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The original sparse representation problem is regularized with a properly designed weighted ℓ1 minimization and effectively solved with existing solver.
In this case, the distortion D l is regularized with a cost that is directly proportional to the distance between the current PTV and the initial PTV of that vertex.
However, even though it is difficult to visually discern the sedimentation process, the large number of scans and data points acquired leads to a well-defined peak in the c(s) analysis, which is regularized with the maximum entropy method with uniform prior so as to extract the least amount of information and broadest distribution consistent with the data.
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We address the balanced clustering problem where cluster sizes are regularized with submodular functions.
Here, the PG and HALS algorithms are regularized with the minimum spectral dispersion constraint.
Also, ill-posed parabolic backward problems in time partial differential equations can be regularized with the aid of integral boundary conditions; see, for example, mathematical models for bacterial self-regularization [10].
And we note that the GIAB callset was regularized with the same variant caller (GATK Haplotype Caller).
Quantum electrodynamics and other gauge field theories relevant in particle physics can be regularized with quantum links along the same lines.
But inhabitants with political power stayed on and the land they occupied has been regularized, with the result that they have become owners of valuable properties, where high-rise apartments are now being built.
After reconstruction, images were regularized with a 3-D gaussian filter of 4 mm full-width at half-maximum to reduce image noise at the voxel level prior to calculation of parametric maps with the SRTM [ 37].
This problem is regularized by means of the Tikhonov method.
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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