Sentence examples for useful for deriving the from inspiring English sources

Individuals with missing trait values are used in FAM-MDR Part I only when they are useful for deriving the relationship matrix, but never for the polygenic calculations themselves.

The following result is useful for deriving the strong duality theorem.

We first give three lemmas useful for deriving the lower bound of the achievable rate of ZF-DPC under DF.

It is expected that the Level-3 data will be useful for deriving the CMVs accurately, except for some of the nightside images.

Based on drift analysis, some useful drift conditions for deriving the time complexity of EAs are studied, including conditions under which an EA will take no more than polynomial time (in problem size) to solve a problem and conditions under which an EA will take at least exponential time (in problem size) to solve a problem.

Some of mathematical formulae that are useful for deriving several results in the text are provided here.

In summary, the method reveals an unprecedented level of detail about the rate of accumulation of intracellular β-catenin, and is useful for deriving quantitative kinetic parameters about the Wnt/β-catenin pathway that may serve as basis for future kinetic modeling of the pathway [15].

We will see in Section 3.3 (and also in Section 7) that the Lie brackets and the Poisson brackets are very useful for deriving higher order optimality conditions in simpler form and for calculating the singular controls.

These assumptions correspond to one ideal LTE OFDM subchannel and, although unrealistic in practice, are useful for deriving capacity equations that can be used for deciding the actual data rate and for simulations deriving an upper bound on throughput.

When known diabetes was excluded from the analysis, results from less than one-third of the countries were useful for deriving a cut point for normal glycemia in FPG and 2-h plasma glucose.

Third, representative task designs can be an important mosaic piece in across-the-board attention theories and highly useful for deriving further testable hypothesis in naturalistic settings.