Permutations algorithms

The most effective is the reciprocal space approach, in which several low Bragg angle peaks are chosen as a basis set, and then an exhaustive permutation-based assignment of various combinations of hkl triplets to each peak from the basis set is carried out. Index permutation algorithms are more complex in realization than direct space algorithms but the former are many orders of magnitude faster than the latter. This occurs because the indices of... 

In the case that the joint or marginal distribution of the test statistics is unknown, p-values can be estimated by resampling methods such as permutation and bootstrap. For example, consider a permutation algorithm to estimate p-values with large biological data in the following manner. First, permute the N sample columns of the data matrix and compute test statistics for each biomarker candidate. Let tij, be test statistics for the th permutation. When repeating this procedure many limes (e.g., B = 100 times), the permutation p-value for hypothesis Hj is... 

Many permutation algorithms have been proposed such as Heap Method, Johnson-Trotter Method, Loopless Johnson-Trotter Method, Ives Method, Alternate Ives Method, Langdon Method, Fischer-Krause Method, etc. The heap method runs faster and is simpler than other methods as presented in [5]. A ladder diagram for heap algorithm is depicted in Fig. 4.5. 

LV Factorization of a Matrix To eveiy m X n matrix A there exists a permutation matrix P, a lower triangular matrix L with unit diagonal elements, and a.nm X n (upper triangular) echelon matrix U such that PA = LU. The Gauss elimination is in essence an algorithm to determine U, P, and L. The permutation matrix P may be needed since it may be necessaiy in carrying out the Gauss elimination to... 

To improve the formatting of the equations that represent a plant, many commercial codes partition the equations into groups of irreducible sets of equations, that is, those that have to be solved simultaneously. If a plant is represented by thousands of equations, the overall time consumed in their solution via either a GRG or SQP algorithm is reduced by partitioning and rearranging the order of the equations with the result indicated in Figure 15.6. Organization of the set of equations into irreducible sets can be carried out by the use of permutation matrices or by one of... 

In the PDS algorithm, a small set of calibration-transfer samples are measured on a primary instrument and a secondary instrument, producing spectral response matrices X, and X2. A permutation matrix F (Procrustes transfer matrix) is used to map spectra measured on the secondary instrument so that they match the spectra measured on the primary instrument. 

The whole GENFIS algorithm not only permutes all valence states of all atoms in the reaction center, it also checks for the fulfillment of the star condition ( ) ... 

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