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Barbara Szyszka - One of the best experts on this subject based on the ideXlab platform.

  • An Interval version of Wendroff’s method for solving the wave equation
    2016
    Co-Authors: Barbara Szyszka
    Abstract:

    The paper is devoted to an implicit Interval method for solving the wave equation. We consider an Interval version of Wendroff’s method, which is constructed so as to include the estimation of the approximation error. The computer calculations were performed in floating Point Interval arithmetic, in order to control the round-off errors, and to obtain a solution, which contains the exact solution, in Interval form.

  • Chosen Interval methods for solving linear Interval systems with special type of matrix
    2013
    Co-Authors: Barbara Szyszka
    Abstract:

    The paper is devoted to chosen direct Interval methods for solving linear Interval systems with special type of matrix. This kind of matrix: band matrix with a parameter, from finite difference problem is obtained. Such linear systems occur while solving one dimensional wave equation (Partial Differential Equations of hyperbolic type) by using the central difference Interval method of the second order. Interval methods are constructed so as the errors of method are enclosed in obtained results, therefore presented linear Interval systems contain elements that determining the errors of difference method. The chosen direct algorithms have been applied for solving linear systems because they have no errors of method. All calculations were performed in floating-Point Interval arithmetic.

  • Interval Versions of Central-Difference Method for Solving the Poisson Equation in Proper and Directed Interval Arithmetic
    Foundations of Computing and Decision Sciences, 2013
    Co-Authors: Tomasz Hoffmann, Andrzej Marciniak, Barbara Szyszka
    Abstract:

    Abstract To study the Poisson equation, the central-difference method is often used. This method has the local truncation error of order O(h2 +k2), where h and k are mesh constants. Using this method in conventional floating-Point arithmetic, we get solutions including the method, representation and rounding errors. Therefore, we propose Interval versions of the central-difference method in proper and directed Interval arithmetic. Applying such methods in floating-Point Interval arithmetic allows one to obtain solutions including all possible numerical errors. We present numerical examples from which it follows that the presented Interval method in directed Interval arithmetic is a little bit better than the one in proper Interval arithmetic, i.e. the Intervals of solutions are smaller. It appears that applying both proper and directed Interval arithmetic the exact solutions belong to the Interval solutions obtained.

  • the central difference Interval method for solving the wave equation
    Parallel Processing and Applied Mathematics, 2011
    Co-Authors: Barbara Szyszka
    Abstract:

    A way of constructing the Interval method of second order for solving one dimensional wave equation is presented in the paper. The central difference Interval method for the hyperbolic Partial Differential Equation is taken into consideration. The suitable Dirichlet and Cauchy conditions are satisfied for the string with fixed endPoints. The estimations of discretization errors are proposed. The method of floating-Point Interval arithmetic is studied. The numerical experiment is presented.

  • PPAM (2) - The central difference Interval method for solving the wave equation
    Parallel Processing and Applied Mathematics, 2011
    Co-Authors: Barbara Szyszka
    Abstract:

    A way of constructing the Interval method of second order for solving one dimensional wave equation is presented in the paper. The central difference Interval method for the hyperbolic Partial Differential Equation is taken into consideration. The suitable Dirichlet and Cauchy conditions are satisfied for the string with fixed endPoints. The estimations of discretization errors are proposed. The method of floating-Point Interval arithmetic is studied. The numerical experiment is presented.

Peter Jonsson - One of the best experts on this subject based on the ideXlab platform.

  • Complexity classification in qualitative temporal constraint reasoning
    Artificial Intelligence, 2004
    Co-Authors: Peter Jonsson, Andrei Krokhin
    Abstract:

    AbstractWe study the computational complexity of the qualitative algebra which is a temporal constraint formalism that combines the Point algebra, the Point-Interval algebra and Allen's Interval algebra. We identify all tractable fragments and show that every other fragment is NP-complete

  • Computational complexity of relating time Points with Interval
    Artificial Intelligence, 1999
    Co-Authors: Peter Jonsson, Thomas Drakengren, Christer Bäckström
    Abstract:

    Abstract Several algebras have been proposed for reasoning about qualitative constraints over the time line. One of these algebras is Vilain's Point–Interval algebra, which can relate time Points with time Intervals. Apart from being a stand-alone qualitative algebra, it is also used as a subalgebra in Meiri's approach to temporal reasoning, which combines reasoning about metric and qualitative temporal constraints over both time Points and time Intervals. While the satisfiability problem for the full Point–Interval algebra is known to be NP-complete, not much is known about its 4 294 967 296 subclasses. This article completely determines the computational complexity of these subclasses and it identifies all of the maximal tractable subalgebras—five in total.

  • TIME - Extending the Point algebra into the qualitative algebra
    Proceedings Ninth International Symposium on Temporal Representation and Reasoning, 1
    Co-Authors: Andrei Krokhin, Peter Jonsson
    Abstract:

    We study the computational complexity of the qualitative algebra which is a temporal formalism that combines the Point algebra, the Point-Interval algebra and Allen's Interval algebra. We identify all tractable fragments containing the Point algebra and show that, for all other fragments containing the Point algebra, the problem is NP-complete.

