New algorithms for approximate Nash equilibria in bimatrix games

We consider the problem of computing additively approximate Nash equilibria in non-cooperative two-player games. We provide a new polynomial time algorithm that achieves an approximation guarantee of 0.36392. Our work improves the previously best known (0.38197¿+¿e)-approximation algorithm of Daskalakis, Mehta and Papadimitriou [6]. First, we provide a simpler algorithm, which also achieves 0.38197. This algorithm is then tuned, improving the approximation error to 0.36392. Our method is relatively fast, as it requires solving only one linear program and it is based on using the solution of an auxiliary zero-sum game as a starting point. The first author was supported by NWO. The second and third author were supported by the EU Marie Curie Research Training Network, contract numbers MRTN-CT-2003-504438-ADONET and MRTN-CT-2004-504438-ADONET respectively

Prélèvement et échantillonnage dans les petits bassins-versants ruraux

Cet article traite de la représentativité des prélèvements d'eau effectués dans le cadre de suivis de bassins versants ou de rivières.Les réflexions proposées sont en premier lieu basées sur des expérimentations de laboratoire et de terrain destinées à comparer divers systèmes et modalités de prélèvements. Les résultats obtenus montrent en particulier que les prélèvements de matières en suspension de dimensions > 100 µm sont peu fiables alors que ce type de particules présente, dans certain cas, une contribution non négligeable aux flux de phosphore total.Les suivis réalisés en divers points représentatifs de petits bassins expérimentaux fournissent des éléments de discussion complémentaires sur le choix des sites des prélèvements et sur les pas de temps de ceux-ci. Nous montrons entre autre, toute l'importance de saisir le début des crues dans les bassins à forte pollution ponctuelle et de considérer des suivis des périodes suffisamment longues pour intégrer les divers fonctionnements hydrochimiques du bassin versant étudié.Water and suspended matter sampling in hydrographic networks is studied through various sampling systems and procedures, and through devices used in fields and in laboratories (fig. 1).Large size particles tend to be underestimated whatever the sampling procedure (manual or automatic) (fig. 2, 3). On the other hand, the sampling for soluble elements and small site particles (less man 50 µm) is very reliable. This is observed in suspended matter concentrations, eg < 2 g.l-1.The largest particles of suspended matter sometimes contribute to nutrient transfer, e.g. phosphorous. This however depends upon the presence of soil microaggregates and nutrient geochemistry. Moreover, natural hydrological variations give rise to another problem for sampling, especially for suspended matter (fig. 7, 9, 10, table 2).Comparatively the variation due to preservation of water is of secondary importance (fig. 11).However, thanks to results from monitoring in experimental watersheds, it is possible to find the best sampling station and the hast time to carry out sampling (fig. 12, 13; fable 3).Duration of survey and intervals between each sample depend, of course, upon the objectives of the study, but also upon watershed characteristics. Considering these characteristics, we propose an example of sampling stategy in the text (table 6, fig. 5)

Is there a reentrant glass in binary mixtures?

By employing computer simulations for a model binary mixture, we show that a reentrant glass transition upon adding a second component only occurs if the ratio $\alpha$ of the short-time mobilities between the glass-forming component and the additive is sufficiently small. For $\alpha \approx 1$, there is no reentrant glass, even if the size asymmetry between the two components is large, in accordance with two-component mode coupling theory. For $\alpha \ll 1$, on the other hand, the reentrant glass is observed and reproduced only by an effective one-component mode coupling theory.Comment: 4 pages, 3 figure

Design of high affinity cyclic pentapeptide ligands for Κ-opioid receptors

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73319/1/j.1399-3011.2005.00295.x.pd