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Finally we remark that (29) and (30) can be efficiently computed with techniques similar to [15].

The cycle C and paths P1 and P2 can be efficiently computed with a classical Breadth First Search.

The features can be efficiently computed with the aid of our specially designed sample collecting user interface.

where n ij denotes the number of words in hypothesis W ij, s ijt can be efficiently computed with the dot product of two vectors, while z ijt requires a lot of computing consideration.

In slice GAC model, a homography is formulated as the rotation of the convolution image of slice and sharp image, and in fiber GAC model, a homography is the inverse polar transform of the convolution of a kernel with the transformed sharp image (please refer to Section 3.2 for detailed proof), in which the convolution operation can be efficiently computed with the help of FFT.

Optimal alignments can be efficiently computed with the Gotoh algorithm (Gotoh, 1982).

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They are efficiently computed with arbitrary precision by integrating a forward sensitivity DAE system that is derived from the original DAE system.

It can be efficiently computed exploiting the relationship with LP methods as R M mvdr ( e jω ) = 1 ∑ k = − M M μ ( k ) e − jωk (34).

Note that the values of ( 2{widehat{omega}}_{dp} ) and ( {widehat{omega}}_p ) can be obtained as the location of the dominant peak of the magnitude squared of the Fourier transform ( {left|mathbf{b}left({omega}_{dp}right){mathbf{y}}_p^2right|}^2 ) and |a H (ω p )Ŝ*Y p |2, which can be efficiently computed by using the FFT with vectors ( {mathbf{y}}_p^2 ) and Ŝ*Y p padded with zeros, respectively.

We also show that the constructed optimization problem can be efficiently computed at a comparable cost with that of the standard Capon beamformer (SCB).

Note that modularity-based community partitions can be efficiently computed for large social networks, and can be constructed even with incomplete network topology data [39].

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