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Finding multiple roots of nonlinear equation systems (NESs) in a single run is one of the most important challenges in numerical computation. We tackle this challenging task by combining the strengths of the repulsion technique, diversity preservation mechanism, and adaptive parameter control. First, the repulsion technique motivates the population to find new roots by repulsing the regions surrounding the previously found roots. However, to find as many roots as possible, algorithm designers need to address a key issue: how to maintain the diversity of the population. To this end, the diversity preservation mechanism is integrated into our approach, which consists of the neighborhood mutation and the crowding selection. In addition, we further improve the performance by incorporating the adaptive parameter control. The purpose is to enhance the search ability and remedy the trial-and-error tuning of the parameters of differential evolution (DE) for different problems. By assembling the above three aspects together, we propose a repulsion-based adaptive DE, called RADE, for finding multiple roots of NESs in a single run. To evaluate the performance of RADE, 30 NESs with diverse features are chosen from the literature as the test suite. Experimental results reveal that RADE is able to find multiple roots simultaneously in a single run on all the test problems. Moreover, RADE is capable of providing better results than the compared methods in terms of both root rate and success rate. [ABSTRACT FROM AUTHOR]

We propose an electronic implementation to record Poincaré sections of dynamical systems exhibiting chaos. Poincaré sections are obtained by sampling and holding the maxima of a sequence of pulses of a chaotic relaxation oscillator versus the same temporal sequence shifted by one unit. By using these sections we are able to detail the transition to chaos via torus breakdown. [ABSTRACT FROM AUTHOR]

The Cucker–Smale flocking model is designed to analyze the velocity and position-control mechanisms in a group of living individuals, such as a flock of birds. In this model, each agent (a bird or fish) adjusts its velocity according to its own velocity and the weighted mean of the relative velocities of the other members of the flock. We herein focus on the simple, distributed, and autonomous nature of the flocking model and apply its operating principles to fair resource allocation for vehicle-mounted mobile relays (VMRs) by considering their need for distributed fair resource allocation in various network topologies. By adaptively adjusting the VMR transmission power, the proposed method effectively alleviates the interference between users in vehicles and users directly connected to the base station. We evaluate the performance of the proposed method in the context of the IEEE 802.16j based system. The achievable bandwidth performance of the proposed method is evaluated relative to that of both the fixed power allocation (FPA) method and the signal-to-interference plus noise ratio (SINR)-based transmit power control method. The result shows that the proposed method adjusts to various network topologies and provides better achievable bandwidth than both the SINR-based method and the FPA method. [ABSTRACT FROM AUTHOR]

Presents the calculation of covering numbers for support vector (SV) machines. Definition of SV; Bounds for SV classes; Example of the application of the result.

Presents a study which derived bounds for the generalization error of kernel machines, such as support vector machines and related regularization networks by obtaining new bounds on their covering numbers. Definitions and notations; Operator theory methods for entropy numbers; Generalization bounds via uniform convergence; Entropy numbers for kernel machines; Discrete spectra of convolution operators; Conclusion.