Idiosyncrasy as an explanation for power laws in nature

Complex systems theory pays much attention to simple mechanisms producing nontrivial patterns, especially power laws. However, power laws with exponent close to one also result from complex mixtures of mechanisms that, in isolation, would not necessarily give this type of distribution. Probably, both paths to the power law are relevant in nature. The second gives a plausible explanation for some instances of power laws emerging in extremely complex systems, such as ecosystems.Comment: To be published in Trends in Mathematics. 6 pages, 0 figure

Endogenous longevity, health and economic growth: a slow growth for a longer life?

We establish a theoretical set-up that is able to endogenously integrate growth and longevity. Our model captures three links between them: a longer life expectancy results in an increase in savings as well as an increase in the workforce, but health and growth compete for resources. We find that the key element is the response of longevity to an increase in health resources. Our model suggests that the first two links could be the most important in poor countries, which could explain their experience of simultaneous increases in growth and life expectancy. The reverse result may apply for developed countries.Government Spending

Skill gaps: existence and efficiency

Given the interdependences between human capital accumulation and technological change, skill gaps may arise in equilibrium. However, they are not necessarily inefficient, and in this paper we present a model in which the simple absence of such a skill gap can be inefficient.efficiency

Apodized Pupil Lyot Coronagraphs for Arbitrary Apertures. IV. Reduced Inner Working Angle and Increased Robustness to Low-Order Aberrations

The Apodized Pupil Lyot Coronagraph (APLC) is a diffraction suppression system installed in the recently deployed instruments Palomar/P1640, Gemini/GPI, and VLT/SPHERE to allow direct imaging and spectroscopy of circumstellar environments. Using a prolate apodization, the current implementations offer raw contrasts down to $10^{-7}$ at 0.2 arcsec from a star over a wide bandpass (20\%), in the presence of central obstruction and struts, enabling the study of young or massive gaseous planets. Observations of older or lighter companions at smaller separations would require improvements in terms of inner working angle (IWA) and contrast, but the methods originally used for these designs were not able to fully explore the parameter space. We here propose a novel approach to improve the APLC performance. Our method relies on the linear properties of the coronagraphic electric field with the apodization at any wavelength to develop numerical solutions producing coronagraphic star images with high-contrast region in broadband light. We explore the parameter space by considering different aperture geometries, contrast levels, dark-zone sizes, bandpasses, and focal plane mask sizes. We present an application of these solutions to the case of Gemini/GPI with a design delivering a $10^{-8}$ raw contrast at 0.19 arcsec and offering a significantly reduced sensitivity to low-order aberrations compared to the current implementation. Optimal solutions have also been found to reach $10^{-10}$ contrast in broadband light regardless of the telescope aperture shape (in particular the central obstruction size), with effective IWA in the $2-3.5\lambda/D$ range, therefore making the APLC a suitable option for the future exoplanet direct imagers on the ground or in space.Comment: 14 pages, 10 figures, accepted in Ap