The value function of an asymptotic exit-time optimal control problem

We consider a class of exit--time control problems for nonlinear systems with a nonnegative vanishing Lagrangian. In general, the associated PDE may have multiple solutions, and known regularity and stability properties do not hold. In this paper we obtain such properties and a uniqueness result under some explicit sufficient conditions. We briefly investigate also the infinite horizon problem

Gravitational lensing and dynamics in SL2S\,J02140-0535: Probing the mass out to large radius

We aim to probe the mass of SL2S\,J02140-0535, a galaxy group at $z$ = 0.44 from the Strong Lensing Legacy Survey (SL2S). We combine strong lensing modeling and dynamical constraints. The strong lensing analysis is based on multi-band HST/ACS observations exhibiting strong lensing features that we have followed-up spectroscopically with VLT/FORS2. To constrain the scale radius of an NFW mass profile that cannot be constrained by strong lensing, we propose a new method by taking advantage of the large-scale dynamical information provided by VLT/FORS2 and KECK/LRIS spectroscopy of group members. In constrast to other authors, we show that the observed lensing features in SL2S\,J02140-0535 belong to different background sources: one at $z$ = 1.7 $\pm$ 0.1 produces three images, while the other at $z$ = 1.023 $\pm$ 0.001 has only a single image. Our unimodal NFW mass model reproduces these images very well. It is characterized by a concentration parameter $c_{200}$ = 6.0 $\pm$ 0.6, which is slightly greater than the value expected from $\Lambda$CDM simulations for a mass of M$_{200}$ $\approx$ 1 $\times$ 10$^{14}$ M_{\sun}. The spectroscopic analysis of group members also reveals a unimodal structure that exhibits no evidence of merging. We compare our dynamic mass estimate with an independent weak-lensing based mass estimate finding that both are consistent. Our combined lensing and dynamical analysis of SL2S\,J02140-0535 demonstrates the importance of spectroscopic information in reliably identifying the lensing features. Our findings argue that the system is a relaxed, massive galaxy group where mass is traced by light. This work shows a potentially useful method for constraining large-scale properties inaccessible to strong lensing, such as the scale radius of the NFW profile.Comment: Accepted for publication in A&

SARCS strong lensing galaxy groups: I - optical, weak lensing, and scaling laws

We present the weak lensing and optical analysis of the SL2S-ARCS (SARCS) sample of strong lens candidates. The sample is based on the Strong Lensing Legacy Survey (SL2S), a systematic search of strong lensing systems in the photometric Canada-France-Hawaii Telescope Legacy Survey (CFHTLS). The SARCS sample focuses on arc-like features and is designed to contain mostly galaxy groups. We briefly present the weak lensing methodology that we use to estimate the mass of the SARCS objects. Among 126 candidates, we obtain a weak lensing detection for 89 objects with velocity dispersions of the Singular Isothermal Sphere mass model ranging from 350 to 1000 km/s with an average value of 600km/s, corresponding to a rich galaxy group (or poor cluster). From the galaxies belonging to the bright end of the group's red sequence (M_i<-21), we derive the optical properties of the SARCS candidates. We obtain typical richnesses of N=5-15 galaxies and optical luminosities of L=0.5-1.5e+12 Lsol (within a radius of 0.5 Mpc). We use these galaxies to compute luminosity density maps, from which a morphological classification reveals that a large fraction of the sample are groups with a complex light distribution, either elliptical or multimodal, suggesting that these objects are dynamically young structures. We finally combine the lensing and optical analyses to draw a sample of 80 most secure group candidates, i.e. weak lensing detection and over-density at the lens position in the luminosity map, to remove false detections and galaxy-scale systems from the initial sample. We use this reduced sample to probe the optical scaling relations in combination with a sample of massive galaxy clusters. We detect the expected correlations over the probed range in mass with a typical scatter of 25% in the SIS velocity dispersion at a given richness or luminosity, making these scaling laws interesting mass proxie

Relation Discovery from Web Data for Competency Management

This paper describes a technique for automatically discovering associations between people and expertise from an analysis of very large data sources (including web pages, blogs and emails), using a family of algorithms that perform accurate named-entity recognition, assign different weights to terms according to an analysis of document structure, and access distances between terms in a document. My contribution is to add a social networking approach called BuddyFinder which relies on associations within a large enterprise-wide "buddy list" to help delimit the search space and also to provide a form of 'social triangulation' whereby the system can discover documents from your colleagues that contain pertinent information about you. This work has been influential in the information retrieval community generally, as it is the basis of a landmark system that achieved overall first place in every category in the Enterprise Search Track of TREC2006

Effect of stand-replacing fires on Mediterranean plant species in their marginal alpine range

In the southern side of the Alps, many relic species with Mediterranean and sub-Mediterranean distribution were described in mild-winter, fire-prone areas. Very few studies have modeled the importance of environmental factors on their distribution. In this paper, we assessed the effect of fire on the occurrence of euri- and steno-Mediterranean (ESM) species in Pinus sylvestris forests of Aosta Valley (Italy), by analyzing vegetation in a chronosequence of six stand-replacing fires (1962-2006). We analyzed species richness along the chronosequence, and modeled it as a function of time since fire, environment, and stand structure. We observed a strong positive association between ESM and total species richness. Temporal vegetation dynamics did not follow the direct succession pattern that is commonly observed in Mediterranean ecosystems. Two distinct maxima of ESM species richness were observed: (1) short lived, ruderal species (32 % of all ESM species) in the early post-fire stages, and (2) dry grassland species (54 %) in intermediate stages. The first were facilitated by the consumption of canopy and litter during fire, while the second by delayed tree canopy closure. In multivariate models of ESM species richness, light and elevation were the only significant predictors. Contrary to expectations, time since fire was not significant. Our study suggests that stand-replacing fires play an important role in preserving Mediterranean species in the study area by maintaining an open canopy, and promote local species diversity