We propose a forecasting approach for solar flares based on data from Solar Cycle 24, taken by the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) mission. In particular, we use the Spaceweather HMI Active Region Patches (SHARP) product that facilitates cut-out magnetograms of solar active regions (AR) in the Sun in near-realtime (NRT), K. Florios cflorios@aueb.gr I. Kontogiannis K. Florios et al.taken over a five-year interval (2012 -2016). Our approach utilizes a set of thirteen predictors, which are not included in the SHARP metadata, extracted from line-of-sight and vector photospheric magnetograms. We exploit several Machine Learning (ML) and Conventional Statistics techniques to predict flares of peak magnitude >M1 and >C1, within a 24 h forecast window. The ML methods used are multi-layer perceptrons (MLP), support vector machines (SVM) and random forests (RF). We conclude that random forests could be the prediction technique of choice for our sample, with the second best method being multi-layer perceptrons, subject to an entropy objective function. A Monte Carlo simulation showed that the best performing method gives accuracy ACC=0.93(0.00), true skill statistic TSS=0.74(0.02) and Heidke skill score HSS=0.49(0.01) for >M1 flare prediction with probability threshold 15% and ACC=0.84(0.00), TSS=0.60(0.01) and HSS=0.59(0.01) for >C1 flare prediction with probability threshold 35%.

The least-squares approach to image deblurring leads to an ill-posed problem. The addition of the nonnegativity constraint, when appropriate, does not provide regularization, even if, as far as we know, a thorough investigation of the illposedness of the resulting constrained least-squares problem has still to be done. Iterative methods, converging to nonnegative least-squares solutions, have been proposed. Some of them have the 'semi-convergence' property, i.e. early stopping of the iteration provides 'regularized' solutions. In this paper we consider two of these methods: the projected Landweber (PL) method and the iterative image space reconstruction algorithm (ISRA). Even if they work well in many instances, they are not frequently used in practice because, in general, they require a large number of iterations before providing a sensible solution. Therefore, the main purpose of this paper is to refresh these methods by increasing their efficiency. Starting from the remark that PL and ISRA require only the computation of the gradient of the functional, we propose the application to these algorithms of special acceleration techniques that have been recently developed in the area of the gradient methods. In particular, we propose the application of efficient step-length selection rules and line-search strategies. Moreover, remarking that ISRA is a scaled gradient algorithm, we evaluate its behaviour in comparison with a recent scaled gradient projection (SGP) method for image deblurring. Numerical experiments demonstrate that the accelerated methods still exhibit the semi-convergence property, with a considerable gain both in the number of iterations and in the computational time; in particular, SGP appears definitely the most efficient one.

Aims. The Spectrometer Telescope for Imaging X-rays (STIX) on Solar Orbiter is a hard X-ray imaging spectrometer, which covers the energy range from 4 to 150 keV. STIX observes hard X-ray bremsstrahlung emissions from solar flares and therefore provides diagnostics of the hottest (⪆10 MK) flare plasma while quantifying the location, spectrum, and energy content of flare-accelerated nonthermal electrons. Methods. To accomplish this, STIX applies an indirect bigrid Fourier imaging technique using a set of tungsten grids (at pitches from 0.038 to 1 mm) in front of 32 coarsely pixelated CdTe detectors to provide information on angular scales from 7 to 180 arcsec with 1 keV energy resolution (at 6 keV). The imaging concept of STIX has intrinsically low telemetry and it is therefore well-suited to the limited resources available to the Solar Orbiter payload. To further reduce the downlinked data volume, STIX data are binned on board into 32 selectable energy bins and dynamically-adjusted time bins with a typical duration of 1 s during flares. Results. Through hard X-ray diagnostics, STIX provides critical information for understanding the acceleration of electrons at the Sun and their transport into interplanetary space and for determining the magnetic connection of Solar Orbiter back to the Sun. In this way, STIX serves to link Solar Orbiter’s remote and in-situ measurements.

In 1993, Snyder et al investigated the maximum-likelihood (ML) approach to the deconvolution of images acquired by a charge-coupled-device camera and proved that the iterative method proposed by Llacer and Nuñez in 1990 can be derived from the expectation-maximization method of Dempster et al for the solution of ML problems. The utility of the approach was shown on the reconstruction of images of the Hubble space Telescope. This problem deserves further investigation because it can be important in the deconvolution of images of faint objects provided by next-generation ground-based telescopes that will be characterized by large collecting areas and advanced adaptive optics. In this paper, we first prove the existence of solutions of the ML problem by investigating the properties of the negative log of the likelihood function. Next, we show that the iterative method proposed by the above-mentioned authors is a scaled gradient method for the constrained minimization of this function in the closed and convex cone of the non-negative vectors and that, if it is convergent, the limit is a solution of the constrained ML problem. Moreover, by looking for the asymptotic behavior in the regime of high numbers of photons, we find an approximation that, as proved by numerical experiments, works well for any number of photons, thus providing an efficient implementation of the algorithm. In the case of image deconvolution, we also extend the method to take into account boundary effects and multiple images of the same object. The approximation proposed in this paper is tested on a few numerical examples.

