Mathematics

Coupling forward-backward with penalty schemes and parallel splitting for constrained variational inequalities

H.Attouch , M.Czarnecki , J.Peypouquet


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We are concerned with the study of a class of forward-backward penalty schemes for solving variational inequalities 0 Ax + NC where H is a real Hilbert space, A : H H is a maximal monotone operator, and NC is the outward normal cone to a closed convex set C H. Let : H R be a convex differentiable function whose gradient is Lipschitz continuous, and which acts as a penalization function with respect to the constraint x C. Given a sequence of penalization parameters which tends to infinity, and a sequence of positive time steps 2 \ 1, we consider the diagonal forward-backward algorithm xn+1 = 1 ). Assuming that satisfies the growth condition limsup n nn < 2/ , we obtain weak ergodic convergence of the sequence to an equilibrium for a general maximal monotone operator A. We also obtain weak convergence of the whole sequence when A is the subdifferential of a proper lower-semicontinuous convex function. As a key ingredient of our analysis, we use the cocoerciveness of the operator. When specializing our results to coupled systems, we bring new light on Passty's Theorem, and obtain convergence results of new parallel splitting algorithms for variational inequalities involving coupling in the constraint. We also establish robustness and stability results that account for numerical approximation errors. An illustration to compressive sensing is given.

Air pollution and children's asthma-related emergency hospital visits in southeastern france

J.Gaudart , J.Mazenq , J.Dubus , D.Andre , A.Nougairede , V.Gilles , G.Noel


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Children's asthma is multifactorial. Environmental factors like air pollution exposure, meteorological conditions, allergens, and viral infections are strongly implicated. However, place of residence has rarely been investigated in connection with these factors. The primary aim of our study was to measure the impact of particulate matter , assessed close to the children's homes, on asthma-related pediatric emergency hospital visits within the Bouches-du-Rhone area in 2013. In a nested case-control study on 3-to 18-year-old children, each control was randomly matched on the emergency room visit day, regardless of hospital. Each asthmatic child was compared to 15 controls. PM10 and PM2. 5, meteorological conditions, pollens, and viral data were linked to ZIP code and analyzed by purpose of emergency visit. A total of 68,897 visits were recorded in children, 1182 concerning asthma. Short-term exposure to PM10 measured near children's homes was associated with excess risk of asthma emergency visits ). Male gender, young age, and temperature were other risk factors. Conversely, wind speed was a protective factor. CONCLUSION:PM10 and certain meteorological conditions near children's homes increased the risk of emergency asthma-related hospital visits in 3-to 18-year-old children in Bouches-du-Rhone. What is Known: A relationship between short-term exposure to air pollution and increase in emergency room visits or hospital admissions as a result of increased pollution levels has already been demonstrated. What is New: This study confirms these results but took into account confounding factors and is based on estimated pollution levels assessed close to the children's homes, rather than those recorded at the hospital. The study area, the Mediterranean, is favorable to creation of secondary pollutants in these sunny and dry seasons.

Crtgeedr: an r package for doubly robust generalized estimating equations estimations in cluster randomized trials with missing data

R.Wang , M.Prague , V.De


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Semi-parametric approaches based on generalized estimating equation are widelyused to analyse correlated outcomes. Most available softwares had been developed forlongitudinal settings. In this paper, we present a R package CRTgeeDR for estimatingparameters in marginal regression in cluster randomized trials. Theory for adjustingfor missing at random outcomes by inverse-probability weighting methods based on the use of a propensity score had been largely studied and implemented. Weexhibit that in CRTs most of the available softwares use an implementation of weightsthat lead to a bias in estimation if a non-independence working correlation structure ischosen. In CRTgeeDR, we solve this problem by using a different implementation whilekeeping the consistency properties of the IPW. Moreover, in CRTs using an augmentedGEE allow to improve efficiency by adjusting for treatment-covariate interactionsand imbalance in baseline covariates between treatment groups using an outcome model. In CRTgeeDR, we extend the abilities of existing packages such as geepack and geeMto allow such data augmentation. Finally, one may want to combine IPW and AUG ina Doubly Robust estimator, which lead to consistent estimation when either thepropensity score or the outcome model corresponds to the true data generation process. The DR approachis implemented in CRTgeeDR. Simulations studies demonstrate the consistency of IPWimplemented in CRTgeeDR and the gains associated with the use of the DR for analyzinga binary outcome using a logit regression. Finally, we reanalyzed data from a sanitationCRT in developing countries with the DRapproach compared to classical GEE and demonstrated a signiffcant intervention effect.
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