Accelerated Projected Gradient Method for Linear Inverse Problems with Sparsity Constraints

Regularization of ill-posed linear inverse problems via $\ell_1$ penalization has been proposed for cases where the solution is known to be (almost) sparse. One way to obtain the minimizer of such an $\ell_1$ penalized functional is via an iterative soft-thresholding algorithm. We propose an alternative implementation to $\ell_1$-constraints, using a gradient method, with projection on $\ell_1$-balls. The corresponding algorithm uses again iterative soft-thresholding, now with a variable thresholding parameter. We also propose accelerated versions of this iterative method, using ingredients of the (linear) steepest descent method. We prove convergence in norm for one of these projected gradient methods, without and with acceleration.Comment: 24 pages, 5 figures. v2: added reference, some amendments, 27 page

The social responsibility imposed to social design moved by sense

Relata a origem do design e seu caráter social desconectado da economia vigente na época. Aborda a preocupação da população atual em relação ao desenvolvimento sustentável, e demonstra que o design social pode contribuir no processo de desenvolvimento econômico, sócio-cultural do país, exemplificando algumas açõe

Taxonomy of asteroid families among the Jupiter Trojans: Comparison between spectroscopic data and the Sloan Digital Sky Survey colors

We present a comparative analysis of the spectral slope and color distributions of Jupiter Trojans, with particular attention to asteroid families. We use a sample of data from the Moving Object Catalogue of the Sloan Digital Sky Survey, together with spectra obtained from several surveys. A first sample of 349 observations, corresponding to 250 Trojan asteroids, were extracted from the Sloan Digital Sky Survey, and we also extracted from the literature a second sample of 91 spectra, corresponding to 71 Trojans. The spectral slopes were computed by means of a least-squares fit to a straight line of the fluxes obtained from the Sloan observations in the first sample, and of the rebinned spectra in the second sample. In both cases the reflectance fluxes/spectra were renormalized to 1 at 6230 $\textrm{\AA}$. We found that the distribution of spectral slopes among Trojan asteroids shows a bimodality. About 2/3 of the objects have reddish slopes compatible with D-type asteroids, while the remaining bodies show less reddish colors compatible with the P-type and C-type classifications. The members of asteroid families also show a bimodal distribution with a very slight predominance of D-type asteroids, but the background is clearly dominated by the D-types. The L4 and L5 swarms show different distributions of spectral slopes, and bimodality is only observed in L4. These differences can be attributed to the asteroid families since the backgraound asteroids show the same slope distribtuions in both swarms. The analysis of individual families indicates that the families in L5 are taxonomically homogeneous, but in L4 they show a mixture of taxonomic types. We discuss a few scenarios that might help to interpret these results.Comment: 20 pages, 15 figures, 2 table

Puzzling asteroid 21 Lutetia: our knowledge prior to the Rosetta fly-by

A wide observational campaign was carried out in 2004-2009 aimed to complete the ground-based investigation of Lutetia prior to the Rosetta fly-by in July 2010. We have obtained BVRI photometric and V-band polarimetric measurements over a wide range of phase angles, and visible and infrared spectra in the 0.4-2.4 micron range. We analyzed them together with previously published data to retrieve information on Lutetia's surface properties. Values of lightcurve amplitudes, absolute magnitude, opposition effect, phase coefficient and BVRI colors of Lutetia surface seen at near pole-on aspect have been determined. We defined more precisely parameters of polarization phase curve and showed their distinct deviation from any other moderate-albedo asteroid. An indication of possible variations both in polarization and spectral data across the asteroid surface was found. To explain features found by different techniques we propose that (i) Lutetia has a non-convex shape, probably due to the presence of a large crater, and heterogeneous surface properties probably related to surface morphology; (ii) at least part of the surface is covered by a fine-grained regolith with particle size less than 20 microns; (iii) the closest meteorite analogues of Lutetia's surface composition are particular types of carbonaceous chondrites or Lutetia has specific surface composition not representative among studied meteorites

Low delta-V near-Earth asteroids: A survey of suitable targets for space missions

