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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.

The effect of chronic oral opioids on hypothalamus-pituitary-gonadal axis in women, and on bone mineral density (BMD) in men and women is not known. The objective of this cross-sectional study was to determine the effect of long-term oral opioids on gonadal status and BMD in male and female patients with chronic non-cancer pain (CNCP). We included 26 community-dwelling CNCP patients, 12 men and 14 premenopausal women, treated with oral opioids for at least one year. We obtained Visual Analogue Scale for pain score, BMD and plasma LH and FSH in all patients; menstrual history and estradiol in women; free androgen index and total and free testosterone in men. Men were older then women (p < 0.05) and had used opioids for a longer period (7.2 ± 3.8 and 4.1 ± 1.8 years, respectively; p < 0.05), but there was no difference in opioid dose or pain score between sexes. The prevalence of hypogonadism was high in men (75 %), while only 21 % of the women reported oligoor amenorrhea indicating hypogonadism (P < 0.01, between sexes). Osteopenia was found in 50 % of men and 21 % of women (p = NS). We conclude that in CNCP patients receiving chronic opioid therapy there is a much higher prevalence of hypogonadism in men then in women. This needs to be considered clinical practice.

Interventions for implementation of thromboprophylaxis in hospitalized patients at risk for venous thromboembolism (Review)

Background Increased vitamin D levels, as reflected by 25-hydroxy vitamin D (25OHD) measurements, have been proposed to protect against COVID-19 based on in vitro, observational, and ecological studies. However, vitamin D levels are associated with many confounding variables, and thus associations described to date may not be causal. Vitamin D Mendelian randomization (MR) studies have provided results that are concordant with large-scale vitamin D randomized trials. Here, we used 2-sample MR to assess evidence supporting a causal effect of circulating 25OHD levels on COVID-19 susceptibility and severity. Methods and findings Genetic variants strongly associated with 25OHD levels in a genome-wide association study (GWAS) of 443,734 participants of European ancestry (including 401,460 from the UK Biobank) were used as instrumental variables. GWASs of COVID-19 susceptibility, hospitalization, and severe disease from the COVID-19 Host Genetics Initiative were used as outcome GWASs. These included up to 14,134 individuals with COVID-19, and up to 1,284,876 without COVID-19, from up to 11 countries. SARS-CoV-2 positivity was determined by laboratory testing or medical chart review. Population controls without COVID-19 were also included in the control groups for all outcomes, including hospitalization and severe disease. Analyses were restricted to individuals of European descent when possible. Using inverse-weighted MR, genetically increased 25OHD levels by 1 standard deviation on the logarithmic scale had no significant association with COVID-19 susceptibility (odds ratio [OR] = 0.95; 95% CI 0.84, 1.08; p = 0.44), hospitalization (OR = 1.09; 95% CI: 0.89, 1.33; p = 0.41), and severe disease (OR = 0.97; 95% CI: 0.77, 1.22; p = 0.77). We used an additional 6 meta-analytic methods, as well as conducting sensitivity analyses after removal of variants at risk of horizontal pleiotropy, and obtained similar results. These results may be limited by weak instrument bias in some analyses. Further, our results do not apply to individuals with vitamin D deficiency. Conclusions In this 2-sample MR study, we did not observe evidence to support an association between 25OHD levels and COVID-19 susceptibility, severity, or hospitalization. Hence, vitamin D supplementation as a means of protecting against worsened COVID-19 outcomes is not supported by genetic evidence. Other therapeutic or preventative avenues should be given higher priority for COVID-19 randomized controlled trials.

Interventions for implementation of thromboprophylaxis in hospitalized patients at risk for venous thromboembolism (Review)