A.k. Zaidi - One of the best experts on this subject based on the ideXlab platform.

  • On temporal logic programming using Petri nets
    IEEE Transactions on Systems Man and Cybernetics - Part A: Systems and Humans, 1999
    Co-Authors: A.k. Zaidi
    Abstract:

    A methodology for modeling temporal (time-sensitive) aspects of discrete-event systems is presented. A formalism of temporal logic which incorporates both Point and Interval descriptions of time is formulated, which is an extension of Alien's Interval logic. A formal axiomatic system of this Point-Interval logic is presented. A graph model is shown to implement the axiomatic system of Point-Interval logic. This graph-based approach transforms the system's specifications given by temporal statements into a graph structure. The graph-based temporal inference engine identifies temporal ambiguities and errors (if present) in the system's specifications, infers new temporal relations among system's Intervals, and identifies the user-defined Intervals of interest.

  • SMC - On spatial modeling of discrete event systems using Point-Interval logic
    SMC'03 Conference Proceedings. 2003 IEEE International Conference on Systems Man and Cybernetics. Conference Theme - System Security and Assurance (Ca, 1
    Co-Authors: A.k. Zaidi, K.h. Rizvi, S.s. Hussain
    Abstract:

    The paper presents a spatial logic, called PISL-2D, and an implementation of its inference engine, called SpInE. The approach can be used to represent spatial knowledge in a 2-dimensional space using a set of qualitative spatial relations. The formalism is based on a Point-Interval logic and a graphical representation, called Point Graphs. The graph representation is used by SpInE to verify and infer spatial knowledge.

Yang Shao-chun - One of the best experts on this subject based on the ideXlab platform.

Jacques Duchene - One of the best experts on this subject based on the ideXlab platform.

  • BIOSTEC (Selected Papers) - Wavelet Transform Analysis of the Power Spectrum of Centre of Pressure Signals to Detect the Critical Point Interval of Postural Control
    Biomedical Engineering Systems and Technologies, 2010
    Co-Authors: Neeraj Kumar Singh, Hichem Snoussi, David J. Hewson, Jacques Duchene
    Abstract:

    The aim of this study was to develop a method to detecting the critical Point Interval (CPI) when sensory feedback is used as part of a closed-loop postural control strategy. Postural balance was evaluated using centre of pressure (COP) displacements from a force plate for 17 control and 10 elderly subjects under eyes open, eyes closed, and vibration conditions. A modified local-maximum-modulus wavelet transform analysis using the power spectrum of COP signals was used to calculate CPI. Lower CPI values indicate increased closed-loop postural control with a quicker response to sensory input. Such a strategy requires greater energy expenditure due to the repeated muscular interventions to remain stable. The CPI for elderly occurred significantly quicker than for controls, indicating tighter control of posture. Similar results were observed for eyes closed and vibration conditions. The CPI parameter can be used to detect differences in postural control due to ageing.

  • Wavelet Transform Analysis of the Power Spectrum of Centre of Pressure Signals to Detect the Critical Point Interval of Postural Control
    2010
    Co-Authors: Neeraj Kumar Singh, Hichem Snoussi, David Hewson, Jacques Duchene
    Abstract:

    The aim of this study was to develop a method to detecting the critical Point Interval (CPI) when sensory feedback is used as part of a closed-loop postural control strategy. Postural balance was evaluated using centre of pressure (COP) displacements from a force plate for 17 control and 10 elderly subjects under eyes open, eyes closed, and vibration conditions. A modified local-maximum-modulus wavelet transform analysis using the power spectrum of COP signals was used to calculate CPI. Lower CPI values indicate increased closed-loop postural control with a quicker response to sensory input. Such a strategy requires greater energy expenditure due to the repeated muscular interventions to remain stable. The CPI for elderly occurred significantly quicker than for controls, indicating tighter control of posture. Similar results were observed for eyes closed and vibration conditions. The CPI parameter can be used to detect differences in postural control due to ageing.

  • Detection of the critical Point Interval of postural control strategy using wavelet transform analysis
    2009
    Co-Authors: Neeraj Kumar Singh, Hichem Snoussi, David Hewson, Jacques Duchene
    Abstract:

    Postural balance is often studied in order to understand the effect of sensory degradation with age. The aim of this study was to develop a new method of detecting the critical Point Interval (CPI) at which sensory feedback is used as part of a closed-loop postural control strategy. Postural balance was evaluated using centre of pressure (COP) displacements measured using a force plate for 17 control subjects and 10 elderly subjects under control (eyes open) and experimental (eyes closed, vibration) conditions. A modified local-maximum-modulus wavelet transform analysis using the power spectrum of COP signals was used to calculate the critical Point when closed-loop control occurs. Lower values of CPI are associated with increased closed-loop postural control, indicating a quicker response to sensory input. This strategy of postural control will require greater energy expenditure due to the repeated muscular interventions in order to remain stable. The CPI for elderly subjects occurred significantly quic er than for control subjects, indicating that posture was more closely controlled. Similar results were observed for eyes closed and vibration conditions. The CPI parameter offers a new method of detecting differences in postural control between different experimental conditions or changes due to ageing.