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Form the matrix C X X, 4 by Equations 13 and 14; Generate four submatrices from Equation 15 and reconstruct the matrix C as: C = C 11 C 12 C 21 C 22 (16).
For example, Candès & Recht [2], and Koltchinskii et al. [5] reconstruct the matrix by assuming that the data structure is low-rank, and this is useful since it enables us to use a popular method of convex optimization.
If c number of rows are compromised, then the attacker would be able to reconstruct the matrix A h. Since A is a (p + 1) × c, the attacker would be able to compute the common keys between p + 1 2 pair of nodes or in other words p + 1 2 links would get exposed.
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Three procedures are used to reconstruct the matrices: the modal (M) method using real natural frequencies, real modes and modal damping factors; Danek's (D) reconstruction from complex eigenvalues and eigenvectors; a reconstruction (E) from complex eigenvalues of the original and constrained system.
In this section, we solve the inverse spectral problem of reconstructing the matrix J by its GSF and we give the structure of GSF.
We can eliminate the signal of interest by reconstructing the matrix Xo leaving out the signal of interest.
In order to avoid the possibility of circularity, for analysis of each regulatory region I excluded the characterized sites from that region and reconstructed the matrix, such that (for example) Bcd sites from the hb anterior activator were not included in the matrix used for analysis of the hb anterior activator.
The computed SVs of the matrix were sorted and the largest k SVs were used to reconstruct the approximated matrix A k as in Equation (2).
In this work, a method is introduced which allows one to reconstruct the transfer matrix of an acoustic two-port from an instationary computation of the response of the two-port to an imposed perturbation of the steady state.
If the peak value of the difference spectrum is (b_{a}), the first a largest singular values are intercepted to reconstruct the Hankel matrix, {mathbf{M}}_{a} = {mathbf{U}}_{a} {varvec{upsigma}}_{a} {mathbf{V}}_{a}^{text{T}} (14).
By localizing fluorescent synaptic puncta optically, and identifying the patterns of pre- and post-synaptic fluorophores at different synapses, one can determine the pre- and post-synaptic cells for each synaptic connection, and, thus, reconstruct the connectivity matrix without tracing neural projections – a task presenting formidable challenge both for conventional serial EM and Brainbow LM.
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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