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As a practical implementation, we have applied this method to analytically design the superresolving three-zone amplitude filters and obtained a complete reshaping of the spatial intensity distribution.
For range-based localization problems, the Cramér Rao lower Bound (CRB) provides an algorithm-independent method to analytically compute a tight lower bound on the square of sensors' localization errors.
This approach is based on a Rayleigh Ritz method to analytically identify the eigenmodes of the structure, which is currently studied for the application as a so-called 'wakefield dechirper'.
Moreover, our deconvolution of the merged data into discrete networks highlights the strength of our method to analytically simplify complex physiological data, and might be scalable to even larger datasets.
Furthermore, the ssLNA provides us not only with a new method to analytically obtain the noise statistics of a coarse-grained network but also with a new simulation tool which replaces conventional SSA simulations with heuristic propensities.
We compare a LPM, a non-linear Support Vector Machine (SVM) with Gaussian kernel [ 29] and a regularized Linear Discriminant Analysis (RLDA) [ 24], where we use a recently developed method to analytically calculate the optimal shrinkage parameter for regularization of LDA [ 30, 31].
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The direct-integration method is a conventional method used to analytically solve the equation of gradually-varied flow (GVF) that is a steady non-uniform flow in an open channel with gradually changes in its water surface elevation.
A distinct feature of the proposed method is to analytically express the flexural rigidity of tapered sections in the stiffness matrices using a series of stiffness factors, such as the αi and βi factors, accurately reflecting the stiffness variation along the member length.
The customized B-spline fitting method used to analytically express the specimen shape and displacement field provides a flexible tool to fit noisy experimental data.
Several methods exist to analytically determine the biogenic and anthropogenic fractions of energy-generating components of MSW.
For adhesive contact, a thermodynamic method is used to analytically obtain the pull-off force required to separate the miniature structure from the substrate.
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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