Information-Based Distance Measures and the Canonical Reflection of View Updates

For the problem of reflecting an update on a database view to the main schema, the constant-complement strategies are precisely those which avoid all update anomalies, and so define the gold standard for well-behaved solutions to the problem. However, the families of view updates which are supported under such strategies are limited, so it is sometimes necessary to go beyond them, albeit in a systematic fashion. In this work, an investigation of such extended strategies is initiated for relational schemata. The approach is to characterize the information content of a database instance, and then require that the optimal reflection of a view update to the main schema embody the least possible change of information. The key property is identified to be strong monotonicity of the view, meaning that view insertions may always be reflected as insertions to the main schema, and likewise for deletions. In that context it is shown that for insertions and deletions, an optimal update, entailing the least change of information, exists and is unique up to isomorphism for wide classes of constraints

Region Operators of Wigner Function: Transformations, Realizations and Bounds

An integral of the Wigner function of a wavefunction |psi >, over some region S in classical phase space is identified as a (quasi) probability measure (QPM) of S, and it can be expressed by the |psi > average of an operator referred to as the region operator (RO). Transformation theory is developed which provides the RO for various phase space regions such as point, line, segment, disk and rectangle, and where all those ROs are shown to be interconnected by completely positive trace increasing maps. The latter are realized by means of unitary operators in Fock space extended by 2D vector spaces, physically identified with finite dimensional systems. Bounds on QPMs for regions obtained by tiling with discs and rectangles are obtained by means of majorization theory.Comment: 16 pages, 4 figures. Hurst Bracken Festschrift, Reports of Mathematical Physics, Feb 2006, to appea

In defense of the epistemic view of quantum states: a toy theory

We present a toy theory that is based on a simple principle: the number of questions about the physical state of a system that are answered must always be equal to the number that are unanswered in a state of maximal knowledge. A wide variety of quantum phenomena are found to have analogues within this toy theory. Such phenomena include: the noncommutativity of measurements, interference, the multiplicity of convex decompositions of a mixed state, the impossibility of discriminating nonorthogonal states, the impossibility of a universal state inverter, the distinction between bi-partite and tri-partite entanglement, the monogamy of pure entanglement, no cloning, no broadcasting, remote steering, teleportation, dense coding, mutually unbiased bases, and many others. The diversity and quality of these analogies is taken as evidence for the view that quantum states are states of incomplete knowledge rather than states of reality. A consideration of the phenomena that the toy theory fails to reproduce, notably, violations of Bell inequalities and the existence of a Kochen-Specker theorem, provides clues for how to proceed with this research program.Comment: 32 pages, REVTEX, based on a talk given at the Rob Clifton Memorial Conference, College Park, May 2003; v2: minor modifications throughout, updated reference

Monte Carlo cluster algorithm for fluid phase transitions in highly size-asymmetrical binary mixtures

Highly size-asymmetrical fluid mixtures arise in a variety of physical contexts, notably in suspensions of colloidal particles to which much smaller particles have been added in the form of polymers or nanoparticles. Conventional schemes for simulating models of such systems are hamstrung by the difficulty of relaxing the large species in the presence of the small one. Here we describe how the rejection-free geometrical cluster algorithm (GCA) of Liu and Luijten [Phys. Rev. Lett 92, 035504 (2004)] can be embedded within a restricted Gibbs ensemble to facilitate efficient and accurate studies of fluid phase behavior of highly size-asymmetrical mixtures. After providing a detailed description of the algorithm, we summarize the bespoke analysis techniques of Ashton et al. [J. Chem. Phys. 132, 074111 (2010)] that permit accurate estimates of coexisting densities and critical-point parameters. We apply our methods to study the liquid--vapor phase diagram of a particular mixture of Lennard-Jones particles having a 10:1 size ratio. As the reservoir volume fraction of small particles is increased in the range 0--5%, the critical temperature decreases by approximately 50%, while the critical density drops by some 30%. These trends imply that in our system, adding small particles decreases the net attraction between large particles, a situation that contrasts with hard-sphere mixtures where an attractive depletion force occurs.Comment: 11 pages, 10 figure

