Sentence examples for description of equation from inspiring English sources

We followed the reviewer's suggestion and rewrite the description of Equation 4 by adding an example to explain it.

From the description of Equation (1), the L1 penalized coefficient vector for our linear model is defined as (2) θ ^ = | | y - H θ | | 2 2 + λ | | θ | | 1 where lambda is the regularization parameter, || θ ||1 is the L1-norm of the parameter vector.

A complete description of equations (1 - 6) is presented in [5].

Additional file 1: Appendices A, B, and C. Detailed description of age-structured multi-state Markov model for estimating PWID population size, detailed description of equations specifying the evidence synthesis model, and methods for and results of sensitivity analyses.

A descriptions of equations implemented for these measures and full details of their context to protein networks in cancer are summarized here [ 53] Tissue specific gene expression data from the Symatlas project [ 24] was analyzed to detect pairwise differential expression across the 79 specific tissues [ 25] (Additional file 8).

In this paper, we review the construction of low-dimensional manifolds of reduced description for equations of chemical kinetics from the standpoint of the method of invariant manifold (MIM).

In addition to Huygens, the Swiss mathematician Jakob Bernoulli and the German mathematician Gottfried Leibniz contributed to the complete description of the equation of the catenary.

Table 1 provides a description of the equation parameters along with the values used in the simulations.

In our description of transport (Equation 2), cargo acts as an unspecific passive tracer.

The abstract description of differential equation systems, with the help of several distinct interfaces, makes it possible to decouple them from a particular type of biological network.

Table 1 Equations and descriptions Description of variable Equations Eq. no.