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We develop a unifying approach to declarative entity linking by introducing the notion of an entity-linking framework and an accompanying notion of the certain links in such a framework. In an entity-linking framework, logic-based constraints are used to express properties of the desired link relations in terms of source relations and, possibly, in terms of other link relations. The definition of the certain links in such a framework makes use of weighted repairs and consistent answers in inconsistent databases. We demonstrate the modeling capabilities of this approach by showing that numerous concrete entity-linking scenarios can be cast as such entity-linking frameworks for suitable choices of constraints and weights. By using the certain links as a measure of expressive power, we investigate the relative expressive power of several entity-linking frameworks and obtain sharp comparisons.

This note focuses on the problem of generalized exponential stability for linear time-varying discrete-time systems in Banach spaces. Characterizations for this concept are presented and connections with the classical concept of exponential stability existent in the literature is pointed out. An illustrative example clarifies the implications between these concepts.

In the present paper the concept of uniform exponential trisplitting for skew-product flows in Banach space is considered. This concept is a generalisation of the well-known concept of uniform exponential trichotomy. Connections between these concepts are presented and some illustrating examples prove that these are distinct. Also, we present necessary and sufficient conditions for the uniform exponential trisplitting concept with invariant and strongly invariant projectors. Finally, a characterisation in terms of Lyapunov sequences is given.

Horadam sequences are second-order linear recurrences in the complex plane which depend on two initial conditions and two recurrence coefficients which are complex numbers. Recently, numerous papers have been devoted to the periodicity of these sequences, as well as to generalizations and applications. In this paper we investigate aspects related to the sequence of rations of consecutive terms and geometric bounds of Horadam sequences. We also propose some directions for further study.

International audience; This paper focuses on the problem of optimal H2H2 filtering for a class of continuous-time stochastic systems without assuming their exponential stability in the mean square sense. Indeed, the stability assumption is relaxed and we assume instead that the Lyapunov operator associated to the dynamical stochastic system is exponentially dichotomic. The optimal solution of the considered optimization problem is expressed in terms of the unique solution of a suitable algebraic Lyapunov equation and the stabilizing solution of a certain algebraic Riccati equation.

We consider a two players linear quadratic differential game associated to a positive θ-periodic dynamical system with jump Markov perturbations. We introduce the concept of stabilizing solution and strong stabilizing solution of the associated system of coupled matrix Riccati differential equations and we will point out the relation between these kinds of solutions. Moreover, we provide a set of conditions which guarantee the existence of strong stabilizing and θ-periodic solution (stabilizing and θ-periodic solution, respectively) of the considered set of coupled matrix Riccati differential equations.

The generalized exponential trichotomy (g.e.t) concept is explored for linear time-varying systems. Characterizations and relations with the notion of uniform exponential trichotomy (u.e.t) in the sense of Elaydi-Janglajew are also provided.

Horadam sequences are second-order recurrences depending on a family of four complex parameters: two initial conditions and two recurrence coefficients. The periodicity conditions, as well as the number and geometric structure of self-repeating Horadam sequences of fixed length have been recently investigated. In this paper various geometric properties of non-homogeneous Horadam sequences are explored, including periodicity conditions and the structure of certain periodic orbits.

The problem of the existence of a Nash equilibrium strategy in a state feedback form is discussed for a class of stochastic linear quadratic two players differential games. It is assumed that only measurements at discrete-time instances of the state parameters are available. Both piecewise continuous admissible strategies as well as piecewise constant admissible strategies are considered.

This paper addresses the problem of optimal H 2 filtering for a class of continuous-time periodic stochastic systems with periodic sampled measurements. The class of admissible filters consist of deterministic continuous-time periodic systems with finite jumps. The optimal solution of the considered optimization problem is obtained by integrating a suitable generalized continuous-time Riccati equation with finite jumps. To illustrate the proposed filtering strategy, we consider a problem of field monitoring where sensors are distributed on a rectangular region in order to estimate the state of a diffusion process. We consider that the sensors and the filter communicate over a communication channel and we assume that the communication channel induces some communication constraints. More specifically, we consider a medium access constraint under which the shared network can only accommodate a limited number of simultaneous communications between components.

