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Quantum games
(2000)
In these lecture notes we investigate the implications of the identification of strategies with quantum operations in game theory beyond the results presented in [J. Eisert, M. Wilkens, and M. Lewenstein, Phys. Rev. Lett. 83, 3077 (1999)]. After introducing a general framework, we study quantum games with a classical analogue in order to flesh out the peculiarities of game theoretical settings in the quantum domain. Special emphasis is given to a detailed investigation of different sets of quantum strategies.
We analyze the variability in the x-ray lightcurves of the black hole candidate Cygnus X-1 by linear and nonlinear time series analysis methods. While a linear model describes the overall second order properties of the observed data well, surrogate data analysis reveals a significant deviation from linearity. We discuss the relation between shot noise models usually applied to analyze these data and linear stochastic autoregressive models. We debate statistical and interpretational issues of surrogate data testing for the present context. Finally, we suggest a combination of tools from linear and nonlinear time series analysis methods as a procedure to test the predictions of astrophysical models on observed data.
An unresolved discussion in contemporary ecology deals with the relative importance of competition along environmental gradients. In deserts, local-scale differences in environmental productivity may be caused by the presence of shrubs, which represent a favorable habitat for annual populations within a nutrient-poor matrix. In this study, we attempted to test the hypothesis that facilitation of desert annuals by shrubs increase the intensity of competition among the annual plants. Such negative indirect effects have so far been ignored in studies about plant-plant interactions. We tested our hypothesis by measuring seedling survival and fecundity of four abundant annual plant species with and without neighbors in open areas and under shrub canopies in a sandy desert area. Our findings did not indicate indirect negative effects of shrubs on their understory annuals. Sensitivity to the presence of neighbors varied between species and surprisingly, the species with the smallest seeds was the only one which was not negatively affected by the presence of neighbors. In contrast to our hypothesis, there was no difference between the habitat types shrubs and openings in absolute and relative competition intensity. Our overall results suggest that negative indirect effects of shrubs are unimportant in determining demographic response of understory annual plants.
Recently, numerous studies have pointed to the importance of positive interactions in natural communities. There is now a broad consensus that the balance between negative and positive interactions should shift along environmental gradients, with competition prevailing under environmentally benign conditions and positive interactions dominating under harsh conditions. A commonly cited example of the importance of facilitation in harsh environments is the preference of desert annual plants for the areas under the canopy of shrubs. The recognition of apparently positive effects of desert shrubs on annuals, however, has been mostly based on density measurements, while fitness parameters of the understory plants have been ignored. Also, the temporal consistency of such effects has not been previously tested. Based on conceptual ideas about the balance between interference and facilitation, we predicted that positive effects of the shrubs on the understory should dominate in dry years, while in favorable years, negative effects would be stronger. We tested our hypothesis by measuring the direction and magnitude of the shrub effect on demographic responses of four desert annual plant species during four consecutive seasons of differing rainfall. The results contradicted our initial hypothesis. Depending on the species, the effect of the shrubs shifted from either negative to neutral or from neutral to positive with increasing annual rainfall. However, this trend was stronger for the effect of shrubs on plant reproductive success than on their densities. Our data highlight the importance of measuring fitness parameters in studies of plant-plant interactions. We suggest that the negative effects of shrubs on plant fitness were due to rainfall interception, while positive effects were related to increased nutrient availability beneath shrubs. However, the mechanisms by which the shrubs and annuals interact can only be resolved using an experimental approach. Our results contradict previous hypotheses about the relative importance of positive and negative interactions along environmental gradients. A simple conceptual model summarizing the proposed role of rainfall in determining the direction of shrub effects on their understory annuals is presented.