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Definition 1: The coherence of a measurement matrix Φ ∈ ℂ m×n is the maximum absolute cross-correlation between the normalized columns: μ Φ = max 1 ≤ l, k ≤ n l ≠ m | 〈 φ l, φ k 〉 | ‖ φ l ‖ 2 ⋅ ‖ φ k ‖ 2. (11).
The lag that gives the maximum absolute cross-correlation is the most likely time lag.
First, with a fixed maximum time delay r, we identify the most likely time delays with the maximum absolute cross-correlation for the interaction between the target gene and each of the other genes.
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A correlation matrix was then constructed using the maximum value of the absolute cross-correlation function between all event pairs.
Characteristics of correlations of wind force components are examined using the absolute ratio of wind forces, phase plane trajectories and (absolute) cross-correlation, and then wind load combinations are examined.
The correction of the absolute cross-correlation amplitude X hence entails subtraction of, followed again by a rescaling step with.
We also observe that in the subset Φ4, when the threshold on the maximum absolute value of the cross-correlation peak decreases, the statistical figures evaluated increase.
De Bruijn sequences are selected in the set Φ8 that includes 7 sequences showing a maximum absolute value of the cross-correlation equal to 12.
This optimum set of perfect periodic autocorrelation sequences has a maximum absolute value of periodic cross-correlation strictly lower than N and close to the well known lower bound SQRT(N).
An iterative (gradient driven), step-refinement, multiscale approach was used to reliably estimate the absolute maxima of the cross-correlation function described by variables representing the 6 degrees of freedom of a rigid body (vertebra).
The partial with the maximum mean cross-correlation r ̄ p is taken as the reference.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com