On the Selection of Optimal Index Configuration in OO Databases

An operation in object-oriented databases gives rise to the processing of a path. Several database operations may result into the same path. The authors address the problem of optimal index configuration for a single path. As it is shown an optimal index configuration for a path can be achieved by splitting the path into subpaths and by indexing each subpath with the optimal index organization. The authors present an algorithm which is able to select an optimal index configuration for a given path. The authors consider a limited number of existing indexing techniques (simple index, inherited index, nested inherited index, multi-index, and multi-inherited index) but the principles of the algorithm remain the same adding more indexing technique

Generalized Conley-Zehnder index

The Conley-Zehnder index associates an integer to any continuous path of symplectic matrices starting from the identity and ending at a matrix which does not admit 1 as an eigenvalue. We give new ways to compute this index. Robbin and Salamon define a generalization of the Conley-Zehnder index for any continuous path of symplectic matrices; this generalization is half integer valued. It is based on a Maslov-type index that they define for a continuous path of Lagrangians in a symplectic vector space $(W,\bar{\Omega})$, having chosen a given reference Lagrangian $V$. Paths of symplectic endomorphisms of $(\R^{2n},\Omega_0)$ are viewed as paths of Lagrangians defined by their graphs in $(W=\R^{2n}\oplus \R^{2n},\bar{\Omega}=\Omega_0\oplus -\Omega_0)$ and the reference Lagrangian is the diagonal. Robbin and Salamon give properties of this generalized Conley-Zehnder index and an explicit formula when the path has only regular crossings. We give here an axiomatic characterization of this generalized Conley-Zehnder index. We also give an explicit way to compute it for any continuous path of symplectic matrices.Comment: arXiv admin note: substantial text overlap with arXiv:1201.372

Weinberg propagator of a free massive particle with an arbitrary spin from the BFV-BRST path integral

The transition amplitude is obtained for a free massive particle of arbitrary spin by calculating the path integral in the index-spinor formulation within the BFV-BRST approach. None renormalizations of the path integral measure were applied. The calculation has given the Weinberg propagator written in the index-free form with the use of index spinor. The choice of boundary conditions on the index spinor determines holomorphic or antiholomorphic representation for the canonical description of particle/antiparticle spin.Comment: 31 pages, Latex, version published in Class. Quantum Gra

Effective and Efficient Similarity Index for Link Prediction of Complex Networks

Predictions of missing links of incomplete networks like protein-protein interaction networks or very likely but not yet existent links in evolutionary networks like friendship networks in web society can be considered as a guideline for further experiments or valuable information for web users. In this paper, we introduce a local path index to estimate the likelihood of the existence of a link between two nodes. We propose a network model with controllable density and noise strength in generating links, as well as collect data of six real networks. Extensive numerical simulations on both modeled networks and real networks demonstrated the high effectiveness and efficiency of the local path index compared with two well-known and widely used indices, the common neighbors and the Katz index. Indeed, the local path index provides competitively accurate predictions as the Katz index while requires much less CPU time and memory space, which is therefore a strong candidate for potential practical applications in data mining of huge-size networks.Comment: 8 pages, 5 figures, 3 table