Einstein Metrics on Group Manifolds and Cosets

It is well known that every compact simple group manifold G admits a bi-invariant Einstein metric, invariant under G_L\times G_R. Less well known is that every compact simple group manifold except SO(3) and SU(2) admits at least one more homogeneous Einstein metric, invariant still under G_L but with some, or all, of the right-acting symmetry broken. (SO(3) and SU(2) are exceptional in admitting only the one, bi-invariant, Einstein metric.) In this paper, we look for Einstein metrics on three relatively low dimensional examples, namely G=SU(3), SO(5) and G_2. For G=SU(3), we find just the two already known inequivalent Einstein metrics. For G=SO(5), we find four inequivalent Einstein metrics, thus extending previous results where only two were known. For G=G_2 we find six inequivalent Einstein metrics, which extends the list beyond the previously-known two examples. We also study some cosets G/H for the above groups G. In particular, for SO(5)/U(1) we find, depending on the embedding of the U(1), generically two, with exceptionally one or three, Einstein metrics. We also find a pseudo-Riemannian Einstein metric of signature (2,6) on SU(3), an Einstein metric of signature (5,6) on G_2/SU(2)_{diag}, and an Einstein metric of signature (4,6) on G_2/U(2). Interestingly, there are no Lorentzian Einstein metrics among our examples.Comment: 23 page

Autoimmunity

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66083/1/j.1365-4362.1981.tb00393.x.pd

Intranasal administration of acetylcholinesterase inhibitors

This short review outlines the rationale, challenges, and opportunities for intranasal acetylcholinesterases, in particular galantamine. An in vitro screening model facilitated the development of a therapeutically viable formulation. In vivo testing confirmed achievement of therapeutically relevant drug levels that matched or exceeded those for oral dosing, with a dramatic reduction in undesired emetic responses. Intranasal drug delivery is an effective option for the treatment of Alzheimer's disease and other central nervous system disorders

Calcium phosphate-hybridized tendon graft to enhance tendon-bone healing two years after ACL reconstruction in goats

Abstract Background We developed a novel technique to improve tendon-bone attachment by hybridizing calcium phosphate (CaP) with a tendon graft using an alternate soaking process. However, the long-term result with regard to the interface between the tendon graft and the bone is unclear. Methods We analyzed bone tunnel enlargement by computed tomography and histological observation of the interface and the tendon graft with and without the CaP hybridization 2 years after anterior cruciate ligament (ACL) reconstruction in goats using EndoButton and the postscrew technique (CaP, n = 4; control, n = 4). Results The tibial bone tunnel enlargement rates in the CaP group were lower than those in the control group (p p p Conclusions The CaP-hybridized tendon graft enhanced the tendon-bone healing 2 years after ACL reconstruction in goats. The use of CaP-hybridized tendon grafts can reduce the bone tunnel enlargement and gap area associated with the direct insertion-like formation in the interface near the joint.</p

Hamiltonian 2-forms in Kahler geometry, III Extremal metrics and stability

This paper concerns the explicit construction of extremal Kaehler metrics on total spaces of projective bundles, which have been studied in many places. We present a unified approach, motivated by the theory of hamiltonian 2-forms (as introduced and studied in previous papers in the series) but this paper is largely independent of that theory. We obtain a characterization, on a large family of projective bundles, of those `admissible' Kaehler classes (i.e., the ones compatible with the bundle structure in a way we make precise) which contain an extremal Kaehler metric. In many cases, such as on geometrically ruled surfaces, every Kaehler class is admissible. In particular, our results complete the classification of extremal Kaehler metrics on geometrically ruled surfaces, answering several long-standing questions. We also find that our characterization agrees with a notion of K-stability for admissible Kaehler classes. Our examples and nonexistence results therefore provide a fertile testing ground for the rapidly developing theory of stability for projective varieties, and we discuss some of the ramifications. In particular we obtain examples of projective varieties which are destabilized by a non-algebraic degeneration.Comment: 40 pages, sequel to math.DG/0401320 and math.DG/0202280, but largely self-contained; partially replaces and extends math.DG/050151

The attachments of the anteromedial and posterolateral fibre bundles of the anterior cruciate ligament: Part 1: tibial attachment.

Accepted versio

Live Imaging of Xwnt5A-ROR2 Complexes

Secreted molecules of the Wnt family regulate key decisions in embryogenesis and adult tissue homeostasis by activating a complex network of Wnt signaling pathways. Although the different branches of Wnt signaling have been studied for more than 25 years, fluorophore tagged constructs for live cell imaging of Wnt molecules activating the Wnt/β-catenin pathway have become available only recently. We have generated a fluorophore tagged Wnt construct of the Xenopus Wnt5a protein (Xwnt5A) with the enhanced green fluorescent protein (EGFP), Xwnt5A-EGFP. This construct activates non-canonical Wnt pathways in an endocytosis dependent manner and is capable of compensating for the loss of endogenous Xwnt5A in Xenopus embryos. Strikingly, non-canonical Wnt pathway activation was restricted to short-range signaling while an inhibitory effect was observed in transwell cell cultures taken as long-range signaling model sytem. We used our Xwnt5A-EGFP construct to analyze in vivo binding of Wnt5A to its co-receptor ROR2 on the microscopic and on the molecular level. On the microscopic level, Xwnt5A-EGFP clusters in the membrane and recruits ROR2-mCherry to these clusters. Applying dual-colour dual-focus line-scanning fluorescence correlation spectroscopy on dorsal marginal zone explants, we identified membrane tethered Xwnt5A-EGFP molecules binding to ROR2-mCherry molecules. Our data favour a model, in which membrane-tethered Wnt-5A recruits ROR2 to form large ligand/receptor clusters and signals in an endocytosis-dependent manner