Optimal eigenvalues estimate for the Dirac operator on domains with boundary

We give a lower bound for the eigenvalues of the Dirac operator on a compact domain of a Riemannian spin manifold under the \MIT bag boundary condition. The limiting case is characterized by the existence of an imaginary Killing spinor.Comment: 10 page

The Maslov index in weak symplectic functional analysis

We recall the Chernoff-Marsden definition of weak symplectic structure and give a rigorous treatment of the functional analysis and geometry of weak symplectic Banach spaces. We define the Maslov index of a continuous path of Fredholm pairs of Lagrangian subspaces in continuously varying Banach spaces. We derive basic properties of this Maslov index and emphasize the new features appearing.Comment: 34 pages, 13 figures, 45 references, to appear in Ann Glob Anal Geom. The final publication will be available at http://www.springerlink.com. arXiv admin note: substantial text overlap with arXiv:math/040613

Gravitational and axial anomalies for generalized Euclidean Taub-NUT metrics

The gravitational anomalies are investigated for generalized Euclidean Taub-NUT metrics which admit hidden symmetries analogous to the Runge-Lenz vector of the Kepler-type problem. In order to evaluate the axial anomalies, the index of the Dirac operator for these metrics with the APS boundary condition is computed. The role of the Killing-Yano tensors is discussed for these two types of quantum anomalies.Comment: 23 page

The spectral shift function and spectral flow

This paper extends Krein's spectral shift function theory to the setting of semifinite spectral triples. We define the spectral shift function under these hypotheses via Birman-Solomyak spectral averaging formula and show that it computes spectral flow.Comment: 47 page

A randomized double-blind control study of early intra-coronary autologous bone marrow cell infusion in acute myocardial infarction: the REGENERATE-AMI clinical trial

Clinical trials suggest that intracoronary delivery of autologous bone marrow-derived cells (BMCs) 1–7 days post-acute myocardial infarction (AMI) may improve left ventricular (LV) function. Earlier time points have not been evaluated. We sought to determine the effect of intracoronary autologous BMC on LV function when delivered within 24 h of successful reperfusion therapy. Methods and results A multi-centre phase II randomized, double-blind, and placebo-controlled trial. One hundred patients with anterior AMI and significant regional wall motion abnormality were randomized to receive either intracoronary infusion of BMC or placebo (1:1) within 24 h of successful primary percutaneous intervention (PPCI). The primary endpoint was the change in left ventricular ejection fraction (LVEF) between baseline and 1 year as determined by advanced cardiac imaging. At 1 year, although LVEF increased compared with baseline in both groups, the between-group difference favouring BMC was small (2.2%; 95% confidence interval, CI: −0.5 to 5.0; P = 0.10). However, there was a significantly greater myocardial salvage index in the BMC-treated group compared with placebo (0.1%; 95% CI: 0.0–0.20; P = 0.048). Major adverse events were rare in both treatment groups. Conclusion The early infusion of intracoronary BMC following PPCI for patients with AMI and regional wall motion abnormality leads to a small non-significant improvement in LVEF when compared with placebo; however, it may play an important role in infarct remodelling and myocardial salvage.UK Stem Cells Foundation, the Heart Cells Foundation, and Barts and the London Charity. Funding to pay the Open Access publication charges for this article was provided by the Barts Cardiovascular Biomedical Research Unit (CVBRU)

Modified differentials and basic cohomology for Riemannian foliations

We define a new version of the exterior derivative on the basic forms of a Riemannian foliation to obtain a new form of basic cohomology that satisfies Poincar\'e duality in the transversally orientable case. We use this twisted basic cohomology to show relationships between curvature, tautness, and vanishing of the basic Euler characteristic and basic signature.Comment: 20 pages, references added, minor corrections mad

A K-theoretical Invariant and Bifurcation for Homoclinics of Hamiltonian Systems

We revisit a K-theoretical invariant that was invented by the first author some years ago for studying multiparameter bifurcation of branches of critical points of functionals. Our main aim is to apply this invariant to investigate bifurcation of homoclinic solutions of families of Hamiltonian systems which are parametrised by tori