Search results for "variant"

An optimized algorithm of image stitching in the case of a multi-modal probe for monitoring the evolution of scars

2013

International audience; We propose a new system that makes possible to monitor the evolution of scars after the excision of a tumorous dermatosis. The hardware part of this system is composed of a new optical innovative probe with which two types of images can be acquired simultaneously: an anatomic image acquired under a white light and a functional one based on autofluorescence from the protoporphyrin within the cancer cells. For technical reasons related to the maximum size of the area covered by the probe, acquired images are too small to cover the whole scar. That is why a sequence of overlapping images is taken in order to cover the required area. The main goal of this paper is to des…

Integrability and Non Integrability of Some n Body Problems

2016

International audience; We prove the non integrability of the colinear 3 and 4 body problem, for any positive masses. To deal with resistant cases, we present strong integrability criterions for 3 dimensional homogeneous potentials of degree −1, and prove that such cases cannot appear in the 4 body problem. Following the same strategy, we present a simple proof of non integrability for the planar n body problem. Eventually, we present some integrable cases of the n body problem restricted to some invariant vector spaces.

Laminations and tilings of the Hyperbolic upper half plane

2005

This thesis is devoted to the study of dynamical systems associated with tilings of theEuclidean plane or of the Hyperbolic half-plane. A such tiling codes an action of a group ofisometries (namely the group of translations of the plane or the group of affine maps) on a compactmetric space $\Omega$ such that the properties of this action are related with the combinatoricproperties of the tiling. The behaviors of the actions obtained by this way are really various. Insome cases, like for example for the Penrose's tiling, this action is free and minimal. This givesto the set $\Omega$ a structure of a specific lamination called {\it solenoid}. This space islocally the product of a Cantor set w…

Compressed Drinfeld associators

2004

Drinfeld associator is a key tool in computing the Kontsevich integral of knots. A Drinfeld associator is a series in two non-commuting variables, satisfying highly complicated algebraic equations - hexagon and pentagon. The logarithm of a Drinfeld associator lives in the Lie algbera L generated by the symbols a,b,c modulo [a,b]=[b,c]=[c,a]. The main result is a description of compressed associators that satisfy the compressed pentagon and hexagon in the quotient L/[[L,L],[L,L]]. The key ingredient is an explicit form of Campbell-Baker-Hausdorff formula in the case when all commutators commute.

On the classification of CAT(0) structures for the 4-string braid group

2005

This paper is concerned with the class of so-called CAT(0) groups, namely, those groups that admit a geometric (i.e., properly discontinuous, co-compact, and isometric) action on some CAT(0) space. More precisely, we are interested in knowing to what extent it is feasible to classify the geometric CAT(0) actions of a given group (up to, say, equivariant homothety of the space). A notable example of such a classification is the flat torus theorem, which implies that the minimal geometric CAT(0) actions of the free abelian group Z (n ≥ 1) are precisely the free actions by translations of Euclidean space E. Typically, however, a given group will have uncountably many nonequivalent actions, mak…

A cubic defining algebra for the Links-Gould polynomial

2012

We define a finite-dimensional cubic quotient of the group algebra of the braid group, endowed with a (essentially unique) Markov trace which affords the Links-Grould invariant of knots and links. We investigate several of its properties, and state several conjectures about its structure.

On listening to atonal variants of two Piano Sonatas by Beethoven

2009

International audience; We investigated the contribution of tonal relationships to the perception of musical ideas and to the feelings of "arousal." Two excerpts of piano sonatas by Beethoven and two atonal variants were used as experimental stimuli. This manipulation destroyed the tonal relationships but preserved both the local and global temporal organization (rhythm and formal). Listeners were asked to indicate the onset of musical ideas, to estimate the arousing properties of the music in a continuous response task, and to rate the similarity of the pieces. A drastic change in the pitch structure strongly affected judgments of similarity. However, it had no effect on the segmentation o…

A new invariant-based method for building biomechanical behavior laws - Application to an anisotropic hyperelastic material with two fiber families

2013

Abstract In this article, we present a general constructive and original approach that allows us to calculate the invariants associated with an anisotropic hyperelastic material made of two families of collagen fibers. This approach is based on mathematical techniques from the theory of invariants: • Definition of the material symmetry group. • Analytical calculation of a set of generators using the Noether’s theorem. • Analytical calculation of an integrity basis. • Comparison between the proposed invariants and the classical ones.

On the projective geometry of entanglement and contextuality

2019

Statistical consequences of the Devroye inequality for processes. Applications to a class of non-uniformly hyperbolic dynamical systems

2005

In this paper, we apply Devroye inequality to study various statistical estimators and fluctuations of observables for processes. Most of these observables are suggested by dynamical systems. These applications concern the co-variance function, the integrated periodogram, the correlation dimension, the kernel density estimator, the speed of convergence of empirical measure, the shadowing property and the almost-sure central limit theorem. We proved in \cite{CCS} that Devroye inequality holds for a class of non-uniformly hyperbolic dynamical systems introduced in \cite{young}. In the second appendix we prove that, if the decay of correlations holds with a common rate for all pairs of functio…