Identification of the multiscale fractional Brownian motion with biomechanical applications

In certain applications, for instance biomechanics, turbulence, finance, or Internet traffic, it seems suitable to model the data by a generalization of a fractional Brownian motion for which the Hurst parameter $H$ is depending on the frequency as a piece-wise constant function. These processes are called multiscale fractional Brownian motions. In this contribution, we provide a statistical study of the multiscale fractional Brownian motions. We develop a method based on wavelet analysis. By using this method, we find initially the frequency changes, then we estimate the different parameters and afterwards we test the goodness-of-fit. Lastly, we give the numerical algorithm. Biomechanical data are then studied with these new tools

Application of plasticity theory to soil behavior : a new sand model

The representation of rheological soil behavior by constitutive equations is a now branch of soil mechanics which has been expanding for 30 years. Based on continuum mechanics, numerical methods (finite elements) and experimental techniques, this now discipline allows practicing engineers to solve complex geotechnical problems. Although all soils are constituted of discrete mineral particles, forces and displacements within them are represented by continuous stresses and strains. Most stress-strain relationships, which describe the soil behavior, are derived from plasticity theory. Originated for metals, the conventional plasticity is presented and illustrated simultaneously with a metal and a soil model. Each plasticity concept may be criticized when applied to soil. A recent theory, called "bounding surface plasticity," generalizes the conventional plasticity and describes more accurately the cyclic responses of metals and clays. This new theory is first presented and linked with the conventional plasticity, then applied to a new material, sand. Step by step a new sand model is constructed, mainly from data analysis with an interactive computer code. In its present development, only monotonic loading s are investigated. In order to verify the model ability to describe sand responses, isotropic, drained and undrained tests on the dense Sacramento River sand are simulated numerically and compared with real test results and predictions with another model. Finally the new constitutive equation, which was formulated in the p-q space for axisymmetric loadings, is generalized in the six-dimensional stress state with the assumption of isotropy and a particular Lode's angle contribution. This new model is ready to be used in finite element codes to represent a sand behavior

Algebraic Properties of Polar Codes From a New Polynomial Formalism

Polar codes form a very powerful family of codes with a low complexity decoding algorithm that attain many information theoretic limits in error correction and source coding. These codes are closely related to Reed-Muller codes because both can be described with the same algebraic formalism, namely they are generated by evaluations of monomials. However, finding the right set of generating monomials for a polar code which optimises the decoding performances is a hard task and channel dependent. The purpose of this paper is to reveal some universal properties of these monomials. We will namely prove that there is a way to define a nontrivial (partial) order on monomials so that the monomials generating a polar code devised fo a binary-input symmetric channel always form a decreasing set. This property turns out to have rather deep consequences on the structure of the polar code. Indeed, the permutation group of a decreasing monomial code contains a large group called lower triangular affine group. Furthermore, the codewords of minimum weight correspond exactly to the orbits of the minimum weight codewords that are obtained from (evaluations) of monomials of the generating set. In particular, it gives an efficient way of counting the number of minimum weight codewords of a decreasing monomial code and henceforth of a polar code.Comment: 14 pages * A reference to the work of Bernhard Geiger has been added (arXiv:1506.05231) * Lemma 3 has been changed a little bit in order to prove that Proposition 7.1 in arXiv:1506.05231 holds for any binary input symmetric channe

Definition, properties and wavelet analysis of multiscale fractional Brownian motion

International audienceIn some applications, for instance finance, biomechanics, turbulence or internet traffic, it is relevant to model data with a generalization of a fractional Brownian motion for which the Hurst parameter $H$ is depending on the frequency. In this contribution, we describe the multiscale fractional Brownian motions which present a parameter $H$ as a piecewise constant function of the frequency. We provide the main properties of these processes: long-memory and smoothness of the paths. Then we propose a statistical method based on wavelet analysis to estimate the different parameters and prove a functional Central Limit Theorem satisfied by the empirical variance of the wavelet coefficients

Histoire sociale et démographie

Jean-Pierre Bardet, directeur d’études avec Cyril Grange, chargé de recherche au CNRS Compte rendu non communiqué

Computer und Stadtgeschichte: das Beispiel Rouen

Gegenstand der Untersuchung sind Urbanisierungs- und Segregationsprozesse am Beispiel der Entwicklung der französischen Stadt Rouen im 18. Jahrhundert. Der Verfasser gibt einen kurzen Einblick in bearbeitete Quellen und Untersuchungsansatz ("Analyse der sozialen Gruppen", "maschinelle Kartierung"). (WZ

Démographie historique

Jean-Pierre Bardet, directeur d’études Lorsque l’enfant grandit Le séminaire de cette année a permis d’approfondir notre réflexion en cours sur l’histoire des grands enfants et des adolescents en poursuivant un dialogue largement amorcé au cours de la précédente année et élargi à l’automne 2000 lors d’un colloque consacré à l’enfance qui a rassemblé un grand nombre de jeunes chercheurs. Au cours de cette année, trois thèmes ont été développés. Le premier a porté sur la définition des âges et ..