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Φ is a K×K Vandermonde matrix of entries (lambda _{j}^{i-1}).
with the associated parameters defined as Φ is a K×K Vandermonde matrix of entries (lambda _{j}^{i-1}).
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].
A Fixed-value Covering Array (CA) denoted by CA N,p,v,t) is an N×p matrix of entries from the set {0,1,⋯, v−1)} such that every set of t-columns contains each possible t-tuple of entries at least a certain number of times (e.g. once).
For each hole, we introduce one two-dimensional matrix of entries D h (j, l), such that D h (j, l) is D(h L 1, j, h L 2, l) of our imaginary four-dimensional matrix.
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Formulating recursion (3) recursing only to entries with the same fixed right ends j and l enables an important optimization: for each j and l, we compute a matrix slice of entries in S that have right ends j − 1 and l − 1 and then derive all D i, j, k, l) from this matrix slice.
Any initial matrix A can be represented as ({mathbf{A}} = {mathbf{P}} - {mathbf{Q}}) where P is a matrix of positive entries and Q is a matrix containing the absolute values of negative entries.
The initial value for the matrix is a matrix of equal entries (normalized by a scalar to satisfy the condition (22)).
Here L = ( A − D ) ⊺ is the graph Laplacian (A is the weighted adjacency matrix of with entries A i j = α k > 0 if there is an edge from node i ( k ) to j ( k ) and zero otherwise, and D is the diagonal matrix such that entry D i i = ∑ j A i j is the out-degree of node i).
To obtain an approximate estimation of how close a given biological process is between S. cerevisiae and another organism we build a matrix of 704×5880 entries.
These were discarded, leaving a genotypic matrix of 191 entries by 314 SNP loci, of which 307 have been placed on the Barchi et al. [ 10] genetic map.
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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