Building with Drones: Accurate 3D Facade Reconstruction using MAVs

Automatic reconstruction of 3D models from images using multi-view Structure-from-Motion methods has been one of the most fruitful outcomes of computer vision. These advances combined with the growing popularity of Micro Aerial Vehicles as an autonomous imaging platform, have made 3D vision tools ubiquitous for large number of Architecture, Engineering and Construction applications among audiences, mostly unskilled in computer vision. However, to obtain high-resolution and accurate reconstructions from a large-scale object using SfM, there are many critical constraints on the quality of image data, which often become sources of inaccuracy as the current 3D reconstruction pipelines do not facilitate the users to determine the fidelity of input data during the image acquisition. In this paper, we present and advocate a closed-loop interactive approach that performs incremental reconstruction in real-time and gives users an online feedback about the quality parameters like Ground Sampling Distance (GSD), image redundancy, etc on a surface mesh. We also propose a novel multi-scale camera network design to prevent scene drift caused by incremental map building, and release the first multi-scale image sequence dataset as a benchmark. Further, we evaluate our system on real outdoor scenes, and show that our interactive pipeline combined with a multi-scale camera network approach provides compelling accuracy in multi-view reconstruction tasks when compared against the state-of-the-art methods.Comment: 8 Pages, 2015 IEEE International Conference on Robotics and Automation (ICRA '15), Seattle, WA, US

X-ray observations of the hot phase in Sgr~A*

We analyze 134 ks Chandra ACIS-I observations of the Galactic Centre (GC) performed in July 2011. The X-ray image with the field of view $17' \times 17'$ contains the hot plasma surrounding the Sgr~A*. The obtained surface brightness map allow us to fit Bondi hot accretion flow to the innermost hot plasma around the GC. We have fitted spectra from region up to $5"$ from Sgr~A* using a thermal bremsstrahlung model and four Gaussian profiles responsible for K$_{\alpha}$ emission lines of Fe, S, Ar, and Ca. The X-ray surface brightness profile up to $3"$ from Sgr~A* found in our data image, was successfully fitted with the dynamical model of Bondi spherical accretion. By modelling the surface brightness profile, we derived the temperature and number density profiles in the vicinity of the black hole. The best fitted model of spherical Bondi accretion shows that this type of flow works only up to $3"$ and implies outer plasma density and temperature to be: $n_{\rm e}^{\rm out}=18.3 \pm {0.1}$ cm$^{-3}$ and $T_{\rm e}^{\rm out}= 3.5 \pm {0.3}$ keV respectively. We show that the Bondi flow can reproduce observed surface brightness profile up to $3"$ from Sgr~A* in the Galactic Center. This result strongly suggests the position of stagnation radius in the complicated dynamics around GC. The Faraday rotation computed from our model towards the pulsar PSR J1745-2900 near the GC agrees with the observed one, recently reported.Comment: 10 pages, 7 figures, accepted for publication in A&

Lattice-switch Monte Carlo

We present a Monte Carlo method for the direct evaluation of the difference between the free energies of two crystal structures. The method is built on a lattice-switch transformation that maps a configuration of one structure onto a candidate configuration of the other by `switching' one set of lattice vectors for the other, while keeping the displacements with respect to the lattice sites constant. The sampling of the displacement configurations is biased, multicanonically, to favor paths leading to `gateway' arrangements for which the Monte Carlo switch to the candidate configuration will be accepted. The configurations of both structures can then be efficiently sampled in a single process, and the difference between their free energies evaluated from their measured probabilities. We explore and exploit the method in the context of extensive studies of systems of hard spheres. We show that the efficiency of the method is controlled by the extent to which the switch conserves correlated microstructure. We also show how, microscopically, the procedure works: the system finds gateway arrangements which fulfill the sampling bias intelligently. We establish, with high precision, the differences between the free energies of the two close packed structures (fcc and hcp) in both the constant density and the constant pressure ensembles.Comment: 34 pages, 9 figures, RevTeX. To appear in Phys. Rev.