Data interpolation is a fundamental data processing tool in scientific studies and engineering applications. However, when interpolating data points on an equidistant grid using polynomials, the so-called Runge phenom...
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Data interpolation is a fundamental data processing tool in scientific studies and engineering applications. However, when interpolating data points on an equidistant grid using polynomials, the so-called Runge phenomenon may occur, making polynomial interpolation unreliable. Although there are some methods proposed to defeat the Runge phenomenon, it is still an open problem which parameter sequence is the globally optimal for overcoming the Runge phenomenon. In this paper, we develop an immunity genetic algorithm based method to solve this problem. Specifically, we first model the Runge-phenomenon-defeating problem as an optimization in which the objective function is the energy of the parametric curve. An immunity genetic algorithm is then devised to determine the best IGA parameter sequence, which minimizes the objective function. The resulting parametric curve overcomes the Runge phenomenon. By performing the proposed immunity genetic searching algorithm starting with some groups of randomly generated parameter sequences, the resulted parameter sequences closely oscillate around the Chebyshev parameter sequence. Therefore, the Chebyshev parameter sequence is most likely the globally optimal sequence conquering the Runge phenomenon. (C) 2015 Elsevier Inc. All rights reserved.
Pseudorandom binary sequences play a significant role in many fields, such as error control coding, spread spectrum communications, and cryptography. In recent years, chaotic system is regarded as an important pseudor...
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Pseudorandom binary sequences play a significant role in many fields, such as error control coding, spread spectrum communications, and cryptography. In recent years, chaotic system is regarded as an important pseudorandom source in the design of pseudorandom bit generators (PRBGs). Among them, most are based on one or more fixed chaotic systems, and the generated binary sequences come to be stationary. However, these kinds of chaotic PRBGs can be attacked by reconstructing the phase space or using some statistical analysis methods. In this study, a scheme for chaotic PRBG based on non-stationary logistic map is proposed. The authors design a dynamic algorithm to change the driven parameter sequence (not random) into a random-like sequence. The variable parameters disrupt the phase space of the system, which can resist the phase space reconstruction attacks effectively. They prove that the non-stationary logistic map is still chaotic under Wiggins' chaos definition. The numerical analysis shows that the generated binary sequences have good cryptographic properties and can pass the well-known statistical tests. The authors' chaotic PRBG based on non-stationary logistic map is a novel scheme in the design of PRBG, and is more secure than the PRBGs based on fixed chaotic systems.
One of the challenging problems with evolutionary computing algorithms is to maintain the balance between exploration and exploitation capability in order to search global optima.A novel convergence track based adapti...
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One of the challenging problems with evolutionary computing algorithms is to maintain the balance between exploration and exploitation capability in order to search global optima.A novel convergence track based adaptive differential evolution(CTbADE)algorithm is presented in this research *** crossover rate and mutation probability parameters in a differential evolution algorithm have a significant role in searching global optima.A more diverse population improves the global searching capability and helps to escape from the local optima *** the convergence path over time helps enhance the searching speed of a differential evolution algorithm for varying *** adaptive powerful parameter-controlled sequences utilized learning period-based memory and following convergence track over time are introduced in this *** proposed algorithm will be helpful in maintaining the equilibrium between an algorithm’s exploration and exploitation capability.A comprehensive test suite of standard benchmark problems with different natures,i.e.,unimodal/multimodal and separable/non-separable,was used to test the convergence power of the proposed CTbADE *** results show the significant performance of the CTbADE algorithm in terms of average fitness,solution quality,and convergence speed when compared with standard differential evolution algorithms and a few other commonly used state-of-the-art algorithms,such as jDE,CoDE,and EPSDE *** algorithm will prove to be a significant addition to the literature in order to solve real time problems and to optimize computationalmodels with a high number of parameters to adjust during the problem-solving process.
The block-diagonal least squares method, which theoretically has specific requirements for the observation data and the spatial distribution of its precision, plays an important role in ultra-high degree gravity field...
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The block-diagonal least squares method, which theoretically has specific requirements for the observation data and the spatial distribution of its precision, plays an important role in ultra-high degree gravity field determination. On the basis of block-diagonal least squares method, three data processing strategies are employed to determine the gravity field models using three kinds of simulated global grid data with different noise spatial distri- bution in this paper. The numerical results show that when we employed the weight matrix corresponding to the noise of the observation data, the model computed by the least squares using the full normal matrix has much higher precision than the one estimated only using the block part of the normal matrix. The model computed by the block-diagonal least squares method without the weight matrix has slightly lower precision than the model computed using the rigorous least squares with the weight matrix. The result offers valuable reference to the using of block-diagonal least squares method in ultra-high gravity model determination.
Our goal is to determine when the trivial extensions of commutative rings by modules are Cohen-Macaulay in the sense of Hamilton and Marley. For this purpose, we provide a generalization of the concept of Cohen-Macaul...
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Our goal is to determine when the trivial extensions of commutative rings by modules are Cohen-Macaulay in the sense of Hamilton and Marley. For this purpose, we provide a generalization of the concept of Cohen-Macaulayness of rings to modules.
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