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where (tilde {A}) is weighted adjacency matrix of directed networks, (tilde { D}_{O}) is the weighted diagonal matrix of out-degrees (or row sum of (tilde {A})) and (tilde {D}_{I}) is the weighted diagonal matrix of in-degrees (or column sum of (tilde {A})).
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The structural proteins of the enamel matrix must have specific protein protein interactions to produce a matrix capable of directing the highly ordered structure of the enamel crystallites.
From these matrices, we have derived the matrix of direct technical coefficients.
where A is the n×n matrix of direct input coefficients.
Then, the entire matrix of direct and indirect coupling loss factors is derived by using a deterministic modal approach.
A linear model of coregionalization (LMC) was fitted to the matrix of direct and cross experimental variograms for the 12 characteristics.
From this definition, w y d can be expressed as: mathop wnolimits_{y}^{d} = hat{eta } cdot y (21 where (mathop eta limits^{ wedge }) is the diagonal matrix of direct water use coefficients and y is the column vector of final demand.
A decomposition by industry is achieved by creating a diagonal matrix of direct impact multipliers (DIMs) which is post-multiplied with the Leontief Inverse: {mathbf{M}}^{i} = {hat{mathbf{f}}} cdot {mathbf{L}} (2 where ({hat{mathbf{f}}}) is a (m + n) × (m + n) matrix with DIMs placed on the diagonal of a (m + n) × (m + n) matrix of zeros.
We focused on the fixed effects model in our exposition, because inconsistency is most easily detectable then [ 1], but note that the proposed forest plot can be adapted to random effects models by assuming that the heterogeneity variance is known and fixed and by adding appropriate elements to the covariance matrix of direct effect estimates.
(A=(a_{ij} inmathbb{R}^{Ntimes N}) is the weighted adjacency matrix of the directed graph (mathscr{G}={V,E}) with the node set V and the link set E: (a_{ij}>0) if there exists a directed link from node j to i at time t; (a_{ij}=0), otherwise.
The algebra graph theory is reviewed and the properties of signless Laplacian matrix of a directed graph are derived.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com