactions are generally limited to relatively small groups of individuals. Here we present a scalable experimental framework for gathering real-time data resolving face-to-face social interactions with tunable spatial and temporal granularities. METHODS AND FINDINGS: We use active Radio Frequency Identification (RFID) devices that assess mutual proximity in a distributed fashion by exchanging low-power radio packets. We analyze the dynamics of person-to-person interaction networks obtained in three high-resolution experiments carried out at different orders of magnitude in community size. The data sets exhibit common statistical properties and lack of a characteristic time scale from 20 seconds to several hours. The association between the number of connections and their duration shows an interesting super-linear behavior, which indicates the possibility of defining super-connectors both in the number and intensity of connections. CONCLUSIONS: Taking advantage of scalability and resolution, this experimental framework allows the monitoring of social interactions, uncovering similarities in the way individuals interact in different contexts, and identifying patterns of super-connector behavior in the community. These results could impact our understanding of all phenomena driven by face-to-face interactions, such as the spreading of transmissible infectious diseases and information.

This paper investigates how the empirical mode decomposition (EMD), a fully data-driven technique recently introduced for decomposing any oscillatory waveform into zero-mean components, behaves in the case of a composite two-tones signal. Essentially two regimes are shown to exist, depending on whether the amplitude ratio of the tones is greater or smaller than unity, and the corresponding resolution properties of the EMD turn out to be in good agreement with intuition and physical interpretation. A refined analysis is provided for quantifying the observed behaviors and theoretical claims are supported by numerical experiments. The analysis is then extended to a nonlinear model where the same two regimes are shown to exist and the resolution properties of the EMD are assessed.

The empirical mode decomposition (EMD) has been introduced quite recently to adaptively decompose nonstationary and/or nonlinear time series. The method being initially limited to real-valued time series, we propose here an extension to bivariate (or complex-valued) time series that generalizes the rationale underlying the EMD to the bivariate framework. Where the EMD extracts zero-mean oscillating components, the proposed bivariate extension is designed to extract zero-mean rotating components. The method is illustrated on a real-world signal, and properties of the output components are discussed. Free Matlab/C codes are available at http://perso.ens-lyon.fr/patrick.flandrin.

During interphase chromosomes decondense, but fluorescent in situ hybridization experiments reveal the existence of distinct territories occupied by individual chromosomes inside the nuclei of most eukaryotic cells. We use computer simulations to show that the existence and stability of territories is a kinetic effect that can be explained without invoking an underlying nuclear scaffold or protein-mediated interactions between DNA sequences. In particular, we show that the experimentally observed territory shapes and spatial distances between marked chromosome sites for human, Drosophila, and budding yeast chromosomes can be reproduced by a parameter-free minimal model of decondensing chromosomes. Our results suggest that the observed interphase structure and dynamics are due to generic polymer effects: confined Brownian motion conserving the local topological state of long chain molecules and segregation of mutually unentangled chains due to topological constraints.

The flat interface between two fluids in a vertically vibrating vessel may be parametrically excited, leading to the generation of standing waves. The equations constituting the stability problem for the interface of two viscous fluids subjected to sinusoidal forcing are derived and a Floquet analysis is presented. The hydrodynamic system in the presence of viscosity cannot be reduced to a system of Mathieu equations with linear damping. For a given driving frequency, the instability occurs only for certain combinations of the wavelength and driving amplitude, leading to tongue-like stability zones. The viscosity has a qualitative effect on the wavelength at onset: at small viscosities, the wavelength decreases with increasing viscosity, while it increases for higher viscosities. The stability threshold is in good agreement with experimental results. Based on the analysis, a method for the measurement of the interfacial tension, and the sum of densities and dynamic viscosities of two phases of a fluid near the liquid-vapour critical point is proposed.

