The wide use of XML for document management and data exchange has created the need to query large repositories of XML data. To efficiently query such large data collections and take advantage of parallelism, we have implemented Apache VXQuery, an ope
n-source scalable XQuery processor. The system builds upon two other open-source frameworks -- Hyracks, a parallel execution engine, and Algebricks, a language agnostic compiler toolbox. Apache VXQuery extends these two frameworks and provides an implementation of the XQuery specifics (data model, data-model dependent functions and optimizations, and a parser). We describe the architecture of Apache VXQuery, its integration with Hyracks and Algebricks, and the XQuery optimization rules applied to the query plan to improve path expression efficiency and to enable query parallelism. An experimental evaluation using a real 500GB dataset with various selection, aggregation and join XML queries shows that Apache VXQuery performs well both in terms of scale-up and speed-up. Our experiments show that it is about 3x faster than Saxon (an open-source and commercial XQuery processor) on a 4-core, single node implementation, and around 2.5x faster than Apache MRQL (a MapReduce-based parallel query processor) on an eight (4-core) node cluster.
We study spectral densities for systems on lattices, which, at a phase transition display, power-law spatial correlations. Constructing the spatial correlation matrix we prove that its eigenvalue density shows a power law that can be derived from the
spatial correlations. In practice time series are short in the sense that they are either not stationary over long time intervals or not available over long time intervals. Also we usually do not have time series for all variables available. We shall make numerical simulations on a two-dimensional Ising model with the usual Metropolis algorithm as time evolution. Using all spins on a grid with periodic boundary conditions we find a power law, that is, for large grids, compatible with the analytic result. We still find a power law even if we choose a fairly small subset of grid points at random. The exponents of the power laws will be smaller under such circumstances. For very short time series leading to singular correlation matrices we use a recently developed technique to lift the degeneracy at zero in the spectrum and find a significant signature of critical behavior even in this case as compared to high temperature results which tend to those of random matrix models.
