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The proof of this claim is similar to that of Lemma 2. In that proof we showed how to transform a sequence of duplicate and delete operations into a sequence of duplicate-delete operations of at most the same cost.
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The rank algorithm transforms a sequence of numbers { x1; x2; x3; …; x n } into a sequence composed of 1 and 0. The transform format is as follows: (5) I n = { 0 ; if x n ≤ x n − 1 ; 1 ; if x n > x n − 1.
The pseudo code of the algorithm for generating K protein-like sequences P1 …, P K of points is as follows: Below we describe the algorithm for transforming a sequence of points P into a protein-like structure P r o t e i n i z e(P).
The main principle of these algorithms is decomposing the computation of the discrete fourier transform of a sequence of length N into smaller discrete fourier transforms see Figure 2. Figure 2 Flow graph of the decimation-in-frequency decomposition of an N -point DFT computation into four (N/4 -point DFT computatioN/4 -point6).
Mallat highlighted that the wavelet transform has a sequence of local maxima that converges to a point at a finer scale even though the function is regular at that point [2, 3].
Then, the original constrained optimization problem is transformed into a sequence of unconstrained optimization problems.
Therefore, each input utterance is transformed into a sequence of acoustic vector [9].
As a result, a single pulse transforms into a sequence of K pulses each of which radiates in a time interval ε k.
The non-linear governing equation is then transformed into a sequence of linear problems having the same stiffness matrix, which can be solved by a classical FEM.
Applying perturbation techniques in the vicinity of this solution, the non-linear governing equation obtained is transformed into a sequence of linear problems having the same stiffness matrix.
By using the SAA, the nonlinear optimal control problem is transformed into a sequence of nonhomogeneous linear two-point boundary value (TPBV) problems.
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