The topological meaning of Levinson's theorem, half-bound states included

We propose to interpret Levinson's theorem as an index theorem. This exhibits its topological nature. It furthermore leads to a more coherent explanation of the corrections due to resonances at thresholds.Comment: 4 page

The Cauchy problems for Einstein metrics and parallel spinors

We show that in the analytic category, given a Riemannian metric $g$ on a hypersurface $M\subset \Z$ and a symmetric tensor $W$ on $M$, the metric $g$ can be locally extended to a Riemannian Einstein metric on $Z$ with second fundamental form $W$, provided that $g$ and $W$ satisfy the constraints on $M$ imposed by the contracted Codazzi equations. We use this fact to study the Cauchy problem for metrics with parallel spinors in the real analytic category and give an affirmative answer to a question raised in B\"ar, Gauduchon, Moroianu (2005). We also answer negatively the corresponding questions in the smooth category.Comment: 28 pages; final versio

Stratification of the orbit space in gauge theories. The role of nongeneric strata

Gauge theory is a theory with constraints and, for that reason, the space of physical states is not a manifold but a stratified space (orbifold) with singularities. The classification of strata for smooth (and generalized) connections is reviewed as well as the formulation of the physical space as the zero set of a momentum map. Several important features of nongeneric strata are discussed and new results are presented suggesting an important role for these strata as concentrators of the measure in ground state functionals and as a source of multiple structures in low-lying excitations.Comment: 22 pages Latex, 1 figur

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

Direct TLR2 Signaling Is Critical for NK Cell Activation and Function in Response to Vaccinia Viral Infection

Natural killer (NK) cells play an essential role in innate immune control of poxviral infections in vivo. However, the mechanism(s) underlying NK cell activation and function in response to poxviruses remains poorly understood. In a mouse model of infection with vaccinia virus (VV), the most studied member of the poxvirus family, we identified that the Toll-like receptor (TLR) 2-myeloid differentiating factor 88 (MyD88) pathway was critical for the activation of NK cells and the control of VV infection in vivo. We further showed that TLR2 signaling on NK cells, but not on accessory cells such as dendritic cells (DCs), was necessary for NK cell activation and that this intrinsic TLR2-MyD88 signaling pathway was required for NK cell activation and played a critical role in the control of VV infection in vivo. In addition, we showed that the activating receptor NKG2D was also important for efficient NK activation and function, as well as recognition of VV-infected targets. We further demonstrated that VV could directly activate NK cells via TLR2 in the presence of cytokines in vitro and TLR2-MyD88-dependent activation of NK cells by VV was mediated through the phosphatidylinositol 3-kinase (PI3K)-extracellular signal-regulated kinase (ERK) pathway. Taken together, these results represent the first evidence that intrinsic TLR signaling is critical for NK cell activation and function in the control of a viral infection in vivo, indicate that multiple pathways are required for efficient NK cell activation and function in response to VV infection, and may provide important insights into the design of effective strategies to combat poxviral infections

Herpes simplex encephalitis is linked with selective mitochondrial damage; a post-mortem and in vitro study

Herpes simplex virus type-1 (HSV-1) encephalitis (HSE) is the most commonly diagnosed cause of viral encephalitis in western countries. Despite antiviral treatment, HSE remains a devastating disease with high morbidity and mortality. Improved understanding of pathogenesis may lead to more effective therapies. Mitochondrial damage has been reported during HSV infection in vitro. However, whether it occurs in the human brain and whether this contributes to the pathogenesis has not been fully explored. Minocycline, an antibiotic, has been reported to protect mitochondria and limit brain damage. Minocycline has not been studied in HSV infection. In the first genome-wide transcriptomic study of post-mortem human HSE brain tissue, we demonstrated a highly preferential reduction in mitochondrial genome (MtDNA) encoded transcripts in HSE cases (n = 3) compared to controls (n = 5). Brain tissue exhibited a significant inverse correlation for immunostaining between cytochrome c oxidase subunit 1 (CO1), a MtDNA encoded enzyme subunit, and HSV-1; with lower abundance for mitochondrial protein in regions where HSV-1 was abundant. Preferential loss of mitochondrial function, among MtDNA encoded components, was confirmed using an in vitro primary human astrocyte HSV-1 infection model. Dysfunction of cytochrome c oxidase (CO), a mitochondrial enzyme composed predominantly of MtDNA encoded subunits, preceded that of succinate dehydrogenase (composed entirely of nuclear encoded subunits). Minocycline treated astrocytes exhibited higher CO1 transcript abundance, sustained CO activity and cell viability compared to non-treated astrocytes. Based on observations from HSE patient tissue, this study highlights mitochondrial damage as a critical and early event during HSV-1 infection. We demonstrate minocycline preserves mitochondrial function and cell viability during HSV-1 infection. Minocycline, and mitochondrial protection, offers a novel adjunctive therapeutic approach for limiting brain cell damage and potentially improving outcome among HSE patients