Equivariant cohomology over Lie groupoids and Lie-Rinehart algebras

Using the language and terminology of relative homological algebra, in particular that of derived functors, we introduce equivariant cohomology over a general Lie-Rinehart algebra and equivariant de Rham cohomology over a locally trivial Lie groupoid in terms of suitably defined monads (also known as triples) and the associated standard constructions. This extends a characterization of equivariant de Rham cohomology in terms of derived functors developed earlier for the special case where the Lie groupoid is an ordinary Lie group, viewed as a Lie groupoid with a single object; in that theory over a Lie group, the ordinary Bott-Dupont-Shulman-Stasheff complex arises as an a posteriori object. We prove that, given a locally trivial Lie groupoid G and a smooth G-manifold f over the space B of objects of G, the resulting G-equivariant de Rham theory of f boils down to the ordinary equivariant de Rham theory of a vertex manifold relative to the corresponding vertex group, for any vertex in the space B of objects of G; this implies that the equivariant de Rham cohomology introduced here coincides with the stack de Rham cohomology of the associated transformation groupoid whence this stack de Rham cohomology can be characterized as a relative derived functor. We introduce a notion of cone on a Lie-Rinehart algebra and in particular that of cone on a Lie algebroid. This cone is an indispensable tool for the description of the requisite monads.Comment: 47 page

Prevention of anxiety among at-risk children: a systematic review and meta-analysis

Background Anxiety disorders are common, often start in childhood and run a chronic course. As such there is a need for effective prevention. Methods We conducted a systematic review and meta-analyses of randomized, controlled trials to prevent the onset of anxiety disorders in ‘at risk’ young people. Diagnostic and symptom outcomes were examined. Putative moderators were tested as was publication bias. Results We included 16 trials (2545 young people). Two trials reported diagnostic outcomes, and significant effects were found for these at end-of-programme (RR = .09, 95%CI = .02 to .16), 6- (RR = .17, 95%CI = .06 to .27) and 12-month (RR = .31, 95%CI .17 to .45) follow-ups. Based on 16 trials, improved anxiety symptoms were significant compared to nonattention controls only, with small effect sizes reported by young people at the end-of-programmes, 6- and 12-month follow-ups; and by parents at the end of the programmes and 12-, but not 6-, month follow-ups. There was no evidence of significant moderation or publication bias. Conclusions Fourteen studies included children and young people who presented with elevated anxiety symptoms, but anxiety disorder was not ruled out in the participants in these studies. Hence, these studies might be reporting results of mixed prevention/early intervention programmes. Prevention programmes that target developmental risk factors, not only disorder maintaining factors, appear most promising. The clinically meaningful impact of anxiety disorder prevention programmes remains unknown

Galois theory and commutators

We prove that the relative commutator with respect to a subvariety of a variety of Omega-groups introduced by the first author can be described in terms of categorical Galois theory. This extends the known correspondence between the Froehlich-Lue and the Janelidze-Kelly notions of central extension. As an example outside the context of Omega-groups we study the reflection of the category of loops to the category of groups where we obtain an interpretation of the associator as a relative commutator.Comment: 14 page

The influence of the preparation methods on the inclusion of model drugs in a β-cyclodextrin cavity

NOTICE: this is the author’s version of a work that was accepted for publication in European Journal of Pharmaceutics and Biopharmaceutics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Eur J Pharm Biopharm. 2009 Feb;71(2):377-386. Epub 2008 Oct 17.The work aims to prove the complexation of two model drugs (ibuprofen, IB and indomethacin, IN) by bcyclodextrin (bCD), and the effect of water in such a process, and makes a comparison of their complexation yields. Two methods were considered: kneading of a binary mixture of the drug, bCD, and inclusion of either IB or IN in aqueous solutions of bCD. In the latter method water was removed by air stream, spray-drying and freeze-drying. To prove the formation of complexes in final products, optical microscopy, UV spectroscopy, IR spectroscopy, DSC, X-ray and NMR were considered. Each powder was added to an acidic solution (pH = 2) to quantify the concentration of the drug inside bCD cavity. Other media (pH = 5 and 7) were used to prove the existence of drug not complexed in each powder, as the drugs solubility increases with the pH. It was observed that complexation occurred in all powders, and that the fraction of drug inside the bCD did not depend neither on the method of complexation nor on the processes of drying considered

