Generalized Forward-Backward Splitting

This paper introduces the generalized forward-backward splitting algorithm for minimizing convex functions of the form $F + \sum_{i=1}^n G_i$, where $F$ has a Lipschitz-continuous gradient and the $G_i$'s are simple in the sense that their Moreau proximity operators are easy to compute. While the forward-backward algorithm cannot deal with more than $n = 1$ non-smooth function, our method generalizes it to the case of arbitrary $n$. Our method makes an explicit use of the regularity of $F$ in the forward step, and the proximity operators of the $G_i$'s are applied in parallel in the backward step. This allows the generalized forward backward to efficiently address an important class of convex problems. We prove its convergence in infinite dimension, and its robustness to errors on the computation of the proximity operators and of the gradient of $F$. Examples on inverse problems in imaging demonstrate the advantage of the proposed methods in comparison to other splitting algorithms.Comment: 24 pages, 4 figure

Low Complexity Regularization of Linear Inverse Problems

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for recovering the unknown signal is to solve a convex optimization problem that enforces some prior knowledge about its structure. This has proved efficient in many problems routinely encountered in imaging sciences, statistics and machine learning. This chapter delivers a review of recent advances in the field where the regularization prior promotes solutions conforming to some notion of simplicity/low-complexity. These priors encompass as popular examples sparsity and group sparsity (to capture the compressibility of natural signals and images), total variation and analysis sparsity (to promote piecewise regularity), and low-rank (as natural extension of sparsity to matrix-valued data). Our aim is to provide a unified treatment of all these regularizations under a single umbrella, namely the theory of partial smoothness. This framework is very general and accommodates all low-complexity regularizers just mentioned, as well as many others. Partial smoothness turns out to be the canonical way to encode low-dimensional models that can be linear spaces or more general smooth manifolds. This review is intended to serve as a one stop shop toward the understanding of the theoretical properties of the so-regularized solutions. It covers a large spectrum including: (i) recovery guarantees and stability to noise, both in terms of $\ell^2$-stability and model (manifold) identification; (ii) sensitivity analysis to perturbations of the parameters involved (in particular the observations), with applications to unbiased risk estimation ; (iii) convergence properties of the forward-backward proximal splitting scheme, that is particularly well suited to solve the corresponding large-scale regularized optimization problem

Multiple regulation of prolactin receptor gene expression in rat liver

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Howling on the edge: Mantled howler monkey (Alouatta palliata) howling behaviour and anthropogenic edge effects in a fragmented tropical rainforest in Costa Rica

The function of long calling is a subject of interest across animal behaviour study, particularly within primatology. Many primate species have male‐specific long‐distance calls, including platyrrhines like the folivorous howler monkey (Alouatta spp.). Howler monkeys may howl to defend resources such as feeding trees or areas of rich vegetation from other monkey groups. This study tests the ecological resource defence hypothesis for howling behaviour in the mantled howler monkey (Alouatta palliata) and investigates how anthropogenic forest fragmentation may influence howling behaviour. More specifically, this study examines how howling bout rate, duration, precursors and tree species richness, DBH, and canopy cover vary in 100 m anthropogenic edge and interior forest zones at La Suerte Biological Research Station (LSBRS), a fragmented tropical rainforest in Costa Rica. Results show that tree species richness and canopy cover are higher in forest interior at this site, suggesting that monkeys should howl at greater rates in the interior to defend access to these higher‐quality vegetation resources. Overall, our results supported the ecological resource defence hypothesis. The main howl precursor was howling from neighbouring groups. Although howling rate did not differ between forest zones, howling bouts from forest interior were longer, had a greater number of howls per bout and were preceded by different precursors than howls from anthropogenic edge zones, including more howls from neighbouring groups. Our findings provide some of the first evidence for behavioural edge effects in primate vocal communication behaviour

Le risque écotoxicologique dans le bassin de la Seine

National audienceLe PIREN-Seine s’intéresse à la présence dans le bassin versant de la Seine de contaminants d’origines agricole, industrielle et domestique depuis une vingtaine d’années. Ces polluants, qui se retrouvent parfois à des concentrations très faibles dans l’eau, peuvent avoir des impacts sur l’homme et l’environnement qui restent peu connus. La présence de ces substances toxiques suscite un intérêt majeur auprès des gestionnaires de la ressource comme des consommateurs. Les perturbations endocriniennes, les effets cancérigènes, la présence de résidus de médicaments sont autant de sujets d’inquiétude largement médiatisés et débattus. Pour garantir la protection de la santé humaine et du milieu aquatique, la réglementation a défini des normes de qualité environnementale, les NQE. En application de la directive cadre sur l’eau, des seuils de concentrations moyennes et maximales ont été édictées par la directive fille 2008/105/EC du 16 décembre 2008 pour les 33 substances prioritaires initialement listées. Des NQE provisoires sont aussi disponibles pour plus de 100 autres substances. Les NQE reposent sur l’évaluation approfondie des effets toxiques en laboratoire de ces molécules. L’écotoxicologie traite des effets toxiques des substances chimiques sur les organismes vivants et l’environnement. Ce thème de recherche est étudié aujourd’hui par les équipes d’écotoxicologie, d’écologie et de chimie du PIREN-Seine, notamment via des études sur trois sites pilotes : le bassin de l’Orge, le bassin de la Vesle et l’axe Seine. Comment mesurer l’impact de ces substances ? Les analyses chimiques étant insuffisantes pour évaluer le risque des substances toxiques dans le milieu, les scientifiques étudient d’autres méthodes. Les bio-essais réalisés en laboratoire en font partie. Regroupant un ensemble très vaste d’essais réalisés sur des échantillons de l’environnement, ils permettent de caractériser le «potentiel toxique», comme la présence des perturbateurs endocriniens et la génotoxicité des masses d’eau. In situ, la bioaccumulation, mesurée sur des organismes «sentinelles» contribue à l’évaluation de l’exposition aux micropolluants. Enfin, les biomarqueurs constituent une solution prometteuse pour diagnostiquer l’impact sur l’environnement des contaminants chimiques