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If we had the internal structure of each subtree k (of Hg k), then we could directly count m ik, and hence formulate the total log-likelihood of the data and estimate the parameters, using Poisson regression, through the usual ML framework.

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These ARs and modified RRs were used to re-evaluate equation (1) and hence formulated E-GAIL-SBSP together with Singapore race-specific estimates of B j and c j (Table  1).

In the general formulation of IFL, hence formulated, an operator O can be marked as independent from any preceding quantifiers of the opposite force, but not from any preceding quantifier having the same force as O.

The optimization is hence formulated to minimize the total sum of variance in the error variables for each enzyme across the k conditions.

As a first step towards that goal, research was conducted to investigate the NSYS due to an incident wave in a shear-type building subjected to full-sine velocity base excitation, to understand the relationships between input excitation, inter-story drifts, story forces, and hence to formulate a procedure to estimate the NSYS along the building height.

While the strengthening effect of mono-dispersed particles has been studied extensively and hence well formulated, a rational and consolidated evaluation of superposed hardening effects of different particle mixtures is still an open problem both experimentally and theoretically.

The GO database was established based on the molecular function, biological process and cellular component [14], and hence proteins formulated in the GO database space would be clustered in a way much better reflecting their subcellular locations, as elucidated in [18].

The bioavailability of paclitaxel is very limited and hence it is formulated in a 1 1 ratio of Cremophor EL and dehydrated ethanol for intravenous administration (Taxol®).

Furthermore, it is impossible to distribute 18 CF3 groups on the surface of C60 without significant steric hindrance, and hence the guidelines formulated for stable addition patterns with fewer CF3 groups are not followed as strictly.

Applying the duality theory of linear programming ([19], Chap. 5), we can exactly get the linear program formulation as P-3, and hence, P-4 is formulated.

Hence, we formulate the computation of the unknown label matrix as a smoothing process on the manifold under the constraint that all observations represent an object of one single class.

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