In the last decades Near-Earth Objects (NEOs) have become very important targets to study, since they can give us clues to the formation, evolution and composition of the Solar System. In addition, they may represent either a threat to humankind, or a repository of extraterrestrial resources for suitable space-borne missions. Within this framework, the choice of next-generation mission targets and the characterisation of a potential threat to our planet deserve special attention. To date, only a small part of the 11,000 discovered NEOs have been physically characterised. From ground and space-based observations one can determine some basic physical properties of these objects using visible and infrared spectroscopy. We present data for 13 objects observed with different telescopes around the world (NASA-IRTF, ESO-NTT, TNG) in the 0.4 - 2.5 um spectral range, within the NEOSURFACE survey (http://www.oa-roma.inaf.it/planet/NEOSurface.html). Objects are chosen from among the more accessible for a rendez-vous mission. All of them are characterised by a delta-V (the change in velocity needed for transferring a spacecraft from low-Earth orbit to rendez-vous with NEOs) lower than 10.5 km/s, well below the Solar System escape velocity (12.3 km/s). We taxonomically classify 9 of these objects for the first time. 11 objects belong to the S-complex taxonomy; the other 2 belong to the C-complex. We constrain the surface composition of these objects by comparing their spectra with meteorites from the RELAB database. We also compute olivine and pyroxene mineralogy for asteroids with a clear evidence of pyroxene bands. Mineralogy confirms the similarity with the already found H, L or LL ordinary chondrite analogues.Comment: 9 pages, 7 figures, to be published in A&A Minor changes by language edito

The Color Distribution in the Edgeworth-Kuiper Belt

We have started since 1997 the Meudon Multicolor Survey of Outer Solar System Objects with the aim of collecting a large and homogeneous set of color data for Trans-Neptunian and Centaurs objects [...] We have a combined sample of 52 B-R color measurements for 8 Centaurs, 22 Classicals, 13 Plutinos, 8 Scattered objects and 1 object with unidentified dynamical class. This dataset is the largest single and homogeneous published dataset to date [...]. A strong (color) correlation with mean excitation velocity points toward a space weathering/impact origin for the color diversity. However, thorough modeling of the collisional/dynamical environment in the Edgeworth-Kuiper belt needs to be done in order to confirm this scenario. We found also that the Classical TNOs consist in the superposition of two distinct populations: the dynamically Cold Classical TNOs (red colors, low i, small sizes) and the dynamically Hot Classical TNOs (diverse colors, moderate and high i, larger sizes). [...] Our specific observation strategy [...] permitted us to highlight a few objects suspected to have true compositional and/or texture variation on their surfaces. These are 1998 HK151, 1999 DF9, 1999 OY3, 2000 GP183, 2000 OK67, and 2001 KA77 and should be prime targets for further observations [...]. Our survey has also highlighted 1998 SN165 whose colors and dynamical properties puts it in a new dynamical class distinct from the Classicals, its previously assigned dynamical class.Comment: Accepted for publication in Astronomical Journal (38 pages, inc. 11 figures

JAK-Inhibitors for the Treatment of Rheumatoid Arthritis : A Focus on the Present and an Outlook on the Future

Janus kinase inhibitors (JAKi) belong to a new class of oral targeted disease-modifying drugs which have recently revolutionized the therapeutic panorama of rheumatoid arthritis (RA) and other immune-mediated diseases, placing alongside or even replacing conventional and biological drugs. JAKi are characterized by a novel mechanism of action, consisting of the intracellular interruption of the JAK-STAT pathway crucially involved in the immune response. The aim of this narrative review is to globally report the most relevant pharmacological features and clinical outcomes of the developed and incoming JAKi for RA, based on the available preclinical and clinical evidence. A total of 219 papers, including narrative and systematic reviews, randomized controlled trials (RCTs), observational studies, case reports, guidelines, and drug factsheets, were selected. The efficacy and safety profile of both the first generation JAKi (baricitinib and tofacitinib) and the second generation JAKi (upadacitinib, filgotinib, peficitinib, decernotinib and itacitinib) were compared and discussed. Results from RCTs and real-life data are encouraging and outline a rapid onset of the pharmacologic effects, which are maintained during the time. Their efficacy and safety profile are comparable or superior to those of biologic agents and JAKi proved to be efficacious when given as monotherapy. Finally, the manufacturing of JAKi is relatively easier and cheaper than that of biologics, thus increasing the number of compounds being formulated and tested for clinical use

