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Cascade transferred a stake worth about $120 million in Coca-Cola Femsaand a holding valued at about $386 million in Grupo Televisa to FrenchGates, according to Bloomberg calculations based on the filings. (Bloomberg) -- Cascade Investment, the holding company created by BillGates, transferred stock in two of Mexico's largest companies to MelindaFrench Gates, bringing the total amount she's received in the past fewdays to more than $2 billion. [Extracted from the article]

We use several quasar samples (Large Bright QSO Survey, Homogeneous Bright QSO Survey, Durham/AAT, and Edinburgh QSO Survey) to determine the density functions and the luminosity evolution of quasars. Combining these different samples and accounting for varying selection criteria require tests of correlation and the determination of density functions for multiply truncated data. We describe new nonparametric techniques for accomplishing these tasks, which have been developed recently by Efron & Petrosian. With these methods, the luminosity evolution can be found through an investigation of the correlation of the bivariate distribution of luminosities and redshifts. Here, one assumes a cosmological model to convert the observed fluxes into luminosities. We use matter-dominated models with either zero cosmological constant or zero spatial curvature. Of the two most commonly used models for luminosity evolution, L[?]ekt(z) and L[?](1+z)k', we find that the second functional form is a better description of the data at all luminosities; we find k'=2.58 ([2.14, 2.91] 1 s region) for the Einstein-de Sitter cosmological model. Using this form of luminosity evolution, we determine a global luminosity function and the evolution of the comoving density for the two types of cosmological models. For the Einstein-de Sitter cosmological model we find a relatively strong increase in comoving density up to z[?]2, at which point the density peaks and begins to decrease rapidly. This is in agreement with results from high-redshift surveys. However, we find that pure luminosity evolution, i.e., constant comoving density, is possible for some cosmological models for 3[?]2. We find that the local luminosity function Ph(L0) exhibits the usual double power-law behavior. The luminosity density (z)=[?]LPs(L, z) dL, where Ps(L, z) is the luminosity function, is found to increase rapidly at low redshift and to reach a peak at around z[?]2. Our results for (z) are compared to results from high-redshift surveys and to the variation of the star formation rate with redshift.

The hypothesis that every theory of quantum gravity in AdS3 is a dimensional reduction of string or M theory leads to a natural conjecture for the density of states of two-dimensional CFTs with a large central charge limit. We prove this conjecture for 2D CFTs which are orbifolds by permutation groups. In particular, we characterize those permutation groups which give CFTs with well-defined large N limits and can thus serve as holographic duals to bulk gravity theories in AdS3. We then show that the holographic dual of a permutation orbifold will have a Hagedorn spectrum in the large N limit. This is evidence that, within this landscape, every theory of quantum gravity with a semiclassical limit is a string theory. [ABSTRACT FROM AUTHOR]

The analytic structure of solutions to the Klein-Gordon equation in a black hole background, as represented by monodromy data, is intimately related to black hole thermodynamics. It encodes the "hidden conformai symmetry" of a nonextremal black hole, and it explains why features of the inner event horizon appear in scattering data such as greybody factors. This indicates that hidden conformai symmetry is generic within a universality class of black holes. [ABSTRACT FROM AUTHOR]

We identify a special information-theoretic property of quantum field theories with holographic duals: the mutual informations among arbitrary disjoint spatial regions A, B, C obey the inequality I(A:B UC)⩾I(A:B) + I(A:C), provided entanglement entropies are given by the Ryu-Takayanagi formula. Inequalities of this type are known as monogamy relations and are characteristic of measures of quantum entanglement. This suggests that correlations in holographic theories arise primarily from entanglement rather than classical correlations. We also show that the Ryu-Takayanagi formula is consistent with all known general inequalities obeyed by the entanglement entropy, including an infinite set recently discovered by Cadney et al.; this constitutes strong evidence in favor of its validity. [ABSTRACT FROM AUTHOR]

Euclidean wormholes--geometries which connect disconnected boundaries--present a challenge to a standard quantum mechanical interpretation of the theory. One potential resolution is that the gravitational path integral computes the ensemble average of many theories. The connected topologies contribute to the simplest possible observable: the free energy, which is computed using a replica trick. This is distinct from the replica trick used to compute entanglement entropies and appears in the computation of any extensive quantity. We argue that both JT gravity and a simplified version of CGHS admit a regime where the contribution of connected replica wormholes to the free energy is larger than that of disconnected topologies. In both theories we find evidence of replica symmetry breaking, which is reminiscent of the behavior of certain spin glasses. We discuss possible insights about ensemble averaging in gravity from this perspective. [ABSTRACT FROM AUTHOR]

A correction to the article "A de Sitter Farey Tail," which published incorrect author affiliations is presented.