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SINDy is a method for learning system of differential equations from data by solving a sparse linear regression optimization problem [Brunton, Proctor, and Kutz, Proc. Natl. Acad. Sci. USA 113, 3932 (2016)PNASA60027-842410.1073/pnas.1517384113]. In this article, we propose an extension of the SINDy method that learns systems of differential equations in cases where some of the variables are not observed. Our extension is based on regressing a higher order time derivative of a target variable onto a dictionary of functions that includes lower order time derivatives of the target variable. We evaluate our method by measuring the prediction accuracy of the learned dynamical systems on synthetic data and on a real data set of temperature time series provided by the Réseau de Transport d'Électricité. Our method provides high quality short-term forecasts and it is orders of magnitude faster than competing methods for learning differential equations with latent variables.

The Reseau de Transport d'Electricit\'e (RTE) is the French main electricity network operational manager and dedicates large number of resources and efforts towards understanding climate time series data. We discuss here the problem and the methodology of grouping and selecting representatives of possible climate scenarios among a large number of climate simulations provided by RTE. The data used is composed of temperature times series for 200 different possible scenarios on a grid of geographical locations in France. These should be clustered in order to detect common patterns regarding temperatures curves and help to choose representative scenarios for network simulations, which in turn can be used for energy optimisation. We first show that the choice of the distance used for the clustering has a strong impact on the meaning of the results: depending on the type of distance used, either spatial or temporal patterns prevail. Then we discuss the difficulty of fine-tuning the distance choice (combined with a dimension reduction procedure) and we propose a methodology based on a carefully designed index., Comment: 19 pages, 14 figures

In this paper, we present a study of the behavior of new RF-exposimeter measurement methods based on linear regression as a function of frequency and distance change. For this, we use a realistic human model (Gustav) exposed to the radiation of a base station antenna. The frequency bands used are GSM, DCS and LTE-Wimax. The distance varies from the near field zone to the far field zone. The errors induced by the human body have been evaluated. The study showed that errors increase with frequency and decrease in Far Field zone. But in general, the proposed methods have a good response to variations in frequency and distance.

In this paper, we consider the estimation of a change-point for possibly high-dimensional data in a Gaussian model, using a maximum likelihood method. We are interested in how dimension reduction can affect the performance of the method. We provide an estimator of the change-point that has a minimax rate of convergence, up to a logarithmic factor. The minimax rate is in fact composed of a fast rate —dimension-invariant— and a slow rate —increasing with the dimension. Moreover, it is proved that considering the case of sparse data, with a Sobolev regularity, there is a bound on the separation of the regimes above which there exists an optimal choice of dimension reduction, leading to the fast rate of estimation. We propose an adaptive dimension reduction procedure based on Lepski’s method and show that the resulting estimator attains the fast rate of convergence. Our results are then illustrated by a simulation study. In particular, practical strategies are suggested to perform dimension reduction.

Calibration of RF exposimeter is a serious problem when conventional measurement methods are used, especially when the morphology of the user, workers or public, changes a lot. In this paper we present a study of the behavior of new measurement methods based on linear regression with respect to morphological change. For this we use three models: Child, Gustav and Emma of different sex, age and dimensions. The study is conducted in the near field for a base station antenna at the DCS band. The study showed a low dependence of the proposed methods on morphology.

We focus on wind power modeling using machine learning techniques. We show on real data provided by the wind energy company Ma{i}a Eolis, that parametric models, even following closely the physical equation relating wind production to wind speed are outperformed by intelligent learning algorithms. In particular, the CART-Bagging algorithm gives very stable and promising results. Besides, as a step towards forecast, we quantify the impact of using deteriorated wind measures on the performances. We show also on this application that the default methodology to select a subset of predictors provided in the standard random forest package can be refined, especially when there exists among the predictors one variable which has a major impact.

