Manifolds with small Dirac eigenvalues are nilmanifolds

a paraitre dans Annals of Global Analysis and GeometryConsider the class of $n$-dimensional Riemannian spin manifolds with bounded sectional curvatures and bounded diameter, and almost non-negative scalar curvature. Let $r=1$ if $n=2,3$ and $r=2^{[n/2]-1}+1$ if $n\geq 4$. We show that if the square of the Dirac operator on such a manifold has $r$ small eigenvalues, then the manifold is diffeomorphic to a nilmanifold and has trivial spin structure. Equivalently, if $M$ is not a nilmanifold or if $M$ is a nilmanifold with a non-trivial spin structure, then there exists a uniform lower bound on the $r$-th eigenvalue of the square of the Dirac operator. If a manifold with almost nonnegative scalar curvature has one small Dirac eigen value, and if the volume is not too small, then we show that the metric is close to a Ricci-flat metric on $M$ with a parallel spinor. In dimension $4$ this implies that $M$ is either a torus or a $K3$-surface

Manifolds with small Dirac eigenvalues are nilmanifolds

Consider the class of n-dimensional Riemannian spin manifolds with bounded sectional curvatures and diameter, and almost non-negative scalar curvature. Let r=1 if n=2,3 and r=2^{[n/2]-1}+1 if n\geq 4. We show that if the square of the Dirac operator on such a manifold has $r$ small eigenvalues, then the manifold is diffeomorphic to a nilmanifold and has trivial spin structure. Equivalently, if M is not a nilmanifold or if M is a nilmanifold with a non-trivial spin structure, then there exists a uniform lower bound on the r-th eigenvalue of the square of the Dirac operator. If a manifold with almost nonnegative scalar curvature has one small Dirac eigenvalue, and if the volume is not too small, then we show that the metric is close to a Ricci-flat metric on M with a parallel spinor. In dimension 4 this implies that M is either a torus or a K3-surface

Patient-specific modeling and analysis of the mitral valve using 3d-tee

Abstract. We describe a system dedicated to the analysis of the complex threedimensional anatomy and dynamics of an abnormal heart mitral valve using three-dimensional echocardiography to characterize the valve pathophysiology. This system is intended to aid cardiothoracic surgeons in conducting preoperative surgical planning and in understanding the outcome of “virtual” mitral valve repairs. This paper specifically addresses the analysis of threedimensional transesophageal echocardiographic imagery to recover the valve structure and predict the competency of a surgically modified valve by computing its closed state from an assumed open configuration. We report on a 3D TEE structure recovery method and a mechanical modeling approach used for the valve modeling and simulation

A Selective ATP-Binding Cassette Subfamily G Member 2 Efflux Inhibitor Revealed via High-Throughput Flow Cytometry

Chemotherapeutics tumor resistance is a principal reason for treatment failure, and clinical and experimental data indicate that multidrug transporters such as ATP-binding cassette (ABC) B1 and ABCG2 play a leading role by preventing cytotoxic intracellular drug concentrations. Functional efflux inhibition of existing chemotherapeutics by these pumps continues to present a promising approach for treatment. A contributing factor to the failure of existing inhibitors in clinical applications is limited understanding of specific substrate/inhibitor/pump interactions. We have identified selective efflux inhibitors by profiling multiple ABC transporters against a library of small molecules to find molecular probes to further explore such interactions. In our primary screening protocol using JC-1 as a dual-pump fluorescent reporter substrate, we identified a piperazine-substituted pyrazolo[1,5-a]pyrimidine substructure with promise for selective efflux inhibition. As a result of a focused structure-activity relationship (SAR)–driven chemistry effort, we describe compound 1(CID44640177), an efflux inhibitor with selectivity toward ABCG2 over ABCB1. Compound 1 is also shown to potentiate the activity of mitoxantrone in vitro as well as preliminarily in vivo in an ABCG2-overexpressing tumor model. At least two analogues significantly reduce tumor size in combination with the chemotherapeutic topotecan. To our knowledge, low nanomolar chemoreversal activity coupled with direct evidence of efflux inhibition for ABCG2 is unprecedented