Exact solutions in a scalar-tensor model of dark energy

We consider a model of scalar field with non minimal kinetic and Gauss Bonnet couplings as a source of dark energy. Based on asymptotic limits of the generalized Friedmann equation, we impose restrictions on the kinetic an Gauss-Bonnet couplings. This restrictions considerable simplify the equations, allowing for exact solutions unifying early time matter dominance with transitions to late time quintessence and phantom phases. The stability of the solutions in absence of matter has been studied.Comment: 30 pages, 2 figures, to appear in JCA

On the Ricci dark energy model

We study the Ricci dark energy model (RDE) which was introduced as an alternative to the holographic dark energy model. We point out that an accelerating phase of the RDE is that of a constant dark energy model. This implies that the RDE may not be a new model of explaining the present accelerating universe.Comment: 8 page

Credit and saving constraints in general equilibrium : evidence from survey data

RESUMEN: En este documento, construimos un modelo de equilibrio general dinámico de agentes heterogéneos en el que las restricciones de ahorro interactúan con las restricciones de crédito. Las restricciones de ahorro en forma de costos fijos para usar el sistema financiero llevan a los hogares a buscar instrumentos de ahorro informales (efectivo) y a un menor ahorro agregado. Las restricciones crediticias inducen una mala asignación de capital entre los productores, lo que a su vez reduce el producto, la productividad y el rendimiento de los instrumentos financieros formales. Calibramos el modelo utilizando datos de encuestas de un país en desarrollo donde las restricciones informales de ahorro y crédito son generalizadas. Nuestros resultados cuantitativos sugieren que eliminar por completo las restricciones de ahorro y crédito puede tener grandes efectos sobre las tasas de ahorro, la producción, la PTF y el bienestar.ABSTRACT: In this paper, we build a heterogeneous agents-dynamic general equilibrium model wherein saving constraints interact with credit constraints. Saving constraints in the form of fixed costs to use the financial system lead households to seek informal saving instruments (cash) and result in lower aggregate saving. Credit constraints induce misallocation of capital across producers that in turn lowers output, productivity, and the return to formal financial instruments. We calibrate the model using survey data from a developing country where informal saving and credit constraints are pervasive. Our quantitative results suggest that completely removing saving and credit constraints can have large effects on saving rates, output, TFP, and welfare. Moreover, we note that a sizable fraction of these gains can be more easily attained by a mix of moderate reforms that lower both types of frictions than by a strong reform on either front

Reconstructing the potentials for the quintessence and tachyon dark energy, from the holographic principle

We propose an holographic quintessence and tachyon models of dark energy. The correspondence between the quintessence and tachyon energy densities with the holographic density, allows the reconstruction of the potentials and the dynamics for the quintessence and tachyon fields, in flat FRW background. The proposed infrared cut-off for the holographic energy density works for two cases of the constant $\alpha$: for $\alpha<1$ we reconstructed the holographic quintessence model in the region before the $\omega=-1$ crossing for the EoS parameter. The cosmological dynamics for $\alpha>1$ was also reconstructed for the holographic quintessence and tachyon models.Comment: 21 pages, 18 figures, 2 table

Super-resolution, Extremal Functions and the Condition Number of Vandermonde Matrices

Super-resolution is a fundamental task in imaging, where the goal is to extract fine-grained structure from coarse-grained measurements. Here we are interested in a popular mathematical abstraction of this problem that has been widely studied in the statistics, signal processing and machine learning communities. We exactly resolve the threshold at which noisy super-resolution is possible. In particular, we establish a sharp phase transition for the relationship between the cutoff frequency ($m$) and the separation ($\Delta$). If $m > 1/\Delta + 1$, our estimator converges to the true values at an inverse polynomial rate in terms of the magnitude of the noise. And when $m < (1-\epsilon) /\Delta$ no estimator can distinguish between a particular pair of $\Delta$-separated signals even if the magnitude of the noise is exponentially small. Our results involve making novel connections between {\em extremal functions} and the spectral properties of Vandermonde matrices. We establish a sharp phase transition for their condition number which in turn allows us to give the first noise tolerance bounds for the matrix pencil method. Moreover we show that our methods can be interpreted as giving preconditioners for Vandermonde matrices, and we use this observation to design faster algorithms for super-resolution. We believe that these ideas may have other applications in designing faster algorithms for other basic tasks in signal processing.Comment: 19 page