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Multiple penalized least squares (MPLS) models are a flexible approach to find adaptive least squares solutions required to be simultaneously sparse and smooth. This is particularly important when addressing real-life inverse problems where there is no ground truth available, such as electrophysiological source imaging. In this work we formalize a modified Newton-Raphson (MNR) algorithm to estimate general MPLS models and propose its extension to perform efficient optimization over the active set of selected features (AMNR). This algorithm can be used to minimize continuously differentiable objective functions with multiple restrictions, including sign constraints. We show that these algorithms provide solutions with acceptable reconstruction in simulated scenarios that do not cope with model assumptions, and for low n/p ratios. We then use both algorithms for estimating different electroencephalography (EEG) inverse models with multiple penalties. We also show how the AMNR allows us to estimate new models in the EEG inverse problem context, such as nonnegative versions of Smooth Garrote and Smooth LASSO. Synthetic data were used for a comparison between solutions obtained using the two algorithms proposed here and the least angle regression (LARS) algorithm, according to well-known quality measures. A visual event-related EEG from healthy young subjects and a resting-state EEG study on the relationship between cognitive ageing and walking speed decline in active elders, were used to illustrate the usefulness of the proposed methods in the analysis of real experimental data.

We present observations and models of the dust environment of activated asteroid P/2013 P5 (PANSTARRS). The object displayed a complex morphology during the observations, with the presence of multiple tails. We combined our own observations, all made with instrumentation attached to the 10.4m Gran Telescopio Canarias (GTC) on La Palma, with previously published Hubble Space Telescope (HST) images to build a model aimed at fitting all the observations. Altogether, the data cover a full 3-month period of observations which can be explained by an intermittent dust loss. The most plausible scenario is that of an asteroid rotating with the spinning axis oriented perpendicular to the orbit plane and loosing mass from the equatorial region, consistent with a rotational break-up. Assuming that the ejection velocity of the particles (v$\sim$0.02-0.05 m s$^{-1}$) corresponds to the escape velocity, the object diameter is constrained to $\sim$30-130 m for bulk densities 3000 to 1000 kg m$^{-3}$., Comment: Accepted by ApJ

Events such as GRB130606A at z=5.91, offer an exciting new window into pre-galactic metal enrichment in these very high redshift host galaxies. We study the environment and host galaxy of GRB 130606A, a high-z event, in the context of a high redshift population of GRBs. We have obtained multiwavelength observations from radio to gamma-ray, concentrating particularly on the X-ray evolution as well as the optical photometric and spectroscopic data analysis. With an initial Lorentz bulk factor in the range \Gamma_0 ~ 65-220, the X-ray afterglow evolution can be explained by a time-dependent photoionization of the local circumburst medium, within a compact and dense environment. The host galaxy is a sub-DLA (log N (HI) = 19.85+/-0.15), with a metallicity content in the range from ~1/7 to ~1/60 of solar. Highly ionized species (N V and Si IV) are also detected. This is the second highest redshift burst with a measured GRB-DLA metallicity and only the third GRB absorber with sub-DLA HI column density. GRB ' lighthouses' therefore offer enormous potential as backlighting sources to probe the ionization and metal enrichment state of the IGM at very high redshifts for the chemical signature of the first generation of stars., Comment: 10 pages, 9 figures, submitted to A&A. Typos corrected