On Improvements to the Analytic Center Cutting Plane Method

In this paper, we explore a weakness of a specific implementation of the analytic center cutting plane method applied to convex optimization problems, which may lead to weaker results than Kelley's cutting plane method. Improvements to the analytic center cutting plane method are suggested, and tested on some example problems.     

Matched/Mismatched interaction of a cyclic hexapeptide with ion pairs containing chiral cations and chiral anions

The binding of a chiral quaternary ammonium ion to a cyclopeptide containing aromatic amino acid subunits is affected not only by the configuration of the cation but also by the configuration of the chiral counterion. Analysis of the binding equilibria shows that complex formation involves interaction of the whole ion pair with the host indicating that steric requirements of the anion influence complex geometry and stability.     

Review of stationary phases for microelectromechanical systems in gas chromatography: feasibility and separations

This review covers the recent development of stationary phases for chip-based gas chromatography (GC). Portable systems for rapid and reliable analysis are urgently needed. One way to achieve this is to miniaturize the entire analysis. Because the column is the central component of the GC system and determines the feasibility and quality of separation, this review focuses on stationary phases reported in the literature and their use in different fields during the last two decades, with emphasis on different methods for introducing the stationary phase into the GC column.     

Solving the p-Median Problem with a Semi-Lagrangian Relaxation

Lagrangian relaxation is commonly used in combinatorial optimization to generate lower bounds for a minimization problem. We study a modified Lagrangian relaxation which generates an optimal integer solution. We call it semi-Lagrangian relaxation and illustrate its practical value by solving large-scale instances of the p-median problem. This work was partially supported by the Fonds National Suisse de la Recherche Scientifique, grant 12-57093.99 and the Spanish government, MCYT subsidy dpi2002-03330.     

One-step stereoselective synthesis and NMR chiral shift properties of a novel hexacoordinated phosphorus cation

[reaction: see text] Tropolone, binol, and PCl(5) react in CH(2)Cl(2) at reflux to generate in one step a novel C(2)-symmetric hexacoordinated phosphorus cation of configuration controlled by the binol ligand. It behaves as an efficient NMR chiral shift agent for chiral anionic phosphate and borate anions.     

Taking into account both preparation and injection in high-performance liquid chromatography linearity studies

As mentioned in International Conference on Harmonisation publications, linearity is a principal parameter in method validation. The most popular statistical tool used is linear least-squares regression. Contrary to what is still very often practiced, the correlation coefficient can in no way be considered as an indicator of the fit quality. There is in fact a test called the "lack-of-fit test" that enables one to answer the question, "Is the linear model adapted to the calibration curve?". However, this test can give erroneous conclusions when, at each level, several sources of variation for the response are influent. It often occurs in high-performance liquid chromatography, as shown in a following example, where the calibration curve is obtained from repeated injections of repeated dilutions of a parent solution. The lack-of-fit test rejected linearity, although it was at least questionable. In fact, the reason for a discrepancy of this kind lies in the presence of a double source of variation: injection and dilution. It is possible to overcome the problem by mixing a nested ANOVA with the standard least-square linear regression. As shown in an example, implementing this methodology for data processing allows one not only to carry out an unbiased lack-of-fit test but also give estimates of the dispersion introduced respectively by the preparation and the injection.     

Strategically zero-sum games: The class of games whose completely mixed equilibria cannot be improved upon

In this paper we propose a new class of games, the “strategically zero-sum games,” which are characterized by a special payoff structure. We show that for a large body of correlation schemes which includes the correlated strategies “à la Aumann”, strategically zero-sum games are exactly these games for which no completely mixed Nash equilibrium can be improved upon.     

An oracle based method to compute a coupled equilibrium in a model of international climate policy

This paper proposes a computational game-theoretic model for the international negotiations that should take place at the end of the period covered by the Kyoto protocol. These negotiations could lead to a self-enforcing agreement on a burden sharing scheme given the necessary global emissions limit that will be imposed when the real extent of climate change is known. The model assumes a non-cooperative behavior of the parties except for the fact that they will be collectively committed to reach a target on total cumulative emissions by the year 2050. The concept of normalized equilibrium, introduced by J.B. Rosen for concave games with coupled constraints, is used to characterize a family of dynamic equilibrium solutions in an m-player game where the agents are (groups of) countries and the payoffs are the welfare gains obtained from a Computable General Equilibrium (CGE) model. The model deals with the uncertainty about climate sensitivity by computing an S-adapted equilibrium. These equilibria are computed using an oracle-based method permitting an implicit definition of the payoffs to the different players, obtained through simulations performed with the global CGE model GEMINI-E3. Partly supported by GICC (French Ministry of Ecology), TOCSIN (EU-044287) and the Swiss-NSF NCCR-Climate program of the Swiss NSF. For helpful comments and discussions, we thank A. Bernard, P. Thalmann, and the anonymous referee.