An introduction to Graph Data Management

A graph database is a database where the data structures for the schema and/or instances are modeled as a (labeled)(directed) graph or generalizations of it, and where querying is expressed by graph-oriented operations and type constructors. In this article we present the basic notions of graph databases, give an historical overview of its main development, and study the main current systems that implement them

Managing polyglot systems metadata with hypergraphs

A single type of data store can hardly fulfill every end-user requirements in the NoSQL world. Therefore, polyglot systems use different types of NoSQL datastores in combination. However, the heterogeneity of the data storage models makes managing the metadata a complex task in such systems, with only a handful of research carried out to address this. In this paper, we propose a hypergraph-based approach for representing the catalog of metadata in a polyglot system. Taking an existing common programming interface to NoSQL systems, we extend and formalize it as hypergraphs for managing metadata. Then, we define design constraints and query transformation rules for three representative data store types. Furthermore, we propose a simple query rewriting algorithm using the catalog itself for these data store types and provide a prototype implementation. Finally, we show the feasibility of our approach on a use case of an existing polyglot system.Peer ReviewedPostprint (author's final draft

Matrix formulation of fuzzy rule-based systems

In this paper, a matrix formulation of fuzzy rule based systems is introduced. A gradient descent training algorithm for the determination of the unknown parameters can also be expressed in a matrix form for various adaptive fuzzy networks. When converting a rule-based system to the proposed matrix formulation, only three sets of linear/nonlinear equations are required instead of set of rules and an inference mechanism. There are a number of advantages which the matrix formulation has compared with the linguistic approach. Firstly, it obviates the differences among the various architectures; and secondly, it is much easier to organize data in the implementation or simulation of the fuzzy system. The formulation will be illustrated by a number of examples

Higher-dimensional models of networks

Networks are often studied as graphs, where the vertices stand for entities in the world and the edges stand for connections between them. While relatively easy to study, graphs are often inadequate for modeling real-world situations, especially those that include contexts of more than two entities. For these situations, one typically uses hypergraphs or simplicial complexes. In this paper, we provide a precise framework in which graphs, hypergraphs, simplicial complexes, and many other categories, all of which model higher graphs, can be studied side-by-side. We show how to transform a hypergraph into its nearest simplicial analogue, for example. Our framework includes many new categories as well, such as one that models broadcasting networks. We give several examples and applications of these ideas