Lax pair and Darboux transformation of noncommutative U(N) principal chiral model

We present a noncommutative generalization of Lax formalism of U(N) principal chiral model in terms of a one-parameter family of flat connections. The Lax formalism is further used to derive a set of parametric noncommutative B\"{a}cklund transformation and an infinite set of conserved quantities. From the Lax pair, we derive a noncommutative version of the Darboux transformation of the model.Comment: 1+20 page

Wiener Reconstruction of Large-Scale Structure from Peculiar Velocities

We present an alternative, Bayesian method for large-scale reconstruction from observed peculiar velocity data. The method stresses a rigorous treatment of the random errors and it allows extrapolation into poorly sampled regions in real space or in k-space. A likelihood analysis is used to determine the fluctuation power spectrum, followed by a Wiener Filter (WF) analysis to obtain the minimum-variance mean fields of velocity and mass density. Constrained Realizations (CR) are then used to sample the statistical scatter about the WF mean field. The WF/CR method is applied as a demonstration to the Mark III data with 1200 km/s, 900 km/s, and 500 km/s resolutions. The main reconstructed structures are consistent with those extracted by the POTENT method. A comparison with the structures in the distribution of IRAS 1.2Jy galaxies yields a general agreement. The reconstructed velocity field is decomposed into its divergent and tidal components relative to a cube of +/-8000 km/s centered on the Local Group. The divergent component is very similar to the velocity field predicted from the distribution of IRAS galaxies. The tidal component is dominated by a bulk flow of 194 +/- 32 km/s towards the general direction of the Shapley concentration, and it also indicates a significant quadrupole.Comment: 28 pages and 8 GIF figures, Latex (aasms4.sty), submitted to ApJ. Postscript version of the figures can be obtained by anonymous ftp from: ftp://alf.huji.ac.il/pub/saleem

Co-evolution of RDF Datasets

Linking Data initiatives have fostered the publication of large number of RDF datasets in the Linked Open Data (LOD) cloud, as well as the development of query processing infrastructures to access these data in a federated fashion. However, different experimental studies have shown that availability of LOD datasets cannot be always ensured, being RDF data replication required for envisioning reliable federated query frameworks. Albeit enhancing data availability, RDF data replication requires synchronization and conflict resolution when replicas and source datasets are allowed to change data over time, i.e., co-evolution management needs to be provided to ensure consistency. In this paper, we tackle the problem of RDF data co-evolution and devise an approach for conflict resolution during co-evolution of RDF datasets. Our proposed approach is property-oriented and allows for exploiting semantics about RDF properties during co-evolution management. The quality of our approach is empirically evaluated in different scenarios on the DBpedia-live dataset. Experimental results suggest that proposed proposed techniques have a positive impact on the quality of data in source datasets and replicas.Comment: 18 pages, 4 figures, Accepted in ICWE, 201