From Atiyah Classes to Homotopy Leibniz Algebras

A celebrated theorem of Kapranov states that the Atiyah class of the tangent bundle of a complex manifold $X$ makes $T_X[-1]$ into a Lie algebra object in $D^+(X)$, the bounded below derived category of coherent sheaves on $X$. Furthermore Kapranov proved that, for a K\"ahler manifold $X$, the Dolbeault resolution $\Omega^{\bullet-1}(T_X^{1,0})$ of $T_X[-1]$ is an $L_\infty$ algebra. In this paper, we prove that Kapranov's theorem holds in much wider generality for vector bundles over Lie pairs. Given a Lie pair $(L,A)$, i.e. a Lie algebroid $L$ together with a Lie subalgebroid $A$, we define the Atiyah class $\alpha_E$ of an $A$-module $E$ (relative to $L$) as the obstruction to the existence of an $A$-compatible $L$-connection on $E$. We prove that the Atiyah classes $\alpha_{L/A}$ and $\alpha_E$ respectively make $L/A[-1]$ and $E[-1]$ into a Lie algebra and a Lie algebra module in the bounded below derived category $D^+(\mathcal{A})$, where $\mathcal{A}$ is the abelian category of left $\mathcal{U}(A)$-modules and $\mathcal{U}(A)$ is the universal enveloping algebra of $A$. Moreover, we produce a homotopy Leibniz algebra and a homotopy Leibniz module stemming from the Atiyah classes of $L/A$ and $E$, and inducing the aforesaid Lie structures in $D^+(\mathcal{A})$.Comment: 36 page

Scale-free static and dynamical correlations in melts of monodisperse and Flory-distributed homopolymers: A review of recent bond-fluctuation model studies

It has been assumed until very recently that all long-range correlations are screened in three-dimensional melts of linear homopolymers on distances beyond the correlation length $\xi$ characterizing the decay of the density fluctuations. Summarizing simulation results obtained by means of a variant of the bond-fluctuation model with finite monomer excluded volume interactions and topology violating local and global Monte Carlo moves, we show that due to an interplay of the chain connectivity and the incompressibility constraint, both static and dynamical correlations arise on distances $r \gg \xi$. These correlations are scale-free and, surprisingly, do not depend explicitly on the compressibility of the solution. Both monodisperse and (essentially) Flory-distributed equilibrium polymers are considered.Comment: 60 pages, 49 figure

Carotid Intima-Media Thickness Progression as Surrogate Marker for Cardiovascular Risk Meta-Analysis of 119 Clinical Trials Involving 100 667 Patients

Background: To quantify the association between effects of interventions on carotid intima-media thickness (cIMT) progression and their effects on cardiovascular disease (CVD) risk. Methods: We systematically collated data from randomized, controlled trials. cIMT was assessed as the mean value at the common-carotid-artery; if unavailable, the maximum value at the common-carotid-artery or other cIMT measures were used. The primary outcome was a combined CVD end point defined as myocardial infarction, stroke, revascularization procedures, or fatal CVD. We estimated intervention effects on cIMT progression and incident CVD for each trial, before relating the 2 using a Bayesian meta-regression approach. Results: We analyzed data of 119 randomized, controlled trials involving 100 667 patients (mean age 62 years, 42% female). Over an average follow-up of 3.7 years, 12 038 patients developed the combined CVD end point. Across all interventions, each 10 μm/y reduction of cIMT progression resulted in a relative risk for CVD of 0.91 (95% Credible Interval, 0.87–0.94), with an additional relative risk for CVD of 0.92 (0.87–0.97) being achieved independent of cIMT progression. Taken together, we estimated that interventions reducing cIMT progression by 10, 20, 30, or 40 μm/y would yield relative risks of 0.84 (0.75–0.93), 0.76 (0.67–0.85), 0.69 (0.59–0.79), or 0.63 (0.52–0.74), respectively. Results were similar when grouping trials by type of intervention, time of conduct, time to ultrasound follow-up, availability of individual-participant data, primary versus secondary prevention trials, type of cIMT measurement, and proportion of female patients. Conclusions: The extent of intervention effects on cIMT progression predicted the degree of CVD risk reduction. This provides a missing link supporting the usefulness of cIMT progression as a surrogate marker for CVD risk in clinical trials