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In this paper we obtain the rates of convergence of the algorithms given in [13] and [14] for an automatic computation of the centered Hausdorff and packing measures of a totally disconnected self-similar set. We evaluate these rates empirically through the numerical analysis of three standard classes of self-similar sets, namely, the families of Cantor type sets in the real line and the plane and the class of Sierpinski gaskets. For these three classes and for small contraction ratios, sharp bounds for the exact values of the corresponding measures are obtained and it is shown how these bounds automatically yield estimates of the corresponding measures, accurate in some cases to as many as 14 decimal places. In particular, the algorithms accurately recover the exact values of the measures in all cases in which these values are known by geometrical arguments. Positive results, which confirm some conjectural values given in [13] and [14] for the measures, are also obtained for an intermediate range of larger contraction ratios. We give an argument showing that, for this range of contraction ratios, the problem is inherently computational in the sense that any theoretical proof, such as those mentioned above, might be impossible, so that in these cases, our method is the only available approach. For contraction ratios close to those of the connected case our computational method becomes intractably time consuming, so the computation of the exact values of the packing and centered Hausdorff measures in the general case, with the open set condition, remains a challenging problem. [ABSTRACT FROM AUTHOR]

Recently, krill herd algorithm (KHA) is proposed for the solution of global optimization problem. Various chaotic maps are considered in the proposed chaotic KHA (CKHA) of the present work to improve the performance of basic KHA method. It is observed that Logistic map based CKHA offers better results as compared other chaotic maps. The performance of the proposed CKHA is tested on standard 26-bus and IEEE 57-bus test power systems for the solution of optimal power flow of power system with different objectives that reflect minimization of fuel cost or active power loss or sum of total voltage deviation. Results obtained by using CKHA are compared to other evolutionary optimization techniques surfaced in the recent state-of-the-art literature. The results presented in this paper show that the proposed CKHA algorithm outperforms the other techniques in terms of convergence rate and global search ability. [ABSTRACT FROM AUTHOR]

Abstract: Parameter estimation for nonlinear differential equations is notoriously difficult because of poor or even no convergence of the nonlinear fit algorithm due to the lack of appropriate initial parameter values. This paper presents a method to gather such initial values by a simple estimation procedure. The method first determines the tangent slope and coordinates for a given solution of the ordinary differential equation (ODE) at randomly selected points in time. With these values the ODE is transformed into a system of equations, which is linear for linear appearance of the parameters in the ODE. For numerically generated data of the Lorenz attractor good estimates are obtained even at large noise levels. The method can be generalized to nonlinear parameter dependency. This case is illustrated using numerical data for a biological example. The typical problems of the method as well as their possible mitigation are discussed. Since a rigorous failure criterion of the method is missing, its results must be checked with a nonlinear fit algorithm. Therefore the method may serve as a preprocessing algorithm for nonlinear parameter fit algorithms. It can improve the convergence of the fit by providing initial parameter estimates close to optimal ones. [Copyright &y& Elsevier]

Abstract: In this paper, some numerical procedures for solving fuzzy first-order initial value problem have been investigated. Sufficiently conditions for stability and convergence of the proposed algorithms are given and their applicability is illustrated with examples. [Copyright &y& Elsevier]

Abstract: This paper addresses the blind identification of single-input multiple-output (SIMO) finite-impulse-response (FIR) systems. We first propose a new adaptive algorithm for the blind identification of SIMO FIR systems. Then, its convergence property is analyzed systematically. It is shown that under some mild conditions, the proposed algorithm is guaranteed to converge in the mean to the true channel impulse responses in both noisy and noiseless cases. Simulations are carried out to demonstrate the theoretical results. [Copyright &y& Elsevier]

Abstract: In this paper a fuzzy control algorithm is used to stabilize the fixed points of a chaotic system. No knowledge of the dynamic equations of the system is needed in this approach and the whole system is considered as a black box. Two main approaches have been investigated: fuzzy clustering and table look up methods. As illustrative examples these methods have been applied to Bonhoeffer van der Pol oscillator and the Henon chaotic system and the convergence toward fixed points is observed. [Copyright &y& Elsevier]