On the viability of m**2 phi**2 and natural inflation

In the context of single field inflation, models with a quadratic potential and models with a natural potential with subplanckian decay constant are in tension with the Planck data. We show that, when embedded in a two-field model with an additional super massive field, they can become consistent with observations. Our results follow if the inflaton is the phase of a complex field (or an angular variable) protected by a mildly broken U(1) symmetry, and the radial component, whose mass is much greater than the Hubble scale, is stabilized at subplanckian values. The presence of the super massive field, besides modifying the effective single field potential, causes a reduction in the speed of sound of the inflaton fluctuations, which drives the prediction for the primordial spectrum towards the allowed experimental values. We discuss these effects also for the linear potential, and show that this model increases its agreement with data as wellComment: 14 pages, 7 figures. v2 added missing abstract in the pdf, references and very minor changes. v3. typos corrected, references adde

Primordial black hole formation with non-Gaussian curvature perturbations

In the context of transient constant-roll inflation near a local maximum, we derive the non-perturbative field redefinition that relates a Gaussian random field with the true non-Gaussian curvature perturbation. Our analysis shows the emergence of a new critical amplitude $\zeta_*$, corresponding to perturbations that prevent the inflaton from overshooting the local maximum, thus becoming trapped in the false minimum of the potential. For potentials with a mild curvature at the local maximum (and thus small non-Gaussianity), we recover the known perturbative field redefinition. We apply these results to the formation of primordial black holes, and discuss the cases for which $\zeta_*$ is smaller or of the same order than the critical value for collapse of spherically symmetric overdensities. In the latter case, we present a simple potential for which the power spectrum needs an amplitude 10 times smaller that in the Gaussian case for producing a sizeable amount of primordial black holes.Comment: 13 pages, 8 figures. v2: expanded explanations + small changes. v3: small typos correcte

The two-field regime of natural inflation

The simplest two-field completion of natural inflation has a regime in which both fields are active and in which its predictions are within the Planck 1-$\sigma$ confidence contour. We show this for the original model of natural inflation, in which inflation is achieved through the explicit breaking of a U(1) symmetry. We consider the case in which the mass coming from explicit breaking of this symmetry is comparable to that from spontaneous breaking, which we show is consistent with a hierarchy between the corresponding energy scales. While both masses are comparable when the observable modes left the horizon, the mass hierarchy is restored in the last e-foldings of inflation, rendering the predictions consistent with the isocurvature bounds. For completeness, we also study the predictions for the case in which there is a large hierarchy of masses and an initial period of inflation driven by the (heavy) radial field.Comment: 18 pages, 9 figure

New Century, Old Disparities: Gender and Ethnic Wage Gaps in Latin America

This paper surveys gender and ethnic wage gaps in 18 Latin American countries, decomposing differences using matching comparisons as a non-parametric alternative to the Blinder-Oaxaca (BO) decomposition. It is found that men earn 9-27 percent more than women, with high cross-country heterogeneity. The unexplained pay gap is higher among older, informal and self-employed workers and those in small firms. Ethnic wage differences are greater than gender differences, and educational attainment differentials play an important role in explaining the gap. Higher ethnic wage gaps are found among males, singleincome generators of households and full-time workers, and in rural areas. An important share of the ethnic wage gap is due to the scarcity of minorities in highpaid positions.gender, ethnicity, wage gaps, Latin America, matching

Socioeconomic health disparities revisited: coping flexibility enhances health-related quality of life for individuals low in socioeconomic status

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Cumulative effects in inflation with ultra-light entropy modes

In multi-field inflation one or more non-adiabatic modes may become light, potentially inducing large levels of isocurvature perturbations in the cosmic microwave background. If in addition these light modes are coupled to the adiabatic mode, they influence its evolution on super horizon scales. Here we consider the case in which a non-adiabatic mode becomes approximately massless ("ultralight") while still coupled to the adiabatic mode, a typical situation that arises with pseudo-Nambu-Goldstone bosons or moduli. This ultralight mode freezes on super-horizon scales and acts as a constant source for the curvature perturbation, making it grow linearly in time and effectively suppressing the isocurvature component. We identify a Stuckelberg-like emergent shift symmetry that underlies this behavior. As inflation lasts for many e-folds, the integrated effect of this source enhances the power spectrum of the adiabatic mode, while keeping the non-adiabatic spectrum approximately untouched. In this case, towards the end of inflation all the fluctuations, adiabatic and non-adiabatic, are dominated by a single degree of freedom.Comment: 27 pages, 1 figure; v2: improved discussions, version published in JCA

New Century, Old Disparities: Gender and Ethnic Wage Gaps in Latin America

This paper surveys gender and ethnic wage gaps in 18 Latin American countries, decomposing differences using matching comparisons as a non-parametric alternative to the Blinder-Oaxaca (BO) decomposition. It is found that men earn 9-27 percent more than women, with high cross-country heterogeneity. The unexplained pay gap is higher among older, informal and self-employed workers and those in small firms. Ethnic wage differences are greater than gender differences, and educational attainment differentials play an important role in explaining the gap. Higher ethnic wage gaps are found among males, single-income generators of households and full-time workers, and in rural areas. An important share of the ethnic wage gap is due to the scarcity of minorities in high-paid positions.gender, ethnicity, wage gaps, Latin America, matching

Natural Compression for Distributed Deep Learning

Modern deep learning models are often trained in parallel over a collection of distributed machines to reduce training time. In such settings, communication of model updates among machines becomes a significant performance bottleneck and various lossy update compression techniques have been proposed to alleviate this problem. In this work, we introduce a new, simple yet theoretically and practically effective compression technique: {\em natural compression (NC)}. Our technique is applied individually to all entries of the to-be-compressed update vector and works by randomized rounding to the nearest (negative or positive) power of two, which can be computed in a "natural" way by ignoring the mantissa. We show that compared to no compression, NC increases the second moment of the compressed vector by not more than the tiny factor \nicefrac{9}{8}, which means that the effect of NC on the convergence speed of popular training algorithms, such as distributed SGD, is negligible. However, the communications savings enabled by NC are substantial, leading to {\em $3$-$4\times$ improvement in overall theoretical running time}. For applications requiring more aggressive compression, we generalize NC to {\em natural dithering}, which we prove is {\em exponentially better} than the common random dithering technique. Our compression operators can be used on their own or in combination with existing operators for a more aggressive combined effect, and offer new state-of-the-art both in theory and practice.Comment: 8 pages, 20 pages of Appendix, 6 Tables, 14 Figure

Literacy Traps: Society-wide Education and Individual Skill Premia

Using a model of O-ring production function, the paper demonstrates how certain communities can get caught in a low-literacy trap in which each individual finds it not worthwhile investing in higher skills because others are not high-skilled. The model sheds light on educational policy. It is shown that policy for promoting human capital has to take the form of a mechanism for solving the coordination failure in people’s choice of educational strategy.education, literacy, O-ring, skill formation, traps