A survey of parallel execution strategies for transitive closure and logic programs

An important feature of database technology of the nineties is the use of parallelism for speeding up the execution of complex queries. This technology is being tested in several experimental database architectures and a few commercial systems for conventional select-project-join queries. In particular, hash-based fragmentation is used to distribute data to disks under the control of different processors in order to perform selections and joins in parallel. With the development of new query languages, and in particular with the definition of transitive closure queries and of more general logic programming queries, the new dimension of recursion has been added to query processing. Recursive queries are complex; at the same time, their regular structure is particularly suited for parallel execution, and parallelism may give a high efficiency gain. We survey the approaches to parallel execution of recursive queries that have been presented in the recent literature. We observe that research on parallel execution of recursive queries is separated into two distinct subareas, one focused on the transitive closure of Relational Algebra expressions, the other one focused on optimization of more general Datalog queries. Though the subareas seem radically different because of the approach and formalism used, they have many common features. This is not surprising, because most typical Datalog queries can be solved by means of the transitive closure of simple algebraic expressions. We first analyze the relationship between the transitive closure of expressions in Relational Algebra and Datalog programs. We then review sequential methods for evaluating transitive closure, distinguishing iterative and direct methods. We address the parallelization of these methods, by discussing various forms of parallelization. Data fragmentation plays an important role in obtaining parallel execution; we describe hash-based and semantic fragmentation. Finally, we consider Datalog queries, and present general methods for parallel rule execution; we recognize the similarities between these methods and the methods reviewed previously, when the former are applied to linear Datalog queries. We also provide a quantitative analysis that shows the impact of the initial data distribution on the performance of methods

A stability with optimality analysis of consensus-based distributed filters for discrete-time linear systems

In this paper we investigate how stability and optimality of consensus-based distributed filters depend on the number of consensus steps in a discrete-time setting for both directed and undirected graphs. By introducing two new algorithms, a simpler one based on dynamic averaging of the estimates and a more complex version where local error covariance matrices are exchanged as well, we are able to derive a complete theoretical analysis. In particular we show that dynamic averaging alone suffices to approximate the optimal centralized estimate if the number of consensus steps is large enough and that the number of consensus steps needed for stability can be computed in a distributed way. These results shed light on the advantages as well as the fundamental limitations shared by all the existing proposals for this class of algorithms in the basic case of linear time-invariant systems, that are relevant for the analysis of more complex situations

LTV stochastic systems stabilization with large and variable input delay

In this paper we propose a solution to the state-feedback and output-feedback stabilization problem for linear time-varying stochastic systems affected by arbitrarily large and variable input delay. It is proved that under the proposed controller the underlying stochastic process is exponentially centered and mean square bounded. The solution is given through a set of delay differential equations with cardinality proportional to the delay bound. The predictor is based on the semigroup generated by the closed-loop system in absence of delay, and its computation is described by a numerically reliable and robust method. In the deterministic case this method generates the same optimal trajectories as in the delay-less case

Stochastic predictor-based leader-following control with input and communication delays

We consider the leader-following control problem on connected directed graphs for stochastic linear agents in the presence of communications and actuator delays. We propose to use a distributed protocol for detecting the distance of agents from the leader and we show that by suitably using this information it is possible to solve efficiently the leader-following control problem by means of predictors, thus recovering results for the single-agent case. The proposed predictor and controller are easy to design and the delay bound that guarantees stability can be computed from closed-form expressions without resorting to LMIs

Empirical vulnerability curves for Italian mansory buildings: evolution of vulnerability model from the DPM to curves as a function of accelertion

In the framework of the emergency management in the case of seismic events, the evaluation of the expected damage represents a basic requirement for risk informed planning. Seismic risk is defined by the probability to reach a level of damage on given exposed elements caused by seismic events occurring in a fixed period and in a fixed area. To this purpose, the expected seismic input, the exposed elements and their vulnerability have to be correctly evaluated. The aim of the research is to define a correct model of vulnerability curves, in PGA, for masonry structures in Italy, by heuristic approach starting from damage probability matrices (DPMs). To this purpose, the PLINIVS database, containing data on major Italian seismic events, has been used and supported by “critical” assumption on missing data. To support the reliability of this assumption, two vulnerability models, considering or not the hypothesis on the missing data, have been estimated and used to calculate the seismic scenario of the L’Aquila 2009 earthquake through the IRMA (Italian Risk MAp) platform. Finally, a comparison between the outcomes elaborated by IRMA platform and the observed damage collected in the AEDES forms, has been done. © 2020, The Author(s)

A new distributed protocol for consensus of discrete-time systems

In this paper, a new distributed protocol is proposed to force consensus in a discrete-time network of scalar agents with an arbitrarily assignable convergence rate. Several simulations validate the performances and the improvements with respect to more standard protocols

Filtering Discrete-Time Systems With Multiplicative Noise in L-2 Spaces With Applications

In this work we adopt a novel formulation of the distributed parameters recursive filter for discrete-time systems evolving in L-2 spaces to widen the class of systems that can be processed by a state estimation algorithm. Starting from a rigorous definition of Kronecker algebra on L-2 spaces that involves both elements and bounded operators of L-2, we provide a computationally efficient solution in the case of linear systems with multiplicative noises. We illustrate the potential application of the approach by developing a case-study concerning the conceptual design of a distributed thermo-couple in the presence of the Nyquist-Johnson noise

Empirical vulnerability curves for Italian mansory buildings: evolution of vulnerability model from the DPM to curves as a function of accelertion

AbstractIn the framework of the emergency management in the case of seismic events, the evaluation of the expected damage represents a basic requirement for risk informed planning. Seismic risk is defined by the probability to reach a level of damage on given exposed elements caused by seismic events occurring in a fixed period and in a fixed area. To this purpose, the expected seismic input, the exposed elements and their vulnerability have to be correctly evaluated. The aim of the research is to define a correct model of vulnerability curves, in PGA, for masonry structures in Italy, by heuristic approach starting from damage probability matrices (DPMs). To this purpose, the PLINIVS database, containing data on major Italian seismic events, has been used and supported by "critical" assumption on missing data. To support the reliability of this assumption, two vulnerability models, considering or not the hypothesis on the missing data, have been estimated and used to calculate the seismic scenario of the L'Aquila 2009 earthquake through the IRMA (Italian Risk MAp) platform. Finally, a comparison between the outcomes elaborated by IRMA platform and the observed damage collected in the AEDES forms, has been done

LQ non-Gaussian Control with I/O packet losses

The paper concerns the Linear Quadratic non-Gaussian (LQnG) sub-optimal control problem when the input and output signals travel through an unreliable network, namely Gilbert-Elliot channels. In particular, the input/output packet losses are modeled by Bernoulli sequences, and we assume that the moments of the non-Gaussian noises up to the fourth order are known. By mean of a suitable rewriting of the system through an intermittent output injection term, and by considering an augmented system with the second-order Kronecker power of the measurements, a simple solution is provided by substituting the Kalman predictor with intermittent observations of the LQG control law with a quadratic optimal predictor. Numerical simulations show the effectiveness of the proposed method

An adaptive POD approximation method for the control of advection-diffusion equations

We present an algorithm for the approximation of a finite horizon optimal control problem for advection-diffusion equations. The method is based on the coupling between an adaptive POD representation of the solution and a Dynamic Programming approximation scheme for the corresponding evolutive Hamilton-Jacobi equation. We discuss several features regarding the adaptivity of the method, the role of error estimate indicators to choose a time subdivision of the problem and the computation of the basis functions. Some test problems are presented to illustrate the method.Comment: 17 pages, 18 figure