Education Composition and Growth: A Pooled Mean Group Analysis of OECD Countries

This paper uses the pooled mean group (PMG) estimator and a dataset restricted to OECD countries to examine the relationship between different levels of education, i.e. between education composition and growth. The PMG estimator allows a greater degree of parameter heterogeneity than the usual estimator procedures used in empirical growth studies by imposing common long run relationships across countries while allowing for heterogeneity in the short run responses and intercepts. Results point to a significant longterm relationship not only between higher education and growth but also between lower schooling levels and growth. This indicates that public spending on education in OECD countries should be spread across the different levels of education in a balanced way.Levels of education, Economic growth, Dynamic heterogeneous panels.

Deterministic Brownian Motion: The Effects of Perturbing a Dynamical System by a Chaotic Semi-Dynamical System

Here we review and extend central limit theorems for highly chaotic but deterministic semi-dynamical discrete time systems. We then apply these results show how Brownian motion-like results are recovered, and how an Ornstein-Uhlenbeck process results within a totally deterministic framework. These results illustrate that the contamination of experimental data by "noise" may, under certain circumstances, be alternately interpreted as the signature of an underlying chaotic process.Comment: 65 pages, 8 figure

Formation of Supermassive Black Holes by Direct Collapse in Pregalactic Halos

We describe a mechanism by which supermassive black holes can form directly in the nuclei of protogalaxies, without the need for seed black holes left over from early star formation. Self-gravitating gas in dark matter halos can lose angular momentum rapidly via runaway, global dynamical instabilities, the so-called "bars within bars" mechanism. This leads to the rapid buildup of a dense, self-gravitating core supported by gas pressure - surrounded by a radiation pressure-dominated envelope - which gradually contracts and is compressed further by subsequent infall. These conditions lead to such high temperatures in the central region that the gas cools catastrophically by thermal neutrino emission, leading to the formation and rapid growth of a central black hole. We estimate the initial mass and growth rate of the black hole for typical conditions in metal-free halos with T_vir ~ 10^4 K, which are the most likely to be susceptible to runaway infall. The initial black hole should have a mass of <~20 solar masses, but in principle could grow at a super-Eddington rate until it reaches ~ 10^4-10^6 solar masses. Rapid growth may be limited by feedback from the accretion process and/or disruption of the mass supply by star formation or halo mergers. Even if super-Eddington growth stops at \~10^3-10^4 solar masses, this process would give black holes ample time to attain quasar-size masses by a redshift of 6, and could also provide the seeds for all supermassive black holes seen in the present universe.Comment: 11 pages, 2 figures, Monthly Notices of the Royal Astronomical Society, in press. Minor revision