On the Impact of Fair Best Response Dynamics

In this work we completely characterize how the frequency with which each player participates in the game dynamics affects the possibility of reaching efficient states, i.e., states with an approximation ratio within a constant factor from the price of anarchy, within a polynomially bounded number of best responses. We focus on the well known class of congestion games and we show that, if each player is allowed to play at least once and at most $\beta$ times any $T$ best responses, states with approximation ratio $O(\beta)$ times the price of anarchy are reached after $T \lceil \log \log n \rceil$ best responses, and that such a bound is essentially tight also after exponentially many ones. One important consequence of our result is that the fairness among players is a necessary and sufficient condition for guaranteeing a fast convergence to efficient states. This answers the important question of the maximum order of $\beta$ needed to fast obtain efficient states, left open by [9,10] and [3], in which fast convergence for constant $\beta$ and very slow convergence for $\beta=O(n)$ have been shown, respectively. Finally, we show that the structure of the game implicitly affects its performances. In particular, we show that in the symmetric setting, in which all players share the same set of strategies, the game always converges to an efficient state after a polynomial number of best responses, regardless of the frequency each player moves with

Edge Partitions of Optimal 22-plane and 33-plane Graphs

A topological graph is a graph drawn in the plane. A topological graph is $k$-plane, $k>0$, if each edge is crossed at most $k$ times. We study the problem of partitioning the edges of a $k$-plane graph such that each partite set forms a graph with a simpler structure. While this problem has been studied for $k=1$, we focus on optimal $2$-plane and $3$-plane graphs, which are $2$-plane and $3$-plane graphs with maximum density. We prove the following results. (i) It is not possible to partition the edges of a simple optimal $2$-plane graph into a $1$-plane graph and a forest, while (ii) an edge partition formed by a $1$-plane graph and two plane forests always exists and can be computed in linear time. (iii) We describe efficient algorithms to partition the edges of a simple optimal $2$-plane graph into a $1$-plane graph and a plane graph with maximum vertex degree $12$, or with maximum vertex degree $8$ if the optimal $2$-plane graph is such that its crossing-free edges form a graph with no separating triangles. (iv) We exhibit an infinite family of simple optimal $2$-plane graphs such that in any edge partition composed of a $1$-plane graph and a plane graph, the plane graph has maximum vertex degree at least $6$ and the $1$-plane graph has maximum vertex degree at least $12$. (v) We show that every optimal $3$-plane graph whose crossing-free edges form a biconnected graph can be decomposed, in linear time, into a $2$-plane graph and two plane forests

On non-L2L^2 solutions to the Seiberg-Witten equations

We show that a previous paper of Freund describing a solution to the Seiberg-Witten equations has a sign error rendering it a solution to a related but different set of equations. The non-$L^2$ nature of Freund's solution is discussed and clarified and we also construct a whole class of solutions to the Seiberg-Witten equations.Comment: 8 pages, Te

Equatorial Annual Oscillation with QBO-driven 5-year Modulation in NCEP Data

An analysis is presented of the zonal wind and temperature variations supplied by the National Center for Environmental Prediction (NCEP), which have been assimilated in the Reanalysis and the Climate Prediction Center (CCP) data sets. The derived zonal-mean variations are employed. Stimulated by modeling studies, the data are separated into the hemispherically symmetric and anti-symmetric components, and spectral analysis is applied to study the annual 12-month oscillation and Quasi-biennial Oscillation (QBO). For data samples that cover as much as 40 years, the results reveal a pronounced 5-year modulation of the symmetric AO in the lower stratosphere, which is confined to equatorial latitudes. This modulation is also inferred for the temperature variations but extends to high latitudes, qualitatively consistent with published model results. A comparison between different data samples indicates that the signature of the 5-year oscillation is larger when the QBO of 30 months is more pronounced. Thus there is circumstantial evidence that this periodicity of the QBO is involved in generating the oscillation. The spectral analysis shows that there is a weak anti-symmetric 5-year oscillation in the zonal winds, which could interact with the large antisymmetric A0 to produce the modulation of the symmetric AO as was shown in earlier modeling studies. According to these studies, the 30-month QBO tends to be synchronized by the equatorial Semi-annual Oscillation (SAO), and this would explain why the inferred 5-year modulation is observed to persist and is phase locked over several cycles

