Selective migration from deprived areas in Northern Ireland and the spatial distribution of inequalities: implications for monitoring health and inequalities in health

Much of the evidence suggesting that inequalities in health have been increasing over the last two decades has come from studies that compared the changes in relative health status of areas over time. Such studies ignore the movement of people between areas. This paper examines the population movement between small areas in Northern Ireland in the year prior to the 1991 census as well as the geographical distribution of migrants to Northern Ireland over the same period. It shows that deprived areas tended to become depopulated and that those who left these areas were the more affluent residents. While immigrants differed a little from the indigenous population, the overall effect of their distribution would be to maintain the geographical socio-economic status quo. The selective movement of people between areas would result in the distribution of health and ill-health becoming more polarized, i.e. produce a picture of widening inequalities between areas even though the distribution between individuals is unchanged. These processes suggest potential significant problems with the area-based approaches to monitoring health and inequalities in health.

Joint measurements and Bell inequalities

Joint quantum measurements of noncommuting observables are possible, if one accepts an increase in the measured variances. A necessary condition for a joint measurement to be possible is that a joint probability distribution exists for the measurement. This fact suggests that there may be a link with Bell inequalities, as these will be satisfied if and only if a joint probability distribution for all involved observables exists. We investigate the connections between Bell inequalities and conditions for joint quantum measurements to be possible. Mermin's inequality for the three-particle Greenberger-Horne-Zeilinger state turns out to be equivalent to the condition for a joint measurement on two out of the three quantum systems to exist. Gisin's Bell inequality for three coplanar measurement directions, meanwhile, is shown to be less strict than the condition for the corresponding joint measurement.

Unconditional constants and polynomial inequalities

If P is a polynomial on Rm of degree at most n then we define the polynomial |P|. Now if B is a convex compact set in Rm, we define the norm ||P||B of P as the maximum of P on B, and then we investigate the inequality || |P| ||B