A generalized Grobman-Hartman theorem

We prove that any generalized hyperbolic operator on any Banach space is structurally stable. As a consequence, we obtain a generalization of the classical Grobman-Hartman theorem.Comment: 9 page

Expansivity and Shadowing in Linear Dynamics

In the early 1970's Eisenberg and Hedlund investigated relationships between expansivity and spectrum of operators on Banach spaces. In this paper we establish relationships between notions of expansivity and hypercyclicity, supercyclicity, Li-Yorke chaos and shadowing. In the case that the Banach space is $c_0$ or $\ell_p$ ($1 \leq p < \infty$), we give complete characterizations of weighted shifts which satisfy various notions of expansivity. We also establish new relationships between notions of expansivity and spectrum. Moreover, we study various notions of shadowing for operators on Banach spaces. In particular, we solve a basic problem in linear dynamics by proving the existence of nonhyperbolic invertible operators with the shadowing property. This also contrasts with the expected results for nonlinear dynamics on compact manifolds, illuminating the richness of dynamics of infinite dimensional linear operators

Epidermal growth factor receptor mediates the vascular dysfunction but not the remodeling induced by aldosterone/salt

Pathophysiological aldosterone (aldo)/mineralocorticoid receptor signaling has a major impact on the cardiovascular system, resulting in hypertension and vascular remodeling. Mineralocorticoids induce endothelial dysfunction, decreasing vasorelaxation in response to acetylcholine and increasing the response to vasoconstrictors. Activation of the epidermal growth factor receptor (EGFR) is thought to mediate the vascular effects of aldo, but this has yet to be demonstrated in vivo. In this study, we analyzed the molecular and functional vascular consequences of aldo-salt challenge in the waved 2 mouse, a genetic model with a partial loss of EGFR tyrosine kinase activity. Deficient EGFR activity is associated with global oxidative stress and endothelial dysfunction. A decrease in EGFR activity did not affect the arterial wall remodeling process induced by aldo-salt. By contrast, normal EGFR activity was required for the aldo-induced enhancement of phenylephrine- and angiotensin II-mediated vasoconstriction. In conclusion, this in vivo study demonstrates that EGFR plays a key role in aldosterone-mediated vascular reactivity

Generalized quasiperiodic Rauzy tilings

We present a geometrical description of new canonical $d$-dimensional codimension one quasiperiodic tilings based on generalized Fibonacci sequences. These tilings are made up of rhombi in 2d and rhombohedra in 3d as the usual Penrose and icosahedral tilings. Thanks to a natural indexing of the sites according to their local environment, we easily write down, for any approximant, the sites coordinates, the connectivity matrix and we compute the structure factor.Comment: 11 pages, 3 EPS figures, final version with minor change

Effective Control of Chronic γ-Herpesvirus Infection by Unconventional MHC Class Ia–Independent CD8 T Cells

Control of virus infection is mediated in part by major histocompatibility complex (MHC) Class Ia presentation of viral peptides to conventional CD8 T cells. Although important, the absolute requirement for MHC Class Ia–dependent CD8 T cells for control of chronic virus infection has not been formally demonstrated. We show here that mice lacking MHC Class Ia molecules (K(b−/−)xD(b−/−) mice) effectively control chronic γ-herpesvirus 68 (γHV68) infection via a robust expansion of β(2)-microglobulin (β(2)-m)-dependent, but CD1d-independent, unconventional CD8 T cells. These unconventional CD8 T cells expressed: (1) CD8αβ and CD3, (2) cell surface molecules associated with conventional effector/memory CD8 T cells, (3) TCRαβ with a significant Vβ4, Vβ3, and Vβ10 bias, and (4) the key effector cytokine interferon-γ (IFNγ). Unconventional CD8 T cells utilized a diverse TCR repertoire, and CDR3 analysis suggests that some of that repertoire may be utilized even in the presence of conventional CD8 T cells. This is the first demonstration to our knowledge that β(2)-m–dependent, but Class Ia–independent, unconventional CD8 T cells can efficiently control chronic virus infection, implicating a role for β(2)-n–dependent non-classical MHC molecules in control of chronic viral infection. We speculate that similar unconventional CD8 T cells may be able to control of other chronic viral infections, especially when viruses evade immunity by inhibiting generation of Class Ia–restricted T cells

Compressed Sensing for Dose Reduction in STEM Tomography

We designed a complete acquisition-reconstruction framework to reduce the radiation dosage in 3D scanning transmission electron microscopy (STEM). Projection measurements are acquired by randomly scanning a subset of pixels at every tilt-view (i.e., random-beam STEM or RB-STEM ). High-quality images are then recovered from the randomly downsampled measurements through a regularized tomographic reconstruction framework. By fulfilling the compressed sensing requirements, the proposed approach improves the reconstruction of heavily-downsampled RB-STEM measurements over the current state-of-the-art technique. This development opens new perspectives in the search for methods permitting lower-dose 3D STEM imaging of electron-sensitive samples without degrading the quality of the reconstructed volume. A Matlab code implementing the proposed reconstruction algorithm has been made available online