Scaling of Information in Turbulence

We propose a new perspective on Turbulence using Information Theory. We compute the entropy rate of a turbulent velocity signal and we particularly focus on its dependence on the scale. We first report how the entropy rate is able to describe the distribution of information amongst scales, and how one can use it to isolate the injection, inertial and dissipative ranges, in perfect agreement with the Batchelor model and with a fBM model. In a second stage, we design a conditioning procedure in order to finely probe the asymmetries in the statistics that are responsible for the energy cascade. Our approach is very generic and can be applied to any multiscale complex system.Comment: in Europhysics Letters, 201

Wavelet-based multifractal analysis of dynamic infrared thermograms to assist in early breast cancer diagnosis

Breast cancer is the most common type of cancer among women and despite recent advances in the medical field, there are still some inherent limitations in the currently used screening techniques. The radiological interpretation of screening X-ray mammograms often leads to over-diagnosis and, as a consequence, to unnecessary traumatic and painful biopsies. Here we propose a computer-aided multifractal analysis of dynamic infrared (IR) imaging as an efficient method for identifying women with risk of breast cancer. Using a wavelet-based multi-scale method to analyze the temporal fluctuations of breast skin temperature collected from a panel of patients with diagnosed breast cancer and some female volunteers with healthy breasts, we show that the multifractal complexity of temperature fluctuations observed in healthy breasts is lost in mammary glands with malignant tumor. Besides potential clinical impact, these results open new perspectives in the investigation of physiological changes that may precede anatomical alterations in breast cancer development

Plankton networks driving carbon export in the oligotrophic ocean

The biological carbon pump is the process by which CO 2 is transformed to organic carbon via photosynthesis, exported through sinking particles, and finally sequestered in the deep ocean. While the intensity of the pump correlates with plankton community composition, the underlying ecosystem structure driving the process remains largely uncharacterized. Here we use environmental and metagenomic data gathered during the Tara Oceans expedition to improve our understanding of carbon export in the oligotrophic ocean. We show that specific plankton communities, from the surface and deep chlorophyll maximum, correlate with carbon export at 150 m and highlight unexpected taxa such as Radiolaria and alveolate parasites, as well as Synechococcus and their phages, as lineages most strongly associated with carbon export in the subtropical, nutrient-depleted, oligotrophic ocean. Additionally, we show that the relative abundance of a few bacterial and viral genes can predict a significant fraction of the variability in carbon export in these regions

Exploring the deviations from scale-invariance of spatial distributions of buildings using a Geographically Weighted Fractal Analysis. An application to twenty French middle-size metropolitan areas

In the early twentieth century a handful of French geographers and historians famously suggested that mainland France comprised two agrarian systems: enclosed field systems with scattered settlements in the central and western France, and openfield systems with grouped settlements in eastern France. This division between grouped and scattered settlements can still be found on the outskirts of urban areas. The objective of this paper is to determine whether the shape of urban areas varies with the type of built patterns in their periphery. To this end, we identify and characterise the local and global deviations from scale-invariance of built patterns in metropolitan France. We propose a new method –Geographically Weighted Fractal Analysis – that can characterize built patterns at a fine spatial resolution without making any a priori distinction between urban patterns and suburban or rural patterns. By applying GWFA to the spatial distribution of buildings throughout mainland France we identify six geographically consistent types of built patterns that are distinctive in the way buildings are either concentrated or dispersed across scales. The relationship between the local built textures and the global shape of twenty metropolitan areas is then analysed statistically. It is found that the proportion of dispersed (or concentrated) outer suburban built patterns in metropolitan areas is closely related to the distance threshold that marks the morphological limit of their urban areas

Spatial distribution of human population in France: exploring the modifiable areal unit problem using multifractal analysis

International audienceCase studies in geography are strongly dependent on the size of the spatial units used for the analysis. This has been expressed as the Modifiable Areal Unit Problem (MAUP): whatever the phenomenon under consideration, it is impossible to identify a single spatial partition that would be most appropriate to analyze it. In this respect, multifractal analysis may be an interesting tool for geographers. It integrates not just a series of nested spatial resolutions, as fractal analysis does, but also a series of points of view about the quantity of information contained in each spatial unit. In this article, we first expose the mathematical bases of multifractal analysis and we describe how it applies to geographical analyses. We insist on the mathematical notion of dimension, which allows us to describe how multifractal parameters can be used to quantify the MAUP. Then, we use the method to characterize the spatial distribution of population density in France. The main result is a typology map of population density that uses the MAUP as a descriptive tool. This map allows the joint identification of several phenomena: the main cities, the rural settlement patterns, and several types of periurban settlement patterns

A Kullback-Leibler divergence measure of intermittency: application to turbulence

For generic systems exhibiting power law behaviors, and hence multiscale dependencies, we propose a new, and yet simple, tool to analyze multifractality and intermittency, after noticing that these concepts are directly related to the deformation of a probability density function from Gaussian at large scales to non-Gaussian at smaller scales. Our framework is based on information theory, and uses Shannon entropy and Kullback-Leibler divergence. We propose an extensive application to three-dimensional fully developed turbulence, seen here as a paradigmatic complex system where intermittency was historically defined. Moreover, the concepts of scale invariance and multifractality were extensively studied in this field and, most importantly, benchmarked. We compute our measure on experimental Eulerian velocity measurements, as well as on synthetic processes and a phenomenological model of fluid turbulence.Our approach is very general and does not require any underlying model of the system, although it can probe the relevance of such a model

Evidence for inherent nonlinearity in temporal rainfall

We examine the underlying structure of high resolution temporal rainfall by comparing the observed series with surrogate series generated by a invertible nonlinear transformation of a linear process. We document that the scaling properties and long range magnitude correlations of high resolution temporal rainfall series are inconsistent with an inherently linear model, but are consistent with the nonlinear structure of a multiplicative cascade model. This is in contrast to current studies that have reported for spatial rainfall a lack of evidence for a nonlinear underlying structure. The proposed analysis methodologies, which consider two-point correlation statistics and also do not rely on higher order statistical moments, are shown to provide increased discriminatory power as compared to standard moment-based analysis

On the nightglow polarisation for space weather exploration

International audienceWe present here observations of the polarisation of four auroral lines in the auroral oval and in the polar cusp using a new ground polarimeter called Petit Cru. Our results confirm the already known polarisation of the red line, and show for the first time that the three other lines observed here (namely 557.7 nm, 391.4 nm and 427.8 nm) are polarised as well up to a few percent. We show that in several circumstances, this polarisation is linked to the local magnetic activity and to the state of the ionosphere through the electron density measured with EISCAT. However, we also show that the contribution of light pollution from nearby cities via scattering can not be ignored and can play an important role in polarisation measurements. This series of observations questions the geophysical origin of the polarisation. It also leaves open its relation to the magnetic field orientation and to the state of both the upper atmosphere and the troposphere

Hair element profile as an indicator of wildlife population health and demographics

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