On the application of the minimum polynomial extrapolation method to incompressible flows with heat transfer

In this paper, the Minimum Polynomial Extrapolation method (MPE) is used to accelerate the convergence of the Characteristic–Based–Split (CBS) scheme for the numerical solution of steady state incompressible flows with heat transfer. The CBS scheme is a fractional step method for the solution of the Navier–Stokes equations while the MPE method is a vector extrapolation method which transforms the original sequence into another sequence converging to the same limit faster then the original one without the explicit knowledge of the sequence generator. The developed algorithm is tested on a two-dimensional benchmark problem (buoyancy–driven convection problem) where the Navier–Stokes equations are coupled with the temperature equation. The obtained results show the feature of the extrapolation procedure to the CBS scheme and the reduction of the computational time of the simulation.     

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.       

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.     

A genetic approach to the design of autonomous agents for futures trading

We propose a genetic algorithm-based method for designing an autonomous trader agent. The task of the proposed method is to find an optimal set of fuzzy if–then rules that best represents the behavior of a target trader agent. A highly profitable trader agent is used as the target in the proposed genetic algorithm. A trading history for the target agent is obtained from a series of futures trading. The antecedent part of fuzzy if–then rules considers time-series data of spot prices, while the consequent part indicates the order of trade (Buy, Sell, or No action) with its degree of certainty. The proposed method determines the antecedent part of fuzzy if–then rules. The consequent part of fuzzy if–then rules is automatically determined from the trading history of the target trader agent. The autonomous trader agent designed by the proposed genetic algorithm consists of a fixed number of fuzzy if–then rules. The decision of the autonomous trader agent is made by fuzzy inference from the time-series data of spot prices. This work was presented in part at the 11th International Symposium on Artificial Life and Robotics, Oita, Japan, January 23–25, 2006     

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.     

A Method of Accelerating Neural Network Learning

The article presents of accelerating neural network learning by the Back Propagation algorithm and one of its fastest modifications – the Levenberg–Marqurdt method. The learning is accelerated by introducing the ‘single-direction’ coefficient of the change of x for calculating its new values (the number of iterations is decreased by approximately 30%). Simulation results of learning neural networks by applying both the classic method and the method of accelerating the procedure are presented.     

Estimation and Ranking of Alternatives under Interval Uncertainty

A method is proposed to estimate and rank alternative decisions with interval representation of their characteristics. The method is verified experimentally. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 148–153, July–August 2005.     

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.     

A Hopfield neural network approach for power optimization of real-time operating systems

The RTOS (Real-Time Operating System) is a critical component in the SoC (System-on-a-Chip), which is the main body for consuming total system energy. Power optimization based on hardware–software partitioning of a RTOS (RTOS–Power partitioning) can significantly minimize the energy consumption of a SoC. This paper presents a new model for RTOS–Power partitioning, which helps in understanding the essence of the RTOS–Power partitioning techniques. A discrete Hopfield neural network approach for implementing the RTOS–Power partitioning is proposed, where a novel energy function, operating equation and coefficients of the neural network are redefined. Simulations are carried out with comparison to other optimization techniques. Experimental results demonstrate that the proposed method can achieve higher energy savings up to 60% at relatively low costs of less than 4k PLBs while increasing the performance compared to the purely software realized SoC–RTOS.     

T–S fuzzy model adopted SLAM algorithm with linear programming based data association for mobile robots

This paper describes a Takagi–Sugeno (T–S) fuzzy model adopted solution to the simultaneous localization and mapping (SLAM) problem with two-sensor data association (TSDA) method. Nonlinear process model and observation model are formulated as pseudolinear models and rewritten with a composite model whose local models are linear according to T–S fuzzy model. Combination of these local state estimates results in global state estimate. This paper introduces an extended TSDA (ETSDA) method for the SLAM problem in mobile robot navigation based on an interior point linear programming (LP) approach. Simulation results are given to demonstrate that the ETSDA method has low computational complexity and it is more accurate than the existing single-scan joint probabilistic data association method. The above system is implemented and simulated with Matlab to claim that the proposed method yet finds a better solution to the SLAM problem than the conventional extended Kalman filter–SLAM algorithm.     

Fokker–Planck approximation of the master equation in molecular biology

The master equation of chemical reactions is solved by first approximating it by the Fokker–Planck equation. Then this equation is discretized in the state space and time by a finite volume method. The difference between the solution of the master equation and the discretized Fokker–Planck equation is analyzed. The solution of the Fokker–Planck equation is compared to the solution of the master equation obtained with Gillespie’s Stochastic Simulation Algorithm (SSA) for problems of interest in the regulation of cell processes. The time dependent and steady state solutions are computed and for equal accuracy in the solutions, the Fokker–Planck approach is more efficient than SSA for low dimensional problems and high accuracy.     