The problem of sampled-data Nash equilibrium strategy in a state feedback setting for a stochastic linear quadratic differential game is addressed. It is assumed that the admissible strategies are constant on the interval between two measurements. The original problem is converted into an equivalent one for a linear stochastic system with finite jumps. This new formulation of the problem allows us to derive necessary and sufficient conditions for the existence of a sampled-data Nash equilibrium strategy in a state feedback form. These conditions are expressed in terms of solvability of a system of interconnected matrix linear differential equations with finite jumps and subject to some algebraic constraints. We provide explicit formulae of the gain matrices of the Nash equilibrium strategy in the class of piece-wise constant strategies in a state feedback form. The gain matrices of the feedback Nash equilibrium strategy are computed based on the solution of the considered system of matrix linear differential equations with finite jumps. For the implementation of these strategies only measurements at discrete-time instances of the states of the dynamical system are required. Finally, we show that under some additional assumptions regarding the sign of the weights matrices in the performance criteria of the two players, there exists a unique piecewise Nash equilibrium strategy in a state feedback form if the maximal length of the sampling period is sufficiently small.

The aim of this paper is to give some characterizations for weak exponential stability properties of evolution operators in Banach spaces. Variants for weak exponential stability of some well-known results in uniform stability theory (Buse and Niculescu (2009) [1] , Daleckij and Krein (1974) [2] , Datko (1973) [3] , Rolewicz (1986) [7] , Stoica and Megan (2009) [8] ) are obtained.

Let B 0 ( D , l 2 ) denote the space of all upper triangular matrices A such that lim r → 1 − ( 1 − r 2 ) ‖ ( A ∗ C ( r ) ) ′ ‖ B ( l 2 ) = 0 . We also denote by B 0 , c ( D , l 2 ) the closed Banach subspace of B 0 ( D , l 2 ) consisting of all upper triangular matrices whose diagonals are compact operators. In this paper we give a duality result between B 0 , c ( D , l 2 ) and the Bergman–Schatten spaces L a 1 ( D , l 2 ) . We also give a characterization of the more general Bergman–Schatten spaces L a p ( D , l 2 ) , 1 ⩽ p ∞ , in terms of Taylor coefficients, which is similar to that of M. Mateljevic and M. Pavlovic [M. Mateljevic, M. Pavlovic, L p -behaviour of the integral means of analytic functions, Studia Math. 77 (1984) 219–237] for classical Bergman spaces.

We present Midas, a system that uses complex data processing to extract and aggregate facts from a large collection of structured and unstructured documents into a set of unified, clean entities and relationships. Midas focuses on data for financial companies and is based on periodic filings with the U.S. Securities and Exchange Commission (SEC) and Federal Deposit Insurance Corporation (FDIC). We show that, by using data aggregated by Midas, we can provide valuable insights about financial institutions either at the whole system level or at the individual company level. The key technology components that we implemented in Midas and that enable the various financial applications are: information extraction, entity resolution, mapping and fusion, all on top of a scalable infrastructure based on Hadoop. We describe our experience in building the Midas system and also outline the key research questions that remain to be addressed towards building a generic, high-level infrastructure for large-scale data integration from public sources.

We present Midas, a system that uses complex data processing to extract and aggregate facts from a large collection of structured and unstructured documents into a set of unified, clean entities and relationships. Midas focuses on data for financial companies and is based on periodic filings with the U.S. Securities and Exchange Commission (SEC) and Federal Deposit Insurance Corporation (FDIC). We show that, by using data aggregated by Midas, we can provide valuable insights about financial institutions either at the whole system level or at the individual company level. To illustrate, we show how co-lending relationships that are extracted and aggregated from EC text filings can be used to construct a network of the major financial institutions. Centrality computations on this network enable us to identify critical hub banks for monitoring systemic risk. Financial analysts or regulators can further drill down into individual companies and visualize aggregated financial data as well as relationships with other companies or people (e.g., officers or directors). The key technology components that we implemented in Midas and that enable the above applications are: information extraction, entity resolution, mapping and fusion, all on top of a scalable infrastructure based on Hadoop.