A robust pseudo-inverse spectral filter applied to the Earth Radiation Budget Experiment (ERBE) scanning channels

Computer simulations of a least squares estimator operating on the ERBE scanning channels are discussed. The estimator is designed to minimize the errors produced by nonideal spectral response to spectrally varying and uncertain radiant input. The three ERBE scanning channels cover a shortwave band a longwave band and a ""total'' band from which the pseudo inverse spectral filter estimates the radiance components in the shortwave band and a longwave band. The radiance estimator draws on instantaneous field of view (IFOV) scene type information supplied by another algorithm of the ERBE software, and on a priori probabilistic models of the responses of the scanning channels to the IFOV scene types for given Sun scene spacecraft geometry. It is found that the pseudoinverse spectral filter is stable, tolerant of errors in scene identification and in channel response modeling, and, in the absence of such errors, yields minimum variance and essentially unbiased radiance estimates

Correlation functions of boundary field theory from bulk Green's functions and phases in the boundary theory

In the context of the bulk-boundary correspondence we study the correlation functions arising on a boundary for different types of boundary conditions. The most general condition is the mixed one interpolating between the Neumann and Dirichlet conditions. We obtain the general expressions for the correlators on a boundary in terms of Green's function in the bulk for the Dirichlet, Neumann and mixed boundary conditions and establish the relations between the correlation functions. As an instructive example we explicitly obtain the boundary correlators corresponding to the mixed condition on a plane boundary $R^d$ of a domain in flat space $R^{d+1}$. The phases of the boundary theory with correlators of the Neumann and Dirichlet types are determined. The boundary correlation functions on sphere $S^d$ are calculated for the Dirichlet and Neumann conditions in two important cases: when sphere is a boundary of a domain in flat space $R^{d+1}$ and when it is a boundary at infinity of Anti-De Sitter space $AdS_{d+1}$. For massless in the bulk theory the Neumann correlator on the boundary of AdS space is shown to have universal logarithmic behavior in all AdS spaces. In the massive case it is found to be finite at the coinciding points. We argue that the Neumann correlator may have a dual two-dimensional description. The structure of the correlators obtained, their conformal nature and some recurrent relations are analyzed. We identify the Dirichlet and Neumann phases living on the boundary of AdS space and discuss their evolution when the location of the boundary changes from infinity to the center of the AdS space.Comment: 32 pages, latex, no figure

Bell inequalities stronger than the CHSH inequality for 3-level isotropic states

We show that some two-party Bell inequalities with two-valued observables are stronger than the CHSH inequality for 3 \otimes 3 isotropic states in the sense that they are violated by some isotropic states in the 3 \otimes 3 system that do not violate the CHSH inequality. These Bell inequalities are obtained by applying triangular elimination to the list of known facet inequalities of the cut polytope on nine points. This gives a partial solution to an open problem posed by Collins and Gisin. The results of numerical optimization suggest that they are candidates for being stronger than the I_3322 Bell inequality for 3 \otimes 3 isotropic states. On the other hand, we found no Bell inequalities stronger than the CHSH inequality for 2 \otimes 2 isotropic states. In addition, we illustrate an inclusion relation among some Bell inequalities derived by triangular elimination.Comment: 9 pages, 1 figure. v2: organization improved; less references to the cut polytope to make the main results clear; references added; typos corrected; typesetting style change

On the Relationship between Convex Bodies Related to Correlation Experiments with Dichotomic Observables

In this paper we explore further the connections between convex bodies related to quantum correlation experiments with dichotomic variables and related bodies studied in combinatorial optimization, especially cut polyhedra. Such a relationship was established in Avis, Imai, Ito and Sasaki (2005 J. Phys. A: Math. Gen. 38 10971-87) with respect to Bell inequalities. We show that several well known bodies related to cut polyhedra are equivalent to bodies such as those defined by Tsirelson (1993 Hadronic J. S. 8 329-45) to represent hidden deterministic behaviors, quantum behaviors, and no-signalling behaviors. Among other things, our results allow a unique representation of these bodies, give a necessary condition for vertices of the no-signalling polytope, and give a method for bounding the quantum violation of Bell inequalities by means of a body that contains the set of quantum behaviors. Optimization over this latter body may be performed efficiently by semidefinite programming. In the second part of the paper we apply these results to the study of classical correlation functions. We provide a complete list of tight inequalities for the two party case with (m,n) dichotomic observables when m=4,n=4 and when min{m,n}<=3, and give a new general family of correlation inequalities.Comment: 17 pages, 2 figure