The Performance of German Firms in the Business-Related Service Sectors Revisited: Differential Evolution Markov Chain Estimation of the Multinomial Probit Model

We outline a new estimation method for the multinomial probit model (MNP). The method is a differential evolution Markov chain algorithm that employs a Metropolis-within-Gibbs sampler with data augmentation and the Geweke–Hajivassiliou–Keane (GHK) probability simulator. The method lifts the curse of dimensionality in numerical integration as it neither requires simulation of the whole likelihood function nor the computation of its analytical or numerical derivatives. The method is applied to an unbalanced panel dataset of firms from the German business-related service sector over the period 1994–2000. In spite of its less restricted character, the MNP model is found not to provide more accurate estimates for explaining the performance of these firms than the multinomial logit model.     

A full-Eulerian solid level set method for simulation of fluid–structure interactions

We present a full Eulerian method, termed solid level set (SLS) method, for modeling of a class of fluid–structure interactions (FSI) problems soft solid body can deform significantly but remains nearly incompressible. The SLS method is based on the unified momentum equation framework in which the solid–fluid interactions are modeled by introducing a solid body force term and a solid–fluid interfacial force term into the Navier–Stokes equation. The key idea of the SLS method is that the deformation of the solid body is no longer tracked using a Lagrangian mesh. Instead, the solid body is tracked by introducing a reference coordinate for describing the reference state of the solid body and by introducing three dynamic level set functions on the Cartesian coordinate and one static level set functions on the reference coordinate. The SLS method is easy to implement and addresses several challenges in the simulation of FSIs in which a fixed Cartesian mesh is used for fluid flow and a Lagrangian mesh is used for tracking the solid deformation. The effectiveness of the SLS method is demonstrated by studying two FSI problems. The method is suitable for studying a wide range of problems in microfluidics, e.g., manipulation of cells in confined space and ink-jet printing of biological samples.     

Neurolinguistic identification of nonlinear dependences

A method is proposed for the identification of nonlinear dependences on the basis of a composition of a fuzzy knowledge base and a neural network. The structure of a neurofuzzy network that is isomorphic to a system of linguistic statements of the form “if-then” is specified, and analytical models for training are obtained. The efficiency of the proposed method of identification is illustrated by a computer experiment. Translatedfrom Kibernetika i Sistemnyi Analiz, No. 2, pp. 37–44, March–April, 2000     

Interpolation and identification problems

The paper refines the relationship between the method of orthogonal moments for the identification of polynomial systems and the method of Lagrange-and Hermite-type operator interpolation in Hilbert space. The identification accuracy is estimated by the interpolation method and the minimum number of input signals that guarantee the prescribed accuracy is determined. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 100–107, May–June 2006.     

A Dynamic Penalty or Projection Method for Incompressible Fluids

In a previous work (Angot et al. in J. Comput. Appl. Math. 226:228–245, 2009), some penalty–projection methods have been tested for the numerical analysis of the Navier-Stokes equations. The purpose of this study is to introduce a variant of the penalty–projection method which allows us to compute the solutions faster than by using the previous solver. This new variant combines dynamically and alternatively a penalty procedure and a projection procedure according to the size of the divergence of the velocity. In other words, this study aims to prove that it is possible to project the intermediate velocity, computed by the first step of the penalty–projection method, only if its divergence is larger than a specified threshold. Theoretical estimates for the new method are given, which are in accordance with the numerical results provided.     

Space–Time Adaptive Solution of First Order PDES

An explicit time-stepping method is developed for adaptive solution of time-dependent partial differential equations with first order derivatives. The space is partitioned into blocks and the grid is refined and coarsened in these blocks. The equations are integrated in time by a Runge–Kutta–Fehlberg (RKF) method. The local errors in space and time are estimated and the time and space steps are determined by these estimates. The method is shown to be stable if one-sided space discretizations are used. Examples such as the wave equation, Burgers’ equation, and the Euler equations in one space dimension with discontinuous solutions illustrate the method.     

Investigation and development of the atlas of chromaticity for formation of raster elements and basic link fragments in synthesizing color halftone images

A direction of improvement of a method for formation of color images on offset plates is proposed. The method and tools developed for synthesizing color images are experimentally tested. Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 99–109, May–June, 2000.     

An asymptotic estimate of the error of eigenvalues in the method of finite elements for the sturm-liouville problem

A scheme of the second order of accuracy for the Sturm—Liouville problem is constructed by the method of finite elements with the use of a special basic system of compact functions. The convergence of the method of finite elements is proved. An exact formula for estimating errors of eigenvalues is obtained. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 28–36, March–Apni, 2000.     

State estimation and filtering in stochastic systems using adequate simplification

The method of order reduction in solving stochastic problems of state estimation and filtering is considered. The method presented concerns the case where mathematical models of objects being studied are defined by systems of nonstationary differential equations. Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 98–102, September–October, 1999.