Compressive ghost imaging

We describe an advanced image reconstruction algorithm for pseudothermal ghost imaging, reducing the number of measurements required for image recovery by an order of magnitude. The algorithm is based on compressed sensing, a technique that enables the reconstruction of an N-pixel image from much less than N measurements. We demonstrate the algorithm using experimental data from a pseudothermal ghost-imaging setup. The algorithm can be applied to data taken from past pseudothermal ghost-imaging experiments, improving the reconstruction's quality.Comment: Comments are welcom

Obtaining imaginary weak values with a classical apparatus: applications for the time and frequency domains

Weak measurements with imaginary weak values are reexamined in light of recent experimental results. The shift of the meter, due to the imaginary part of the weak value, is derived via the probability of postselection, which allows considering the meter as a distribution of a classical variable. The derivation results in a simple relation between the change in the distribution and its variance. By applying this relation to several experimental results, in which the meter involved the time and frequency domains, it is shown to be especially suitable for scenarios of that kind. The practical and conceptual implications of a measurement method, which is based on this relation, are discussed.Comment: 4 pages, 1 figure, close to published versio

Budget Feasible Mechanisms

We study a novel class of mechanism design problems in which the outcomes are constrained by the payments. This basic class of mechanism design problems captures many common economic situations, and yet it has not been studied, to our knowledge, in the past. We focus on the case of procurement auctions in which sellers have private costs, and the auctioneer aims to maximize a utility function on subsets of items, under the constraint that the sum of the payments provided by the mechanism does not exceed a given budget. Standard mechanism design ideas such as the VCG mechanism and its variants are not applicable here. We show that, for general functions, the budget constraint can render mechanisms arbitrarily bad in terms of the utility of the buyer. However, our main result shows that for the important class of submodular functions, a bounded approximation ratio is achievable. Better approximation results are obtained for subclasses of the submodular functions. We explore the space of budget feasible mechanisms in other domains and give a characterization under more restricted conditions

Bijective Mappings Of Meshes With Boundary And The Degree In Mesh Processing

This paper introduces three sets of sufficient conditions, for generating bijective simplicial mappings of manifold meshes. A necessary condition for a simplicial mapping of a mesh to be injective is that it either maintains the orientation of all elements or flips all the elements. However, these conditions are known to be insufficient for injectivity of a simplicial map. In this paper we provide additional simple conditions that, together with the above mentioned necessary conditions guarantee injectivity of the simplicial map. The first set of conditions generalizes classical global inversion theorems to the mesh (piecewise-linear) case. That is, proves that in case the boundary simplicial map is bijective and the necessary condition holds then the map is injective and onto the target domain. The second set of conditions is concerned with mapping of a mesh to a polytope and replaces the (often hard) requirement of a bijective boundary map with a collection of linear constraints and guarantees that the resulting map is injective over the interior of the mesh and onto. These linear conditions provide a practical tool for optimizing a map of the mesh onto a given polytope while allowing the boundary map to adjust freely and keeping the injectivity property in the interior of the mesh. The third set of conditions adds to the second set the requirement that the boundary maps are orientation preserving as-well (with a proper definition of boundary map orientation). This set of conditions guarantees that the map is injective on the boundary of the mesh as-well as its interior. Several experiments using the sufficient conditions are shown for mapping triangular meshes. A secondary goal of this paper is to advocate and develop the tool of degree in the context of mesh processing

On Scale Versus Conformal Symmetry in Turbulence

We consider the statistical description of steady state fully developed incompressible fluid turbulence at the inertial range of scales in any number of spatial dimensions. We show that turbulence statistics is scale but not conformally covariant, with the only possible exception being the direct enstrophy cascade in two space dimensions. We argue that the same conclusions hold for compressible non-relativistic turbulence as well as for relativistic turbulence. We discuss the modification of our conclusions in the presence of vacuum expectation values of negative dimension operators. We consider the issue of non-locality of the stress-energy tensor of inertial range turbulence field theory.Comment: 4 pages, revtex, ref. added. We discuss the modification of our conclusions in the presence of vacuum expectation values of negative dimension operator

Spontaneous Symmetry Breaking, Conformal Anomaly and Incompressible Fluid Turbulence

We propose an effective conformal field theory (CFT) description of steady state incompressible fluid turbulence at the inertial range of scales in any number of spatial dimensions. We derive a KPZ-type equation for the anomalous scaling of the longitudinal velocity structure functions and relate the intermittency parameter to the boundary Euler (A-type) conformal anomaly coefficient. The proposed theory consists of a mean field CFT that exhibits Kolmogorov linear scaling (K41 theory) coupled to a dilaton. The dilaton is a Nambu-Goldstone gapless mode that arises from a spontaneous breaking due to the energy flux of the separate scale and time symmetries of the inviscid Navier-Stokes equations to a K41 scaling with a dynamical exponent $z=\frac{2}{3}$. The dilaton acts as a random measure that dresses the K41 theory and introduces intermittency. We discuss the two, three and large number of space dimensions cases and how entanglement entropy can be used to characterize the intermittency strength.Comment: 27 pages, revtex; added discussions, added formulas, added referenc