Beyond convergence rates: Exact recovery with Tikhonov regularization with sparsity constraints

The Tikhonov regularization of linear ill-posed problems with an $\ell^1$ penalty is considered. We recall results for linear convergence rates and results on exact recovery of the support. Moreover, we derive conditions for exact support recovery which are especially applicable in the case of ill-posed problems, where other conditions, e.g. based on the so-called coherence or the restricted isometry property are usually not applicable. The obtained results also show that the regularized solutions do not only converge in the $\ell^1$-norm but also in the vector space $\ell^0$ (when considered as the strict inductive limit of the spaces $\R^n$ as $n$ tends to infinity). Additionally, the relations between different conditions for exact support recovery and linear convergence rates are investigated. With an imaging example from digital holography the applicability of the obtained results is illustrated, i.e. that one may check a priori if the experimental setup guarantees exact recovery with Tikhonov regularization with sparsity constraints

"TNOs are Cool": A survey of the trans-Neptunian region X. Analysis of classical Kuiper belt objects from Herschel and Spitzer observations

The classical Kuiper belt contains objects both from a low-inclination, presumably primordial, distribution and from a high-inclination dynamically excited population. Based on a sample of classical TNOs with observations at thermal wavelengths we determine radiometric sizes, geometric albedos and thermal beaming factors as well as study sample properties of dynamically hot and cold classicals. Observations near the thermal peak of TNOs using infra-red space telescopes are combined with optical magnitudes using the radiometric technique with near-Earth asteroid thermal model (NEATM). We have determined three-band flux densities from Herschel/PACS observations at 70.0, 100.0 and 160.0 $\mu$m and Spitzer/MIPS at 23.68 and 71.42 $\mu$m when available. We have analysed 18 classical TNOs with previously unpublished data and re-analysed previously published targets with updated data reduction to determine their sizes and geometric albedos as well as beaming factors when data quality allows. We have combined these samples with classical TNOs with radiometric results in the literature for the analysis of sample properties of a total of 44 objects. We find a median geometric albedo for cold classical TNOs of 0.14 and for dynamically hot classical TNOs, excluding the Haumea family and dwarf planets, 0.085. We have determined the bulk densities of Borasisi-Pabu (2.1 g/cm^3), Varda-Ilmare (1.25 g/cm^3) and 2001 QC298 (1.14 g/cm^3) as well as updated previous density estimates of four targets. We have determined the slope parameter of the debiased cumulative size distribution of dynamically hot classical TNOs as q=2.3 +- 0.1 in the diameter range 100<D<500 km. For dynamically cold classical TNOs we determine q=5.1 +- 1.1 in the diameter range 160<D<280 km as the cold classical TNOs have a smaller maximum size.Comment: 22 pages, 7 figures Accepted to be published in Astronomy and Astrophysic

Linearly constrained evolutions of critical points and an application to cohesive fractures

We introduce a novel constructive approach to define time evolution of critical points of an energy functional. Our procedure, which is different from other more established approaches based on viscosity approximations in infinite dimension, is prone to efficient and consistent numerical implementations, and allows for an existence proof under very general assumptions. We consider in particular rather nonsmooth and nonconvex energy functionals, provided the domain of the energy is finite dimensional. Nevertheless, in the infinite dimensional case study of a cohesive fracture model, we prove a consistency theorem of a discrete-to-continuum limit. We show that a quasistatic evolution can be indeed recovered as a limit of evolutions of critical points of finite dimensional discretizations of the energy, constructed according to our scheme. To illustrate the results, we provide several numerical experiments both in one and two dimensions. These agree with the crack initiation criterion, which states that a fracture appears only when the stress overcomes a certain threshold, depending on the material