Robustness to Strategic Uncertainty (Revision of DP 2010-70)

We model a player’s uncertainty about other players’ strategy choices as smooth probability distributions over their strategy sets. We call a strategy profile (strictly) robust to strategic uncertainty if it is the limit, as uncertainty vanishes, of some sequence (all sequences) of strategy profiles, in each of which every player’s strategy is optimal under under his or her uncertainty about the others. We derive general properties of such robustness, and apply the definition to Bertrand competition games and the Nash demand game, games that admit infinitely many Nash equilibria. We show that our robustness criterion selects a unique Nash equilibrium in the Bertrand games, and that this agrees with recent experimental findings. For the Nash demand game, we show that the less uncertain party obtains the bigger share.Nash equilibrium;refinement;strategic uncertainty;price competition;Bertrand competition;bargaining;Nash demand game

Relations between topography, wetlands, vegetation cover and stream water chemistry in boreal headwater catchments in Sweden

International audienceA large part of the spatial variation of stream water chemistry is found in headwater streams and small catchments. To understand the dominant processes, taking place in small and heterogeneous catchments, spatial and temporal data with high resolution is needed. In most cases available map data has too low quality and resolution to successfully be used in environmental assessments and modelling. In this study 18 forested catchments (1?4 km2) were selected within a 120×50 km area in the county of Värmland in western Sweden. The aim was to test if topographic and vegetation variables derived from official datasets were correlated to stream water chemistry, represented by DOC, Al, Fe and Si content. A GIS was used to analyse the elevation characteristics, generate topographic indices and calculate the percentage of wetlands and a number of vegetation classes. The results clearly show that the topography has a major influence on the occurrence of wetlands, which has a major influence on stream water chemistry. There were very strong correlations between mean slope and percentage wetland, percentage wetland and DOC, mean slope and DOC and mean topographic wetness index and DOC. The conclusion was that official topographic data, despite uncertain or low quality and resolution, could be useful in the prediction of headwater chemistry in boreal forested catchments

A microfluidic device for the study of the orientational dynamics of microrods

We describe a microfluidic device for studying the orientational dynamics of microrods. The device enables us to experimentally investigate the tumbling of microrods immersed in the shear flow in a microfluidic channel with a depth of 400 mu and a width of 2.5 mm. The orientational dynamics was recorded using a 20 X microscopic objective and a CCD camera. The microrods were produced by shearing microdroplets of photocurable epoxy resin. We show different examples of empirically observed tumbling. On the one hand we find that short stretches of the experimentally determined time series are well described by fits to solutions of Jeffery's approximate equation of motion [Jeffery, Proc. R. Soc. London. 102 (1922), 161-179]. On the other hand we find that the empirically observed trajectories drift between different solutions of Jeffery's equation. We discuss possible causes of this orbit drift.Comment: 11 pages, 8 figure

Second look at the spread of epidemics on networks

In an important paper, M.E.J. Newman claimed that a general network-based stochastic Susceptible-Infectious-Removed (SIR) epidemic model is isomorphic to a bond percolation model, where the bonds are the edges of the contact network and the bond occupation probability is equal to the marginal probability of transmission from an infected node to a susceptible neighbor. In this paper, we show that this isomorphism is incorrect and define a semi-directed random network we call the epidemic percolation network that is exactly isomorphic to the SIR epidemic model in any finite population. In the limit of a large population, (i) the distribution of (self-limited) outbreak sizes is identical to the size distribution of (small) out-components, (ii) the epidemic threshold corresponds to the phase transition where a giant strongly-connected component appears, (iii) the probability of a large epidemic is equal to the probability that an initial infection occurs in the giant in-component, and (iv) the relative final size of an epidemic is equal to the proportion of the network contained in the giant out-component. For the SIR model considered by Newman, we show that the epidemic percolation network predicts the same mean outbreak size below the epidemic threshold, the same epidemic threshold, and the same final size of an epidemic as the bond percolation model. However, the bond percolation model fails to predict the correct outbreak size distribution and probability of an epidemic when there is a nondegenerate infectious period distribution. We confirm our findings by comparing predictions from percolation networks and bond percolation models to the results of simulations. In an appendix, we show that an isomorphism to an epidemic percolation network can be defined for any time-homogeneous stochastic SIR model.Comment: 29 pages, 5 figure

