Using a model of cellular automata and classification methods for prediction of time series with memory

The paper deals with the problem of prediction of time series with memory for which classical prediction methods are frequently inadequate. A method is proposed that is based on a model of cellular automata, classification methods, and fuzzy set theory. The accuracy of models based on this method is estimated. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 43–54, November–December 2006.     

Necessary and sufficient optimality conditions of a design decision on the structure of a local computer network

A problem of nonlinear programming with Boolean variables is considered, for which the possibility of extension of the optimality conditions of solving a special problem of nonlinear programming (with continuous variables) is shown by statistical estimation of possible design decisions. This contributed to the solution of the initial problem by simpler methods. Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 133–137, September–October, 1999.     

Optimizing a mathematical model of a 3D body surface

A general method is proposed to select the number and arrangement of horizontal and vertical sections of a surface sufficient to describe this surface by splines of two variables with an accuracy sufficient from the technological point of view. An analytical review is given to methods that can be used to solve the problem posed (spline-interpolation, spline-interlineation of functions, R-functions, the theory of polynomial operator interpolation). The results of a computation experiment are presented. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 103–112, January–February 2006.     

Algebraic Fractional-Step Schemes for Time-Dependent Incompressible Navier–Stokes Equations

The numerical investigation of a recent family of algebraic fractional-step methods (the so called Yosida methods) for the solution of the incompressible time-dependent Navier–Stokes equations is presented. A comparison with the Karniadakis–Israeli–Orszag method Karniadakis et al. (1991, J. Comput. Phys. 97, 414–443) is carried out. The high accuracy in time of these schemes well combines with the high accuracy in space of spectral methods.     

Identification of parameters in a dynamic problem of elasticity for a body with an inclusion

Explicit expressions for gradients of residual functionals are obtained for the identification of the parameters of elastic dynamic deformation of multicomponent bodies by gradient methods. The technique is based on the solutions of conjugate problems found using the theory of optimal control over states of multicomponent distributed systems that is developed by the authors. Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 75–97, May–June 2OO9.     

Phase Portrait Modeling of a Nonlinear System with a Dynamic Fuzzy Network

Fuzzy logic and neural networks are two important technologies for modeling and control of dynamical systems and have been constrained by the non-dynamical nature of their some popular architectures. There exist problems such as large rule bases (i.e., curse of dimensionality), long training times, the need to determine buffer lengths. This article proposes to overcome these major problems in phase portrait modeling of a nonlinear system with a dynamic fuzzy network (DFN) with unconstrained connectivity and with dynamic fuzzy processing units called “feurons”. Nonlinear physical system properties can be encapsulated by DFN. As an example, DFN has been used as the modeler for some nonlinear physical system such as chaotic, limit cycle, oscillator. The minimization of an integral quadratic performance index subject to dynamic equality constraints is considered for a phase portrait modeling application. For gradient computation adjoint sensitivity method has been used. Its computational complexity is significantly less than direct sensitivity method, but it requires a backward integration capability. We used first and approximate second order gradient-based methods including Broyden–Fletcher–Golfarb–Shanno algorithm to update the parameters of the dynamic fuzzy networks yielding faster rate of convergence     

Substantiation of a criterion of metrological reliability of measuring instruments

The choice of a criterion of metrological reliability of measuring instruments is founded. Redundant measurement methods are used that make it possible to determine the current values of the parameters of the conversion function being used at any moment of operation of a measuring instrument. Based on the results of intermediate measurements of correcting physical values, an equation of quantities that describe the conversion function parameters is obtained. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 181–184, September–October 2008.     

Generating customized yet factually consistent information: a constraint satisfaction approach

We present an information customization framework that leverages a hybrid of adaptive hypermedia and intelligent techniques, in particular constraint satisfaction methods, to generate customized and factually consistent information based on a user profile. Information customization is modeled as a constraint satisfaction problem, whereby a solution is derived by (a) satisfying user-model constraints to select a user-specific set of ‘information snippets’; and (b) establishing inter-snippet consistency to ensure that all snippets are compatible with each other. Our approach takes the unique step of establishing factually consistency – via the satisfaction of inter-snippet constraints – between heterogeneous information snippets. A customized information package is generated by systematically synthesizing the set of user-specific and factually consistent information snippets. The featured information customization framework incorporates variations of various search and constraint satisfaction methods. The work is applied in an E-Healthcare setting leading to the generation of customized healthcare information.     

On the calculation of unperturbed amplitude scattering of a quantum particle on a complicated object

A model realizing a simple numerical solution algorithm of the direct quantum scattering problem for a neutral nonrelativistic particle, is suggested. The particle interacts with N ~ 10⁵–10⁷ disordered centers. The selected interval of the number N is some neighborhood of the application limit of iteration methods within the bounds of the suggested scheme. The model results in the linear algebraic system with a dimension that is 2–4 orders of magnitude lower than the number N.     