Bounds on the Complexity of Halfspace Intersections when the Bounded Faces have Small Dimension

We study the combinatorial complexity of D-dimensional polyhedra defined as the intersection of n halfspaces, with the property that the highest dimension of any bounded face is much smaller than D. We show that, if d is the maximum dimension of a bounded face, then the number of vertices of the polyhedron is O(n^d) and the total number of bounded faces of the polyhedron is O(n^d^2). For inputs in general position the number of bounded faces is O(n^d). For any fixed d, we show how to compute the set of all vertices, how to determine the maximum dimension of a bounded face of the polyhedron, and how to compute the set of bounded faces in polynomial time, by solving a polynomial number of linear programs

Back-reaction of a conformal field on a three-dimensional black hole

The first order corrections to the geometry of the (2+1)-dimensional black hole due to back-reaction of a massless conformal scalar field are computed. The renormalized stress energy tensor used as the source of Einstein equations is computed with the Green function for the black-hole background with transparent boundary conditions. This tensor has the same functional form as the one found in the nonperturbative case which can be exactly solved. Thus, a static, circularly symmetric and asymptotically anti-de Sitter black hole solution of the semiclassical equations is found. The corrections to the thermodynamic quantities are also computed.Comment: 12 pages, RevTeX, no figure

Greedy Randomized Adaptive Search and Variable Neighbourhood Search for the minimum labelling spanning tree problem

This paper studies heuristics for the minimum labelling spanning tree (MLST) problem. The purpose is to find a spanning tree using edges that are as similar as possible. Given an undirected labelled connected graph, the minimum labelling spanning tree problem seeks a spanning tree whose edges have the smallest number of distinct labels. This problem has been shown to be NP-hard. A Greedy Randomized Adaptive Search Procedure (GRASP) and a Variable Neighbourhood Search (VNS) are proposed in this paper. They are compared with other algorithms recommended in the literature: the Modified Genetic Algorithm and the Pilot Method. Nonparametric statistical tests show that the heuristics based on GRASP and VNS outperform the other algorithms tested. Furthermore, a comparison with the results provided by an exact approach shows that we may quickly obtain optimal or near-optimal solutions with the proposed heuristics

Random perfect lattices and the sphere packing problem

Motivated by the search for best lattice sphere packings in Euclidean spaces of large dimensions we study randomly generated perfect lattices in moderately large dimensions (up to d=19 included). Perfect lattices are relevant in the solution of the problem of lattice sphere packing, because the best lattice packing is a perfect lattice and because they can be generated easily by an algorithm. Their number however grows super-exponentially with the dimension so to get an idea of their properties we propose to study a randomized version of the algorithm and to define a random ensemble with an effective temperature in a way reminiscent of a Monte-Carlo simulation. We therefore study the distribution of packing fractions and kissing numbers of these ensembles and show how as the temperature is decreased the best know packers are easily recovered. We find that, even at infinite temperature, the typical perfect lattices are considerably denser than known families (like A_d and D_d) and we propose two hypotheses between which we cannot distinguish in this paper: one in which they improve Minkowsky's bound phi\sim 2^{-(0.84+-0.06) d}, and a competitor, in which their packing fraction decreases super-exponentially, namely phi\sim d^{-a d} but with a very small coefficient a=0.06+-0.04. We also find properties of the random walk which are suggestive of a glassy system already for moderately small dimensions. We also analyze local structure of network of perfect lattices conjecturing that this is a scale-free network in all dimensions with constant scaling exponent 2.6+-0.1.Comment: 19 pages, 22 figure