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where A ̂ is matrix of dimension 2p+n x ×n y.
Y =, bx, +, varepsilon, (3)where Y is matrix of measured values, matrix of independent variables.
with σ p,q =[σ p,⋯,σ q ], and C the normalization constant, Φ is a Vandermonde matrix of entries (lambda _{j}^{i-1}), E is matrix of entries (e^{frac {-lambda _{j}}{sigma _{i}}}), and (xi (lambda _{i}) = lambda _{i}^{N-K}) [30, Table I].
The energy function F MS (C) of the Chan Vese model is defined as: begin{aligned} F^{MS} (C) & = mu L(C) + nu area insideC) & quad + lambda_{1} int_{insideC} {(u - c_{1} )^{2} } {text{d}}x{text{d}}y & quad + lambda_{2} int_{outsideC} {(u - c_{2} )^{2} } {text{d}}x{text{d}}y end{aligned} (1 where C is the ranging closed curve and u is matrix of the image.
In order to identify genes which were widely represented across all organisms, a phylogenetic profile, which is matrix of the presence/absence of genes across all organisms, was created (Table S2).
Here, X is matrix of gene expression data, P(X | G) means the (marginal) likelihood probability, and P G) means a prior distribution over network structure G. Based on the above discussion, the combined score measure consists of two parts: one is the approximate likelihood, and the other is the network prior information.
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EDMs are matrices of squared distances between points.
"Most companies like ours are matrixes of regions and product lines.
EPS compounds are matrixes of polysaccharides linked to protein and other biomolecules, which could be ionized.
Let, and be matrices of appropriate dimensions and assume is symmetric, satisfying, then (2.12).
Images in this article are matrices of 8-bit luminance values.
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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