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The rank function is discontinuous and nonconvex, thus the general RCOPs are classified as NP-hard in most of the cases.
Each aspect attempts to improve the under-approximation of winning regions or decrease the rank function by simplifying the structure of the parity game.
This algorithm includes two sub-algorithms: the first is to define the PGEA energy and entropy, a rank function, and a niche function and then calculate the rank function values of every particle in the phase space; the second is to solve for the optimal Pareto front of a multi-objective optimization problem.
Alia, E. Martinelli, Sign detection in residue arithmetic units, Journal of Systems Architecture 45 (1998) 251] is incorrect because the interpretation and the derivation of the rank function is wrong.
We exploit the vector space model for generating index and query, and our new-designed KDO algorithm is utilized for providing keyword weight, so that the rank function not only considers about the relevance between query and document, but also takes into account the document quality.
In the regularization, trace norm is used as a rank function.
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Finally, attribute reduction is equivalently formulated with rank functions and closure operators of matroids.
For its design we formulate a methodology using ideas from the back-propagation algorithm and robust techniques to circumvent the non-differentiability of rank functions.
In addition, we compute the rank combination by averaging the rank functions (r_P) and (r_Q), to give us the score function of the rank combination, (s_{RC}).
The values of the score function s are sorted from highest to lowest to obtain the rank functions r p and r q, respectively (see Fig. 3).
The regions of the intersection are ranked according to their score (descending order) to give rank functions rx'(d) and ry'(d).
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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