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Based on the random matrix model, we can build statistical models using massive datasets across the power grid, and employ hypothesis testing for anomaly detection. First, the aim of this paper is to make the first attempt to apply the recent free probability result in extracting big data analytics, in particular data fusion. The nature of this work is basic in that new algorithms and analytics tools are proposed to pave the way for the future's research. Second, using the new analytic tool, we are able to make some discovery related to anomaly detection that is very difficult for other approaches. To our best knowledge, there is no similar report in the literature. Third, both linear and nonlinear polynomials of large random matrices can be handled in this new framework. Simulations demonstrate the following: Compared with the linearity, nonlinearity is more flexible in problem modeling and closer to the nature of the reality. In some sense, some other nonlinear matrix polynomials may be more effective for the power grid, Comment: 8 pages, 5 figures

The domestication and development of cattle has considerably impacted human societies, but the histories of cattle breeds have been poorly understood especially for African, Asian, and American breeds. Using genotypes from 43,043 autosomal single nucleotide polymorphism markers scored in 1,543 animals, we evaluate the population structure of 134 domesticated bovid breeds. Regardless of the analytical method or sample subset, the three major groups of Asian indicine, Eurasian taurine, and African taurine were consistently observed. Patterns of geographic dispersal resulting from co-migration with humans and exportation are recognizable in phylogenetic networks. All analytical methods reveal patterns of hybridization which occurred after divergence. Using 19 breeds, we map the cline of indicine introgression into Africa. We infer that African taurine possess a large portion of wild African auroch ancestry, causing their divergence from Eurasian taurine. We detect exportation patterns in Asia and identify a cline of Eurasian taurine/indicine hybridization in Asia. We also identify the influence of species other than Bos taurus in the formation of Asian breeds. We detect the pronounced influence of Shorthorn cattle in the formation of European breeds. Iberian and Italian cattle possess introgression from African taurine. American Criollo cattle are shown to be of Iberian, and not African, decent. Indicine introgression into American cattle occurred in the Americas, and not Europe. We argue that cattle migration, movement and trading followed by admixture have been important forces in shaping modern bovine genomic variation., Comment: 38 pages, 15 figures. Various changes made to respond to peer reviews. Mostly, arguments were clarified and additional f-statistics were added