Robustness to Strategic Uncertainty (Revision of DP 2010-70)

We model a player’s uncertainty about other players’ strategy choices as smooth probability distributions over their strategy sets. We call a strategy profile (strictly) robust to strategic uncertainty if it is the limit, as uncertainty vanishes, of some sequence (all sequences) of strategy profiles, in each of which every player’s strategy is optimal under under his or her uncertainty about the others. We derive general properties of such robustness, and apply the definition to Bertrand competition games and the Nash demand game, games that admit infinitely many Nash equilibria. We show that our robustness criterion selects a unique Nash equilibrium in the Bertrand games, and that this agrees with recent experimental findings. For the Nash demand game, we show that the less uncertain party obtains the bigger share.

Evolution of glutamate dehydrogenase genes: evidence for lateral gene transfer within and between prokaryotes and eukaryotes

BACKGROUND: Lateral gene transfer can introduce genes with novel functions into genomes or replace genes with functionally similar orthologs or paralogs. Here we present a study of the occurrence of the latter gene replacement phenomenon in the four gene families encoding different classes of glutamate dehydrogenase (GDH), to evaluate and compare the patterns and rates of lateral gene transfer (LGT) in prokaryotes and eukaryotes. RESULTS: We extend the taxon sampling of gdh genes with nine new eukaryotic sequences and examine the phylogenetic distribution pattern of the various GDH classes in combination with maximum likelihood phylogenetic analyses. The distribution pattern analyses indicate that LGT has played a significant role in the evolution of the four gdh gene families. Indeed, a number of gene transfer events are identified by phylogenetic analyses, including numerous prokaryotic intra-domain transfers, some prokaryotic inter-domain transfers and several inter-domain transfers between prokaryotes and microbial eukaryotes (protists). CONCLUSION: LGT has apparently affected eukaryotes and prokaryotes to a similar extent within the gdh gene families. In the absence of indications that the evolution of the gdh gene families is radically different from other families, these results suggest that gene transfer might be an important evolutionary mechanism in microbial eukaryote genome evolution

Models for the magnetic ac susceptibility of granular superferromagnetic CoFe/Al2_2O3_3

The magnetization and magnetic ac susceptibility, $\chi = \chi' - i \chi''$, of superferromagnetic systems are studied by numerical simulations. The Cole-Cole plot, $\chi''$ vs. $\chi'$, is used as a tool for classifying magnetic systems by their dynamical behavior. The simulations of the magnetization hysteresis and the ac susceptibility are performed with two approaches for a driven domain wall in random media. The studies are motivated by recent experimental results on the interacting nanoparticle system Co$_{80}$Fe$_{20}$/Al$_{2}$O$_{3}$ showing superferromagnetic behavior. Its Cole-Cole plot indicates domain wall motion dynamics similarly to a disordered ferromagnet, including pinning and sliding motion. With our models we can successfully reproduce the features found in the experimental Cole-Cole plots.Comment: 8 pages, 6 figure

Memory Effect, Rejuvenation and Chaos Effect in the Multi-layer Random Energy Model

We introduce magnetization to the Multi-layer Random Energy Model which has a hierarchical structure, and perform Monte Carlo simulation to observe the behavior of ac-susceptibility. We find that this model is able to reproduce three prominent features of spin glasses, i.e., memory effect, rejuvenation and chaos effect, which were found recently by various experiments on aging phenomena with temperature variations.Comment: 10 pages, 14 figures, to be submitted to J. Phys. Soc. Jp

Nonexistence of Generalized Apparent Horizons in Minkowski Space

We establish a Positive Mass Theorem for initial data sets of the Einstein equations having generalized trapped surface boundary. In particular we answer a question posed by R. Wald concerning the existence of generalized apparent horizons in Minkowski space