Simulation of Motion of a Collection of Rigid Bodies,Taking into Account Their Collisions and Joints

Existing methods of simulation of motion of rigid bodies are considered that take into account collisions and joints of such bodies. A new fast universal fixed-step-size algorithm of speed constraints is proposed. This algorithm combines all the advantages of well-known algorithms and is deprived of their drawbacks. Using a modified Dantzig method, the upper time estimate equal to O(4k) is obtained for the algorithm. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 29–38, July–August 2005.     

Estimation of the number of “good” permutatio with applications to cryptography

The authors propose two methods of estimating the number of so-called “good” permutations, which are defined in the article. The nature of both methods is statistical, but their methodologies are completely different. The use of these methods is illustrated by the example of the permutation length N = 25, which is of intense interest in cryptography. Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 10–16, September–October, 1999.     

The Neural Network Approach to Input–Output Analysis for Economic Systems

Economic practitioners in China are giving up the classical Leontief’s Input–Output analysis methods. This paper offers an alternative method of input–output analysis. The proposed method is based on the layered neural network model. It shows that neural networks method can be useful for input–output analysis for a dynamic economic system.       

Sensitivity analysis of coupled structural–acoustic systems subjected to stochastic excitation

A development for computing the acoustic pressure spectral density and its sensitivity of coupled structural–acoustic systems subjected to stochastic excitation is presented. Previous work in the area of structural–acoustic response considered systems subject to deterministic excitations. The response computation depends on the excitation; therefore, new methods are developed to account for stochastic excitation. The structural–acoustic response is calculated using finite element methods and stochastic analysis techniques. An accurate and highly efficient algorithm series for structural stationary random response analysis, pseudo excitation method (PEM) is used. Numerical examples are given to demonstrate the effectiveness of the methods and the program.     

Approximate solution of a class of optimal control problems in domains of arbitrary form

A combination of both fictitious domain and net methods is used for solution of optimal-control problems for elliptic systems. The proposed difference scheme has an order of accuracy ofO(h ^1/2) in the net norm L₂. Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 138–146, January–February, 2000.     

An a posteriori error estimate and a comparison theorem for the nonconforming <Emphasis Type="Italic">P</Emphasis><Subscript>1</Subscript> element

A posteriori error estimates for the nonconforming P ₁ element are easily determined by the hypercircle method via Marini’s observation on the relation to the mixed method of Raviart–Thomas. Another tool is Ainsworth’s application of the hypercircle method to mixed methods. The relation on the finite element solutions is also extended to an a priori relation of the errors, and the errors of four different finite element methods can be compared.      

On High Order Strong Stability Preserving Runge–Kutta and Multi Step Time Discretizations

Strong stability preserving (SSP) high order time discretizations were developed for solution of semi-discrete method of lines approximations of hyperbolic partial differential equations. These high order time discretization methods preserve the strong stability properties–in any norm or seminorm—of the spatial discretization coupled with first order Euler time stepping. This paper describes the development of SSP methods and the recently developed theory which connects the timestep restriction on SSP methods with the theory of monotonicity and contractivity. Optimal explicit SSP Runge–Kutta methods for nonlinear problems and for linear problems as well as implicit Runge–Kutta methods and multi step methods will be collected     

An evaluative study on ESO and SIMP for optimising a cantilever tie—beam

We examine both the evolutionary structural optimisation (ESO) and solid isotropic microstructure with penalisation (SIMP) methodologies by investigating a cantilever tie–beam. Initially, both ESO and SIMP produce designs with higher objective function values relative to a previously published ‘intuitive’ design. However, after careful investigation of the numerical parameters such as the initial design domain and the mesh size, both methods obtain designs that have lower objective function values relative to the intuitive design. Thus, a clearer understanding of the numerical parame- ters and their influence on optimisation methods is achieved.     

Stabilization by Local Projection for Convection–Diffusion and Incompressible Flow Problems

We give a survey on recent developments of stabilization methods based on local projection type. The considered class of problems covers scalar convection–diffusion equations, the Stokes problem and the linearized Navier–Stokes equations. A new link of local projection to the streamline diffusion method is shown. Numerical tests for different type of boundary layers arising in convection–diffusion problems illustrate the stabilizing properties of the method.     

Choosing the parameter of a modified additive-averaged splitting algorithm

The problem-solving time and the solution accuracy are expressed as functions of a parameter. An optimization problem of choosing the parameter using a “time cost–solution accuracy” criterion is considered. A Pareto-optimal set of solutions is obtained. The best value of the parameter is chosen by the ideal-point method. Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 98–105, July–August 2009.