Stokes Inversion based on Convolutional Neural Networks

Spectropolarimetric inversions are routinely used in the field of Solar Physics for the extraction of physical information from observations. The application to two-dimensional fields of view often requires the use of supercomputers with parallelized inversion codes. Even in this case, the computing time spent on the process is still very large. Our aim is to develop a new inversion code based on the application of convolutional neural networks that can quickly provide a three-dimensional cube of thermodynamical and magnetic properties from the interpretation of two-dimensional maps of Stokes profiles. We train two different architectures of fully convolutional neural networks. To this end, we use the synthetic Stokes profiles obtained from two snapshots of three-dimensional magneto-hydrodynamic numerical simulations of different structures of the solar atmosphere. We provide an extensive analysis of the new inversion technique, showing that it infers the thermodynamical and magnetic properties with a precision comparable to that of standard inversion techniques. However, it provides several key improvements: our method is around one million times faster, it returns a three-dimensional view of the physical properties of the region of interest in geometrical height, it provides quantities that cannot be obtained otherwise (pressure and Wilson depression) and the inferred properties are decontaminated from the blurring effect of instrumental point spread functions for free. The code is provided for free on a specific repository, with options for training and evaluation.Comment: 18 pages, 14 figures, accepted for publication in Astronomy & Astrophysic

Enhancing SDO/HMI images using deep learning

The Helioseismic and Magnetic Imager (HMI) provides continuum images and magnetograms with a cadence better than one per minute. It has been continuously observing the Sun 24 hours a day for the past 7 years. The obvious trade-off between full disk observations and spatial resolution makes HMI not enough to analyze the smallest-scale events in the solar atmosphere. Our aim is to develop a new method to enhance HMI data, simultaneously deconvolving and super-resolving images and magnetograms. The resulting images will mimic observations with a diffraction-limited telescope twice the diameter of HMI. Our method, which we call Enhance, is based on two deep fully convolutional neural networks that input patches of HMI observations and output deconvolved and super-resolved data. The neural networks are trained on synthetic data obtained from simulations of the emergence of solar active regions. We have obtained deconvolved and supper-resolved HMI images. To solve this ill-defined problem with infinite solutions we have used a neural network approach to add prior information from the simulations. We test Enhance against Hinode data that has been degraded to a 28 cm diameter telescope showing very good consistency. The code is open source.Comment: 13 pages, 10 figures. Accepted for publication in Astronomy & Astrophysic

Type O pure radiation metrics with a cosmological constant

In this paper we complete the integration of the conformally flat pure radiation spacetimes with a non-zero cosmological constant $\Lambda$, and $\tau \ne 0$, by considering the case $\Lambda +\tau\bar\tau \ne 0$. This is a further demonstration of the power and suitability of the generalised invariant formalism (GIF) for spacetimes where only one null direction is picked out by the Riemann tensor. For these spacetimes, the GIF picks out a second null direction, (from the second derivative of the Riemann tensor) and once this spinor has been identified the calculations are transferred to the simpler GHP formalism, where the tetrad and metric are determined. The whole class of conformally flat pure radiation spacetimes with a non-zero cosmological constant (those found in this paper, together with those found earlier for the case $\Lambda +\tau\bar\tau = 0$) have a rich variety of subclasses with zero, one, two, three, four or five Killing vectors

Redefining monetary policy rules: A threshold approach

In this paper, we try to analyse the extent to which a redefinition of the monetary policy rule would help to avoid the zero-lower bound, as well as to explore the conditions needed to avoid that constraint. To that aim, we estimate the threshold values of the key variables of the policy rule: the inflation gap and the output gap. The threshold model allows us to know which are the turning points from which the relationship between the key variables and the interest rate revert. In the Eurozone countries, we have found that the inflation gap always contributes to increasing the nominal interest rate. On the contrary, the output gap works differently when it reaches values above or below the threshold value, which would favour the reduction of the interest rates towards the zero levelSpanish Ministry of Economy, Industry and Competitiveness through the project ECO2015-65826-