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This matrix of weighted scores is the regressor in the PLS model against the measured properties of the mixture.

The Laplacian energy is defined as EL(G)="∑iλi2, where λi's are eigenvalues of the Laplacian matrix of weighted network G.

From the matrix of exports by trade partner a weighted matrix was obtained, which was multiplied by the GDP growth of each trade partner, giving a matrix of weighted partner growth for each country in each time period.

The above process could be denoted as xt + 1 = Px t, where P represents the matrix of transition probability, which is column-normalized matrix of weighted adjacency matrix of network graph G.

Nucleotide sequence of rat GFAP gene (Gene ID: 24387, Chromosome: 10; NC_005109.3) was scanned on NUBIscan against matrix of weighted PPAR γ half sites from previously mentioned experimental data.

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Since the Laplacian matrices of weighted networks usually have complex eigenvalues, the problem of complex synchronized regions should be investigated carefully.

The labelled locations are distributed in a grid with cells measuring 500 × 500 m in order to aggregate the individual level data and to create origin-destination matrices of weighted connections between home and work locations.

The cells of the matrix consist of weighted term-frequency (T-F) and inverse document frequency (IDF) matrix described in the previous section.

This is done by replacing focal points of conjoined bases of one problem by matrix analogs of weighted zeros of Wronskians of conjoined bases of two different problems.

Relative oscillation theory adds new aspects to the classical oscillation results by showing that matrix analogs of weighted zeros [6 10] of the Wronskian for suitable solutions of (1.1), (1.2) can be used to count the difference between the numbers of finite eigenvalues of problems (1.1), (1.2).

It is shown that the proposed new estimator of the covariance matrix of the weighted AUC estimators is always positive semidefinite.

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