1,206 research outputs found
Uniform growth of groups acting on Cartan-Hadamard spaces
Let be an -dimensional simply connected manifold of pinched sectional
curvature . There exist a positive constant such
that for any finitely generated discrete group acting on , then
either is virtually nilpotent or the algebraic entropy
Testing the isotropy of high energy cosmic rays using spherical needlets
For many decades, ultrahigh energy charged particles of unknown origin that
can be observed from the ground have been a puzzle for particle physicists and
astrophysicists. As an attempt to discriminate among several possible
production scenarios, astrophysicists try to test the statistical isotropy of
the directions of arrival of these cosmic rays. At the highest energies, they
are supposed to point toward their sources with good accuracy. However, the
observations are so rare that testing the distribution of such samples of
directional data on the sphere is nontrivial. In this paper, we choose a
nonparametric framework that makes weak hypotheses on the alternative
distributions and allows in turn to detect various and possibly unexpected
forms of anisotropy. We explore two particular procedures. Both are derived
from fitting the empirical distribution with wavelet expansions of densities.
We use the wavelet frame introduced by [SIAM J. Math. Anal. 38 (2006b) 574-594
(electronic)], the so-called needlets. The expansions are truncated at scale
indices no larger than some , and the distances between
those estimates and the null density are computed. One family of tests (called
Multiple) is based on the idea of testing the distance from the null for each
choice of , whereas the so-called PlugIn approach is
based on the single full expansion, but with thresholded wavelet
coefficients. We describe the practical implementation of these two procedures
and compare them to other methods in the literature. As alternatives to
isotropy, we consider both very simple toy models and more realistic
nonisotropic models based on Physics-inspired simulations. The Monte Carlo
study shows good performance of the Multiple test, even at moderate sample
size, for a wide sample of alternative hypotheses and for different choices of
the parameter . On the 69 most energetic events published by the
Pierre Auger Collaboration, the needlet-based procedures suggest statistical
evidence for anisotropy. Using several values for the parameters of the
methods, our procedures yield -values below 1%, but with uncontrolled
multiplicity issues. The flexibility of this method and the possibility to
modify it to take into account a large variety of extensions of the problem
make it an interesting option for future investigation of the origin of
ultrahigh energy cosmic rays.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS619 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Differentiable Rigidity under Ricci curvature lower bound
In this article we prove a differentiable rigidity result. Let and
be two closed -dimensional Riemannian manifolds ()
and be a continuous map of degree . We furthermore assume that
the metric is real hyperbolic and denote by the diameter of
. We show that there exists a number such that if the Ricci curvature of the metric is bounded below by
and its volume satisfies \vol_g (Y)\leqslant (1+\varepsilon)
\vol_{g_0} (X) then the manifolds are diffeomorphic. The proof relies on
Cheeger-Colding's theory of limits of Riemannian manifolds under lower Ricci
curvature bound.Comment: 33 pages, 1 dessi
L'informatique oblige à repenser la classification des sciences : questions à Gilles Dowek. On a longtemps confondu l'informatique avec ses usages, questions à Gérard Berry ; propos recueillis par Dominique Chouchan
National audienceL'informatique est-elle une science ? Discipline encore jeune, une soixantaine d'années d'existence seulement, son statut épistémologique se démarque de celui des sciences plus anciennes
Application of coding theory to interconnection networks
AbstractWe give a few examples of applications of techniques and results borrowed from error-correcting codes to problems in graphs and interconnection networks. The degree and diameter of Cayley graphs with vertex set (Z2Z)r are investigated. The asymptotic case is dealt with in Section 2. The robustness, or fault tolerance, of the n-cube interconnection network is studied in Section 3
Rigidity of amalgamated product in negative curvature
International audienceLet be the fundamental group of a compact n-dimensional riemannian manifold X of sectional curvature bounded above by -1. We suppose that is a free product of its subgroup A and B over the amalgamated subgroup C. We prove that the critical exponent of C satisfies . The equality happens if and only if there exist an embedded compact hypersurface Y in X , totally geodesic, of constant sectional curvature -1, with fundamental group C and which separates X in two connected components whose fundamental groups are A and B. Similar results hold if is an HNN extension, or more generally if acts on a simplicial tree without fixed point
Poincar\'e inequality on complete Riemannian manifolds with Ricci curvature bounded below
We prove that complete Riemannian manifolds with polynomial growth and Ricci
curvature bounded from below, admit uniform Poincar\'e inequalities. A global,
uniform Poincar\'e inequality for horospheres in the universal cover of a
closed, -dimensional Riemannian manifold with pinched negative sectional
curvature follows as a corollary.Comment: 20 pages, 2 fugure
3D Facial Visualization Through Adaptive Spread Spectrum Synchronous Scalable (A4S) Data Hiding
International audienceAn adaptive spread spectrum synchronous scalable(A4S) data hiding strategy is being put forward to integrate the disparate 3D facial visualization data, into a single JPEG2000 format file with the aim to cater diverse clients in various bandwidth scenarios. The method is both robust and imperceptible in the sense that the robustness of the spread spectrum (SS) is coupled with the removable embedding that ensures highest possible visualization quality. The SS embedding of the DWT-domain 2.5D facial model is carried out in the transform domain YCrCb components, of the 2D texture, from the coding stream of JPEG2000 codec just after the DWT stage. High depth map quality is ensured through the adaptation of synchronization during embedding that would exclude some highest frequency subbands. The results show that the method can be exploited for video-surveillance and video-conference applications
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