Solar flares originate from magnetically active regions but not all solar active regions give rise to a flare. Therefore, the challenge of solar flare prediction benefits by an intelligent computational analysis of physics-based properties extracted from active region observables, most commonly line-ofsight or vector magnetograms of the active-region photosphere. For the purpose of flare forecasting, this study utilizes an unprecedented 171 flare-predictive active region properties, mainly inferred by the Helioseismic and Magnetic Imager onboard the Solar Dynamics Observatory (SDO/HMI) in the course of the European Union Horizon 2020 FLARECAST project. Using two different supervised machine learning methods that allow feature ranking as a function of predictive capability, we show that: i) an objective training and testing process is paramount for the performance of every supervised machine learning method; ii) most properties include overlapping information and are therefore highly redundant for flare prediction; iii) solar flare prediction is still -and will likely remain -a predominantly probabilistic challenge. Nishizuka et al 2018) within the recent field of space weather forecasting that relies on the availability of two ingredients; one observational and one computational. First, it is well-established that solar active regions (ARs) exclusively host major flares and therefore flare prediction needs experimental data on AR properties, associated to the photospheric and coronal magnetic field; however, coronal information has only recently started being used in the form of EUV images given as input to a deep learning network by Nishizuka et al (2018). Second, this information on AR magnetic properties can be processed for prediction purposes by means of a computational method for data analysis; machine learning has recently offered strong candidates for such methods.Since February 2010, the Helioseismic and Magnetic Imager onboard the Solar Dynamics Observatory (SDO/HMI) (Scherrer et al 2012) is providing both line-of-sight and vector magnetograms of the full solar disk at a (vector magnetogram) cadence of 12 minutes. SDO/HMI magnetograms can be used for solar flare prediction according to two different approaches. First, HMI magnetograms are utilized to calculate a variety of properties either from the line-of-sight component only, from the radial component only, or from all three vector components. Various single-valued quantities, hereafter referred to as features, can be calculated from these property images through a variety of techniques (e.g., thresholding, feature recognition, etc), such that calculation of one physical property may provide multiple features as inputs to machine learning (i.e., image maximum, total, and moments). Of course, additional features that are not derived from property images may also contribute to the input dataset. Second, from a deep learning perspective, HMI images can be given as input to Convolutional Neural Networks (CNNs) that automatically perform a probabilistic f...

Aims. To study the acceleration and propagation of bremsstrahlung-producing electrons in solar flares, we analyze the evolution of the flare loop size with respect to energy at a variety of times. A GOES M3.7 loop-structured flare starting around 23:55 on 2002 April 14 is studied in detail using Ramaty High Energy Solar Spectroscopic Imager (RHESSI) observations. Methods. We construct photon and mean-electron-flux maps in 2-keV energy bins by processing observationally-deduced photon and electron visibilities, respectively, through several image-processing methods: a visibility-based forward-fit (FWD) algorithm, a maximum entropy (MEM) procedure and the uv-smooth (UVS) approach. We estimate the sizes of elongated flares (i.e., the length and width of flaring loops) by calculating the second normalized moments of the intensity in any given map. Employing a collisional model with an extended acceleration region, we fit the loop lengths as a function of energy in both the photon and electron domains. Results. The resulting fitting parameters allow us to estimate the extent of the acceleration region which is between ∼13 arcsec and ∼19 arcsec. Both forward-fit and uv-smooth algorithms provide substantially similar results with a systematically better fit in the electron domain. Conclusions. The consistency of the estimates from these methods provides strong support that the model can reliably determine geometric parameters of the acceleration region. The acceleration region is estimated to be a substantial fraction (∼1/2) of the loop extent, indicating that this dense flaring loop incorporates both acceleration and transport of electrons, with concurrent thick-target bremsstrahlung emission.

We introduce a hybrid approach to solar flare prediction, whereby a supervised regularization method is used to realize feature importance and an unsupervised clustering method is used to realize the binary flare/no-flare decision. The approach is validated against NOAA SWPC data.

This paper introduces a novel compartmental model describing the excretion of 18F-fluoro-deoxyglucose (FDG) in the renal system and a numerical method based on the maximum likelihood for its reduction. This approach accounts for variations in FDG concentration due to water re-absorption in renal tubules and the increase of the bladder's volume during the FDG excretion process. From the computational viewpoint, the reconstruction of the tracer kinetic parameters is obtained by solving the maximum likelihood problem iteratively, using a non-stationary, steepest descent approach that explicitly accounts for the Poisson nature of nuclear medicine data. The reliability of the method is validated against two sets of synthetic data realized according to realistic conditions. Finally we applied this model to describe FDG excretion in the case of animal models treated with metformin. In particular we show that our approach allows the quantitative estimation of the reduction of FDG de-phosphorylation induced by metformin.