Families of Group Actions, Generic Isotriviality, and Linearization

We study families of reductive group actions on A2 parametrized by curves and show that every faithful action of a non-finite reductive group on A3 is linearizable, i.e. G-isomorphic to a representation of G. The difficulties arise for non-connected groups G. We prove a Generic Equivalence Theorem which says that two affine mor- phisms p: S → Y and q: T → Y of varieties with isomorphic (closed) fibers become isomorphic under a dominant ́etale base change φ : U → Y . A special case is the following result. Call a morphism φ: X → Y a fibration with fiber F if φ is flat and all fibers are (reduced and) isomorphic to F. Then an affine fibration with fiber F admits an ́etale dominant morphism μ: U → Y such that the pull-back is a trivial fiber bundle: U ×Y X ≃ U × F . As an application we give short proofs of the following two (known) results: (a) Every affine A1-fibration over a normal variety is locally trivial in the Zariski-topology; (b) Every affine A2-fibration over a smooth curve is locally trivial in the Zariski-topology

The NHS performance framework: taking account of economic behaviour

The provision of quantitative information has been given a key role in securing good performance in the new NHS. A new National Performance Framework has been proposed encompassing a number of dimensions of performance. Whilst this approach to managing the NHS is welcomed, it is essential to understand the strengths and limitations intrinsic to the use of performance indicators for this purpose. In particular, complex behavioural consequences may arise in response to the collection and dissemination of performance data, some of which may be unintended, potentially dysfunctional and damaging for the NHS. Results from a recent study on the performance of NHS Trusts are used to illustrate the sort of unintended side-effects which occur within the current system and which may in principle be replicated in the new system in future. Whilst the possibility of such consequences does not invalidate the potential of the new Performance Framework to secure the desired changes in the NHS, it does suggest that careful attention needs to be paid to the assessment of unanticipated side-effects.performance, NHS Trusts

A Solidification Phenomenon in Random Packings

We prove that uniformly random packings of copies of a certain simply-connected figure in the plane exhibit global connectedness at all sufficiently high densities, but not at low densities

Wage Labour Rates in Upper Canada, 1818-1840

Despite the heavy influx of immigrants into Upper Canada from 1815 to 1840, wage rates remained in general surprisingly stable. On the one hand, the range of rates offered to skilled tradesmen, such as carpenters and blacksmiths, narrowed with a gradual downward trend. Fluctuation over time of farm labourers' wages was less than variation due to distance from points of entry and seasonal employment. Day labourers' wages, on the other hand, seem to have actually increased marginally. Although female servants started with lower wages and saw the rate fall over time, male servants' wages rose to the general level of unskilled men's rates. These trends point to a steadier demand for male labour as the province became more heavily populated. En dépit de l’afflux massif d’immigrants venus s’établir dans le Haut-Canada entre 1815 et 1840, la plupart des taux de salaires y sont demeurés étonnamment stables. Une grande partie des ouvriers qualifiés, tels les charpentiers et les forgerons, ont connu une réduction graduelle de l’éventail des salaires offerts. Par ailleurs, les salaires des ouvriers agricoles ont varié davantage en fonction de l’éloignement des points d’arrivée et des saisons que selon le cours des années. Pour ce qui est des journaliers agricoles, leurs salaires semblent avoir augmenté de façon marginale. Quant aux gages des domestiques masculins, ils se sont élevés au niveau des salaires des ouvriers masculins non spécialisés, tandis que les gages des domestiques féminines, déjà moins élevés au point de départ, se sont détériorés avec le temps. Ces tendances laissent supposer que la demande de main-d’oeuvre masculine s’est régularisée au fur et à mesure que la population augmentait