Les representations sociales sont a la base de notre vie psychique. C’est a elles que nous faisons le plus facilement et le plus spontanement appel pour nous reperer dans notre environnement physique et humain. Situees a l’interface du psychologique et du sociologique, elles sont enracinees au cœur du dispositif social. Quelles representations de l’autre et des relations sociales englobent-elles ? En quoi constituent-elles des elements fondamentaux de notre epistemologie, et notamment de l’elaboration du sens commun ?

The Personal Dosimeter is a portable device that allows measurement of electromagnetic field levels. In this work we propose a new method for non-invasive evaluation of the whole body averaged body specific absorption rate of the human body (${SAR}_{wba}$) from only the personal dosimeter measurement. This new method is based on linear regression to reduce errors due to the presence of the human body on the measurement. The results show a SAR assessment with very low error rates in the order of 5%, a reduction in the average error of 5 times for a morphology of a middle adult man and 9 times for a morphology of a child of 10 years old.

In this work, we present a study of the behavior of new measurement methods based on linear regression with respect to morphological, frequency and separation distance change. For this we use three models: Child, Gustav and Emma of different sex, age and dimensions.The study is conducted in the near field for a base station antenna at the DCS band. The study showed a low dependence of the proposed methods on morphology. After this, we study the frequency dependence of the RF exposimeter error and the effect of the distance between the sources and the human body. The frequency bands used are GSM, DCS and LTE-Wimax. The distance varies from the near field zone to the far field zone. The study showed that errors increase with frequency and decrease in Far Field zone. The main original contribution of the proposed approach is that the procedure of calibration of the personal exposimeter is based on statistical analyzes taking into account morphology, frequency and distance between the body and the source of exposure.

A total of three measurement methods are presented for low-voltage cables characterization in the frequency band used for power line communication (9–500 kHz). In this paper, the cables are considered as composed of a set of simple transmission lines free from mutual coupling. The characteristic impedance and propagation constant as a function of the frequency have been assessed. In the first method, an LCR meter has been used to measure the input impedance of the cable, while the output is step-by-step short and open circuited. In the second method, a network analyzer in a reflection mode is used to measure the input impedance. The third method consists of measuring the scattering matrix (S-matrix) of the cable using a network analyzer. These measurement methods have been validated and compared using a well-known coaxial cable. In addition, the measurement reproducibility and the drift of the measuring devices are evaluated. Finally, two power low-voltage cable technologies, underground cable and overhead line twisted cable, are characterized by the most accurate method. The cables losses have been also investigated .

Antenna arrays for directionnding (DF) are usually designed and tested in controlled environments such as anechoic chambers. However, antenna pattern may change signicantly when antennas are placed in their operational environment. In such perturbing close context, the antennas calibration validity becomes a major issue which can lead to DF performance degradation and costly recalibration process. This paper presents an innovative design and implementation of a non-disturbing solution for quasi-real time antenna monitoring. The proposed system is based on optically modulated scattering (OMS) technique. Its capacity to detect the presence of various types of obstacles, which signicantly perturb the antenna radiation pattern, is evaluated. A relation between monitoring mode and DF mode measurement signals is established. Finally, a design and sizing of the overall system is proposed.

We consider the problem of estimating the density of observations taking values in classical or nonclassical spaces such as manifolds and more general metric spaces. Our setting is quite general but also sufficiently rich in allowing the development of smooth functional calculus with well localized spectral kernels, Besov regularity spaces, and wavelet type systems. Kernel and both linear and nonlinear wavelet density estimators are introduced and studied. Convergence rates for these estimators are established, which are analogous to the existing results in the classical setting of real-valued variables.

Climate analysis is extremely useful to understand better the differences of electricity consumption within the French territory and to help electricity consumption forecasts. Using a large historical data base of 14 years of meteorological observations, this work aims to study a segmentation of the French territory based on functional time series of temperature and wind. In a first step, 14 clustering instances, one for each year, have been performed using, for each instance, one year of data. Each year, the clustering exhibits several homogeneous and spatially connected regions. Benefits of this approach let to study the stability of the previous regions over the years and to highlight the inter-annual variability of the French climate. A final aggregation of all clustering instances shows a segmentation map in easily interpretable, geographically connected climate zones over the last years. Especially, we observe that the number of clusters remains extremely stable through the years. Exhibiting stable homogeneous regions bring then some valuable knowledge for potentially installing new wind or solar farms on the French territory.