A joint estimator is presented for the two parameters that define the long-range dependence phenomenon in the simplest case. The estimator is based on the coefficients of a discrete wavelet decomposition, improving a wavelet-based estimator of the scaling parameter (Abry and Veitch 1998), as well as extending it to include the associated power parameter. An important feature is its conceptual and practical simplicity, consisting essentially in measuring the slope and the intercept of a linear fit after a discrete wavelet transform is performed, a very fast (O(n)) operation. Under well-justified technical idealizations the estimator is shown to be unbiased and of minimum or close to minimum variance for the scale parameter, and asymptotically unbiased and efficient for the second parameter. Through theoretical arguments and numerical simulations it is shown that in practice, even for small data sets, the bias is very small and the variance close to optimal for both parameters. Closed-form expressions are given for the covariance matrix of the estimator as a function of data length, and are shown by simulation to be very accurate even when the technical idealizations are not satisfied. Comparisons are made against two maximum-likelihood estimators. In terms of robustness and computational cost the wavelet estimator is found to be clearly superior and statistically its performance is comparable. We apply the tool to the analysis of Ethernet teletraffic data, completing an earlier study on the scaling parameter alone.

We explain the emergence of organized structures in two-dimensional turbulent flows by a theory of equilibrium statistical mechanics. This theory takes into account all the known constants of the motion for the Euler equations. The microscopic states are all the possible vorticity fields, while a macroscopic state is defined as a probability distribution of vorticity at each point of the domain, which describes in a statistical sense the fine-scale vorticity fluctuations. The organized structure appears as a state of maximal entropy, with the constraints of all the constants of the motion. The vorticity field obtained as the local average of this optimal macrostate is a steady solution of the Euler equation. The variational problem provides an explicit relationship between stream function and vorticity, which characterizes this steady state. Inertial structures in geophysical fluid dynamics can be predicted, using a generalization of the theory to potential vorticity.

Genomes of eukaryotes are partitioned into domains of functionally distinct chromatin states. These domains are stably inherited across many cell generations and can be remodeled in response to developmental and external cues, hence contributing to the robustness and plasticity of expression patterns and cell phenotypes. Remarkably, recent studies indicate that these 1D epigenomic domains tend to fold into 3D topologically associated domains forming specialized nuclear chromatin compartments. However, the general mechanisms behind such compartmentalization including the contribution of epigenetic regulation remain unclear. Here, we address the question of the coupling between chromatin folding and epigenome. Using polymer physics, we analyze the properties of a block copolymer model that accounts for local epigenomic information. Considering copolymers build from the epigenomic landscape of Drosophila, we observe a very good agreement with the folding patterns observed in chromosome conformation capture experiments. Moreover, this model provides a physical basis for the existence of multistability in epigenome folding at sub-chromosomal scale. We show how experiments are fully consistent with multistable conformations where topologically associated domains of the same epigenomic state interact dynamically with each other. Our approach provides a general framework to improve our understanding of chromatin folding during cell cycle and differentiation and its relation to epigenetics.

The generalized entropies of Renyi inspire new measures for estimating signal information and complexity in the time-frequency plane. When applied to a time-frequency representation (TFR) from Cohen's class or the affine class, the Renyi entropies conform closely to the notion of complexity that we use when visually inspecting time-frequency images. These measures possess several additional interesting and useful properties, such as accounting and cross-component and transformation invariances, that make them natural for time-frequency analysis. This paper comprises a detailed study of the properties and several potential applications of the Renyi entropies, with emphasis on the mathematical foundations for quadratic TFRs. In particular, for the Wigner distribution, we establish that there exist signals for which the measures are not well defined.

We study experimentally the propagation of high-amplitude compressional waves in a chain of beads in contact, submitted or not to a small static force. In such a system, solitary waves have been theoretically predicted by Nesterenko [J. Appl. Mech. Tech. Phys. (USSR) 5, 733 (1984)]. We have built an impact generator in order to create high-amplitude waves in the chain. We observe the propagation of isolated nonlinear pulses, measure their velocity as a function of their maximum amplitude, for different applied static forces, and record their shape. In all experiments, we find good agreement between our observations and the theoretical predictions of the above reference, without using any adjustable parameter in the data analysis. We also show that the velocity measurements taken at three different nonzero applied static forces all lie on a single curve, when expressed in rescaled variables. The size of the pulses is typically one-tenth the total length of the chain. All the measurements support the identification of these isolated nonlinear pulses with the solitary waves predicted by Nesterenko.

