Uneven state distribution of homicides in Brazil and their effect on life expectancy, 2000–2015: a cross-sectional mortality study

ObjectiveTo determine cause-specific and age-specific contributions to life expectancy changes between 2000 and 2015, separately by state and sex in Brazil, with a focus on homicides.DesignRetrospective cross-sectional demographic analysis of mortality.Setting and populationBrazilian population by age, sex and state from 2000 to 2015.Main outcome measureUsing mortality data from the Brazilian Mortality Information System and population estimates from the National Statistics Office, we used death distribution methods and the linear integral decomposition model to estimate levels and changes in life expectancy. We also examine how multiple causes of death, including those attributable to homicides and amenable/avoidable mortality, contributed to these changes from 2000 to 2015.ResultsBetween 2000 and 2015, life expectancy in Brazil increased from 71.5 to 75.1 years. Despite state-level variation in gains, life expectancy increased in almost all states over this period. However across Brazil, homicide mortality contributed, to varying degrees, to either attenuated or decreased male life expectancy gains. In Alagoas in 2000–2007 and Sergipe in 2007–2015, homicides contributed to a reduction in life expectancy of 1.5 years, offsetting gains achieved through improvements due to medically amenable causes. In the period 2007–2015, male life expectancy could have been improved by more than half a year in 12 of Brazil’s states if homicide mortality had remained at the levels of 2007.ConclusionsHomicide mortality appears to offset life expectancy gains made through recent improvements to mortality amenable to medical services and public health interventions, with considerable subnational heterogeneity in the extent of this phenomenon. Efforts combating the causes of homicides can increase life expectancy beyond what has been achieved in recent decades.

Bloch wave homogenisation of quasiperiodic media

Quasiperiodic media is a class of almost periodic media which is generated from periodic media through a ‘cut and project’ procedure. Quasiperiodic media displays some extraordinary optical, electronic and conductivity properties which call for the development of methods to analyse their microstructures and effective behaviour. In this paper, we develop the method of Bloch wave homogenisation for quasiperiodic media. Bloch waves are typically defined through a direct integral decomposition of periodic operators. A suitable direct integral decomposition is not available for almost periodic operators. To remedy this, we lift a quasiperiodic operator to a degenerate periodic operator in higher dimensions. Approximate Bloch waves are obtained for a regularised version of the degenerate operator. Homogenised coefficients for quasiperiodic media are obtained from the first Bloch eigenvalue of the regularised operator in the limit of regularisation parameter going to zero. A notion of quasiperiodic Bloch transform is defined and employed to obtain homogenisation limit for an equation with highly oscillating quasiperiodic coefficients.

THE CONTINUOUS SPECTRUM IN DISCRETE SERIES BRANCHING LAWS

If G is a reductive Lie group of Harish-Chandra class, H is a symmetric subgroup, and π is a discrete series representation of G, the authors give a condition on the pair (G, H) which guarantees that the direct integral decomposition of π|H contains each irreducible representation of H with finite multiplicity. In addition, if G is a reductive Lie group of Harish-Chandra class, and H ⊂ G is a closed, reductive subgroup of Harish-Chandra class, the authors show that the multiplicity function in the direct integral decomposition of π|H is constant along "continuous parameters". In obtaining these results, the authors develop a new technique for studying multiplicities in the restriction π|H via convolution with Harish-Chandra characters. This technique has the advantage of being useful for studying the continuous spectrum as well as the discrete spectrum.