Vivre ensemble implique une part inevitable de conflit car celui-ci fait partie des formes « normales » et meme necessaires de la relation a l’autre au meme titre que la bonne entente. Beaucoup de facteurs y concourent : la divergence d’interets, de points de vue ; la defense identitaire, territoriale ou ethique ; le desir de pouvoir et de possession... Pourtant, il fait souvent peur car il genere des affects negatifs (anxiete, colere, peur du rejet...). A l’inverse, certains s’installent durablement dans le conflit et n’arrivent plus a en sortir. Car une fois declenche, un conflit a tendance a s’autoentretenir. Cependant, il peut jouer un role positif. C’est souvent l’occasion de redefinir les bases de la relation.

International audience; —A matrix method which takes into account the probe positioning errors in cylindrical and spherical near-field (NF) measurement techniques is proposed. The near-field irregularities made impossible the determination of the cylindrical or spherical wave expansion from the measured data using classical techniques based on 2D Discrete Fourier Transformation (2D-DFT) in cylindrical case (CC) and orthogonality properties in spherical case (SC). The irregularities can be randomly distributed but known and the matrix method expresses the linear relation between the measured near-field and the corresponding cylindrical or spherical modal expansion coefficients. Once the coefficients of the cylindrical and the spherical wave expansions are known the far-field of the antenna under test (AUT) is easily determined. Accuracy of the matrix method is numerically studied as a function of the irregularities magnitude and for different noise levels (data Signal to Noise Ratio). Also, experimental results have shown the efficiency of the proposed technique.

As the use of electromagnetic fields (EM) by radiofrequency (RF) has increased along with increased use of mobile phones, the potential health risks have also been widely discussed. In this study, the effect of fixing metal braces on teeth, was examined by giving the variation of the specific absorption rate (SAR) distribution and antenna parameters. Three halfwave dipole antennas were used as the exposure source for the GSM-900, DCS-1800 and 5G-3600 Mhz frequency bands, in the presence of a three-dimensional 3-D heterogeneous model of the human head named Zubal. All simulations are performed with CST Microwave Studio 2017.

This paper presents measurement technique for antenna pattern including gain on planar near field ranges. Although rigorous formalism exists, this formalism is not commonly used due to its complexity. Simplified equations are derived in particular antenna under test (AUT) polarizations and kind of probe corresponding to the most common cases. Application of the technique to a reflector antenna (about 30 dB @ 12 GHz) is described. Analysis of measured results is carried out to illustrate a comparison of accuracy of this technique with results obtained with a compact range.

International audience; Objective: As well known, using a single body worn sensor exposimeter introduces systematic errors on the measurement of the incident free space electric field strength. This is because the body creates around it high, intermediate and low level field zones, which depend on the direction of arrival of the incident field. The goal of this work is to propose an efficient method for the reduction of these errors. Methods: After classifying the perturbations induced by the body on the measured electric and magnetic fields thanks to realistic numerical simulations, we then propose a two-sensor setup in conjunction with simple semi-empirical correction formulas, in order to compensate these perturbations. Results: At 942 MHz, when the two sensors are placed in any opposite sides of the body at chest height, the worst case, maximum and average errors respectively decrease to 12% and 3% compared to 83% and 22% for measurement techniques using a single sensor, or 32% and 11% when using the average value of the measurements. Conclusion: The error related to the measurement in the presence of the body was significantly reduced by the proposed method making use of two opposite sensors, E-field and H-field at the chest. Significance: The conformity of exposure to EMF in terms of reference values according to the ICNIRP is given in the abscence of the human body. The interest of this work lies in the reduction of the errors made when measuring the field in the presence of the body.

