Sentence examples for matrices with as from inspiring English sources

Anderson and May [18] described "who-acquires-infection-from-whom" matrices with as many unique elements as risks of infection, but Nold [45] formulated mixing as a convex combination of age-specific activities (number of contacts per person per day) and constant preference (proportion with others in the same group), and Jacquez et al. [46] allowed preference to vary with age.

We look for Φ matrices with as few rows as possible which can guarantee the invertibility, stability, and robustness of the sampling process for the class of sparse inputs.

The inner wall is composed of a protein matrix embedded with as well as coated with lipids, while the outer wall is composed of quinone tanned proteins as well as protein-tyrosine crosslinks.

Assume that, and each contain elements and that is an matrix with iterations as before.

These rules are given in the form of incidence matrices with nodes as columns and connections or arcs as rows (each element represents the role of a connection), and some additional textual descriptions.

This implies that, where denotes a matrix with as the th line and th column entry.

Step 3: Cross all zeros in the matrix with as few lines (horizontal and/or vertical only) as possible.

To this end, we note that if is rank deficient, (i.e., ), are the eigenvalues of, where is a diagonal matrix with as its diagonal elements, and is a complex Gaussian matrix with statistically independent, zero-mean, unit-variance elements.

For graphic representation the matrix was blurred using a convolution matrix, with as kernel the 3x3 matrix [0.05 0.05 0.05; 0.05 0.05 0.05; 0.05 0.05 0.05].

To achieve this, we produced a matrix with as many columns as sets of 50 consecutive SNPs that can be built from the genotype file, and as many rows as animals in the analysis.

where and are two circulant matrices with and as their first columns, respectively; is the unitary discrete Fourier transform matrix with ; is an additive white Gaussian noise (AWGN) vector with zero mean and covariance matrix.