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The FWI is formulated as a nonlinear optimization problem that traditionally uses local (derivative-based) minimization to find the scalar field of properties that best represents the field seismic data. This problem has a high computational cost and accuracy limited to local minima, in addition to suffering from a slow convergence rate (Cycle Skipping). Therefore, we developed a two-phase hybrid optimization algorithm based on DFO algorithms. The first use global minimization and clustering technique. The second use local minimization. In phase 1 we adopted the modified PSO and K-means algorithms and in phase 2, we adopted the ANMS. We call the hybrid algorithm of the PSO-Kmeans-ANMS. Where K-means is responsible for dividing swarms of particles into 2 clusters at every instant. This strategy aims to automatically balance the mechanisms of exploration and exploitation of the parameter search space by the hybrid algorithm, allowing one to find more precise solutions and consequently improving its convergence. The PSO-Kmeans-ANMS algorithm was validated on the set of 12 benchmark functions and applied to the FWI 1D problem. We compared PSO-Kmeans-ANMS with classic PSO, modified PSO, and ANMS algorithms. The metrics used were are the average execution time and the success rate (an error of ± 4% of the optimal solution). In all validation experiments and the FWI application, the PSO-Kmeans-ANMS performed well in terms of robustness and computational efficiency. In the case of FWI, there was a significant reduction in computational cost, thus presenting a relevant result. [ABSTRACT FROM AUTHOR]

Byline: Raad Yahya Qassim, Gilberto Corso, Liacir dos Santos Lucena, Zieli Dutra Thome The objective of this paper is to review the application of data envelopment analysis to performance evaluation of electricity distribution. After introducing the basic concepts and models of data envelopment analysis, work on its application in electricity distribution is discussed via a number of case studies. Suggestions for further research are presented, with a view to enhancing the use of data envelopment analysis in electrical energy distribution.

We study the Projection of Lucena Network PLN : a planar network whose nodes coincide with the sites of the square lattice. The PLN has one internal parameter ρ , for ρ → 1 the network resembles a symmetric regular lattice with almost none highly connected node while ρ → 0 is more asymmetric and there are several highly connected nodes. We estimate P ( r ) , the probability of a node be connected to another node at distance r . The PLN follows the fractal scaling P ( r ) ∝ r − δ with 3 < δ < 4 according to ρ . For ρ → 1 we have δ close to 4 which is a signature of short range interactions, while ρ → 0 shows δ → 3 and has long range interactions. In addition, the fractal dimension, d f , of the PLN behaves as: for ρ → 1 , d f = 2 , the dimension of the embedding space while for ρ → 0 , d f increases and the PLN shares some similarities with a small world graph. [ABSTRACT FROM AUTHOR]

Abstract: The hierarchical property for a general class of networks stands for a power-law relation between clustering coefficient, and connectivity : . This relation is empirically verified in several biologic and social networks, as well as in random and deterministic network models, in special for hierarchical networks. In this work we show that the hierarchical property is also present in a Lucena network. To create a Lucena network we use the dual of a multifractal lattice ML, the vertices are the sites of the ML and links are established between neighbouring lattices, therefore this network is space filling and planar. Besides a Lucena network shows a scale-free distribution of connectivity. We deduce a relation for the maximal local clustering coefficient of a vertex in a planar graph. This condition expresses that the number of links among neighbour, , of a vertex is equal to its connectivity , that means: . The Lucena network fulfils the condition independent of and the anisotropy of ML. In addition, implies the threshold for the hierarchical property for any scale-free planar network. [Copyright &y& Elsevier]