Linearity validation

Each of these two QSAR model searches led to pools of several thousands of statistically valid linear equations, expressing the estimate of the Cox2 pICso value as linear combinations of molecular descriptors selected by a Genetic Algorithm (GA) [57,... 

Remark 8 The master problem consists of valid linear supports, and hence relaxations of the nonlinear functions, for all points xk that result from fixing y = yk Y as stated by (6.20). As a result it represents a relaxation of the original MINLP model (6.13), and hence it is a lower bound on its solution, and it is identical to its solution if all supports are included. 

Validation (linear) n = 488 Overall 56% correct (91% for degrad, fast 127 chem.) (44% for degrad, slow 361 chem.)... 

Section VII.C). When multiple choices are possible, one can. in fact, develop valid linear outer approximations that properly bound the nonconvex solution space in the MILP master problem. As for the process unit nodes, the mass balances are expressed in terms of component flows rather than in terms of fractional compositions. Finally, the right-hand side in the linearizations of the process units are modified to ensure that nonzero flows are attained when the 0-1 variable is set to zero. 

For the example validation, linearity will be analyzed within each assay and across all four assays. For the second analysis, as mentioned before, the RMSE can be used as a measure of... 

Notice we have zeros below the diagonal of the first four rows and columns. We know by inspection that these reactions are linearly independent, which is why we wrote them in the first place, So the rank of V is four. See Exercise 2.9 for a proof that there are no other valid linearly independent reactions among these species and elements. 

In the steady state, if the Fick law were valid, linear gradients would be established. By using thin laminae (9) of rubber joined in series, one can determine the actual concentration gradients existing in the membranes. That there is not a linear gradient at high relative humidities is shown by Fig. 153, in... 

In many cases, it may not be possible to obtain a valid linear regression model, and it may be necessary to perform nonlinear regression. In general, since nonlinear regression can handle an arbitrarily complex function, there is really no need to make any simplifications about the form of the regression model. Therefore, the model to be identified can be written as... 

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