Capturing Topology in Graph Pattern Matching

Graph pattern matching is often defined in terms of subgraph isomorphism, an NP-complete problem. To lower its complexity, various extensions of graph simulation have been considered instead. These extensions allow pattern matching to be conducted in cubic-time. However, they fall short of capturing the topology of data graphs, i.e., graphs may have a structure drastically different from pattern graphs they match, and the matches found are often too large to understand and analyze. To rectify these problems, this paper proposes a notion of strong simulation, a revision of graph simulation, for graph pattern matching. (1) We identify a set of criteria for preserving the topology of graphs matched. We show that strong simulation preserves the topology of data graphs and finds a bounded number of matches. (2) We show that strong simulation retains the same complexity as earlier extensions of simulation, by providing a cubic-time algorithm for computing strong simulation. (3) We present the locality property of strong simulation, which allows us to effectively conduct pattern matching on distributed graphs. (4) We experimentally verify the effectiveness and efficiency of these algorithms, using real-life data and synthetic data.Comment: VLDB201

Superconductivity and local-moment magnetism in Eu(Fe0.89_{0.89}Co0.11_{0.11})2_{2}As2_{2}

We report the measurements of resistivity and magnetization under magnetic fields parallel and perpendicular to the basal plane, respectively, on a cobalt-doped Eu(Fe$_{0.89}$Co$_{0.11}$)$_{2}$As$_{2}$ single crystal. We observed a resistivity drop at $T_c\sim$ 21 K, which shifts toward lower temperatures under external fields, suggesting a superconducting transition. The upper critical fields near $T_c$ show large anisotropy, in contrast with those of other '122' FeAs-based superconductors. Low-field magnetic susceptibility data also show evidence of superconductivity below 21 K. Instead of expected zero-resistance below $T_c$, however, a resistivity reentrance appears at 17 K under zero field, coincident with the magnetic ordering of Eu$^{2+}$ moments. Based on the temperature and field dependences of anisotropic magnetization, a helical magnetic structure for the Eu$^{2+}$ spins is proposed. External magnetic fields easily changes the helimagnetism into a ferromagnetism with fully polarized Eu$^{2+}$ spins, accompanying by disappearance of the resistivity reentrance. Therefore, superconductivity coexists with ferromagnetic state of Eu$^{2+}$ spins under relatively low magnetic field. The magnetic and superconducting phase diagrams are finally summarized for both $H\parallel ab$ and $H\parallel c$.Comment: 8 pages, 10 figure

Spin-1/2 XYZ model revisit: general solutions via off-diagonal Bethe ansatz

The spin-1/2 XYZ model with both periodic and anti-periodic boundary conditions is studied via the off-diagonal Bethe ansatz method. The exact spectra of the Hamiltonians and the Bethe ansatz equations are derived by constructing the inhomogeneous T-Q relations, which allow us to treat both the even N (the number of lattice sites) and odd N cases simultaneously in an unified approach.Comment: 20 pages, 3 tables, published version, numerical check is adde

Exact solution of the spin-s Heisenberg chain with generic non-diagonal boundaries

The off-diagonal Bethe ansatz method is generalized to the high spin integrable systems associated with the su(2) algebra by employing the spin-s isotropic Heisenberg chain model with generic integrable boundaries as an example. With the fusion techniques, certain closed operator identities for constructing the functional T-Q relations and the Bethe ansatz equations are derived. It is found that a variety of inhomogeneous T-Q relations obeying the operator product identities can be constructed. Numerical results for two-site s=1 case indicate that an arbitrary choice of the derived T-Q relations is enough to give the complete spectrum of the transfer matrix.Comment: 26 pages, 2 tables, 1 figure, published versio