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No abstract

L(R)R becomes a nondegenerate real quadratic form.. Such a form. has a signature (r/, r_), where r/ is the number of positive eigenvalues and r_ is the number of negative eigenvalues we also call this the signature of L. Of course, r-r++r_ is the rank of L since L is nondegenerate. L is indefinite if r/ r_ =0.Let (+, --} be a group with two elements, with identity +. We define two natural homomorphisms det, spin O(L(R)R)--.{ +, } as follows det (a) is the sign of the determinant of a, and spin (a) is the sign of the real spinor norm. of a. More precisely, since the Cartan-Dieudonn theorem guarantees that O(L(R)R) is generated by reflections in non-isotropic elements, if a is the reflection in x e L(R)R, then det (a)= --, while spin (a)-+ (or --) if q(x)>O (or q(x)O).These homomorphisms lead to our natural subgroups o O(L(R)R). Define O//(L(R)R) to be the kernel o (det, spin). For a, e {+,--} with (a, ):/:(+, +)we then define a group O(L(R)R) containing O//(L(R)R) by specifying that O(L(R)R)/O//(L(R)R) be generated by any element a e O(L(R)R) such that det (a)=a and spin (a)=fl. (If no such element exists, which can only happen if L is definite, we set O(L(R)R)=O//(L(R)R).

HIV-associated neurocognitive disorders (HAND) describes different levels of neurocognitive impairment, which are a common complication of HIV infection. The most severe of these, HIV-associated dementia (HIV D), has decreased in incidence since the introduction of combination antiretroviral therapy (cART), while an increase in the less severe, minor neurocognitive disorder (MND), is now seen. The neuropathogenesis of HAND is not completely understood, however macrophages (MΦ)s/microglia are believed to play a prominent role in the development of the more severe HIV-D. Here, we report evidence of neuroinflammation in autopsy tissues from patients with HIV infection and varying degrees of neurocognitive impairment but without HIV encephalitis (HIVE). MΦ/microglial and astrocyte activation is less intense but similar to that seen in HIVE, one of the neuropathologies underlying HIV-D. MΦs and microglia appear to be activated, as determined by CD163, CD16 and HLA-DR expression, many having a rounded or ramified morphology with thickened processes, classically associated with activation. Astrocytes also show considerable morphological alterations consistent with an activated state and have increased expression of GFAP and vimentin, as compared to seronegative controls. Interestingly, in some areas, astrocyte activation appears to be limited to perivascular locations, suggesting events at the blood-brain barrier may influence astrocyte activity. In contrast to HIVE, productive HIV infection was not detectable by tyramide signal-amplified immunohistochemistry or in situ hybridization in the CNS of HIV infected persons without encephalitis. These findings suggest significant CNS inflammation, even in the absence of detectable virus production, is a common mechanism between the lesser and more severe HIV-associated neurodegenerative disease processes and supports the notion that MND and HIV-D are a continuum of the same disease process.