Suggestion, hypnosis and hypnotherapy: a survey of use, knowledge and attitudes of anaesthetists

Publisher's copy made available with the permission of the publisher © Australian Society of AnaesthetistsClinical hypnosis is a skill of using words and gestures (frequently called suggestions) in particular ways to achieve specific outcomes. It is being increasingly recognised as a useful intervention for managing a range of symptoms, especially pain and anxiety. We surveyed all 317 South Australian Fellows and trainees registered with ANZCA to determine their use, knowledge of, and attitudes towards positive suggestion, hypnosis and hypnotherapy in their anaesthesia practice. The response rate was 218 anaesthetists (69%). The majority of respondents (63%) rated their level of knowledge on this topic as below average. Forty-eight per cent of respondents indicated that there was a role for hypnotherapy in clinical anaesthesia, particularly in areas seen as traditional targets for the modality, i.e. pain and anxiety states. Nearly half of the anaesthetists supported the use of hypnotherapy and positive suggestions within clinical anaesthesia. Those respondents who had experience of clinical hypnotherapy were more likely to support hypnosis teaching at undergraduate or postgraduate level when compared with those with no experience.http://www.aaic.net.au/Article.asp?D=200408

Hot dense capsule implosion cores produced by z-pinch dynamic hohlraum radiation

Hot dense capsule implosions driven by z-pinch x-rays have been measured for the first time. A ~220 eV dynamic hohlraum imploded 1.7-2.1 mm diameter gas-filled CH capsules which absorbed up to ~20 kJ of x-rays. Argon tracer atom spectra were used to measure the Te~ 1keV electron temperature and the ne ~ 1-4 x10^23 cm-3 electron density. Spectra from multiple directions provide core symmetry estimates. Computer simulations agree well with the peak compression values of Te, ne, and symmetry, indicating reasonable understanding of the hohlraum and implosion physics.Comment: submitted to Phys. Rev. Let

Global embedding of the Kerr black hole event horizon into hyperbolic 3-space

An explicit global and unique isometric embedding into hyperbolic 3-space, H^3, of an axi-symmetric 2-surface with Gaussian curvature bounded below is given. In particular, this allows the embedding into H^3 of surfaces of revolution having negative, but finite, Gaussian curvature at smooth fixed points of the U(1) isometry. As an example, we exhibit the global embedding of the Kerr-Newman event horizon into H^3, for arbitrary values of the angular momentum. For this example, considering a quotient of H^3 by the Picard group, we show that the hyperbolic embedding fits in a fundamental domain of the group up to a slightly larger value of the angular momentum than the limit for which a global embedding into Euclidean 3-space is possible. An embedding of the double-Kerr event horizon is also presented, as an example of an embedding which cannot be made global.Comment: 16 pages, 13 figure

Singular forces and point-like colloids in lattice Boltzmann hydrodynamics

We present a second-order accurate method to include arbitrary distributions of force densities in the lattice Boltzmann formulation of hydrodynamics. Our method may be used to represent singular force densities arising either from momentum-conserving internal forces or from external forces which do not conserve momentum. We validate our method with several examples involving point forces and find excellent agreement with analytical results. A minimal model for dilute sedimenting particles is presented using the method which promises a substantial gain in computational efficiency.Comment: 22 pages, 9 figures. Submitted to Phys. Rev.

Gas loading of graphene-quartz surface acoustic wave devices

Copyright © 2013 AIP PublishingGraphene was transferred to the propagation path of quartz surface acoustic wave devices and the attenuation due to gas loading of air and argon measured at 70 MHz and 210 MHz and compared to devices with no graphene. Under argon loading, there was no significant difference between the graphene and non-graphene device and the values of measured attenuation agree well with those calculated theoretically. Under air loading, at 210 MHz, there was a significant difference between the non-graphene and graphene devices, with the average value of attenuation obtained with the graphene devices being approximately twice that obtained from the bare quartz devices.Royal Societ