A selection procedure with no optimization step called LOLA, for Learning Out of Leaders with Adaptation is proposed. LOLA is an auto-driven algorithm with two thresholding steps. The consistency of the LOL procedure (the non adaptive version of LOLA) is proved under sparsity conditions and simulations are conducted to illustrate the practical good performances of LOLA. The behavior of the algorithm is studied when instrumental variables are artificially added without a priori significant connection to the model. Finally, the problem of empirically verifying the conditional convergence hypothesis used in economics concerning the growth rate is studied. To avoid unnecessary discussion about the choice and the pertinence of instrumental variables, the model is embedded in a very high dimensional setting. Using the LOLA algorithm, a solution for modeling the link between the growth rate and the initial level of the gross domestic product is provided and the convergence hypothesis is empirically proved.

A matrix method is developed to calculate the antennas radiation pattern from near-field data measured over arbitrary surfaces. The principle of the matrix method is to determine the modal expansion coefficients by solving a system of linear equations. The number of required measured samples is deduced from the number of modes considering the cylindrical or the spherical wave expansion of antenna radiated fields. Once the modal coefficients are known, the far field of the antenna under test (AUT) is obtained. The matrix method has been implemented, and its potentialities are evaluated using two specific arbitrary surfaces (square section cylinder surrounding the AUT and a closed cylinder). Numerical (dipoles array) and experimental (base station antenna) results are provided to illustrate the efficiency and the stability of the proposed method.

International audience

International audience; A mobile telephone user's exposure to the radio-frequency electromagnetic field depends heavily on the power their telephone radiates, which can vary widely according to requests from the base station. This study presents the design and development of a system called SYstem for Radiated POwer Measurement (SYRPOM), which measures the power radiated by a mobile telephone. This study also describes the tests carried out on the system itself and gives the results of two measuring campaigns it has been possible to perform in this way. The first such campaign consisted of assessing the mean power received by a typical mobile telephone user carrying out various activities. The second campaign was aimed at (1) comparing the mean radiated power when stationary and when moving and (2) assessing and contrasting different models of handsets in terms of the mean radiated power. The SYRPOM has proved to be a flexible, easy-to-use high-performance and innovative tool for carrying out this kind of studies.

The uncertainty on the far field, obtained from antenna planar near field measurements, due to the limitation of the dynamic range is investigated by means of numerical analysis. The dynamic range is usually limited by the noise and the receiver nonlinearity. The noise floor limits low level signals and the receiver nonlinearity degrades high level signals. Consequently, the effects of noise and nonlinearity were studied and a quantitative evaluation was established.

A matrix method is developed to calculate the antennas radiation pattern from near-field (NF) data measured over arbitrary surfaces. The principle of the matrix method is to determine the modal expansion coefficients (MEC) by solving a system of linear equations. The number of required measured samples is deduced from the number of modes considering the cylindrical wave expansion (CWE) of antenna radiated fields. Once the modal coefficients are known, the far-field (FF) of the antenna under test (AUT) is obtained. The matrix method has been implemented, and its potentialities are evaluated using a specific arbitrary surface (square section cylinder surrounding the AUT). Numerical (dipoles array) and experimental (base station antenna) results are provided to illustrate the efficiency and the stability of the proposed method.

The uncertainty on the far field, obtained from antenna planar near field measurements, due to position errors is investigated by means of numerical analysis. These errors include periodic and random errors in both transverse and longitudinal directions. The errors' behavior was established and the most critical mechanical errors were determined.

In this paper we present a matrix method which takes into account the probe positioning errors in spherical near-field (NF) measurement. The NF irregularities made the determination of the spherical wave expansion (SWE) from the measured data using the Fast Fourier Transformation (FFT) impossible. The irregularities can be randomly distributed but known. The matrix method expresses the linear relation between the measured NF and the corresponding SWE coefficients. The accuracy of the proposed method is numerically studied as a function of the irregularities magnitude and for different noise levels (data Signal to Noise Ratio). Also, experimental results have shown the efficiency of the proposed technique.

