The VORTEX project: first results and perspectives

(abridged) Vortex coronagraphs are among the most promising solutions to perform high contrast imaging at small angular separations. They feature a very small inner working angle, a clear 360 degree discovery space, have demonstrated very high contrast capabilities, are easy to implement on high-contrast imaging instruments, and have already been extensively tested on the sky. Since 2005, we have been designing, developing and testing an implementation of the charge-2 vector vortex phase mask based on concentric subwavelength gratings, referred to as the Annular Groove Phase Mask (AGPM). Science-grade mid-infrared AGPMs were produced in 2012 for the first time, using plasma etching on synthetic diamond substrates. They have been validated on a coronagraphic test bench, showing broadband peak rejection up to 500:1 in the L band, which translates into a raw contrast of about $6\times 10^{-5}$ at $2 \lambda/D$. Three of them have now been installed on world-leading diffraction-limited infrared cameras (VLT/NACO, VLT/VISIR and LBT/LMIRCam). During the science verification observations with our L-band AGPM on NACO, we observed the beta Pictoris system and obtained unprecedented sensitivity limits to planetary companions down to the diffraction limit ($0.1''$). More recently, we obtained new images of the HR 8799 system at L band during the AGPM first light on LMIRCam. After reviewing these first results obtained with mid-infrared AGPMs, we will discuss the short- and mid-term goals of the on-going VORTEX project, which aims to improve the performance of our vortex phase masks for future applications on second-generation high-contrast imagers and on future extremely large telescopes (ELTs).Comment: To appear in SPIE proceedings vol. 914

COVID-19 symptoms at hospital admission vary with age and sex: results from the ISARIC prospective multinational observational study

Background: The ISARIC prospective multinational observational study is the largest cohort of hospitalized patients with COVID-19. We present relationships of age, sex, and nationality to presenting symptoms. Methods: International, prospective observational study of 60 109 hospitalized symptomatic patients with laboratory-confirmed COVID-19 recruited from 43 countries between 30 January and 3 August 2020. Logistic regression was performed to evaluate relationships of age and sex to published COVID-19 case definitions and the most commonly reported symptoms. Results: ‘Typical’ symptoms of fever (69%), cough (68%) and shortness of breath (66%) were the most commonly reported. 92% of patients experienced at least one of these. Prevalence of typical symptoms was greatest in 30- to 60-year-olds (respectively 80, 79, 69%; at least one 95%). They were reported less frequently in children (≤ 18 years: 69, 48, 23; 85%), older adults (≥ 70 years: 61, 62, 65; 90%), and women (66, 66, 64; 90%; vs. men 71, 70, 67; 93%, each P < 0.001). The most common atypical presentations under 60 years of age were nausea and vomiting and abdominal pain, and over 60 years was confusion. Regression models showed significant differences in symptoms with sex, age and country. Interpretation: This international collaboration has allowed us to report reliable symptom data from the largest cohort of patients admitted to hospital with COVID-19. Adults over 60 and children admitted to hospital with COVID-19 are less likely to present with typical symptoms. Nausea and vomiting are common atypical presentations under 30 years. Confusion is a frequent atypical presentation of COVID-19 in adults over 60 years. Women are less likely to experience typical symptoms than men

Continuous-time systems that solve computational problems

The concept of using continuous-time dynamical systems (described by ordinary differential equations) in order to solve computational problems is discussed, with an emphasis on convergence analysis and design procedures. The continuous-time approach is illustrated on concrete examples related to the computation of eigenvalues and eigenvectors of matrices

Noisy independent component analysis as a method of rotating the factor scores

Noisy independent component analysis (ICA) is viewed as a method of factor rotation in exploratory factor analysis (EFA). Starting from an initial EFA solution, rather than rotating the loadings towards simplicity, the factors are rotated orthogonally towards independence. An application to Thurstone's box problem in psychometrics is presented using a new data matrix containing measurement error. Results show that the proposed rotational approach to noisy ICA recovers the components used to generate the mixtures quite accurately and also produces simple loadings

Robust low-rank matrix completion by Riemannian optimization

Low-rank matrix completion is the problem where one tries to recover a low-rank matrix from noisy observations of a subset of its entries. In this paper, we propose RMC, a new method to deal with the problem of robust low-rank matrix completion, i.e., matrix completion where a fraction of the observed entries are corrupted by non-Gaussian noise, typically outliers. The method relies on the idea of smoothing the `1 norm and using Riemannian optimization to deal with the low-rank constraint. We first state the algorithms as the successive minimization of smooth approximations of the `1 norm and we analyze its convergence by showing the strict decrease of the objective function. We then perform numerical experiments on synthetic data and demonstrate the effectiveness on the proposed method on the Netflix dataset

On the Continuity of the Tangent Cone to the Determinantal Variety

Tangent and normal cones play an important role in constrained optimization to describe admissible search directions and, in particular, to formulate optimality conditions. They notably appear in various recent algorithms for both smooth and nonsmooth low-rank optimization where the feasible set is the set Rm×n≤r of all m × n real matrices of rank at most r. In this paper, motivated by the convergence analysis of such algorithms, we study, by computing inner and outer limits, the continuity of the correspondence that maps each X∈Rm×n≤r to the tangent cone to Rm×n≤r at X. We also deduce results about the continuity of the corresponding normal cone correspondence. Finally, we show that our results include as a particular case the a-regularity of the Whitney stratification of Rm×n≤r following from the fact that this set is a real algebraic variety, called the real determinantal variety