On The Complexity and Completeness of Static Constraints for Breaking Row and Column Symmetry

We consider a common type of symmetry where we have a matrix of decision variables with interchangeable rows and columns. A simple and efficient method to deal with such row and column symmetry is to post symmetry breaking constraints like DOUBLELEX and SNAKELEX. We provide a number of positive and negative results on posting such symmetry breaking constraints. On the positive side, we prove that we can compute in polynomial time a unique representative of an equivalence class in a matrix model with row and column symmetry if the number of rows (or of columns) is bounded and in a number of other special cases. On the negative side, we show that whilst DOUBLELEX and SNAKELEX are often effective in practice, they can leave a large number of symmetric solutions in the worst case. In addition, we prove that propagating DOUBLELEX completely is NP-hard. Finally we consider how to break row, column and value symmetry, correcting a result in the literature about the safeness of combining different symmetry breaking constraints. We end with the first experimental study on how much symmetry is left by DOUBLELEX and SNAKELEX on some benchmark problems.Comment: To appear in the Proceedings of the 16th International Conference on Principles and Practice of Constraint Programming (CP 2010

Review of operational aspects of initial experiments utilizing the U.S. MLS

An exercise to support the Federal Aviation Administration in demonstrating the U.S. candidate for an international microwave landing system (MLS) was conducted by NASA. During this demonstration the MLS was utilized to provide the TCV Boeing 737 research airplane with guidance for automatic control during transition from conventional RNAV to MLS RNAV in curved, descending flight; flare; touchdown; and roll-out. Flight profiles, system configuration, displays, and operating procedures used in the demonstration are described, and preliminary results of flight data analysis are discussed. Recent experiences with manually controlled flight in the NAFEC MLS environment are also discussed. The demonstration shows that in automatic three-dimensional flight, the volumetric signal coverage of the MLS can be exploited to enable a commercial carrier class airplane to perform complex curved, descending paths with precision turns into short final approaches terminating in landing and roll-out, even when subjected to strong and gusty tail and cross wind components and severe wind shear

The extinction and dust-to-gas structure of the planetary nebula NGC 7009 observed with MUSE

The large field and wavelength range of MUSE is well suited to mapping Galactic planetary nebulae (PN). The bright PN NGC 7009 was observed with MUSE on the VLT during the Science Verification of the instrument in seeing of 0.6". Emission line maps in hydrogen Balmer and Paschen lines were formed from analysis of the MUSE cubes. The measured electron temperature and density from the MUSE cube were employed to predict the theoretical hydrogen line ratios and map the extinction distribution across the nebula. After correction for the interstellar extinction to NGC 7009, the internal dust-to-gas ratio (A_V/N_H) has been mapped for the first time in a PN. The extinction map of NGC 7009 has considerable structure, broadly corresponding to the morphological features of the nebula. A large-scale feature in the extinction map, consisting of a crest and trough, occurs at the rim of the inner shell. The nature of this feature was investigated and instrumental and physical causes considered; no convincing mechanisms were identified to produce this feature, other than mass loss variations in the earlier asymptotic giant branch phase. The dust-to-gas ratio A_V/N_H increases from 0.7 times the interstellar value to >5 times from the centre towards the periphery of the ionized nebula. The integrated A_V/N_H is about 2 times the mean ISM value. It is demonstrated that extinction mapping with MUSE provides a powerful tool for studying the distribution of PN internal dust and the dust-to-gas ratio. (Abridged.)Comment: 10 pages, 7 figures. Accepted by A&

Collision of High Frequency Plane Gravitational and Electromagnetic Waves

We study the head-on collision of linearly polarized, high frequency plane gravitational waves and their electromagnetic counterparts in the Einstein-Maxwell theory. The post-collision space-times are obtained by solving the vacuum Einstein-Maxwell field equations in the geometrical optics approximation. The head-on collisions of all possible pairs of these systems of waves is described and the results are then generalised to non-linearly polarized waves which exhibit the maximum two degrees of freedom of polarization.Comment: Latex file, 17 pages, accepted for publication in International Journal of Modern Physics

Demonstration of decomposition and optimization in the design of experimental space systems

Effective design strategies for a class of systems which may be termed Experimental Space Systems (ESS) are needed. These systems, which include large space antenna and observatories, space platforms, earth satellites and deep space explorers, have special characteristics which make them particularly difficult to design. It is argued here that these same characteristics encourage the use of advanced computer-aided optimization and planning techniques. The broad goal of this research is to develop optimization strategies for the design of ESS. These strategics would account for the possibly conflicting requirements of mission life, safety, scientific payoffs, initial system cost, launch limitations and maintenance costs. The strategies must also preserve the coupling between disciplines or between subsystems. Here, the specific purpose is to describe a computer-aided planning and scheduling technique. This technique provides the designer with a way to map the flow of data between multidisciplinary analyses. The technique is important because it enables the designer to decompose the system design problem into a number of smaller subproblems. The planning and scheduling technique is demonstrated by its application to a specific preliminary design problem

High Resolution CO and H2 Molecular Line Imaging of a Cometary Globule in the Helix Nebula

We report high resolution imaging of a prominent cometary globule in the Helix nebula in the CO J=1-0 (2.6 mm) and H2 v=1-0 S(1) (2.12 micron) lines. The observations confirm that globules consist of dense condensations of molecular gas embedded in the ionized nebula. The head of the globule is seen as a peak in the CO emission with an extremely narrow line width (0.5 km/s) and is outlined by a limb-brightened surface of H2 emission facing the central star and lying within the photo-ionized halo. The emission from both molecular species extends into the tail region. The presence of this extended molecular emission provides new constraints on the structure of the tails, and on the origin and evolution of the globules.Comment: 12 pages, 3 figures. To appear in The Astrophysical Journal Letter

Sensitivity of nonlinear photoionization to resonance substructure in collective excitation

Collective behaviour is a characteristic feature in many-body systems, important for developments in fields such as magnetism, superconductivity, photonics and electronics. Recently, there has been increasing interest in the optically nonlinear response of collective excitations. Here we demonstrate how the nonlinear interaction of a many-body system with intense XUV radiation can be used as an effective probe for characterizing otherwise unresolved features of its collective response. Resonant photoionization of atomic xenon was chosen as a case study. The excellent agreement between experiment and theory strongly supports the prediction that two distinct poles underlie the giant dipole resonance. Our results pave the way towards a deeper understanding of collective behaviour in atoms, molecules and solid-state systems using nonlinear spectroscopic techniques enabled by modern short-wavelength light sources

KMS states on Quantum Grammars

We consider quantum (unitary) continuous time evolution of spins on a lattice together with quantum evolution of the lattice itself. In physics such evolution was discussed in connection with quantum gravity. It is also related to what is called quantum circuits, one of the incarnations of a quantum computer. We consider simpler models for which one can obtain exact mathematical results. We prove existence of the dynamics in both Schroedinger and Heisenberg pictures, construct KMS states on appropriate C*-algebras. We show (for high temperatures) that for each system where the lattice undergoes quantum evolution, there is a natural scaling leading to a quantum spin system on a fixed lattice, defined by a renormalized Hamiltonian.Comment: 22 page