The personal radiofrequency dosimeters are increasingly used for the workers exposure estimation to the electromagnetic radiations in terms of reference level of the fields. The presence of the human body at the vicinity of dosimeter compromises its measurement accuracy. In this paper, the study of interaction between personal radiofrequency dosimeter and human body is presented. First, we deal with the error introduced by the presence of the body and an approach to reduce this impact by adding elements in the dosimeter structure. Indeed, by introducing a metal ground plane and optimizing the height of antenna-ground plane, we can estimate at 10 % close the level of incidental field, that is to say a considerable reduction impact of the body on the dosimeter. We also study the stability of the intrinsic characteristics of the dosimeter (isotropy and front to back ratio). Different simulations were performed in the GSM 900 band with the finite integration technique. In the context of the design of worn-body radiofrequency dosimeters it’s very useful to master these interaction results.

Constructing a good approximation to a function of many variables suffers from the “curse of dimensionality”. Namely, functions on ℝN with smoothness of order s can in general be captured with accuracy at most O(n−s/N) using linear spaces or nonlinear manifolds of dimension n. If N is large and s is not, then n has to be chosen inordinately large for good accuracy. The large value of N often precludes reasonable numerical procedures. On the other hand, there is the common belief that real world problems in high dimensions have as their solution, functions which are more amenable to numerical recovery. This has led to the introduction of models for these functions that do not depend on smoothness alone but also involve some form of variable reduction. In these models it is assumed that, although the function depends on N variables, only a small number of them are significant. Another variant of this principle is that the function lives on a low dimensional manifold. Since the dominant variables (respectively the manifold) are unknown, this leads to new problems of how to organize point queries to capture such functions. The present paper studies where to query the values of a ridge function f(x)=g(a⋅x) when both a∈ℝN and g∈C[0,1] are unknown. We establish estimates on how well f can be approximated using these point queries under the assumptions that g∈Cs[0,1]. We also study the role of sparsity or compressibility of a in such query problems.

L’identite subjective se construit en grande partie dans le contact avec les autres ; la quete de reconnaissance identitaire constitue donc une des dynamiques fondamentales des relations interpersonnelles. Cette quete peut revetir des formes variees qui se declinent en une serie de «besoins» identitaires et territoriaux qui sont autant de sources de conflits possibles. Cette etude montre que ces conflits s’inscrivent dans un contexte social et relationnel et s’articulent a plusieurs niveaux: celui de la protection (de soi et de son territoire) et des mecanismes de defense relationnels; celui de la definition de la relation et des rapports de places; celui des representations sociales liees a la culture des protagonistes (culture ethnique ou familiale, groupes d’appartenance ou de reference...). Ils s’ancrent aussi dans l’histoire personnelle des individus et dans les scenarios de vie qu’ils ont forges, scenarios qui les conduisent a s’engager dans des voies relationnelles qui ne les satisfont que partiellement mais qu’ils croient inexorables.

International audience; —The matrix method for the calculation of antenna far-field using irregularly distributed near-field measurement data is presented. The matrix method is based on the determination of the plane wave expansion (PWE) coefficients from the irregular near-field samples using a matrix form that connects the radiated field with the corresponding plane wave spectrum. The plane wave spectrum is used to determine the far-field of the antenna under test (AUT). The matrix method has been implemented, and its potentialities are presented. The validations using analytical radiating model (dipoles array) and experimental measurement (X band standard gain horn antenna) results have demonstrated the efficiency and stability of the proposed method.

We study the regularity of centered Gaussian processes $$(Z_x( \omega ))_{x\in M}$$ , indexed by compact metric spaces $$(M, \rho )$$ . It is shown that the almost everywhere Besov regularity of such a process is (almost) equivalent to the Besov regularity of the covariance $$K(x,y) = {\mathbb E}(Z_x Z_y)$$ under the assumption that (i) there is an underlying Dirichlet structure on M that determines the Besov regularity, and (ii) the operator K with kernel K(x, y) and the underlying operator A of the Dirichlet structure commute. As an application of this result, we establish the Besov regularity of Gaussian processes indexed by compact homogeneous spaces and, in particular, by the sphere.