Reconstruction of graded groupoids from graded Steinberg algebras

We show how to reconstruct a graded ample Hausdorff groupoid with topologically principal neutrally-graded component from the ring structure of its graded Steinberg algebra over any commutative integral domain with 1, together with the embedding of the canonical abelian subring of functions supported on the unit space. We deduce that diagonal-preserving ring isomorphism of Leavitt path algebras implies $C^*$-isomorphism of $C^*$-algebras for graphs $E$ and $F$ in which every cycle has an exit. This is a joint work with Joan Bosa, Roozbeh Hazrat and Aidan Sims.Universidad de Málaga. Campus de Excelencia internacional Andalucía Tec

Strict \infty-groupoids are Grothendieck \infty-groupoids

We show that there exists a canonical functor from the category of strict \infty-groupoids to the category of Grothendieck \infty-groupoids and that this functor is fully faithful. As a main ingredient, we prove that free strict \infty-groupoids on a globular pasting scheme are weakly contractible.Comment: 22 pages, v2: revised according to referee's comments, in particular: new organization of the pape

Tensor products of Leavitt path algebras

We compute the Hochschild homology of Leavitt path algebras over a field $k$. As an application, we show that $L_2$ and $L_2\otimes L_2$ have different Hochschild homologies, and so they are not Morita equivalent; in particular they are not isomorphic. Similarly, $L_\infty$ and $L_\infty\otimes L_\infty$ are distinguished by their Hochschild homologies and so they are not Morita equivalent either. By contrast, we show that $K$-theory cannot distinguish these algebras; we have $K_*(L_2)=K_*(L_2\otimes L_2)=0$ and $K_*(L_\infty)=K_*(L_\infty\otimes L_\infty)=K_*(k)$.Comment: 10 pages. Added hypothesis to Corolary 4.5; Example 5.2 expanded, other cosmetic changes, including an e-mail address and some dashes. Final version, to appear in PAM

Populating an economic model with health state utility values: moving towards better practice

Background: When estimating health state utility values (HSUV) for multiple health conditions, the alternative models used to combine these data can produce very different values. Results generated using a baseline of perfect health are not comparable with those generated using a baseline adjusted for not having the health condition taking into account age and gender. Despite this, there is no guidance on the preferred techniques that should be used and very little research describing the effect on cost per QALY results. Methods: Using a cardiovascular disease (CVD) model and cost per QALY thresholds, we assess the consequence of using different baseline health state utility profiles (perfect health, individuals with no history of CVD, general population) in conjunction with three models (minimum, additive, multiplicative) frequently used to estimate proxy scores for multiple health conditions. Results: Assuming a baseline of perfect health ignores the natural decline in quality of life associated with co-morbidities, over-estimating the benefits of treatment to such an extent it could potentially influence a threshold policy decision. The minimum model biases results in favour of younger aged cohorts while the additive and multiplicative technique produced similar results. Although further research in additional health conditions is required to support our findings, this pilot study highlights the urgent need for analysts to conform to an agreed reference case and provides initial recommendations for better practice. We demonstrate that in CVD, if data are not available from individuals without the health condition, HSUVs from the general population provide a reasonable approximation