Remarks on existence and uniqueness of Cournot–Nash equilibria in the non-potential case

This article is devoted to various methods (optimal transport, fixed-point, ordinary differential equations) to obtain existence and/or uniqueness of Cournot–Nash equilibria for games with a continuum of players with both attractive and repulsive effects. We mainly address separable situations but for which the game does not have a potential, contrary to the variational framework of Blanchet and Carlier (Optimal transport and Cournot–Nash equilibria, 2012). We also present several numerical simulations which illustrate the applicability of our approach to compute Cournot–Nash equilibria.     

Dominance-based heuristics for one-machine total cost scheduling problems

We study the one-machine scheduling problem with release dates and we look at several objective functions including total (weighted) tardiness and total (weighted) completion time. We describe dominance rules for these criteria, as well as techniques for using these dominance rules to build heuristic solutions. We use them to improve certain well-known greedy heuristic algorithms from the literature. Finally, we introduce a Tabu Search method with a neighborhood based on our dominance rules. Experiments show the effectiveness of our techniques in obtaining very good solutions for all studied criteria.     

On a weighted total variation minimization problem

The present article is devoted to the study of a constrained weighted total variation minimization problem, which may be viewed as a relaxation of a generalized Cheeger problem and is motivated by landslide modeling. Using the fact that the set of minimizers is invariant by a wide class of monotone transformations, we prove that level sets of minimizers are generalized Cheeger sets and obtain qualitative properties of the minimizers: they are all bounded and all achieve their essential supremum on a set of positive measure.     

Absolute rate constants for the gas‐phase ozonolysis of isoprene and methylbutenol

The reactions of the biogenic organic compounds isoprene and 2‐methyl‐3‐buten‐2‐ol (MBO) with ozone have been investigated under controlled conditions for pressure (atmospheric pressure) and temperature (293 ± 2 K), using FTIR spectrometry. CO was added to scavenge hydroxyl radical formation during the ozonolysis experiments. Reaction rate constants were determined by absolute rate technique, by measuring both ozone and the organic compound concentrations. The measured values were k₁ = (1.19 ± 0.09) × 10^?17 cm³ molecule^?1 s^?1 for the reaction between ozone and isoprene and k₂ = (8.3 ± 1.0) × 10_?18 cm³ molecule^?1 s^?1 for the reaction between ozone and MBO. © 2004 Wiley Periodicals, Inc. Int J Chem Kinet 36: 152–156 2004     

Scheduling subject to nonrenewable-resource constraints

Polynomially bounded solution methods are presented to solve a class of precedence constrained scheduling problems in which each job requires a certain amount of nonrenewable resource that is being consumed during its execution.     

In vitro 4 MHz NMR proton relaxation times and in vitro mechanical behavior at low extension of human common carotid arterial wall

We investigated the influence of the biomechanical behavior of human common carotid arterial wall on the NMR proton relaxation times using a Bruker Minispec at 4 MHz. The study was limited to low extension in simple longitudinal elongation of the carotid wall (the maximum loading stretch ratio being 40%). Twenty-five carotid samples divided into 2 longitudinal strips were tested. The first strip was used to determine the nondimensional elastic parameter alpha according to the mechanical model of Fung. The second strip was used to measure the proton relaxation times. T1 value was 316.8 ms +/- 27.6 and T2 value was 59.9 ms +/- 6.8. A significant linear correlation was found between T1 and Ln alpha (p = 0.02). T1 and T2 were not correlated to the age but linearly correlated to the tissue water content (p less than 0.0001), however the age and alpha were not correlated to the tissue water content. These results may reflect the differences in the amount of water binding sites of the elastin which is involved in the elasticity of the carotid wall at low extension.     

An automated image-processing strategy to analyze dynamic arterial spin labeling perfusion studies. Application to human skeletal muscle under stress

Arterial spin labeling (ASL) perfusion measurements allow the follow-up of muscle perfusion with high temporal resolution during a stress test. Automated image processing is proposed to estimate perfusion maps from ASL images. It is based on two successive analyses: at first, automated rejection of the image pairs between which a large displacement is detected is performed, followed by factor analysis of the dynamic data and cluster analysis to classify pixels with large signal variation characteristic of vessels. Then, after masking these "vascular" pixels, factor analysis and cluster analysis are further applied to separate the different muscles between low or high perfusion increase, yielding a functional map of the leg. Data from 10 subjects (five normal volunteers and five elite sportsmen) had been analyzed. Resulting time perfusion curves from a region of interest (ROI) in active muscles show a good accordance whether extracted with automated processing or with manual processing. This method of functional segmentation allows automated suppression of vessels and fast visualization of muscles with high, medium or low perfusion, without any a priori knowledge.