A-branes and Noncommutative Geometry

We argue that for a certain class of symplectic manifolds the category of A-branes (which includes the Fukaya category as a full subcategory) is equivalent to a noncommutative deformation of the category of B-branes (which is equivalent to the derived category of coherent sheaves) on the same manifold. This equivalence is different from Mirror Symmetry and arises from the Seiberg-Witten transform which relates gauge theories on commutative and noncommutative spaces. More generally, we argue that for certain generalized complex manifolds the category of generalized complex branes is equivalent to a noncommutative deformation of the derived category of coherent sheaves on the same manifold. We perform a simple test of our proposal in the case when the manifold in question is a symplectic torus.Comment: 15 pages, late

Generalized Paxos Made Byzantine (and Less Complex)

One of the most recent members of the Paxos family of protocols is Generalized Paxos. This variant of Paxos has the characteristic that it departs from the original specification of consensus, allowing for a weaker safety condition where different processes can have a different views on a sequence being agreed upon. However, much like the original Paxos counterpart, Generalized Paxos does not have a simple implementation. Furthermore, with the recent practical adoption of Byzantine fault tolerant protocols, it is timely and important to understand how Generalized Paxos can be implemented in the Byzantine model. In this paper, we make two main contributions. First, we provide a description of Generalized Paxos that is easier to understand, based on a simpler specification and the pseudocode for a solution that can be readily implemented. Second, we extend the protocol to the Byzantine fault model

Environmental protection and the generalized system of preferences : a legal and appropriate linkage?

This article will question the legality of measures of environmental ‘conditionality’ in the Generalized System of Preferences [GSP] of the European Community [EC]. The GSP is a GATT/WTO authorized scheme which permits developed nations to grant non-reciprocal tariff preferences in favour of developing countries. The objectives of the GSP are primarily development-oriented in that it aims to increase the export earnings of developing countries, promote their industrialization and accelerate rates of economic growth. A recent case taken in the WTO examined the legal contours of the grant of tariff preferences and it is in the light of this that this article will examine the so-called ‘special incentive arrangements’ of the reformed EC GSP which offers additional tariff preferences to developing countries on the ‘condition’ that they adhere to specified standards of environmental protection

The Legendre Transform in Non-additive Thermodynamics and Complexity

We present an argument which purports to show that the use of the standard Legendre transform in non-additive Statistical Mechanics is not appropriate. For concreteness, we use as paradigm, the case of systems which are conjecturally described by the (non-additive) Tsallis entropy. We point out the form of the modified Legendre transform that should be used, instead, in the non-additive thermodynamics induced by the Tsallis entropy. We comment on more general implications of this proposal for the thermodynamics of "complex systems".Comment: 23 pages. LaTeX2e. No figure

Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime

We propose that holographic entanglement entropy can be calculated at arbitrary orders in the bulk Planck constant using the concept of a "quantum extremal surface": a surface which extremizes the generalized entropy, i.e. the sum of area and bulk entanglement entropy. At leading order in bulk quantum corrections, our proposal agrees with the formula of Faulkner, Lewkowycz, and Maldacena, which was derived only at this order; beyond leading order corrections, the two conjectures diverge. Quantum extremal surfaces lie outside the causal domain of influence of the boundary region as well as its complement, and in some spacetimes there are barriers preventing them from entering certain regions. We comment on the implications for bulk reconstruction.Comment: 28 pages, 6 figures. Version 3: typos fixed, minor changes to reference

Multi-Trace Operators and the Generalized AdS/CFT Prescription

We show that multi-trace interactions can be consistently incorporated into an extended AdS/CFT prescription involving the inclusion of generalized boundary conditions and a modified Legendre transform prescription. We find new and consistent results by considering a self-contained formulation which relates the quantization of the bulk theory to the AdS/CFT correspondence and the perturbation at the boundary by double-trace interactions. We show that there exist particular double-trace perturbations for which irregular modes are allowed to propagate as well as the regular ones. We perform a detailed analysis of many different possible situations, for both minimally and non-minimally coupled cases. In all situations, we make use of a new constraint which is found by requiring consistence. In the particular non-minimally coupled case, the natural extension of the Gibbons-Hawking surface term is generated.Comment: 27 pages, LaTeX, v.2:minor changes, v.3:comments added, v.4:several new results, discussions, references and a section of Conclusions added. Previous results unchanged, v.5: minor changes. Final version to be published in Phys.Rev.

On the Existence of the Logarithmic Correction Term in Black Hole Entropy-Area Relation

In this paper we consider a model universe with large extra dimensions to obtain a modified black hole entropy-area relation. We use the generalized uncertainty principle to find a relation between the number of spacetime dimensions and the presence or vanishing of logarithmic prefactor in the black hole entropy-area relation. Our calculations are restricted to the microcanonical ensembles and we show that in the modified entropy-area relation, the microcanonical logarithmic prefactor appears only when spacetime has an even number of dimensions.Comment: 9 Pages, No Figure