Linear Datalog and Bounded Path Duality of Relational Structures

In this paper we systematically investigate the connections between logics with a finite number of variables, structures of bounded pathwidth, and linear Datalog Programs. We prove that, in the context of Constraint Satisfaction Problems, all these concepts correspond to different mathematical embodiments of a unique robust notion that we call bounded path duality. We also study the computational complexity implications of the notion of bounded path duality. We show that every constraint satisfaction problem \csp(\best) with bounded path duality is solvable in NL and that this notion explains in a uniform way all families of CSPs known to be in NL. Finally, we use the results developed in the paper to identify new problems in NL

Relational Foundations For Functorial Data Migration

We study the data transformation capabilities associated with schemas that are presented by directed multi-graphs and path equations. Unlike most approaches which treat graph-based schemas as abbreviations for relational schemas, we treat graph-based schemas as categories. A schema $S$ is a finitely-presented category, and the collection of all $S$-instances forms a category, $S$-inst. A functor $F$ between schemas $S$ and $T$, which can be generated from a visual mapping between graphs, induces three adjoint data migration functors, $\Sigma_F:S$-inst$\to T$-inst, $\Pi_F: S$-inst $\to T$-inst, and $\Delta_F:T$-inst $\to S$-inst. We present an algebraic query language FQL based on these functors, prove that FQL is closed under composition, prove that FQL can be implemented with the select-project-product-union relational algebra (SPCU) extended with a key-generation operation, and prove that SPCU can be implemented with FQL

Online Matrix Completion Through Nuclear Norm Regularisation

It is the main goal of this paper to propose a novel method to perform matrix completion on-line. Motivated by a wide variety of applications, ranging from the design of recommender systems to sensor network localization through seismic data reconstruction, we consider the matrix completion problem when entries of the matrix of interest are observed gradually. Precisely, we place ourselves in the situation where the predictive rule should be refined incrementally, rather than recomputed from scratch each time the sample of observed entries increases. The extension of existing matrix completion methods to the sequential prediction context is indeed a major issue in the Big Data era, and yet little addressed in the literature. The algorithm promoted in this article builds upon the Soft Impute approach introduced in Mazumder et al. (2010). The major novelty essentially arises from the use of a randomised technique for both computing and updating the Singular Value Decomposition (SVD) involved in the algorithm. Though of disarming simplicity, the method proposed turns out to be very efficient, while requiring reduced computations. Several numerical experiments based on real datasets illustrating its performance are displayed, together with preliminary results giving it a theoretical basis.Comment: Corrected a typo in the affiliatio

Calculus and Algebra for Distributed Data Management

The sharing of content by communities of users (e.g., scientists) in a P2P context remains cumbersome. We argue that main reasons for this is the lack of calculus and algebra for distributed data management. We present the ActiveXML language that extends the XML language with features to handle distribution. More precisely, ActiveXML documents are XML documents with a special syntax for specifying the embedding of Web service calls, e.g. XML queries such as XQueries. We also present ActiveXML algebra that extends ActiveXML notably with explicit control of data exchanges. ActiveXML algebra allows describing query plans, and exchanging them between peers

Les connaissances de la toile

How to manage knowledge on the Web.Comment: in French; Cultures num\'eriques, \'education aux m\'edias et \`a l'information (2013

First-Order Query Evaluation with Cardinality Conditions

We study an extension of first-order logic that allows to express cardinality conditions in a similar way as SQL's COUNT operator. The corresponding logic FOC(P) was introduced by Kuske and Schweikardt (LICS'17), who showed that query evaluation for this logic is fixed-parameter tractable on classes of structures (or databases) of bounded degree. In the present paper, we first show that the fixed-parameter tractability of FOC(P) cannot even be generalised to very simple classes of structures of unbounded degree such as unranked trees or strings with a linear order relation. Then we identify a fragment FOC1(P) of FOC(P) which is still sufficiently strong to express standard applications of SQL's COUNT operator. Our main result shows that query evaluation for FOC1(P) is fixed-parameter tractable with almost linear running time on nowhere dense classes of structures. As a corollary, we also obtain a fixed-parameter tractable algorithm for counting the number of tuples satisfying a query over nowhere dense classes of structures

Path constraints in semistructured databases

AbstractWe investigate a class of path constraints that is of interest in connection with both semistructured and structured data. In standard database systems, constraints are typically expressed as part of the schema, but in semistructured data there is no explicit schema and path constraints provide a natural alternative. As with structured data, path constraints on semistructured data express integrity constraints associated with the semantics of data and are important in query optimization. We show that in semistructured databases, despite the simple syntax of the constraints, their associated implication problem is r.e. complete and finite implication problem is co-r.e. complete. However, we establish the decidability of the implication and finite implication problems for several fragments of the path constraint language and demonstrate that these fragments suffice to express important semantic information such as extent constraints, inverse relationships, and local database constraints commonly found in object-oriented databases

The effect of elevated temperature exposure on the fracture toughness of solid wood and structural wood composites

This is the author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Springer and can be found at: http://www.springer.com/life+sciences/forestry/journal/226.Fracture toughness of wood and wood composites has traditionally been characterized by a stress intensity factor, an initiation strain energy release rate (G[subscript init]) or a total energy to fracture (G[subscript f]). These parameters provide incomplete fracture characterization for these materials because the toughness changes as the crack propagates. Thus for materials such as wood, oriented strand board (OSB), plywood and laminated veneer lumber (LVL), it is essential to characterize the fracture properties during crack propagation by measuring a full crack resistant or R curve. This study used energy methods during crack propagation to measure full R curves and then compared the fracture properties of wood and various wood-based composites such as, OSB, LVL and plywood. The effect of exposure to elevated temperature on fracture properties of these materials was also studied. The steady state energy release rate (G[subscript SS]) of wood was lower than that of wood composites such as LVL, plywood and OSB. The resin in wood composites provides them with a higher fracture toughness compared to solid lumber. Depending upon the internal structure of the material the mode of failure also varied. With exposure to elevated temperatures, G[subscript SS] for all materials decreased while the failure mode remained the same. The scatter associated with conventional bond strength tests, such as internal bond (IB) and bond classification tests, renders any statistical comparison using those tests difficult. In contrast, fracture tests with R curve analysis may provide an improved tool for characterization of bond quality in wood composites