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The sum-product algorithm can be simplified using a mathematical approximation, which is called the min-sum algorithm [8].

Although the paranasal sinuses are a complex framework of air cavities, widely variable in number and size, their anatomy may be simplified using a schematic approach based on drainage pathways.

It is absolutely necessary for complex information to be simplified using a multi-level analysis to reduce complex information to the simplest level.

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This cascade form can be simplified using an equivalent transfer function G(s) as shown at the bottom of the Figure 4(a).

A fuel vaporization and expansion modeling, which has been simplified using a Dimensional Analysis, is presented.

First, the electrode geometry and material composition are simplified using a thermally equivalent model.

The questions were based on the wording of the validated version of the M.I.N.I. (Lecrubier et al. 1997; Sheehan et al. 1998) with slight changes after Phase I. Compared with the original structured diagnostic interview version of the M.I.N.I., this self-questionnaire version was simplified using a points system for scoring.

Data on environmental temperature and rain patterns were simplified using a principal component analysis that produced two main components, one clearly related to temperature (CC1) and another strongly related to rain patterns (CC2, Table 1, see Methods for details).

When the observations are independent (a reasonable assumption for one measurement per person), V is a diagonal matrix and many of the elements of are 0. In this special case, the estimating equations for α can be simplified using with a corresponding n length vector for s, an n length vector for, and an n x n matrix for.

This method is based on a novel use of piecewise linear approximations to characteristic functions along a grid, and its computation may be simplified using complex arithmetic.

This is a time-consuming and error-prone task that might be simplified using automated or semi-automated inhibition zone readers.

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