A Differentiable Homotopy to Compute Nash Equilibria of n-Person Games

The literature on the computation of Nash equilibria in n-person games is dominated by simplicial methods. This paper is the first to introduce a globally convergent algorithm that fully exploits the differentiability present in the problem. It presents an everywhere differentiable homotopy to do the computations. The homotopy path can therefore be followed by several numerical techniques. Moreover, instead of computing some Nash equilibrium, the algorithm is constructed in such a way that it computes the Nash equilibrium selected by the tracing procedure of Harsanyi and Selten. As a by-product of our proofs it follows that for a generic game the tracing procedure defines an unique feasible path. The numerical performance of the algorithm is illustrated by means of several examples.microeconomics ;

Galactic annihilation emission from nucleosynthesis positrons

The Galaxy hosts a widespread population of low-energy positrons revealed by successive generations of gamma-ray telescopes through a bright annihilation emission from the bulge region, with a fainter contribution from the inner disk. The exact origin of these particles remains currently unknown. We estimate the contribution to the annihilation signal of positrons generated in the decay of radioactive 26Al, 56Ni and 44Ti. We adapted the GALPROP propagation code to simulate the transport and annihilation of radioactivity positrons in a model of our Galaxy. Using plausible source spatial distributions, we explored several possible propagation scenarios to account for the large uncertainties on the transport of ~1MeV positrons in the interstellar medium. We then compared the predicted intensity distributions to the INTEGRAL/SPI observations. We obtain similar intensity distributions with small bulge-to-disk ratios, even for extreme large-scale transport prescriptions. At least half of the positrons annihilate close to their sources, even when they are allowed to travel far away. In the high-diffusion, ballistic case, up to 40% of them escape the Galaxy. In proportion, this affects bulge positrons more than disk positrons because they are injected further off the plane in a tenuous medium, while disk positrons are mostly injected in the dense molecular ring. The predicted intensity distributions are fully consistent with the observed longitudinally-extended disk-like emission, but the transport scenario cannot be strongly constrained by the current data. Nucleosynthesis positrons alone cannot account for the observed annihilation emission in the frame of our model. An additional component is needed to explain the strong bulge contribution, and the latter is very likely concentrated in the central regions if positrons have initial energies in the 100keV-1MeV range.Comment: 16 pages, 7 figures, accepted for publication in A&

Effect of reinforcing submicron SiC particles on the wear of electrolytic NiP coatings Part 1. Uni-directional sliding

As-plated and annealed NiP coatings and composite NiP-SiC coatings were investigated in uni-directional ball-on-disc sliding tests. Abrasive wear was noticed in the case of composite NiP coatings containing submicron SiC particles, whereas in NiP coatings oxidational wear was active. The addition of submicron SiC particles not only increases the hardness of these electrolytic coatings but also hinders the formation of an oxide film in the sliding wear track. As a consequence, the wear loss on as-plated NiP coatings is not markedly reduced by the addition of SiC particles. On the contrary, a heat treatment at 420 °C for 1 h decreases the wear loss on both pure NiP and composite NiP-SiC coatings. During that heat treatment, Ni3P precipitates are formed in the NiP matrix and owing to this fact, the hardness of both pure NiP and composite NiP-SiC coatings increases. However, the heat treatment of composite NiP-SiC coatings induces the sensitivity for crack formation in the NiP matrix around these SiC particles. As a result, the pull out of SiC particles in the wear track occurs easily during sliding, and the wear loss of composite NiP-SiC coatings remains above the wear loss on NiP coatings

Effect of reinforcing submicron SiC particles on the wear of electrolytic NiP coatings Part 2: Bi-directional sliding

As-plated and heat-treated electrodeposited NiP and composite NiP-SiC coatings were investigated in bi-directional ball-on-disc sliding tests. All tests were performed under gross slip conditions. Heat treatment decreases the wear volume loss during fretting in ambient air for all coatings investigated. Heat-treated NiP coating has a lower wear volume loss compared to composite NiP-SiC coatings for all sliding tests. The wear rate at the bi-directional sliding test was found to be lower relative to the wear rate at uni-directional sliding test

Stochastic Resonance in a simple model of magnetic reversals

We discuss the effect of stochastic resonance in a simple model of magnetic reversals. The model exhibits statistically stationary solutions and bimodal distribution of the large scale magnetic field. We observe a non trivial amplification of stochastic resonance induced by turbulent fluctuations, i.e. the amplitude of the external periodic perturbation needed for stochastic resonance to occur is much smaller than the one estimated by the equilibrium probability distribution of the unperturbed system. We argue that similar amplifications can be observed in many physical systems where turbulent fluctuations are needed to maintain large scale equilibria.Comment: 6 page

Non equilibrium thermodynamics and cosmological pancakes formation

We investigate the influence of non equilibrium thermodynamics on cosmological structure formation. In this paper, we consider the collapse of planar perturbations usually called "Zel'dovich pancakes". We have developed for that purpose a new two fluids (gas and dark matter) hydrodynamical code, with three different thermodynamical species: electrons, ions and neutral particles (T_e\ne T_i \ne T_n). We describe in details the complex structure of accretion shock waves. We include several relevant processes for a low density, high temperature, collisional plasma such as non-equilibrium chemical reactions, cooling, shock heating, thermal energy equipartition between electrons, ions and neutral particles and electronic conduction. We find two different regions in the pancake structure: a thermal precursor ahead of the compression front and an equipartition wave after the compression front where electrons and ions temperatures differ significantly. This complex structure may have two interesting consequences: pre-heating of unshocked regions in the vicinity of massive X-ray clusters and ions and electrons temperatures differences in the outer regions of X-rays clusters.Comment: 30 pages, including 8 figures, accepted for publication in The Astrophysical Journa

Cutting the Climate-Development Gordian Knot - Economic options in a politically constrained world

Combating climate change cannot but be a cooperative venture amongst nations. Together with the problem posed by the withdrawal of the US from the Kyoto Protocol, the key challenge for winning the battle is the involvement of developing countries in efforts to alter their GHGs emissions trends. This involvement is necessary technically but also politically to bring the largest emitter of the planet back on the battle field. In the first section we draw on history to outline the intellectual underpinning of North/South divide around climate affairs. In the second section we show the economic basis for a leverage effect between development and climate policies. The third section ventures to propose some guidance to develop a viable climate regime strong enough to support an ambitious effort to decarbonize economies and we show that the Kyoto framework, once re-interpreted and amended is not so far from this working drawing.climate policy; development

Weak lensing B-modes on all scales as a probe of local isotropy

This article derives a multipolar hierarchy for the propagation of the weak-lensing shear and convergence in a general spacetime. The origin of B-modes, in particular on large angular scales, is related to the local isotropy of space. Known results assuming a Friedmann-Lema\^itre background are naturally recovered. The example of a Bianchi I spacetime illustrates our formalism and its implications for future observations are stressed.Comment: 10 pages, 2 figures. Replaced to match published versio