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In practical application, we can replace the module A 3 by an optimal compression rate matrix indexed by the sparsity order ρ and the SNR vector γ, which can be stored in the computer's memory.

We also sometimes think of an element (T in mathrm {End}_{mathbb {K}}(mathbb {K}[X])) as a matrix indexed by X, and define (T_{xy} in mathbb {K}) as its entry at ((x,y ) in X times X), so that (T delta _y) = sum _{xin X} T_{xy} delta _x ) for any (y in X).

We assume g is represented as K α, where K is an n× n kernel matrix indexed by the observed SNP covariates.

Hereafter, we denote K as the kernel matrix indexed by the observed covariate; and K i, j) indicates particular elements of K; K is the infinite dimensional Gaussian kernel, or the 3 p ×3 p dimensional kernel for the diffusion kernel.

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After full synchronization of the machines' respective weights, the recorded traces are stored in a matrix T indexed by ti,j as described in Eq. (7).

The contact map representation is a 2D matrix X indexed by the residues i∈ L and j∈ R from the interacting proteins L and R. Entry X i, j in contact map X is defined as (1) which is the minimum distance between all heavy atoms, h i and h j, of residues i and j.

Matrix H is indexed by (h_{i,k^{prime }}) where its rows are the number of traces gathered 1≤i≤I and its columns are the possible keys in a key space of a cryptosystem 0≤key≤K′−1 indexed as k′=key+1.

Starting with a set of training sequences all containing, and aligned on, a common functional site, we generate the PWC matrix V, a two-dimensional matrix of counts that is indexed by k-mer and relative position, respectively.

PWC results in a two-dimensional matrix (V ), in which rows are indexed by k-mer and columns are indexed by position relative to a functional site.

The confusion matrix has two dimensions: one indexed by the actual class and the other indexed by the class predicted by the classifier (Deng et al. 2016).

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