Averaging Life Expectancy

More than 50 years ago a peculiar feature of averages was pointed out by Cohen and Nagel (1934, p. 449) in their well-known book on logic. Their example happened to be mortality from tuberculosis; Blacks in Richmond, Virginia, had a lower rate than Blacks in New York; Whites in Richmond had a lower rate than Whites in New York; yet the overall rate for Richmond was higher than that in New York. Many other examples of the paradox have subsequently been pointed out, and some general theory has been presented by Colin Blyth. If this were only an arithmetical curiosity no one would care much about it, but in fact its very possibility is a troubling consideration for all numerical comparisons. If recognizing Blacks and Whites reverses the standing of New York and Richmond, how do we know that recognizing some further breakdown will not reverse the standing once again? This paper presents a different paradox, but one that is also threatening to the drawing of conclusions from numerical data. To follow Cohen and Nagel's example but disregarding the distinction between Blacks and Whites, the arithmetic average mortality (expressed as a death rate) of Richmond and New York combined will always fall between the rate for New York and that for Richmond. The result of a linear averaging process cannot fall outside the units averaged. This is no longer true when a non-linear form of average is used -- the present paper shows a hypothetical example for a harmonic mean. There are many questions that require non-linear averaging. One such is life expectancy, that is a weighted function of the usual (age-specific) rates, but the weighting is nonlinear. The authors came on this paradox in studying life expectancy for women in the Soviet Union as projected to the year 2020. All of the republics fall between 77.713 and 78.026, but the figure for the USSR comes out to 77.632. This is not an error due to rounding; it is not due to Simpson's paradox that would result from internal heterogeneity in the several republics; it is due to the nonlinear weighting implicit in the calculation of the life expectancy

Starburst-driven Starbursts in the Heart of Ultraluminous Infrared Galaxies

There is increasing evidence for the presence of blue super star clusters in the central regions of ultraluminous infrared galaxies like Arp 220. Ultraluminous galaxies are thought to be triggered by galaxy mergers, and it has often been argued that these super star clusters may form during violent collisions between gas clouds in the final phase of the mergers. We now investigate another set of models which differ from previous ones in that the formation of the super star clusters is linked directly to the very intense starburst occurring at the very center of the galaxy. Firstly we show that a scenario in which the super star clusters form in material compressed by shock waves originating from the central starburst is implausible because the objects so produced are much smaller than the observed star clusters in Arp 220. We then investigate a scenario (based on the Shlosman-Noguchi model) in which the infalling dense gas disk is unstable gravitationally and collapses to form massive gaseous clumps. Since these clumps are exposed to the external high pressure driven by the superwind (a blast wave driven by a collective effect of a large number of supernovae in the very core of the galaxy), they can collapse and then massive star formation may be induced in them. The objects produced in this kind of collapse have properties consistent with those of the observed super star clusters in the center of Arp 220.Comment: 13 pages, 1 figure, ApJ (Letters) in pres

Irreversibility and the arrow of time in a quenched quantum system

Irreversibility is one of the most intriguing concepts in physics. While microscopic physical laws are perfectly reversible, macroscopic average behavior has a preferred direction of time. According to the second law of thermodynamics, this arrow of time is associated with a positive mean entropy production. Using a nuclear magnetic resonance setup, we measure the nonequilibrium entropy produced in an isolated spin-1/2 system following fast quenches of an external magnetic field and experimentally demonstrate that it is equal to the entropic distance, expressed by the Kullback-Leibler divergence, between a microscopic process and its time-reverse. Our result addresses the concept of irreversibility from a microscopic quantum standpoint.Comment: 8 pages, 7 figures, RevTeX4-1; Accepted for publication Phys. Rev. Let

Local Swift-BAT active galactic nuclei prefer circumnuclear star formation

We use Herschel data to analyze the size of the far-infrared 70micron emission for z<0.06 local samples of 277 hosts of Swift-BAT selected active galactic nuclei (AGN), and 515 comparison galaxies that are not detected by BAT. For modest far-infrared luminosities 8.5<log(LFIR)<10.5, we find large scatter of half light radii Re70 for both populations, but a typical Re70 <~ 1 kpc for the BAT hosts that is only half that of comparison galaxies of same far-infrared luminosity. The result mostly reflects a more compact distribution of star formation (and hence gas) in the AGN hosts, but compact AGN heated dust may contribute in some extremely AGN-dominated systems. Our findings are in support of an AGN-host coevolution where accretion onto the central black hole and star formation are fed from the same gas reservoir, with more efficient black hole feeding if that reservoir is more concentrated. The significant scatter in the far-infrared sizes emphasizes that we are mostly probing spatial scales much larger than those of actual accretion, and that rapid accretion variations can smear the distinction between the AGN and comparison categories. Large samples are hence needed to detect structural differences that favour feeding of the black hole. No size difference AGN host vs. comparison galaxies is observed at higher far-infrared luminosities log(LFIR)>10.5 (star formation rates >~ 6 Msun/yr), possibly because these are typically reached in more compact regions in the first place.Comment: 7 pages, 3 figures, accepted for publication in Astronomy & Astrophysic

Reducing Vulnerability in Critical Life Course Phases through Enhancing Human Capital

In this paper we examine selected types of vulnerability over the human life course with a specific focus on differentials not only by age and gender -- as is conventionally done in demography -- but also by level of education and with a focus on health. Starting with the newborn and vulnerability in terms of infant and child mortality, we refer to the level of education of the mother. In reference to young people's susceptibility to unemployment after leaving school, we take into account the education of the women and men themselves. Proceeding further in the life course, we next consider vulnerability to becoming disabled in the age group 30-74 according to the education level of the studied persons themselves. Finally, the last section studies differential vulnerability at the national level using the time series of deaths from disasters where the aggregate levels of education at a national level are being taken into account. We conclude that over the entire life cycle of individuals, the changes in behavior that tend to be associated with more education (of mothers or the persons themselves) can be viewed as a potent factor in reducing child mortality, reducing the risk for unemployment at young age, reducing the vulnerability to natural disasters, and finally reducing the risk of falling into disability. These general long-term benefits of near-term investments in education hold for individuals as well as for entire societies

Fractional Langevin equation

We investigate fractional Brownian motion with a microscopic random-matrix model and introduce a fractional Langevin equation. We use the latter to study both sub- and superdiffusion of a free particle coupled to a fractal heat bath. We further compare fractional Brownian motion with the fractal time process. The respective mean-square displacements of these two forms of anomalous diffusion exhibit the same power-law behavior. Here we show that their lowest moments are actually all identical, except the second moment of the velocity. This provides a simple criterion which enables to distinguish these two non-Markovian processes.Comment: 4 page

Electromagnetic transitions in an effective chiral Lagrangian with the eta-prime and light vector mesons

We consider the chiral Lagrangian with a nonet of Goldstone bosons and a nonet of light vector mesons. The mixing between the pseudoscalar mesons eta and eta-prime is taken into account. A novel counting scheme is suggested that is based on hadrogenesis, which conjectures a mass gap in the meson spectrum of QCD in the limit of a large number of colors. Such a mass gap would justify to consider the vector mesons and the eta-prime meson as light degrees of freedom. The complete leading order Lagrangian is constructed and discussed. As a first application it is tested against electromagnetic transitions of light vector mesons to pseudoscalar mesons. Our parameters are determined by the experimental data on photon decays of the omega, phi and eta-prime meson. In terms of such parameters we predict the corresponding decays into virtual photons with either dielectrons or dimuons in the final state.Comment: 17 pages, extended discussion on mixin