Measuring Polynomial Invariants of Multi-Party Quantum States

We present networks for directly estimating the polynomial invariants of multi-party quantum states under local transformations. The structure of these networks is closely related to the structure of the invariants themselves and this lends a physical interpretation to these otherwise abstract mathematical quantities. Specifically, our networks estimate the invariants under local unitary (LU) transformations and under stochastic local operations and classical communication (SLOCC). Our networks can estimate the LU invariants for multi-party states, where each party can have a Hilbert space of arbitrary dimension and the SLOCC invariants for multi-qubit states. We analyze the statistical efficiency of our networks compared to methods based on estimating the state coefficients and calculating the invariants.Comment: 8 pages, 4 figures, RevTex4, v2 references update

Cosmological post-Newtonian expansions to arbitrary order

We prove the existence of a large class of one parameter families of solutions to the Einstein-Euler equations that depend on the singular parameter \ep=v_T/c (0<\ep < \ep_0), where $c$ is the speed of light, and $v_T$ is a typical speed of the gravitating fluid. These solutions are shown to exist on a common spacetime slab M\cong [0,T)\times \Tbb^3, and converge as \ep \searrow 0 to a solution of the cosmological Poisson-Euler equations of Newtonian gravity. Moreover, we establish that these solutions can be expanded in the parameter \ep to any specified order with expansion coefficients that satisfy \ep-independent (nonlocal) symmetric hyperbolic equations

Exponential Decay for Small Non-Linear Perturbations of Expanding Flat Homogeneous Cosmologies

It is shown that during expanding phases of flat homogeneous cosmologies all small enough non-linear perturbations decay exponentially. This result holds for a large class of perfect fluid equations of state, but notably not for very ``stiff'' fluids as the pure radiation case

On the Definition of Averagely Trapped Surfaces

Previously suggested definitions of averagely trapped surfaces are not well-defined properties of 2-surfaces, and can include surfaces in flat space-time. A natural definition of averagely trapped surfaces is that the product of the null expansions be positive on average. A surface is averagely trapped in the latter sense if and only if its area $A$ and Hawking mass $M$ satisfy the isoperimetric inequality $16\pi M^2 > A$, with similar inequalities existing for other definitions of quasi-local energy.Comment: 4 page

No one knows which city has the highest concentration of fine particulate matter

This is the final version. Available from the publisher via the DOI in this record.Exposure to ambient fine particulate matter (PM2.5) is the leading global environmental risk factor for mortality and disease burden, with associated annual global welfare costs of trillions of dollars. Examined within is the ability of current data to answer a basic question about PM2.5, namely the location of the city with the highest PM2.5 concentration. The ability to answer this basic question serves as an indicator of scientific progress to assess global human exposure to air pollution and as an important component of efforts to reduce its impacts. Despite the importance of PM2.5, we find that insufficient monitoring data exist to answer this basic question about the spatial pattern of PM2.5 at the global scale. Only 24 of 234 countries have more than 3 monitors per million inhabitants, while density is an order of magnitude lower in the vast majority of the world's countries, with 141 having no regular PM2.5 monitoring at all. The global mean population distance to nearest PM2.5 monitor is 220 km, too large for exposure assessment. Efforts to fill in monitoring gaps with estimates from satellite remote sensing, chemical transport modeling, and statistical models have biases at individual monitor locations that can exceed 50 μg m−3. Progress in advancing knowledge about the global distribution of PM2.5 will require a harmonized network that integrates different types of monitoring equipment (regulatory networks, low-cost monitors, satellite remote sensing, and research-grade instrumentation) with atmospheric and statistical models. Realization of such an integrated framework will facilitate accurate identification of the location of the city with the highest PM2.5 concentration and play a key role in tracking the progress of efforts to reduce the global impacts of air pollution.Natural Sciences and Engineering Research Council of CanadaDepartment of Biotechnology on ‘Air Pollution and Human Health

Global existence and asymptotic behaviour in the future for the Einstein-Vlasov system with positive cosmological constant

The behaviour of expanding cosmological models with collisionless matter and a positive cosmological constant is analysed. It is shown that under the assumption of plane or hyperbolic symmetry the area radius goes to infinity, the spacetimes are future geodesically complete, and the expansion becomes isotropic and exponential at late times. This proves a form of the cosmic no hair theorem in this class of spacetimes

Turbulent dispersion from tall stack in the unstable boundary layer: a comparison between Gaussian and K-diffusion modelling for non buoyant emissions

Most air quality dispersionmo dels used for regulatory applications are based onGaussianan d K-diffusionform ulations. The reliability of such models strongly depends on how dispersion parameters and eddy diffusivities are computed on the basis of the update understanding of the Planetary Boundary Layer (PBL) meteorology. In this paper, we compare the performances in simulating pollutants released from continuous point source, by using some Gaussian and K-diffusion models with different assumptions concerning the parameterisation of the dispersionpro cesses. Results show that the Gaussianmo del, inwhic h the dispersion parameters are directly related to spectral peak of turbulence energy, gives the best overall performances. This could be due to a more realistic description of spreading processes occurring into the PBL. This suggests that, in the context of the regulatory applications, this model cangiv e the best combinationb etweengroun d level concentration estimates and computer requirements

Trapped surfaces and spherical closed cosmologies

This article gives necessary and sufficient conditions for the formation of trapped surfaces in spherically symmetric initial data defined on a closed manifold. Such trapped surfaces surround a region in which there occurs an enhancement of matter over the average. The conditions are posed directly in terms of physical variables and show that what one needs is a relatively large amount of excess matter confined to a small volume. The expansion of the universe and an outward flow of matter oppose the formation of trapped surfaces; an inward flow of matter helps. The model can be regarded as a Friedmann-Lema\^\i tre-Walker cosmology with localized spherical inhomogeneities. We show that the total excess mass cannot be too large.Comment: 36 page

Global existence of classical solutions to the Vlasov-Poisson system in a three dimensional, cosmological setting

The initial value problem for the Vlasov-Poisson system is by now well understood in the case of an isolated system where, by definition, the distribution function of the particles as well as the gravitational potential vanish at spatial infinity. Here we start with homogeneous solutions, which have a spatially constant, non-zero mass density and which describe the mass distribution in a Newtonian model of the universe. These homogeneous states can be constructed explicitly, and we consider deviations from such homogeneous states, which then satisfy a modified version of the Vlasov-Poisson system. We prove global existence and uniqueness of classical solutions to the corresponding initial value problem for initial data which represent spatially periodic deviations from homogeneous states.Comment: 23 pages, Latex, report #

Optical scalars in spherical spacetimes

Consider a spherically symmetric spacelike slice through a spherically symmetric spacetime. One can derive a universal bound for the optical scalars on any such slice. The only requirement is that the matter sources satisfy the dominant energy condition and that the slice be asymptotically flat and regular at the origin. This bound can be used to derive new conditions for the formation of apparent horizons. The bounds hold even when the matter has a distribution on a shell or blows up at the origin so as to give a conical singularity