264 research outputs found
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 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
Recommended from our members
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 is depending on the frequency. In this contribution, we describe the multiscale fractional Brownian motions which present a parameter 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
DĂ©mographie 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 ..
- …