We show that the classical Heisenberg antiferromagnet on a Kagom\'e lattice is an example of a spin nematic. By calculating the effects of thermal fluctuations around ground states, and by Monte Carlo simulations, we find entropically driven, local spin-nematic order at low temperature T with a correlation length which is divergent in the limit T\ensuremath{\rightarrow}0. Dynamical correlations are also studied, within the harmonic approximation, in the nematically ordered states.

BACKGROUND: Contacts between patients, patients and health care workers (HCWs) and among HCWs represent one of the important routes of transmission of hospital-acquired infections (HAI). A detailed description and quantification of contacts in hospitals provides key information for HAIs epidemiology and for the design and validation of control measures. METHODS AND FINDINGS: We used wearable sensors to detect close-range interactions ("contacts") between individuals in the geriatric unit of a university hospital. Contact events were measured with a spatial resolution of about 1.5 meters and a temporal resolution of 20 seconds. The study included 46 HCWs and 29 patients and lasted for 4 days and 4 nights. 14,037 contacts were recorded overall, 94.1% of which during daytime. The number and duration of contacts varied between mornings, afternoons and nights, and contact matrices describing the mixing patterns between HCW and patients were built for each time period. Contact patterns were qualitatively similar from one day to the next. 38% of the contacts occurred between pairs of HCWs and 6 HCWs accounted for 42% of all the contacts including at least one patient, suggesting a population of individuals who could potentially act as super-spreaders. CONCLUSIONS: Wearable sensors represent a novel tool for the measurement of contact patterns in hospitals. The collected data can provide information on important aspects that impact the spreading patterns of infectious diseases, such as the strong heterogeneity of contact numbers and durations across individuals, the variability in the number of contacts during a day, and the fraction of repeated contacts across days. This variability is however associated with a marked statistical stability of contact and mixing patterns across days. Our results highlight the need for such measurement efforts in order to correctly inform mathematical models of HAIs and use them to inform the design and evaluation of prevention strategies.

We report the observation of dynamo action in the von Kármán sodium experiment, i.e., the generation of a magnetic field by a strongly turbulent swirling flow of liquid sodium. Both mean and fluctuating parts of the field are studied. The dynamo threshold corresponds to a magnetic Reynolds number R(m) approximately 30. A mean magnetic field of the order of 40 G is observed 30% above threshold at the flow lateral boundary. The rms fluctuations are larger than the corresponding mean value for two of the components. The scaling of the mean square magnetic field is compared to a prediction previously made for high Reynolds number flows.

An integrable deformation of the type IIB ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{\mathrm{S}}^{5}$ superstring action is presented. The deformed field equations, Lax connection, and $\ensuremath{\kappa}$-symmetry transformations are given. The original $\mathfrak{psu}(2,2|4)$ symmetry is expected to become $q$ deformed.

BACKGROUND: The spread of infectious diseases crucially depends on the pattern of contacts between individuals. Knowledge of these patterns is thus essential to inform models and computational efforts. However, there are few empirical studies available that provide estimates of the number and duration of contacts between social groups. Moreover, their space and time resolutions are limited, so that data are not explicit at the person-to-person level, and the dynamic nature of the contacts is disregarded. In this study, we aimed to assess the role of data-driven dynamic contact patterns between individuals, and in particular of their temporal aspects, in shaping the spread of a simulated epidemic in the population. METHODS: We considered high-resolution data about face-to-face interactions between the attendees at a conference, obtained from the deployment of an infrastructure based on radiofrequency identification (RFID) devices that assessed mutual face-to-face proximity. The spread of epidemics along these interactions was simulated using an SEIR (Susceptible, Exposed, Infectious, Recovered) model, using both the dynamic network of contacts defined by the collected data, and two aggregated versions of such networks, to assess the role of the data temporal aspects. RESULTS: We show that, on the timescales considered, an aggregated network taking into account the daily duration of contacts is a good approximation to the full resolution network, whereas a homogeneous representation that retains only the topology of the contact network fails to reproduce the size of the epidemic. CONCLUSIONS: These results have important implications for understanding the level of detail needed to correctly inform computational models for the study and management of real epidemics. Please see related article BMC Medicine, 2011, 9:88.