Gluck twist on a certain family of 2-knots

We show that by performing the Gluck twist along the 2-knot $K^2_{pq}$ derived from two ribbon presentations of the ribbon 1-knot $K(p,q)$ we get the standard 4-sphere $S^4$. In the proof we apply Kirby calculus.Comment: 11 pages, 12 figure

The twistor geometry of three-qubit entanglement

A geometrical description of three qubit entanglement is given. A part of the transformations corresponding to stochastic local operations and classical communication on the qubits is regarded as a gauge degree of freedom. Entangled states can be represented by the points of the Klein quadric ${\cal Q}$ a space known from twistor theory. It is shown that three-qubit invariants are vanishing on special subspaces of ${\cal Q}$. An invariant vanishing for the $GHZ$ class is proposed. A geometric interpretation of the canonical decomposition and the inequality for distributed entanglement is also given.Comment: 4 pages RevTeX

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 $\delta$

NS Fivebrane and Tachyon Condensation

We argue that a semi-infinite D6-brane ending on an NS5-brane can be obtained from the condensation of the tachyon on the unstable D9-brane of type IIA theory. The construction uses a combination of the descriptions of these branes as solitons of the worldvolume theory of the D9-brane. The NS5-brane, in particular, involves a gauge bundle which is operator valued, and hence is better thought of as a gerbe.Comment: 20 pages, harvma

Metamaterial-based graphene thermal emitter

This is the final version of the article. Available from Tsinghua University Press / Springer Verlag via the DOI in this record.The publisher's erratum to this article is in ORE: http://hdl.handle.net/10871/34353A thermal emitter composed of a frequency-selective surface metamaterial layer and a hexagonal boron nitride-encapsulated graphene filament is demonstrated. The broadband thermal emission of the metamaterial (consisting of ring resonators) was tailored into two discrete bands, and the measured reflection and emission spectra agreed well with the simulation results. The high modulation frequencies that can be obtained in these devices, coupled with their operation in air, confirm their feasibility for use in applications such as gas sensing.C.S., I.J.L. and G.R.N. acknowledge financial support from the Engineering and Physical Sciences Research Council (EPSRC) of the United Kingdom via the Centre for Doctoral Training in Electromagnetic Metamaterials (No. EP/L015331/1). G.R.N. also acknowledges the support of EPSRC via a Fellowship in Frontier Manufacturing (No. EP/J018651/1)

Does Ideology Matter in Bankruptcy? Voting Behavior on the Courts of Appeals

This Article empirically examines whether courts of appeals judges cast ideological votes in the bankruptcy context. The empirical study is unique insofar as it is the first to examine the voting behavior of circuit court judges in bankruptcy cases. More importantly, it focuses on a particular type of dispute that arises in bankruptcy: debt-dischargeability determinations. The study implements this focused approach in order to reduce heterogeneity in result. We find, contrary to our hypotheses, no evidence that circuit court judges engage in ideological voting in bankruptcy cases. We also find, however, non-ideological factors—including the race of the judge and the disposition of the case by lower courts—that substantially influence the voting pattern of the judges in our study. The Article makes three broad contributions. First, it indicates that bankruptcy voting is comparatively non-ideological, at least at the level of the courts of appeals. Second, by identifying the influence of certain non-ideological factors on voting behavior, the Article suggests avenues for profitable future research. And third, the Article makes a methodological contribution through its fine-grained approach, which demonstrates the importance of focusing on particular legal issues in order to reduce heterogeneity in, and bolster the reliability of, findings from empirical legal studies

Where are the Hedgehogs in Nematics?

In experiments which take a liquid crystal rapidly from the isotropic to the nematic phase, a dense tangle of defects is formed. In nematics, there are in principle both line and point defects (``hedgehogs''), but no point defects are observed until the defect network has coarsened appreciably. In this letter the expected density of point defects is shown to be extremely low, approximately $10^{-8}$ per initially correlated domain, as result of the topology (specifically, the homology) of the order parameter space.Comment: 6 pages, latex, 1 figure (self-unpacking PostScript)

A Direct Reduction from k-Player to 2-Player Approximate Nash Equilibrium

We present a direct reduction from k-player games to 2-player games that preserves approximate Nash equilibrium. Previously, the computational equivalence of computing approximate Nash equilibrium in k-player and 2-player games was established via an indirect reduction. This included a sequence of works defining the complexity class PPAD, identifying complete problems for this class, showing that computing approximate Nash equilibrium for k-player games is in PPAD, and reducing a PPAD-complete problem to computing approximate Nash equilibrium for 2-player games. Our direct reduction makes no use of the concept of PPAD, thus eliminating some of the difficulties involved in following the known indirect reduction.Comment: 21 page

Quantum strategies

We consider game theory from the perspective of quantum algorithms. Strategies in classical game theory are either pure (deterministic) or mixed (probabilistic). We introduce these basic ideas in the context of a simple example, closely related to the traditional Matching Pennies game. While not every two-person zero-sum finite game has an equilibrium in the set of pure strategies, von Neumann showed that there is always an equilibrium at which each player follows a mixed strategy. A mixed strategy deviating from the equilibrium strategy cannot increase a player's expected payoff. We show, however, that in our example a player who implements a quantum strategy can increase his expected payoff, and explain the relation to efficient quantum algorithms. We prove that in general a quantum strategy is always at least as good as a classical one, and furthermore that when both players use quantum strategies there need not be any equilibrium, but if both are allowed mixed quantum strategies there must be.Comment: 8 pages, plain TeX, 1 figur