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

A new formulation of compartmental epidemic modelling for arbitrary distributions of incubation and removal times

The paradigm for compartment models in epidemiology assumes exponentially distributed incubation and removal times, which is not realistic in actual populations. Commonly used variations with multiple exponentially distributed variables are more flexible, yet do not allow for arbitrary distributions. We present a new formulation, focussing on the SEIR concept that allows to include general distributions of incubation and removal times. We compare the solution to two types of agent-based model simulations, a spatially homogeneous one where infection occurs by proximity, and a model on a scale-free network with varying clustering properties, where the infection between any two agents occurs via their link if it exists. We find good agreement in both cases. Furthermore a family of asymptotic solutions of the equations is found in terms of a logistic curve, which after a non-universal time shift, fits extremely well all the microdynamical simulations. The formulation allows for a simple numerical approach; software in Julia and Python is provided.Comment: 21 pages, 11 figures. v2 matches published version: improved presentation (including title, abstract and references), results and conclusions unchange

The Yang-Mills gradient flow and SU(3) gauge theory with 12 massless fundamental fermions in a colour-twisted box

We perform the step-scaling investigation of the running coupling constant, using the gradient-flow scheme, in SU(3) gauge theory with twelve massless fermions in the fundamental representation. The Wilson plaquette gauge action and massless unimproved staggered fermions are used in the simulations. Our lattice data are prepared at high accuracy, such that the statistical error for the renormalised coupling, g_GF, is at the subpercentage level. To investigate the reliability of the continuum extrapolation, we employ two different lattice discretisations to obtain g_GF. For our simulation setting, the corresponding gauge-field averaging radius in the gradient flow has to be almost half of the lattice size, in order to have this extrapolation under control. We can determine the renormalisation group evolution of the coupling up to g^2_GF ~ 6, before the onset of the bulk phase structure. In this infrared regime, the running of the coupling is significantly slower than the two-loop perturbative prediction, although we cannot draw definite conclusion regarding possible infrared conformality of this theory. Furthermore, we comment on the issue regarding the continuum extrapolation near an infrared fixed point. In addition to adopting the fit ansatz a'la Symanzik for performing this task, we discuss a possible alternative procedure inspired by properties derived from low-energy scale invariance at strong coupling. Based on this procedure, we propose a finite-size scaling method for the renormalised coupling as a means to search for infrared fixed point. Using this method, it can be shown that the behaviour of the theory around g^2_GF ~ 6 is still not governed by possible infrared conformality.Comment: 24 pages, 6 figures; Published version; Appendix A added for tabulating data; One reference included; Typos correcte

Dynamical meson-baryon resonances with chiral Lagrangians

The s-wave meson-baryon interaction is studied using the lowest-order chiral Lagrangian in a unitary coupled-channels Bethe-Salpeter equation. In the strangeness $S=-1$ sector the low-energy $K^- p$ dynamics leads to the dynamical generation of the $\Lambda(1405)$ as a ${\bar K}N$ state, along with a good description of the $K^- p$ scattering observables. At higher energies, the $\Lambda(1670)$ is also found to be generated dynamically as a $K \Xi$ quasibound state for the first time. For strangeness S=0, it is the $S_{11}(1535)$ resonance that emerges from the coupled-channels equations, leading to a satisfactory description of meson-baryon scattering observables in the energy region around the $S_{11}(1535)$. We speculate on the possible dynamical generation of $\Xi$ resonances within the chiral $S=-2$ sector as ${\bar K} \Lambda$ or ${\bar K} \Sigma$ quasibound states.Comment: 8 pages, 5 figures, Talk given at NSTAR2001, Workshop on the Physics of Excited Nucleons, Mainz (Germany), March 7-10, to be published in World Scientifi

The Resonance Overlap and Hill Stability Criteria Revisited

We review the orbital stability of the planar circular restricted three-body problem, in the case of massless particles initially located between both massive bodies. We present new estimates of the resonance overlap criterion and the Hill stability limit, and compare their predictions with detailed dynamical maps constructed with N-body simulations. We show that the boundary between (Hill) stable and unstable orbits is not smooth but characterized by a rich structure generated by the superposition of different mean-motion resonances which does not allow for a simple global expression for stability. We propose that, for a given perturbing mass $m_1$ and initial eccentricity $e$, there are actually two critical values of the semimajor axis. All values $a a_{\rm unstable}$ are unstable in the Hill sense. The first limit is given by the Hill-stability criterion and is a function of the eccentricity. The second limit is virtually insensitive to the initial eccentricity, and closely resembles a new resonance overlap condition (for circular orbits) developed in terms of the intersection between first and second-order mean-motion resonances.Comment: 33 pages, 14 figures, accepte