Uniform growth of groups acting on Cartan-Hadamard spaces

Let $X$ be an $n$-dimensional simply connected manifold of pinched sectional curvature $-a^2 \leq K \leq -1$. There exist a positive constant $C(n,a)$ such that for any finitely generated discrete group $\Gamma$ acting on $X$, then either $\Gamma$ is virtually nilpotent or the algebraic entropy $Ent (\Gamma) \geq C(n,a)$

Differentiable Rigidity under Ricci curvature lower bound

In this article we prove a differentiable rigidity result. Let $(Y, g)$ and $(X, g_0)$ be two closed $n$-dimensional Riemannian manifolds ($n\geqslant 3$) and $f:Y\to X$ be a continuous map of degree $1$. We furthermore assume that the metric $g_0$ is real hyperbolic and denote by $d$ the diameter of $(X,g_0)$. We show that there exists a number $\varepsilon:=\varepsilon (n, d)>0$ such that if the Ricci curvature of the metric $g$ is bounded below by $-n(n-1)$ 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

Rigidity of amalgamated product in negative curvature

International audienceLet $\Gamma$ be the fundamental group of a compact n-dimensional riemannian manifold X of sectional curvature bounded above by -1. We suppose that $\Gamma$ is a free product of its subgroup A and B over the amalgamated subgroup C. We prove that the critical exponent $\delta(C)$ of C satisfies $\delta(C) \geq n-2$. 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 $\Gamma$ is an HNN extension, or more generally if $\Gamma$ 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, $n$-dimensional Riemannian manifold with pinched negative sectional curvature follows as a corollary.Comment: 20 pages, 2 fugure

Spatial hearing rendering in wireless microphone systems for binaural hearing aids

In 2015, 360 million people, including 32 million children, were suffering from hearing impairment all over the world. This makes hearing disability a major worldwide issue. In the US, the prevalence of hearing loss increased by 160% over the past generations. However, 72% of the 34 million impaired American persons (11% of the population) still have an untreated hearing loss. Among the various current solutions alleviating hearing disability, hearing aid is the only non-invasive and the most widespread medical apparatus. Combined with hearing aids, assisting listening devices are a powerful answer to address the degraded speech understanding observed in hearing-impaired subjects, especially in noisy and reverberant environments. Unfortunately, the conventional devices do not accurately render the spatial hearing property of the human auditory system, weakening their benefits. Spatial hearing is an attribute of the auditory system relying on binaural hearing. With 2 ears, human beings are able to localize sounds in space, to get information about the acoustic surroundings, to feel immersed in environments... Furthermore, it strongly contributes to speech intelligibility. It is hypothesized that recreating an artificial spatial perception through the hearing aids of impaired people might allow for recovering a part of these subjects' hearing performance. This thesis investigates and supports the aforementioned hypothesis with both technological and clinical approaches. It reveals how certain well-established signal processing methods can be integrated in some assisting listening devices. These techniques are related to sound localization and spatialization. Taking into consideration the technical constraints of current hearing aids, as well as the characteristics of the impaired auditory system, the thesis proposes a novel solution to restore a spatial perception for users of certain types of assisting listening devices. The achieved results demonstrate the feasibility and the possible implementation of such a functionality on conventional systems. Additionally, this thesis examines the relevance and the efficiency of the proposed spatialization feature towards the enhancement of speech perception. Via a clinical trial involving a large number of patients, the artificial spatial hearing shows to be well appreciated by disabled persons, while improving or preserving their current hearing abilities. This can be considered as a prominent contribution to the current scientific and technological knowledge in the domain of hearing impairment

Etching suspended superconducting hybrid junctions from a multilayer

A novel method to fabricate large-area superconducting hybrid tunnel junctions with a suspended central normal metal part is presented. The samples are fabricated by combining photo-lithography and chemical etch of a superconductor - insulator - normal metal multilayer. The process involves few fabrication steps, is reliable and produces extremely high-quality tunnel junctions. Under an appropriate voltage bias, a significant electronic cooling is demonstrated

Spin-Valve Effect of the Spin Accumulation Resistance in a Double Ferromagnet - Superconductor Junction

We have measured the transport properties of Ferromagnet - Superconductor nanostructures, where two superconducting aluminum (Al) electrodes are connected through two ferromagnetic iron (Fe) ellipsoids in parallel. We find that, below the superconducting critical temperature of Al, the resistance depends on the relative alignment of the ferromagnets' magnetization. This spin-valve effect is analyzed in terms of spin accumulation in the superconducting electrode submitted to inverse proximity effect