The fundamental pro-groupoid of an affine 2-scheme

A natural question in the theory of Tannakian categories is: What if you don't remember \Forget? Working over an arbitrary commutative ring $R$, we prove that an answer to this question is given by the functor represented by the \'etale fundamental groupoid \pi_1(\spec(R)), i.e.\ the separable absolute Galois group of $R$ when it is a field. This gives a new definition for \'etale \pi_1(\spec(R)) in terms of the category of $R$-modules rather than the category of \'etale covers. More generally, we introduce a new notion of "commutative 2-ring" that includes both Grothendieck topoi and symmetric monoidal categories of modules, and define a notion of $\pi_1$ for the corresponding "affine 2-schemes." These results help to simplify and clarify some of the peculiarities of the \'etale fundamental group. For example, \'etale fundamental groups are not "true" groups but only profinite groups, and one cannot hope to recover more: the "Tannakian" functor represented by the \'etale fundamental group of a scheme preserves finite products but not all products.Comment: 46 pages + bibliography. Diagrams drawn in Tik

Indirect comparison of interventions using published randomised trials: systematic review of PDE-5 inhibitors for erectile dysfunction

BACKGROUND: There are no randomised and properly blinded trials directly comparing one PDE-5 inhibitor with another in a normal home setting. Valid indirect comparisons with a common comparator must examine equivalent doses, similar duration, similar populations, with the same outcomes reported in the same way. METHODS: Published randomised, double-blind trials of oral PDE-5 inhibitors for erectile dysfunction were sought from reference lists in previous reviews and electronic searching. Analyses of efficacy and harm were carried out for each treatment, and results compared where there was a common comparator and consistency of outcome reporting, using equivalent doses. RESULTS: Analysis was limited by differential reporting of outcomes. Sildenafil trials were clinically and geographically more diverse. Tadalafil and vardenafil trials tended to use enriched enrolment. Using all trials, the three interventions were similar for consistently reported efficacy outcomes. Rates of successful intercourse for sildenafil, tadalafil and vardenafil were 65%, 62%, and 59%, with placebo rates of 23–28%. The rates of improved erections were 76%, 75% and 71%, respectively, with placebo rates of 22–24%, and NNTs of 1.9 or 2.0. Reporting of withdrawals was less consistent, but all-cause withdrawals for sildenafil, tadalafil and vardenafil were 8% 13% and 20%. All three drugs were well tolerated, with headache being the most commonly reported event at 13–17%. There were few serious adverse events. CONCLUSION: There were differences between trials in outcomes reported, limiting comparisons, and the most useful outcomes were not reported. For common outcomes there was similar efficacy between PDE-5 inhibitors

Hardness, function, emotional well-being, satisfaction and the overall sexual experience in men using 100-mg fixed-dose or flexible-dose sildenafil citrate

The prescribing information for sildenafil citrate (VIAGRA, Pfizer, New York, NY, USA) recommends flexible dosing (50 mg initially, adjusted to 100 or 25 mg based on effectiveness and tolerability) in most men with erectile dysfunction (ED). In many men, however, 100 mg may be the most appropriate initial dose because it would reduce the need for titration and could prevent discouragement and treatment abandonment should 50 mg be insufficient. Results of two previously published double-blind, placebo-controlled sildenafil trials of similar design except for a fixed-dose vs flexible-dose regimen were analyzed. Relative to the flexible-dose, approximately one-third more men were satisfied with an initial and fixed dose of 100 mg. In addition, tolerability was similar, and improvements from baseline in outcomes on validated, ED-specific, patient-reported questionnaires were either similar (erectile function and the percentage of completely hard and fully rigid erections) or greater (emotional well-being and the overall sexual experience). The similarity in outcomes is not surprising given that almost 90% of the men in the flexible-dose trial titrated to 100 mg after 2 weeks. These data suggest prescription of an initial dose of 100 mg for men with ED, except in those for whom it is inappropriate

Identifying Highly Conserved and Highly Differentiated Gene Ontology Categories in Human Populations

Detecting and interpreting certain system-level characteristics associated with human population genetic differences is a challenge for human geneticists. In this study, we conducted a population genetic study using the HapMap genotype data to identify certain special Gene Ontology (GO) categories associated with high/low genetic difference among 11 Hapmap populations. Initially, the genetic differences in each gene region among these populations were measured using allele frequency, linkage disequilibrium (LD) pattern, and transferability of tagSNPs. The associations between each GO term and these genetic differences were then identified. The results showed that cellular process, catalytic activity, binding, and some of their sub-terms were associated with high levels of genetic difference, and genes involved in these functional categories displayed, on average, high genetic diversity among different populations. By contrast, multicellular organismal processes, molecular transducer activity, and some of their sub-terms were associated with low levels of genetic difference. In particular, the neurological system process under the multicellular organismal process category had low levels of genetic difference; the neurological function also showed high evolutionary conservation between species in some previous studies. These results may provide a new insight into the understanding of human evolutionary history at the system-level