Approximations of standard equivalence relations and Bernoulli percolation at p\_u

The goal of this note is to announce certain results in orbit equivalence theory, especially concerning the approximation of p.m.p. standard equivalence relations by increasing sequence of sub-relations, with applications to the behavior of the Bernoulli percolation on graphs at the threshold pu. R\'esum\'e en Fran\c{c}ais. Approximations de relations d'\'equivalence standards et percolation de Bernoulli \`a p\_u

COCYCLE SUPERRIGIDITY FOR TRANSLATION ACTIONS OF PRODUCT GROUPS

International audienceLet G be either a profinite or a connected compact group, and Γ, Λ be finitely generated dense subgroups. Assuming that the left translation action of Γ on G is strongly ergodic, we prove that any cocycle for the left-right translation action of Γ × Λ on G with values in a countable group is " virtually " cohomologous to a group homomorphism. Moreover , we prove that the same holds if G is a (not necessarily compact) connected simple Lie group provided that Λ contains an infinite cyclic subgroup with compact closure. We derive several applications to OE-and W *-superrigidity. In particular, we obtain the first examples of compact actions of F2 × F2 which are W *-superrigid

Einstein-Maxwell theory and the Weyl double copy

The Weyl double copy relates vacuum solutions in general relativity to Abelian gauge fields in Minkowski spacetime. In a previous work, we showed how the Weyl double copy can be extended to provide a treatment of external gravitational sources consistent with the classical Kerr-Schild double copy. Using this generalization, here we provide a complete double-copy analysis of electrovacuum Petrov type-D spacetimes. This includes the first analysis of the charged C metric, whose single-copy interpretation invokes the two-potential formalism of electrodynamics. We also present the first double-copy prescription for the Ricci spinor, which for nonaccelerating spacetimes, takes a form similar to the original double-copy relation for the Weyl spinor

Sources in the Weyl Double Copy

The Weyl double copy relates exact solutions in general relativity to exact solutions in gauge theory, formulated in the spinorial language. To date, the Weyl double copy is understood and employed only for vacuum spacetimes, and hence only to vacuum gauge theories. In this Letter, we propose an extension to the Weyl double copy that provides a systematic procedure for treating gravitational sources. We show that this extended Weyl double copy gives a new perspective to the Kerr-Newman black hole and the general class of Petrov type D electrovac spacetimes

The stringy origins of Galileons and their novel limit

We show generalized Galileons — a particular subclass of Horndeski gravity — arise from a consistent Kaluza-Klein reduction of the low-energy effective action of heterotic string theory to first order in α'. This suggests Horndeski theories of gravity have a string-theoretic origin. The form of the Galileonic terms is precisely fixed by parameters of the embedding spacetime, so that only a specific subset of Horndeski theories is permitted by string theory. A novel limit of the model is considered by performing a dimensionfulrescaling of α'

Isometries and the double copy

In the standard derivation of the Kerr-Schild double copy, the geodicity of the Kerr-Schild vector and the stationarity of the spacetime are presented as assumptions that are necessary for the single copy to satisfy Maxwell's equations. However, it is well known that the vacuum Einstein equations imply that the Kerr-Schild vector is geodesic and shear-free, and that the spacetime possesses a distinguished vector field that is simultaneously a Killing vector of the full spacetime and the flat background, but need not be timelike with respect to the background metric. We show that the gauge field obtained by contracting this distinguished Killing vector with the Kerr-Schild graviton solves the vacuum Maxwell equations, and that this definition of the Kerr-Schild double copy implies the Weyl double copy when the spacetime is Petrov type D. When the Killing vector is taken to be timelike with respect to the background metric, we recover the familiar Kerr-Schild double copy, but the prescription is well defined for any vacuum Kerr-Schild spacetime and we present new examples where the Killing vector is null or spacelike. While most examples of physical interest are type D, vacuum Kerr-Schild spacetimes are generically of Petrov type II. We present a straightforward example of such a spacetime and study its double copy structure. Our results apply to real Lorentzian spacetimes as well as complex spacetimes and real spacetimes with Kleinian signature, and provide a simple correspondence between real and self-dual vacuum Kerr-Schild spacetimes. This correspondence allows us to study the double copy structure of a self-dual analog of the Kerr spacetime. We provide evidence that this spacetime may be diffeomorphic to the self-dual Taub-NUT solution.Comment: 28 pages; Matches version to appear in JHE

The use of oral fluids to monitor key pathogens in porcine respiratory disease complex.

BACKGROUND: The usefulness of oral fluid (OF) sampling for surveillance of infections in pig populations is already accepted but its value as a tool to support investigations of porcine respiratory disease complex (PRDC) has been less well studied. This study set out to describe detection patterns of porcine reproductive and respiratory syndrome virus (PRRSV), porcine circovirus type 2 (PCV2), swine influenza virus type A (SIV) and Mycoplasma hyopneumoniae (M. hyo) among farms showing differing severity of PRDC. The study included six wean-to-finish pig batches from farms with historical occurrence of respiratory disease. OF samples were collected from six pens every two weeks from the 5th to the 21st week of age and tested by real time PCR for presence of PRRSV, SIV and M. hyo and by quantitative real time PCR for PCV2. Data was evaluated alongside clinical and post-mortem observations, mortality rate, slaughter pathology, histopathology, and immunohistochemistry testing data for PCV2 antigen where available. RESULTS: PRRSV and M. hyo were detectable in OF but with inconsistency between pens at the same sampling time and within pens over sequential sampling times. Detection of SIV in clinical and subclinical cases showed good consistency between pens at the same sampling time point with detection possible for periods of 2-4 weeks. Quantitative testing of OF for PCV2 indicated different patterns and levels of detection between farms unaffected or affected by porcine circovirus diseases (PCVD). There was good correlation of PCR results for multiple samples collected from the same pen but no associations were found between prevalence of positive test results and pen location in the building or sex of pigs. CONCLUSIONS: Detection patterns for PRRSV, SIV and M. hyo supported the effectiveness of OF testing as an additional tool for diagnostic investigation of PRDC but emphasised the importance of sampling from multiple pens and on multiple occasions. Preliminary evidence supported the measurement of PCV2 load in pooled OF as a tool for prediction of clinical or subclinical PCVD at farm level