Six-month ground-based water vapour raman lidar measurements over Athens, Greece and system validation

Water vapour is one of the most important greenhouse gases, since it causes about two third of the natural greenhouse effect of the Earth's atmosphere. To improve the understanding of the role of the water vapour in the atmosphere, extensive water vapour profiles with high spatio-temporal resolution are therefore necessary. A ground-based Raman lidar system is used to perform water vapour measurements in Athens, Greece (37.9°N, 23.6°E, 200 m asi.). Water vapour mixing ratio measurements are retrieved from simultaneous inelastic H2O and N2 Raman backscatter lidar signals at 387 nm (from atmospheric N2) and 407 nm (from H2O). Systematic measurements are performed since September 2006. A new algorithm is used to retrieve water vapour vertical profiles in the lower troposphere (0.5-5 km range height asl.). The lidar observations are complemented with radiosonde measurements. Radiosonde data are obtained daily (at 00:00 UTC and 12:00 UTC) from the Hellenic Meteorological Service (HMS) of Greece which operates a meteorological station at the "Hellinikon" airport (37. 54° N, 23.44° E, 15m asl) in Athens, Greece. First results of the systematic intercomparison between water vapour profiles derived simultaneously by the Raman lidar and by radiosondes are presented and discussed

An Empirical Study of Finding Approximate Equilibria in Bimatrix Games

While there have been a number of studies about the efficacy of methods to find exact Nash equilibria in bimatrix games, there has been little empirical work on finding approximate Nash equilibria. Here we provide such a study that compares a number of approximation methods and exact methods. In particular, we explore the trade-off between the quality of approximate equilibrium and the required running time to find one. We found that the existing library GAMUT, which has been the de facto standard that has been used to test exact methods, is insufficient as a test bed for approximation methods since many of its games have pure equilibria or other easy-to-find good approximate equilibria. We extend the breadth and depth of our study by including new interesting families of bimatrix games, and studying bimatrix games upto size $2000 \times 2000$. Finally, we provide new close-to-worst-case examples for the best-performing algorithms for finding approximate Nash equilibria

Outlier resistant filtering and smoothing

AbstractWe consider a stationary Gaussian information process transmitted through an additive noise channel. We assume that the noise and information processes are mutually independent, and we model the noise process as nominally Gaussian with additive outliers. For the above system model, we first develop a theory for outlier resistant filtering and smoothing operations. We then design specific such nonlinear operations, and we study their performance. The performance criteria are the asymptotic mean squared error at the Gaussian nominal model, the breakdown point, and the influence function. We find that the proposed operations combine excellent performance at the nominal model with strong resistance to outliers

Approximate well-supported Nash equilibria in symmetric bimatrix games

The $\varepsilon$-well-supported Nash equilibrium is a strong notion of approximation of a Nash equilibrium, where no player has an incentive greater than $\varepsilon$ to deviate from any of the pure strategies that she uses in her mixed strategy. The smallest constant $\varepsilon$ currently known for which there is a polynomial-time algorithm that computes an $\varepsilon$-well-supported Nash equilibrium in bimatrix games is slightly below $2/3$. In this paper we study this problem for symmetric bimatrix games and we provide a polynomial-time algorithm that gives a $(1/2+\delta)$-well-supported Nash equilibrium, for an arbitrarily small positive constant $\delta$

On the Approximation Performance of Fictitious Play in Finite Games

We study the performance of Fictitious Play, when used as a heuristic for finding an approximate Nash equilibrium of a 2-player game. We exhibit a class of 2-player games having payoffs in the range [0,1] that show that Fictitious Play fails to find a solution having an additive approximation guarantee significantly better than 1/2. Our construction shows that for n times n games, in the worst case both players may perpetually have mixed strategies whose payoffs fall short of the best response by an additive quantity 1/2 - O(1/n^(1-delta)) for arbitrarily small delta. We also show an essentially matching upper bound of 1/2 - O(1/n)

Polylogarithmic Supports are required for Approximate Well-Supported Nash Equilibria below 2/3

In an epsilon-approximate Nash equilibrium, a player can gain at most epsilon in expectation by unilateral deviation. An epsilon well-supported approximate Nash equilibrium has the stronger requirement that every pure strategy used with positive probability must have payoff within epsilon of the best response payoff. Daskalakis, Mehta and Papadimitriou conjectured that every win-lose bimatrix game has a 2/3-well-supported Nash equilibrium that uses supports of cardinality at most three. Indeed, they showed that such an equilibrium will exist subject to the correctness of a graph-theoretic conjecture. Regardless of the correctness of this conjecture, we show that the barrier of a 2/3 payoff guarantee cannot be broken with constant size supports; we construct win-lose games that require supports of cardinality at least Omega((log n)^(1/3)) in any epsilon-well supported equilibrium with epsilon < 2/3. The key tool in showing the validity of the construction is a proof of a bipartite digraph variant of the well-known Caccetta-Haggkvist conjecture. A probabilistic argument shows that there exist epsilon-well-supported equilibria with supports of cardinality O(log n/(epsilon^2)), for any epsilon> 0; thus, the polylogarithmic cardinality bound presented cannot be greatly improved. We also show that for any delta > 0, there exist win-lose games for which no pair of strategies with support sizes at most two is a (1-delta)-well-supported Nash equilibrium. In contrast, every bimatrix game with payoffs in [0,1] has a 1/2-approximate Nash equilibrium where the supports of the players have cardinality at most two.Comment: Added details on related work (footnote 7 expanded