Scene-adapted plug-and-play algorithm with convergence guarantees

Recent frameworks, such as the so-called plug-and-play, allow us to leverage the developments in image denoising to tackle other, and more involved, problems in image processing. As the name suggests, state-of-the-art denoisers are plugged into an iterative algorithm that alternates between a denoising step and the inversion of the observation operator. While these tools offer flexibility, the convergence of the resulting algorithm may be difficult to analyse. In this paper, we plug a state-of-the-art denoiser, based on a Gaussian mixture model, in the iterations of an alternating direction method of multipliers and prove the algorithm is guaranteed to converge. Moreover, we build upon the concept of scene-adapted priors where we learn a model targeted to a specific scene being imaged, and apply the proposed method to address the hyperspectral sharpening problem

Unplugging the Universe: the neglected electromagnetic consequence of decoupling

This letter concentrates on the non-equilibrium evolution of magnetic field structures at the onset of recombination, when the charged particle current densities decay as neutrals are formed. We consider the effect that a decaying magnetic flux has on the acceleration of particles via the transient induced electric field. Since the residual charged-particle number density is small as a result of decoupling, we shall consider the magnetic and electric fields essentially to be imposed, neglecting the feedback from any minority accelerated population. We find that the electromagnetic treatment of this phase transition can produce energetic electrons scattered throughout the Universe. Such particles could have a significant effect on cosmic evolution in several ways: (i) their presence could delay the effective end of the recombination era; (ii) they could give rise to plasma concentrations that could enhance early gravitational collapse of matter by opposing cosmic expansion to a greater degree than neutral matter could; (iii) they could continue to be accelerated, and become the seed for reionisation at the later epoch $z \approx 10$.Comment: 4 pages, no figure

On the changes in the physical properties of the ionized region around the Weigelt structures in Eta Carinae over the 5.54-yr spectroscopic cycle

We present HST/STIS observations and analysis of two prominent nebular structures around the central source of Eta Carinae, the knots C and D. The former is brighter than the latter for emission lines from intermediate or high ionization potential ions. The brightness of lines from intermediate and high ionization potential ions significantly decreases at phases around periastron. We do not see conspicuous changes in the brightness of lines from low ionization potential (<13.6 eV) that the total extinction towards the Weigelt structures is that the total extinction towards the Weigelt structures is AsubV =2/0. that the total extinction towards the Weigelt structures is AV = 2.0. Weigelt C and D are characterized by an electron density of that the total extinction towards the Weigelt structures is AV = 2.0. Weigelt C and D are characterized by an electron density of 10exp6.9 cm-3 that does not significantly change throughout the orbital cycle. The electron temperature varies from 5500 K (around periastron) to 7200 K (around apastron). The relative changes in the brightness of He I lines are well reproduced by the variations in the electron temperature alone. We found that, at phases around periastron, the electron temperature seems to be higher for Weigelt C than that of D. The Weigelt structures are located close to the Homunculus equatorial plane, at a distance of about 1240 AU from the central source. From the analysis of proper motion and age, the Weigelt complex can be associated with the equatorial structure called the Butterfly Nebula surrounding the central binary system.Comment: 19 pages, 18 figure

Problem-based learning and applied mathematics

Problem-based learning (PBL) is a teaching method that appeared in the early 1960s and is widely applied in distinct areas nowadays. In the presented manuscript, we describe a PBL methodology use restricted to applied mathematics for problem solving among a group of engineering students in a Portuguese university. In the pandemic context, it was a huge challenge both for the students and for the teacher. Supported by the available literature, the experiment was defined. As it is well known, teachers are not only knowledge transmitters but also designers of teaching initiatives. Thus, teachers and students both have a large role in PBL methodologies, where collaboration, reflection and concepts discussion are essential. In the presented pedagogical challenge, students were devoted to integrating the previous knowledge acquired and the one acquired during the project. This process improved their new competences—both personal and team work. Despite being a recent pedagogical method, PBL is revealed to be an important teaching tool.info:eu-repo/semantics/publishedVersio

The three-dimensional structure of the Eta Carinae Homunculus

We investigate, using the modeling code SHAPE, the three-dimensional structure of the bipolar Homunculus nebula surrounding Eta Carinae, as mapped by new ESO VLT/X-Shooter observations of the H2 $\lambda=2.12125$ micron emission line. Our results reveal for the first time important deviations from the axisymmetric bipolar morphology: 1) circumpolar trenches in each lobe positioned point-symmetrically from the center and 2) off-planar protrusions in the equatorial region from each lobe at longitudinal (~55 degrees) and latitudinal (10-20 degrees) distances from the projected apastron direction of the binary orbit. The angular distance between the protrusions (~110 degrees) is similar to the angular extent of each polar trench (~130 degrees) and nearly equal to the opening angle of the wind-wind collision cavity (~110 degrees). As in previous studies, we confirm a hole near the centre of each polar lobe and no detectable near-IR H2 emission from the thin optical skirt seen prominently in visible imagery. We conclude that the interaction between the outflows and/or radiation from the central binary stars and their orientation in space has had, and possibly still has, a strong influence on the Homunculus. This implies that prevailing theoretical models of the Homunculus are incomplete as most assume a single star origin that produces an axisymmetric nebula. We discuss how the newly found features might be related to the Homunculus ejection, the central binary and the interacting stellar winds. We also include a 3D printable version of our Homunculus model.Comment: 14 pages, 7 color figures, 1 interactive 3D figure (Figure 5, requires Adobe Reader), published in MNRAS. A 3D printable version of our Homunculus model can be downloaded from http://svs.gsfc.nasa.gov/vis/a010000/a011500/a011568/Eta_Car_Homunuculus_3D_model.zip or from the 'Supporting Information' link in the electronic version of the MNRAS articl

Esquemas de cruzamentos em gado de leite.

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